15 students and 13 teachers went on a field trip to an art museum. Student tickets cost $4 each, and adult tickets cost $9 each. How much did the museum tickets cost in all?​

The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

[tex](x - 8)^{2} = 144[/tex]

The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -

[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]

[tex]x^{2} + 64 + 16x = 144[/tex]

[tex]x^{2} + 16x + 64 - 144 = 0[/tex]

[tex]x^{2} + 16x - 80 = 0[/tex]

[tex]x^{2} + 20x - 4x - 80 = 0[/tex]

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

d. 20 feet by 20 feet

Solve problems on area of lawn -

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P = 180 - (125 + 30)

P = 180 - 155

P = 25 degrees

Thus :

P = 25/180 n radian

P = 5/36 n

Which mean the first option is the correct answer.

Answer:3/7

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

change all denominators to 21

{21 is the lcd of all the numbers)

17/21 x 1= 17/21

1/3 x 7 = 7/21

5/7 x 3 = 15/21

17/21 + 7/21 - 15/21

24/21-5/21

9/21

reduce by three

9/21÷3

3/7

The area of the circular section is 3.14 square units

The given parameters are:

Radius, r = 1 kilometre

Rewrite the above properly as follows

So, we have

r = 1 kilometre

The area of the circular section is:

A = πr^2

So, we have

A = 3.14 * 1^2

Evaluate the exponent

So, we have

A = 3.14 * 1

Evaluate the product

So, we have

A = 3.14

Hence, the area of the circular section is 3.14 square units

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The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

In the question,

the given expression is [tex]-24\frac{1}{2} +16.15-4[/tex] , solving further we get

= -49/2 + 16.15 - 4       ...(as [tex]24\frac{1}{2} = \frac{49}{2}[/tex]  )

= -24.5 + 12.15

= -12.35

In option(A) we have ,

=[tex]24\frac{1}{2} -16.15+4[/tex]

= 49/2 -16.15 +4

= 24.5 -16.15 +4

= 8.35 + 4

= 12.35

In option(B) we have ,

= 16.15 - 28.5

= -12.35

In option(C) we have ,

= -28.5 + 16.15

= -12.35

In option(D) we have ,

[tex]=-20\frac{1}{2} +16.5[/tex]

= -41/2 + 16.5     ...( as [tex]20\frac{1}{2} = \frac{41}{2}[/tex] )

= -20.5 + 16.5

= -4

In option(E) we have ,

[tex]=12.15-24\frac{1}{2}[/tex]

= 12.15 - 49/2

= 12.15 - 24.5

= -12.35

As we can see that from all the option , only option(B), option(C) and option(E) matches with the given expression .

Therefore , The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

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The regions is represented as :

   A = p - p ∩ q ,  B = p ∩ q  and   C = q - p ∩ q

According to the question we have been given the Venn diagram with two regions p and q.

We need to find the representation of regions A, B and C.

As we can from the diagram,

  region A is the area where the only p statement is there which exclude the B region . That is A is area of difference.

So it can be represented as

                   A = p - p ∩ q

  region B is the intersection of p and q.

So it can be represented by

                  B = p ∩ q

region C is the area where only q statement is there and excludes the intersection region. That is C is area of difference

So it can be represented as

                  C = q - p ∩ q

Hence the regions is represented as

                  A = p - p ∩ q

                  B = p ∩ q

                  C = q - p ∩ q

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Answer:its a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer is in the pic.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]

Use the trigonometric identities to prove the given equation:

[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]

                 [tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]

Answer:The answer would be 8

Step-by-step explanation:You would have to do 8/-2+2 and that would leave you with 8 because -2+2 is 0.

Answer:

The first answer is correct

Step-by-step explanation:

y = mx + b is the slope intercept form of a line

15x - 5y = 30  Subtract 15x from both sides

-5y = -15x + 60  Divide both sides by -5

y = 3x -6  The -6 is your y-intercept.  It is the point (0.-6)  We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.

The x-intercept is when y = 0

y = 3x -6

0 = 3x - 6 Add 6 to both sides

6 = 3x  Divide both side by 3

2 = x This is the point (2,0)

We could have taken the original equation and set x=0 and y=0

15x - 5y = 30

15(0) - 5y = 30

-5y = 30  Divide both sides by -5

y = -6

15x -5y = 30

15x - 5(0) = 30

15x = 30  Divide both sides by 15

x = 2

-

The Lateral surface of the triangular pyramid = 6 cm²

The lateral surface of a triangular pyramid is the area of the three triangular surfaces of the triangular pyramid, which excludes the area of the base.

The area of each triangular face = area of triangle = 1/2(base)(height).

Given the following as shown in the diagram:

Height of the triangular face = 7.2 cm

Base length of the triangular face = 5 cm

Lateral surface of the triangular pyramid = 3(1/2 × base × height)

Plug in the values

Lateral surface of the triangular pyramid = 3(1/2 × 5 × 7.2)

Lateral surface of the triangular pyramid = 3(18)

Lateral surface of the triangular pyramid = 6 cm²

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Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex]

to rationalise the denominator multiply numerator/ denominator by [tex]\sqrt{5}[/tex]

= [tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]

= [tex]\frac{\sqrt{75} }{5}[/tex]

= [tex]\frac{\sqrt{25(3)} }{5}[/tex]

= [tex]\frac{5\sqrt{3} }{5}[/tex]

= [tex]\sqrt{3}[/tex]

7.5% = 0.075

0.075 x 123.28 = 9.246

So, the tax will be $9.20.

Total cost would be $132.48.

Answer:

8

Step-by-step explanation:

I attached my answer........

Answer
(-3) - (-10) = 7

|7| = 7

7

Answer:

x = -6

Step-by-step explanation:

Distribute where possible

5x - 30 + 8 = 7x - 10

Combine like terms

5x - 22 = 7x - 10

Subtract 7x from both sides and add 22 to both sides

-2x = 12

x = -6

Answer:

The distance would be 118

Step-by-step explanation:

The easiest way I solve the distance between a negative number and a positive number is by adding the negative (but making it a positive) and the positive together. If you add 55 and 63 you would get 118. And 118 is the distance between -55 and 63.

I hope this helps!! :)

Answer:

5

Step-by-step explanation:

Every number from the absolute sign will be positive.

The value of (gof)(-2) for the given values of f(x) and g(x) is 60.

A Composite function may be defined as a function which is formed from the operation of combination of two functions. If f(x) and g(x) are two functions, then the composite functions of the given functions are fog(x) that is f(g(x)) and gof(x) that is g(f(x)).

It is given in the question that f(x) = -2x + 7 and g(x) = x² - 6x + 5.

Now, gof(x) = g(f(x)) = (-2x + 7)² - 6(-2x + 7) + 5

gof(x) = 4x² + 49 - 28x + 12x - 42 + 5

gof(x) = 4x² - 16x + 12

gof(-2) = 4(-2)² - 16(-2) + 12

gof(-2) = 16 + 32 + 12

=>gof(-2) = 60

Therefore, the value of gof(-2) is equal to 60.

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According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

Answer:

y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Step-by-step explanation:

Look at (-3,3) and (2,7)

So the line rises 4 units and runs 5 units, then slope is 4/5

using m = 4/5, y = 3, x = -3

y = mx + b

3 = 4/5(-3) + b

3 = -12/5 + b

b = 15/5 + 12/5 = 27/5

so y = 4/5x + 27/5

or 5y = 4x + 27

or 5y - 4x = 27

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

Answer:

$448.766754 per week or $448

Step-by-step explanation:

i gotchu

theres 52.1429 weeks

divide 23,400 by 52.1429

u get $448.766754 per week

Answer:

[tex] - 2x - h[/tex]

Step-by-step explanation:

We are given a function [tex]g(x)=2-x^2[/tex]. We want to find [tex](g(x+h)-g(x))/h[/tex] To do so, first we need to work out the numerator

[tex]g(x+h)=2-(x+h)^2[/tex]. Therefore

[tex]g(x+h)-g(x)\implies 2-x^2-2xh-h^2-2x-x^2[/tex]

like terms cancel out leaving us with

So,

[tex] \displaystyle\frac{g(x + h) + g(x)}{h} = \frac{ h( - 2x - h )}{h} = \boxed{ - 2x - h}[/tex]

Let us assume the given number is x.

If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:

= (x-5) × 2

Formation of equation:

The number decreased by 5 can be written as: x - 5

Now, to double it, we will multiply it by 2 = (x-5) × 2

Therefore, we have the algebraic form of the given condition as :

= (x-5) × 2

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Answer:

2,440 acres of old-growth trees.

Step-by-step explanation:

61,000*0.04=2,440

There are 2,440 acres of old-growth trees.

Hope this helps!

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The value of equation for x is x > 0.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

|5-2x| > 5

To solve for let us take x on one side.

So, Subtracting 5 both the side we get,

|5 - 2x - 5| > 5 - 5

Simplifying we get,

|-2x| > 0

Extracting mod we get,

2x > 0

Now since 2 > 0 which is true,

Thus, x > 0

So, the value of equation for x is x > 0.

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The value of the Z - Score is a -1.5.

According to the statement

We have to find that the z-score of the company.

So, For this purpose, we know that the

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

From the given information:

The annual salaries of all employees at a financial company are normally distributed with a mean Mu = $34,000 and a standard deviation Sigma = $4,000.

Then

Let X = annual salaries of all employees at a financial company

And

The z score probability distribution for the normal distribution is given by:

Z - Score = Annual salary - mean / s.d.

Then substitute the values

Z - Score = 28,000 - 34,000/ 4000

Z -Score = -6/4

Z -Score = -1.5.

So, The value of the Z - Score is a -1.5.

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[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]