Answer: 85
To solve this, we need to calculate the height of the triangle. To do this, we divide the triangle verticaly, in two right triangles.
So, we have the hypotenuse of the two smaller triangles is 14. The short leg is half the side of the big triangle: 14/2=7 and the long leg is the height of the triangle and what we want to know.
By the pythagorean theorem:
[tex]14^2=7^2+x^2[/tex][tex]x=\sqrt[]{14^2-7^2}=7\sqrt[]{3}[/tex]And now we use the formula for the area of a triangle:
[tex]A=\frac{b\cdot h}{2}=\frac{7\cdot7\sqrt[]{3}}{2}=\frac{49\sqrt[]{3}}{2}[/tex]This is the area of each of the smaller triangles. To get the area of the big triangle, we add up the two smaller areas:
[tex]\frac{49\sqrt[]{3}}{2}+\frac{49\sqrt[]{3}}{2}=49\sqrt[]{3}[/tex]rounded to the nearest tenth is 85
Find the total surface area of the cone. Use the r button on your calculator. altitude = 13 cm, diameter = 11 cm, slant height = 15 cm
In general, the area of a cone is given by the formula below
[tex]\begin{gathered} A=\pi r^2+\pi rl \\ r\rightarrow\text{ radius} \\ l\rightarrow\text{ slant height} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} r=\frac{11}{2}=5.5 \\ l=15 \\ \Rightarrow A=\pi *5.5^2+\pi *5.5*15 \\ \Rightarrow A=112.75\pi \end{gathered}[/tex]Rounding to two decimal places,
[tex]\Rightarrow A\approx354.22[/tex]The answer is approximately 354.22 cm^, option D.razy GolfmathsdivThe current value of a baseball card is 60 times its original value v (in dollars). The baseball card is worth$15. Write and solve an equation to find the original value of the baseball card.Equation:= 15Original value: $
Answer:
Equation: 60v = 15
Original value: $0.25.
Step-by-step explanation:
Current value: $15
Original value: v
The current value is 60 times the original value.
So, the equation is:
Equation: 60v = 15
Now we solve the equation to find the original value.
60v = 15
v = 15/60
v = 0.25
Original value: $0.25.
Write the following sentence using mathematical symbols:
n is greater than or equal to 0.
The sentence using mathematical symbols would form an inequality as; n ≥ 0.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. The Set of such values is; called the solution set to the considered equation or inequality.
We need to write a sentence using mathematical symbols:
Given that "n is greater than or equal to 0"
The inequality form as;
n ≥ 0
Therefore, the sentence using mathematical symbols would form an inequality as; n ≥ 0.
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HELP PLSSSSSSSSSSSSSS
Answer: 64
Step-by-step explanation:
Length x width x higth= volume
4 x 8 x 2 = 64
Answer:
4 cm
Step-by-step explanation:
First, find the volume of the rectangular prism.
4*8*2=32*2=64 cm^-3
Now, the formula for the volume of the cube is:
Volume = side ^ 3
We know the volume is 64 cm^3, so plug it in to the equation:
64 = side ^ 3
take the cube root of both sides
4 = side
Use the sketch tool to mark the picture with the given information. Then choose what postulate proves the triangles congruent.
We choose ASA Postulate to prove this triangle congruent.
In the given question given that
[tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
So [tex]m\angle BAC\cong m\angle DAC[/tex]
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
So [tex]m\angle BCA\cong m\angle DCA[/tex]
Then [tex]AC\cong AC[/tex]
Then [tex]\triangle BAC\cong \triangle DAC[/tex]
There given postulate are AAS, ASA, SSS, SAS.
We have proved using the ASA postulate.
Now describing the ASA postulate.
ASA means Angle-Side-Angle Postulate.
According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Hence, we choose ASA Postulate to prove this triangle congruent.
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: 0, ordered pair: (−3,−8)
The equation (in slope-intercept form) of the line as described whose slope is; 0 and passes through the point given is; y = -8.
What is the equation of the line whose slope is; 0 and passes through the point given;It follows from the task content that the equation of the line whose slope is; 0 and passes through the point; (-3, -8) is to be determined.
Hence, from the slope formula;
slope, m = ∆y/∆x
Therefore; 0 = ∆y/∆x
By cross-multiplication; we have;
∆y = 0
Recall, ∆y = y - y1 = y - (-8)
y - (-8) = 0
y + 8 = 0
y = -8.
Therefore, it follows that the equation of the line described is; y = -8.
Consequently, the line in discuss is a horizontal line.
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HELP ASAP
Solve z3 = 27.
z = 9
z = −9
z = 3
z = ±3
Answer:
the answer is 3
Step-by-step explanation:
Jose invests $8,216 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. What will the account balance be after 11 years?
After 11 years, the account balance is $17,704.987. (approx.)
Compound interest is defined.The principle of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate compound interest.
The principal of the loan plus compound interest will then be what is left.
Given,
P = $8,216 for the principal value.
Interest rate, r = 7% or 0.07.
Period, with t = 11.
Interest applied n times every time period, or 12 times.
As far as we are aware, A = P(1 + r/n) n*t
where A is the whole sum.
Fill out the formula with the values,
=> A = 8216(1 + 0.07/12) ^ 11*12
= 8216((12 + 0.07)/12) ^ 132
Upon calculation, we obtain,
≅ $17,704.987
As a result, after 11 years, the account will have a balance of $17,704.987 (about).
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a1 = 1; d = 3a1 = 1; d = −3a1 = 17; d = 3a1 = 17; d = −3
Given:
A graph is given and the points on the graph are as:
(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)
Required:
To determine the value of
[tex]a_1[/tex]and d for the given sequence.
Explanation:
We can observe from the graph that the given sequence is an arithmetic sequence.
Here
[tex]a_1[/tex]represent the first value and d represent the common ratio.
So the values are as:
[tex]\begin{gathered} a_1=1 \\ d=14-17=\text{ -3} \end{gathered}[/tex]Final Answer:
[tex]a_{1=1},\text{ d = -3}[/tex]The second option is the correct answer.
If Y (-7, -4) and Z (5, 2), find the slope of a line perpendicular to YZ
Answer:
slope of perpendicular line = - 2
Step-by-step explanation:
calculate the slope of YZ using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )
[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30.
Answer: One pair of skates costs a total of $3
Step-by-step explanation: 30 (Total) - 9 (Fee) ÷ 7 (Pairs of skates)
Total - Free ÷ Pair of skates
The data represents the number of cars that the sales staff at Templeton Motors sold this week.
4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3
Which line plot correctly displays the data?
OA.
Formula Sheet
3.
Number of Cars Sold
X X
X X X
X X X X X X
+++
AHH
+
0 1 2 3 4 5 6 7 8 9 10
X
Number of Cars Sold
X X X X X X X
H
0 1 2 3 4 5 6 7 8 9 10
OC.
OD.
←
Number of Cars Sold
X X
X X X
X X X X X X X
++
0 1 2 3 4 5 6 7 8 9 10
X X
Number of Cars Sold
X X
X X X
H11
0 1 2 3 4 5 6 7 8 9 10
The line plot that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.
How to Represent a Data on a Line Plot?A line plot is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the line plot.
The dots on each data point on the line plot corresponds to the frequency of a data point in a data distribution.
Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:
2 - 1 dot
3 - 3 dots
4 - 3 dots
5 - 2 dots
6 - 1 dot
7 - 1 dot
8 - 1 dots
Thus, the line plot that correctly represents these data points alongside their frequencies is: A.
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HELP ASAP WILL GIVE BRAINLEST
How many times larger is (1.064 x 10^1) than (7 x 10^−1)?
0.152
15.2
6.58
7.448
1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
We'll apply division by splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
Let 7 x 10⁻¹ be x times the number 1.064 x 10¹.
The value of x is obtained by taking the ratio of 1.064 x 10¹ and 7 x 10⁻¹.
x = 1.064 x 10¹ / 7 x 10⁻¹
x = 15.2
Thus,1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.
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Your friend has a coln that is not fair. It comes up heads 70% of the time and talls 30% of the time. You flip it twice. Let Xbe the number of heads that come up. Find the probability distribution for X
Let X be the number of heads that come up
[tex]\begin{gathered} \text{Probability of head = 70\% = }\frac{70}{100} \\ \text{Probability of tail = 30\% = }\frac{30}{100} \end{gathered}[/tex]Step 1: Write out the formula for the binomial probability distribution
[tex]P_x=^nC_xp^xq^{n-x}[/tex][tex]undefined[/tex]Someone please help me with this!
The width of the chest is 14.7 inches.
What is a Rectangular Prism?A rectangular prism is a three-dimensional form with six faces, where all of the faces (top, bottom, and lateral faces) are rectangles and all pairings of opposite faces are congruent. The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.Given:
The volume of rectangular prism = 10368 cubic inches or 6 cubic feet
Height of rectangular prism = 24 inches
It is mentioned that the chest will be twice as long as it is wide.
Let the width of the chest be x inches, so its length is 2x inches.
The volume of the chest = length × width × height
Substituting the values,
10368 = 2x × x × 24
10368 = 2x²× 24
x² = 10368/48
x = √216
x ≅ 14.7 inches ( to the nearest tenth of an inch)
Therefore, the width of the chest is 14.7 inches.
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Please solve for x using steps 1/3x= 1/3+6/x
You have the following algebraic equation:
1/3x = 1/3 + 6/x
In order to solve the previous equation you first multiply both sides of the equation by x, thus, you can quit x denominators in the equation. Proceed as follow:
1/3x = 1/3 + 6/x multiply by x both sides
1/3 = x/3 + 6 multiply by 3 both sides
1 = x + 18 subtract 18 both sides
1 - 18 = x + 18 - 18
-17 = x
-17 = x is the same as x = -17. The solution to the given equation is x = -17.
The difference of seven times a number and five is one hundred find the number
Let the number be x
seven times the number = 7x
The difference of seven times a number and five is one hundred. It means that
7x - 5 = 100
7x = 100 + 5
7x = 105
x = 105/7
x = 15
The number is 15
The directress of a parabola is represented by the linear equation y=2, and its vertex is located at (3,1).Both of these attributes of the parabola are graphed below. which of the following is the equation that represents this parabola?
The directrix of the parabola is at y = 2 and its vertex is at (-3,1). Since the directrix is below the vertex, we can say that the parabola will open downwards. The general form to find the equation of the parabola given the directrix and vertex is
[tex]y=-(x-h)^2+k[/tex]The value of h for the problem is -3 while the value of k for the problem is 1. Substitute it on the equation above, we get
[tex]\begin{gathered} y=-(x-(-3))^2+1 \\ y=-(x+3)^2+1 \end{gathered}[/tex]Hence, the answer to this problem is option 2. Note that the equation started in a negative sign because the parabola opens downwards.
(1/5) -1 as the exponent
Answer:
1/5
Step-by-step explanation:
Which graph represents the solution set of the system of inequalities-2x+y<_4 y>x+2
The graph of the solution set of the system of inequalities y > x + 2 and
- 2x + y ≤ 4 is shown in figure.
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequalities is,
⇒ y > x + 2
And, - 2x + y ≤ 4
Now,
The inequality is,
⇒ - 2x + y ≤ 4
Add 2x both side, we get;
⇒ - 2x + y + 2x ≤ 4 + 2x
⇒ y ≤ 2x + 4
And, The second inequality is;
⇒ y > x + 2
So, Plot the graph of the inequalities y ≤ 2x + 4 and y > x + 2.
We get the solution set of the system of inequalities.
Which is shown in figure.
Thus, The graph of the solution set of the system of inequalities y > x + 2 and - 2x + y ≤ 4 is shown in figure.
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write down in terms of n, an expression for the nth term of the following sequences
-7,-12,-17,-22,-27
The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
The sequence is -7, -12, -17, -22, -27...
The first term = -7
The common difference = The second term - The first term
= -12 - (-7)
= -12+7
= -5
The nth term of the sequence = a+(n-1)d
Where a is the first term
d is the common difference
n is the n terms
Substitute the values in the equation
The nth term of the sequence = -7+(n-1)-5
= -7-5n+5
= -5n-2
Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
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a cylinder had a radius of 3 and height of 2 need answer quick
To find the volume of a cylinder with radius 3 and height 3
we will use the formular below:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question, r=3 and h = 2
substitute the value into the formula
[tex]V=\pi(3)^2\times2[/tex][tex]V=18\pi[/tex]If we substitute the value of pie = 22/7
Then,
[tex]V=18\times\frac{22}{7}[/tex][tex]V\approx56.57\text{ cubic unit}[/tex]Mrs. Smith wants to buy floor covering for her master bedroom. The dimensions of the master bedroom are 11yd by 7yd. The floor covering is sold in square meters. How many square meters of floor covering will she need?
She will need ____ square meters.
Round answer to the nearest hundredth as needed.
Mrs. Smith will need 64m² of floor covering for her master bedroom.
The length L of the bedroom is 11 yards,
The breadth B of the bedroom is 7 yards.
The floor covering is available only in square meters.
As we know,
One yard = 0.9144 meters.
the length of the bedroom in meter is,
Length L = 0.091144 x 11
Length L = 10.02 meters.
the breadth of the bedroom in meters is,
Breadth B = 0.91144 x 7
Breadth = 6.38 meters.
the Area of Rectangular master bedroom in Meter square is,
Area = Length x Breadth
Area of the bedroom = 10.02 x 6.38
Area of the bedroom = 63.92 m²
Area of floor covering required = Area of the master bedroom.
Area of the floor covering required = 63.92 m².
Rounding off to nearest hundredth = 64m²
Mrs. Smith will need 64m² of floor covering.
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X Consider lines L and M on the graph below. Which of the following BEST describes the slope of these two lines? y L М. 10 9 8 7 6 5 3 2 1 X 0 1 2 3 4 5 6 7 8 9 10 L has a greater slope than M. Land M have the same slope. M has a greater slope than L.
since they are parellel lines, we conclude that they have the same slope, the second option is the correct one.
(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)
Explanation:
We have two equation of line. Both lines intersect at a point.
The point of intersection of two graphs, is the solution of the graph.
At this point, both will have same x and y values
Tracing the graph:
The point of intersection occurs at x = -2, y = 2
Hence, the solution is at (-2, 2)
please help! what are the x and y values
Answer:
1, -2
0, -4
-1,-6
-2,-8
Don buys a shirt for $24.85. His friend Daryl spends $3.15 more for his shirt. Sean paid the same price as Daryl for his shirt but bought 2. How much did Sean spend for his 2 shirts?
Solution
- Don buys a shirt for $24.85.
- Daryl spends $3.15 more for his shirt. This means that Daryl spends
[tex]\$24.85+\$3.15=\$28[/tex]- Thus, Daryl spends $28 on his shirt.
- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.
- Sean bought two shirts, thus, Sean spends:
[tex]\$28+\$28=\$56[/tex]Final Answer
Sean spends $56 on his 2 shirts
Find the suma1 = -26/5 , d = -5/3 , n = 10
The sum of the arithmentic series is -127
Step - by - Step Explanation
What to find? The sum of the arithmetic series.
Parameter Given:
a₁ = -26/5 , d=-5/3 , n=10
To find the sum of the arithmetic series we will use the formula below:
[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]Substitute the values and evaluate.
[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]=-127
A shopper pushes a grocery cart with a force F of 50 N downward and to the right, as shown in the figure below. The anglethe handle makes with the horizontal is 37°, and the cart is moved 14 m. Find the work W done, in joules (1).Ed
Solution
For this case we can create the following plot:
We want to find the work so we can use this formula:
[tex]W=Fd\cos \theta[/tex]Replacing we got:
[tex]W=50\cdot14m\cdot\cos 37=559.04J[/tex]Solve the equation for y in terms of x. In other words, algebraicallyrearrange the equation so that the y variable is by itself one side of theequation. Type your answer in the form y = mx + b. If you have a valuethat is not an integer then type it rounded to the nearest hundredth. Donot put spaces between your characters.4.2 + 2y = 8y = ?4x+2y=8
Given:
[tex]4x+2y=8[/tex]Solve the equation for y,
[tex]\begin{gathered} 4x+2y=8 \\ Subtract\text{ -4 from both sides} \\ 4x+2y-4x=8-4x \\ 2y=8-4x \\ \text{Divide by 2 on both side} \\ \frac{2y}{2}=\frac{8-4x}{2} \\ y=\frac{8}{2}-\frac{4x}{2} \\ y=4-2x \\ \text{ express the equation in the form y=mx+b} \\ y=-2x+4 \end{gathered}[/tex]Answer: y = -2x +4