Pls help I am stuck thank you so much
The perimeter of shape C is 30 cm shorter than the total perimeter of A and B.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
Hence the perimeter of each shape is given as follows:
A = 2 x (5 + 12) = 34 cm.B = 2 x (4 + 9) = 26 cm.C = 12 + 5 + 9 + 4 = 30 cm.Then the difference is given as follows:
34 + 26 - 30 = 30 cm.
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Jalen bought a new iPad. The screen has a perimeter of inches 36 inches and an area of 80 square inches. What are the dimensions of the iPad’s screen?
Let's assume the dimensions of the iPad's screen are represented by length (L) and width (W). We can use the given information to set up two equations.
Perimeter equation:
The perimeter of a rectangle is given by the formula: 2(L + W). In this case, the perimeter is given as 36 inches.
So, 2(L + W) = 36.
Area equation:
The area of a rectangle is given by the formula: L * W. In this case, the area is given as 80 square inches.
So, L * W = 80.
We now have a system of two equations:
2(L + W) = 36
L * W = 80
From equation 1, we can simplify it to L + W = 18 and rewrite it as L = 18 - W.
Now substitute this value of L into equation 2:
(18 - W) * W = 80
Expanding the equation:
18W - W^2 = 80
Rearranging the equation to quadratic form:
W^2 - 18W + 80 = 0
Factoring or using the quadratic formula, we find the two possible values for W.
The solutions are W = 8 and W = 10.
Now we can substitute these values back into the equation L = 18 - W to find the corresponding values of L.
For W = 8:
L = 18 - 8 = 10
For W = 10:
L = 18 - 10 = 8
Therefore, the dimensions of the iPad's screen can be either 8 inches by 10 inches or 10 inches by 8 inches.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in ΔSTU is in the range (2, 32).
Given that ΔSTU is a triangle,
ST = 15,
US = x,
UT = 17.
We need to find the length of x in the triangle STU.
To solve this question, we need to apply the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Therefore, using this theorem, we get:
ST + US > UT => 15 + x > 17
=> x > 17 - 15
=> x > 2US + UT > ST
=> x + 17 > 15 => x > 15 - 17
=> x > -2UT + ST > US
=> 17 + 15 > x
=> 32 > x
In this case ST = 15, US = x, UT = 17. Let's apply the triangle inequality to the sides of the triangle STU:
ST + US > UT
15 + x > 17
Simplify the inequality:
x > 17 - 15
x > 2
Triangle STU is valid The length of US(x) must be greater than 2 to be a perfect triangle.
However, without further information, we cannot determine the exact value of x.
You can specify any value greater than 2.
Therefore, from the above conditions, we conclude that 2 < x < 32.
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Does anybody know the answer i need. It quick!!!!!
The area of the triangle in this problem is given as follows:
34 ft².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The parameters for this problem are given as follows:
b = 10 ft, h = 6.8 ft.
Hence the area is given as follows:
A = 0.5 x 10 x 6.8
A = 34 ft².
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Consider a graph of the function y = x² in xy-plane. The minimum distance between point (0, 4) on the y-axis and points on the graph is [1-2] You should rationalize the denominator in the answer. PLEASE HELP ME
The minimum distance between the point (0, 4) on the y-axis and points on the graph is 4.
To find the minimum distance between the point (0, 4) on the y-axis and points on the graph of the function y = x², we can use the concept of perpendicular distance.
The distance between a point (x, y) on the graph and the point (0, 4) is given by the formula:
distance = √((x - 0)² + (y - 4)²) = √(x² + (y - 4)²)
Substituting the function y = x² into the distance formula, we get:
distance = √(x² + (x² - 4)²) = √(x² + (x⁴ - 8x² + 16))
Simplifying further, we have:
distance = √(x⁴ + x² - 8x² + 16) = √(x⁴ - 7x² + 16)
To find the minimum distance, we need to minimize the expression x⁴ - 7x² + 16. Since this is a quadratic-like expression, we can use calculus to find the minimum.
Taking the derivative of x⁴ - 7x² + 16 with respect to x, we get:
d/dx (x⁴ - 7x² + 16) = 4x³ - 14x
Setting the derivative equal to zero to find critical points:
4x³ - 14x = 0
Factorizing, we have:
2x(2x² - 7) = 0
This gives us two critical points: x = 0 and x = ±√(7/2).
Next, we evaluate the expression x⁴ - 7x² + 16 at these critical points and the endpoints of the interval:
f(0) = 0⁴ - 7(0)² + 16 = 16
f(±√(7/2)) = (√(7/2))⁴ - 7(√(7/2))² + 16 ≈ 4.157
Comparing these values, we find that the minimum distance occurs at x = 0, giving us a minimum distance of √(0⁴ - 7(0)² + 16) = √16 = 4.
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For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Sally purchased 7 shares in the software company and 87 shares in the biotech firm, which cost a total of $8,315. At the same time, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech firm. How much did each share cost?
The cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
Let's denote the cost of one share in the software company as 'x' dollars and the cost of one share in the biotech company as 'y' dollars.
According to the given information, Sally purchased 7 shares in the software company and 87 shares in the biotech company, which cost a total of $8,315. We can express this as the following equation:
7x + 87y = 8315 ----(Equation 1)
Similarly, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech company. This can be represented as the following equation:
84x + 50y = 7338 ----(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.
Multiply Equation 1 by 50 and Equation 2 by 87 to eliminate the 'y' terms:
350x + 4350y = 415750 ----(Equation 3)
7308x + 4350y = 638526 ----(Equation 4)
Now, subtract Equation 3 from Equation 4:
(7308x + 4350y) - (350x + 4350y) = 638526 - 415750
Simplifying the equation:
7308x - 350x = 222776
6958x = 222776
Divide both sides of the equation by 6958:
x = 222776 / 6958
x = 32
Now that we have the value of 'x', we can substitute it back into either Equation 1 or Equation 2 to solve for 'y'. Let's substitute it into Equation 1:
7(32) + 87y = 8315
224 + 87y = 8315
87y = 8315 - 224
87y = 8091
Divide both sides of the equation by 87:
y = 8091 / 87
y ≈ 93
Therefore, the cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
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Suppose that the relation H is defined as follows. H = {(9, 3), (8, p), (3, q), (8, 0)) Give the domain and range of H. Write your answers using set notation.
Answer:
See below
Step-by-step explanation:
Domain would be all the x-values, so this is {3, 8, 8, 9}
Range would be all the y-values, so this is {0, 3, p, q}
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There is just one solution to this system. The answer is (460/7), (-13/7), and (-24/7). The correct answer is option A.
Given the system of equations as X+ y- z=63x- y+ z=2x- 4y+ 2z-34.We have to use row operations to solve this system of equations. Let us start by writing down the augmented matrix of the given system of equations. [1, 1, -1 | 6][3, -1, 1 | 2][1, -4, 2 | -34]
The first step is to change the first element of the second row to zero. For that, we subtract three times the first row from the second row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][1, -4, 2 | -34]
Now, we need to change the first element of the third row to zero. For that, we subtract the first row from the third-row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, -5, 3 | -40]
The next step is to change the second element of the third row to zero. For that, we add 5/4 times the second row to the third row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, 0, 7 | -24]
Now, we solve the system of equations using back-substitution. We have 7z = -24 ⇒ z = -24/7
Substituting this value of z in the second equation, we get -4y = 4 - z = 4 + 24/7 = 52/7⇒ y = -13/7
Substituting these values of y and z in the first equation, we get x = 63 - y + z = 63 + 13/7 - 24/7 = 460/7Thus, the solution of the given system of equations is (x, y, z) = (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
The given system of equations is solved using row operations. It is found that this system has exactly one solution which is (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
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What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
Total Amount Interest Amount
compounded annually
compounded semiannually
compounded quarterly
V
Answer:
The total amount with annual compounding is 23,304.79 .
The interest with annual compounding is $18,304.79.
The total amount with semi annual compounding is 24,005.10.
The interest with semi annual compounding is $19,005.10.
The total amount with quarterly compounding is 24,377.20.
The interest with quarterly compounding is $19,377.20.
What are the total amount and interest?
The formula for determining the total amount is:
FV = PV(1 + r/m)^nm
Where:
FV =total amount
PV = amount deposited
r = interest rate
n = number of years
m = number of compounding
Interest = FV - amount deposited
FV = 5000 x (1.08)^20 = 23,304.79
Interest = 23,304.79 - 5000 = $18,304.79
FV =5000 x (1.08/2)^(2 x 20) =24,005.10
Interest = 24,005.10 - 5000 = $19,005.10
FV =5000 x (1.08/4)^(20 x 4) =24,377.20
Interest = 24,377.20 - 5000 = $19,377.20
Step-by-step explanation:
(2x5)(10x−2) simplified
Answer:
200x - 40 (5x-1)
Step-by-step explanation:
2 x 10 = 20
20 x 10 = 200
20 x -2 = -40
200 - 40 = 100 - 20, 50 - 10, 20 - 4, 10 - 2, 5 -1
so the answer is either 5x - 1 or 200x - 40
pls help me with this!!!!
Answer:
The equation of a hyperbola with co-vertices at (0, 7) and (0, -7) and a transverse axis that is 12 units long is:
x²/36 - y²/49 = 1.
Therefore, the correct equation is: x²/36 - y²/49 = 1.
Determine the surface area and volume Note: The base is a square.
The volume of the can is approximately 304 cubic centimeters.
To determine the surface area and volume of the can, we need to consider the properties of a cylinder with a square base.
Surface Area:
The surface area of the can consists of three parts: the square base and the two circular faces.
a) Square Base:
The base of the can is a square, so its area is given by the formula:
Area = side^2.
Since the diameter of the can is 8 centimeters, the side of the square base is also 8 centimeters.
Therefore, the area of the square base is 8 cm [tex]\times[/tex] 8 cm = 64 square centimeters.
b) Circular Faces:
The can has two circular faces, one at the top and one at the bottom.
The formula for the area of a circle is[tex]A = \pi \times r^2,[/tex] where r is the radius. The radius of the can is half the diameter, which is 8 cm / 2 = 4 cm.
Thus, the area of each circular face is [tex]\pi \times (4 cm)^2 = 16\pi[/tex] square centimeters.
To find the total surface area, we sum the areas of the square base and the two circular faces:
Total Surface Area = Square Base Area + 2 [tex]\times[/tex] Circular Face Area
[tex]= 64 cm^2 + 2 \times 16\pi cm^2[/tex]
≈ [tex]64 cm^2 + 100.48 cm^2[/tex]
≈[tex]164.48 cm^2[/tex]
Therefore, the surface area of the can is approximately 164.48 square centimeters.
Volume:
The volume of the can is given by the formula:
Volume = base area [tex]\times[/tex] height.
Since the base is a square, the base area is equal to the side^2, which is 8 cm [tex]\times[/tex] 8 cm = 64 square centimeters.
The height of the can is the height we calculated earlier, which is approximately 4.75 centimeters.
Volume = Base Area [tex]\times[/tex] Height
[tex]= 64 cm^2 \times4.75[/tex] cm
≈ 304 [tex]cm^3[/tex]
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find surface area and volume
The surface area and volume of the composite solid is are 1720ft² and 3563.33 ft³ respectively.
What is volume and surface area of composite solid?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of the solid = lateral area of pyramid + surface area of cuboid
lateral area of pyramid = 4 × 1/2 bh
= 4 × 1/2 × 10× 12
= 120×2 = 240 ft²
Surface area of the cuboid = 2( 100+ 320+ 320)
= 2( 740)
= 1480 ft²
Surface area of the composite solid = 240 + 1480
= 1720 ft²
Volume of the composite solid = volume of cuboid + volume of pyramid
volume of cuboid = 10×10×32 = 3200ft²
volume of pyramid = 1/3base area × height
height of the pyramid is calculated as;
diagonal of base = √ 10²+10²
= √200
= 14.14
h² = 13²-7.07²
h² = 169 - 49.98
h² = 119.02
h = 10.9 ft
Volume of pyramid = 1/3 × 100 × 10.9
= 363.33 ft³
Volume of the composite solid = 3200+363.33
= 3563.33 ft³
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Answer:
(a) The graph is an exponential growth curve.
(b) f(0) = 2, f(1) = 10
(c) The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
Step-by-step explanation:
Given function:
[tex]k(x)=2(5)^x[/tex]
[tex]\hrulefill[/tex]
Part (a)The graph is an exponential growth curve.
The curve begins in quadrant II, crosses the y-axis at (0, 2) into quadrant I, and increases rapidly as x increases.
In general, an exponential growth function is in the form:
[tex]\boxed{y = ab^x}[/tex]
where:
a is the y-intercept.b is the base.In this case, the y-intercept is 2 and the base is 5.
As the value of a is positive, and the value of b is greater than 1, it indicates exponential growth.
[tex]\hrulefill[/tex]
Part (b)The term "second coordinates" refers to the y-values of the points on a graph.
To find the second coordinates of the points with first coordinates 0 and 1, substitute x = 0 and x = 1 into the function and solve.
[tex]\begin{aligned}k(0)&=2(5)^{0}\\&=2(1)\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}k(1)&=2(5)^{1}\\&=2(5)\\&=10\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part (c)The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
As 2(5)ˣ > 0, the graph is entirely above the x-axis.
The end behaviour of the function is:
As x → -∞, k(x) → 0.As x → ∞, k(x) → ∞.Therefore, the graph increases from left to right.
In y = 2(5)ˣ, the base is 5, but it is multiplied by 2. This means that for every unit increase in x, the corresponding y-value is doubled compared to the graph of y = 5ˣ. Therefore, the multiplication by 2 makes the graph of y = 2(5)ˣ steeper than the graph of y = 5ˣ.
The graph is completely on the x-axis; It then increases from left to right. it is less steep that y = 5ˣ
The values are (0, 2) and (1, 10)
How to determine the shape of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2(5ˣ)
The above function is an exponential growth curve
This means that
The graph is completely on the x-axisIt then increases from left to rightit is less steep that y = 5ˣCalculating the values of the functionHere, we have
f(x) = 2(5ˣ)
This gives
f(0) = 2(5⁰)
f(0) = 2
f(1) = 2(5¹)
f(1) = 10
So, the values are (0, 2) and (1, 10)
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1. 20x + 14y +6z
2.6x + 2y
3. 1/2(6n - 12m)
Answer:
1. linear equation
2. linear equation
3. algebraic equation
Step-by-step explanation:
1. The expression 20x + 14y + 6z represents a linear equation with three variables: x, y, and z. It consists of three terms: 20x, 14y, and 6z. The coefficients of these terms are 20, 14, and 6 respectively. This equation represents a plane in a three-dimensional coordinate system, where the variables x, y, and z determine the position on the plane.
2. The expression 6x + 2y represents a linear equation with two variables: x and y. It consists of two terms: 6x and 2y. The coefficients of these terms are 6 and 2 respectively. This equation represents a straight line in a two-dimensional coordinate system, where the variables x and y determine the position on the line.
3. The expression 1/2(6n - 12m) represents an algebraic equation with two variables: n and m. It consists of one term: 6n - 12m. The coefficient of this term is 1/2. This equation represents a relationship between the variables n and m, where n and m could be any real numbers.
What are these three answers?
The true options are:
A. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
E. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Option A represents the original statement accurately. It states that if a number is negative (p), then the additive inverse is positive (q). This corresponds to the implication p → q, where the antecedent is p and the consequent is q.
Option B represents the inverse of the original statement. It states that if a number is not negative (~p), then the additive inverse is not positive (~q). This is the negation of the original statement and can be written as ~p → ~q.
Option C represents the converse of the original statement. It states that if the additive inverse is not positive (~q), then the number is not negative (~p). The converse swaps the positions of the antecedent and consequent, resulting in ~q → ~p.
Options D and E are not true. Option D represents the contrapositive of the original statement, which would be if the additive inverse is not positive (~q), then the number is not negative (~p). However, the contrapositive should have the negation of both the antecedent and the consequent, so the correct contrapositive would be ~q → ~p.
Option E incorrectly represents the converse by stating that if the additive inverse is negative (q), then the number is positive (p), which is not an accurate representation of the converse.
In summary, the true options are A, B, and C, as they accurately represent the original statement, its inverse, and its converse, respectively.
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The complete question is :
Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.
A. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
C. If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
D. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
E. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Escriba el tipo de variable y nivel de medición para la siguiente grupo de variables : A) tipo de medallas a prueba olímpica. B) Volumen de agua en un tanque
The type of medals is a categorical nominal variable, while the volume of water is a numerical continuous variable.
How can these variables be classified?Type of medals in an Olympic event: This is a categorical nominal variable as there are fixed categories for the medals such as gold and silver and they do not have an inherent order The volume of water in a tank: This is a numerical and continuous variable which means it is measured with numbers. Moreover, it is continuous as it is obtained by measuring.Note: This question is in Spanish, here is the question in English:
Write the type of variable and level of measurement for the following group of variables: A) type of medals at Olympic test. B) Volume of water in a tank
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Charimaya is running a race around a square track of length 75 m. Find the distance covered by her at the end of her fifth round.
At the end of her fifth round, Charimaya would have covered a distance of 1500 meters.
To find the distance covered by Charimaya at the end of her fifth round, we need to calculate the total distance covered in one round and then multiply it by five.
Given that the track is square-shaped with a length of 75 m, we know that all four sides of the track are equal in length.
To calculate the distance covered in one round, we need to find the perimeter of the square track. Since all sides are equal, we can simply multiply the length of one side by 4.
The length of one side of the square track is 75 m. Therefore, the perimeter of the track is:
Perimeter = 4 × 75 m = 300 m
So, Charimaya covers a distance of 300 m in one round.
To find the distance covered at the end of her fifth round, we multiply the distance covered in one round by 5:
Distance covered in 5 rounds = 300 m × 5 = 1500 m
Therefore, at the end of her fifth round, Charimaya would have covered a distance of 1500 meters.
It's worth noting that since the track is square-shaped, each round consists of running along all four sides of the track.
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2 times the cube root of 72 divided by the cube root of 3888
Step-by-step explanation:
0.52913368398
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what is this solution to the problem of ? 12÷132
Answer:
0.090909
Step-by-step explanation:
I used a calculator
Find the value of the combination. 13C5
Answer:
[tex]_{13}C_5=1287[/tex]
Step-by-step explanation:
[tex]\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\\\\_{13}C_5=\frac{13!}{5!(13-5)!}\\\\_{13}C_5=\frac{13!}{5!\cdot8!}\\\\_{13}C_5=\frac{13*12*11*10*9}{5*4*3*2*1}\\\\_{13}C_5=\frac{154440}{120}\\\\_{13}C_5=1287[/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(13 - 5)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(8)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times \cancel{8!}}{5! \times \cancel{8!}} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 }{5 \times 4 \times 3 \times 2 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 110 \times 9 }{20 \times 6 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 990 }{20 \times 6 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{154440 }{120 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = 1287 \\ [/tex]
on #5
Find the measure of the indicated are.
90°
80°
100°
70°
H
40°
The measure of the Intercepted arc having an inscribed angle of 40 degrees is 80 degrees.
What is the measure of the intercepted arc?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the figure:
Inscribed angle = 40 degrees
Intercepted arc = ?
Plug the given value into the above formula and solve for the arc:
Inscribed angle = 1/2 × intercepted arc.
40 = 1/2 × intercepted arc
Multiply both sides by 2:
40 × 2 = 2 × 1/2 × intercepted arc
40 × 2 = intercepted arc
Intercepted arc = 80°
Therefoore, the Intercepted arc is 80 degrees.
Option B) 80° is the correct answer.
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Pamela bought a cat carrier to take her new kitten, Muffinnette, to the vet. The carrier is shaped like a rectangular prism that is 15 inches long, 9 1/2
inches wide, and 10 inches tall.
Which equation can you use to find the volume of the cat carrier, V?
What is the volume of the cat carrier?
What is the formula?
What do the V’s equal?
Answer:
60 cm³
Step-by-step explanation:
volume of a rectangular pyramid
v = ( l * w * h ) / 3
v = ( 4 * 5 * 9 ) / 3
v = 60
A water slide is a straight ramp 20 m long that starts from the top of a tower 18 m high. Find the angle the slide forms with the tower. Approximate to the nearest degree.
The angle the slide forms with the tower is approximately 41 degrees (rounded to the nearest degree).
To find the angle the slide forms with the tower, we can use trigonometric ratios. Let's consider the right triangle formed by the height of the tower (18 m), the length of the slide (20 m), and the angle we want to find.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the tower (18 m) and the adjacent side is the length of the slide (20 m). Therefore:
tan(angle) = 18/20
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(18/20)
Using a calculator, we find that arctan(18/20) is approximately 40.56 degrees.
Therefore, the angle the slide forms with the tower is approximately 41 degrees (rounded to the nearest degree).
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(08.01 MC)
A function is shown: f(x) = 4x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
Of(x) = (4x + 1)(4x - 1)
Of(x) = (2x + 1)(2x - 1)
f(x) = 4(x²+1)
f(x) = 2(x²-1)
The equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b): Of(x) = (4x + 1)(4x - 1).
The correct answer to the given question is option a or b.
The given function is f(x) = 4x² - 1. We need to choose the equivalent function that best shows the x-intercepts on the graph.The x-intercepts are the points where the graph of a function intersects the x-axis. At the x-intercepts, the value of y is zero.
Therefore, to find the x-intercepts, we need to solve the equation f(x) = 0 for x. The function f(x) = 4x² - 1 can be factored as:(2x + 1)(2x - 1)
To find the x-intercepts, we set f(x) = 0:4x² - 1 = 0(2x + 1)(2x - 1) = 0So, either 2x + 1 = 0 or 2x - 1 = 0. Solving these equations, we get:
x = -1/2 or x = 1/2
These are the x-intercepts of the graph of f(x) = 4x² - 1.Now, let's look at the given options and determine which one shows the x-intercepts on the graph:
Option (a):
Of(x) = (4x + 1)(4x - 1)
This is the factored form of f(x) = 4x² - 1. It correctly shows the x-intercepts.
Option (b):
Of(x) = (2x + 1)(2x - 1)
This is the same as option (a) and correctly shows the x-intercepts.
Option (c): f(x) = 4(x² + 1)
This function does not have any x-intercepts. It has a minimum value of 4 at x = 0.
Option (d): f(x) = 2(x² - 1)
This function has x-intercepts at x = -1 and x = 1. It does not show the x-intercepts of the given function.
Therefore, the equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b):
Of(x) = (4x + 1)(4x - 1).
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Please please help me!!
What can you conclude about the population
density from the table provided?
Region A
Region B
Region C
Region D
Population
20,178
1,200
13,475
6,980
Area (km²)
521
451
395
426
Answer:
Region A: 20,178 people/521 km²
= 38.7 people/km²
Region B: 1,200 people/451 km²
= 2.7 people/km²
Region C: 13,475 people/395 km²
= 34.1 people/km²
Region D: 6,980 people/426 km²
= 16.4 people/km²
The regions, in order from the most densely populated to the least densely populated: A, C, D, B
Evaluate the given expression for x=7
Answer:
63
Step-by-step explanation:
Given the expression:
[tex]\displaystyle{x^2+3x-7}[/tex]
Substitute x = -7:
[tex]\displaystyle{7^2+3(7)-7}[/tex]
Evaluate:
[tex]\displaystyle{(7)(7)+3(7)-7}\\\\\displaystyle{=49+21-7}\\\\\displaystyle{=63}[/tex]
You pick a card at random. Without putting the first card back, you pick a second card at random.
6,7,8,9
What is the probability of picking a 6 and then picking a 9?
(Write you answer as a fraction or whole number)
NEED ASAP PLS!!!!!
Answer:
1/12 is the correct answer
In a group of 105 students, 70 students passed Mathematics, 60 students passed History and 45 students passed Geography; 30 students passed Mathematics and History, 35 students passed History and Geography, 25 passed Mathematics and Geography and 15 passed all three subjects. Draw a Venn Diagram to illustrate this information. Find the number of students who
a) Passed at least one subjects
b) Passed exactly two subjects
c) Passed Geography and failed Mathematics
d) Passed all three subjects e) Failed Mathematics given that they passed History
answer pls
a) Passed at least one subject: 100 students
b) Passed exactly two subjects: 90 students
c) Passed Geography and failed Mathematics: 20 students
d) Passed all three subjects: 15 students
e) Failed Mathematics given that they passed History: 30 students.
To solve this problem, let's draw a Venn diagram to visualize the information given:
In the Venn diagram above, the circles represent the three subjects: Mathematics (M), History (H), and Geography (G). The numbers outside the circles represent the students who did not pass that particular subject, and the numbers inside the circles represent the students who passed the subject. The numbers in the overlapping regions represent the students who passed multiple subjects.
Now, let's answer the questions:
a) Passed at least one subject:
To find the number of students who passed at least one subject, we add the number of students in each circle (M, H, and G), subtract the students who passed two subjects (since they are counted twice), and add the students who passed all three subjects.
Total = M + H + G - (M ∩ H) - (M ∩ G) - (H ∩ G) + (M ∩ H ∩ G)
Total = 70 + 60 + 45 - 30 - 25 - 35 + 15
Total = 100
Therefore, 100 students passed at least one subject.
b) Passed exactly two subjects:
To find the number of students who passed exactly two subjects, we sum the students in the overlapping regions (M ∩ H, M ∩ G, and H ∩ G).
Total = (M ∩ H) + (M ∩ G) + (H ∩ G)
Total = 30 + 25 + 35
Total = 90
Therefore, 90 students passed exactly two subjects.
c) Passed Geography and failed Mathematics:
To find the number of students who passed Geography and failed Mathematics, we subtract the number of students in the intersection of M and G from the number of students who passed Geography.
Total = G - (M ∩ G)
Total = 45 - 25
Total = 20
Therefore, 20 students passed Geography and failed Mathematics.
d) Passed all three subjects:
To find the number of students who passed all three subjects, we look at the overlapping region (M ∩ H ∩ G).
Total = (M ∩ H ∩ G)
Total = 15
Therefore, 15 students passed all three subjects.
e) Failed Mathematics given that they passed History:
To find the number of students who failed Mathematics given that they passed History, we subtract the number of students in the intersection of M and H from the number of students who passed History.
Total = H - (M ∩ H)
Total = 60 - 30
Total = 30
Therefore, 30 students failed Mathematics given that they passed History.
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