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The perimeter of a shape is 15 cm and the area is 25 cm^2

Find the area of the larger shape if it is being enlarged by a scale factor of 6​

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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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.

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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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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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]

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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Answer:

60 cm³

Step-by-step explanation:

volume of a rectangular pyramid

v = ( l * w * h ) / 3

v = ( 4 * 5 * 9 ) / 3

v = 60

The measure of the Intercepted arc having an inscribed angle of 40 degrees is 80 degrees.

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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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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Answer:

1/12 is the correct answer

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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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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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.

The height, h, of the cylinder is approximately 1.27 centimeters when the volume is 100 cm^3 and the radius is 5 cm, rounded to the nearest tenth.

To find the height, h, of the cylinder, we can rearrange the formula for the volume of a cylinder:

V = πr^2h

Given that the volume, V, is 100 cm^3 and the radius, r, is 5 cm, we can substitute these values into the formula:

100 = π(5^2)h

Simplifying further:

100 = 25πh

To solve for h, divide both sides of the equation by 25π:

100 / (25π) = h

To calculate the value, we'll use an approximation for π as 3.14:

100 / (25 * 3.14) ≈ h

Simplifying:

100 / 78.5 ≈ h

h ≈ 1.27 cm

Therefore, when the volume is 100 cm3 and the radius is 5 cm, the cylinder's height, h, is about 1.27 centimetres, rounded to the closest tenth.

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Answer:

0.090909

Step-by-step explanation:

I used a calculator

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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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:

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]

Answer:

-9 is less than x, which is less than or equal to 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Domain is where the function exists for x.

The functions domain goes in terms of x goes from -9 to 11 not including -9 and including 11.

Interval notation:

-9 < x ≤ 11

Set notation:

(-9, 11]

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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The area of the triangle in this problem is given as follows:

34 ft².

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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The 90% confidence interval for the population variance (σ^2) is approximately [7.19, 20.19].

To construct a 90% confidence interval for the population variance (σ^2), given a sample size of 20 and a sample variance (s^2) of 12.5, we need to utilize the chi-square distribution.

The formula for constructing a confidence interval for the population variance is:

[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]

Where n is the sample size, s^2 is the sample variance, χ^2_upper is the upper critical value from the chi-square distribution, and χ^2_lower is the lower critical value from the chi-square distribution.

For a 90% confidence interval, we need to find the critical values from the chi-square distribution that correspond to the upper and lower tails of 5% each (since the confidence level is divided equally into two tails).

(a) Degrees of freedom:

The degrees of freedom (df) for the chi-square distribution is equal to n - 1. In this case, n = 20, so df = 20 - 1 = 19.

(b) Chi-square critical values:

We need to find the upper and lower critical values from the chi-square distribution table for df = 19 and a significance level of 0.05/2 = 0.025 (for each tail).

From the chi-square distribution table or using a statistical software, the upper critical value for a significance level of 0.025 and df = 19 is approximately 32.852. Similarly, the lower critical value is also approximately 8.907.

(c) Confidence interval calculation:

Substituting the values into the formula, we can construct the confidence interval:

[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]

[ (20 - 1) * 12.5 / 32.852, (20 - 1) * 12.5 / 8.907 ]

[ 19 * 12.5 / 32.852, 19 * 12.5 / 8.907 ]

[ 7.19, 20.19 ]

Therefore, the [7.19, 20.19] is roughly inside the 90% confidence interval for the population variance (2).

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Question

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample​ variance, s^2​, is determined to be 12.5.Complete parts​ (a) through​ (c).Construct a​ 90% confidence interval for

σ2 if the sample​ size, n, is 20.

Answer:

B :3

Step-by-step explanation:

good luck <3

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}

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.

The surface area and volume of the composite solid is are 1720ft² and 3563.33 ft³ respectively.

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:

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

Step-by-step explanation:

0.52913368398

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The perimeter of shape C is 30 cm shorter than the total perimeter of A and B.

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:

Then the difference is given as follows:

34 + 26 - 30 = 30 cm.

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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]

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:

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]

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]

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:

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)

From 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

Here, 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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