Keeping the properties of exponents in mind, to what power must you raise the expression 7 to get 7 as the result?

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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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:

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]

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:

(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and  Tcritical = 3.143

In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds

we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas

Mean, xbar = 1.01

Standard deviation, s = 0.29

Sample size, n = 7

Confidence interval  : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 7 - 1 = 6

Hence Tcritical = 3.143

Margin of Error = 3.143 * 0.29/sqrt(6)

Margin of error = 0.37211

Lower boundary = (1.01 - 0.37211) = 0.63789

Upper boundary = (1.01 + 0.37211) = 1.38211

(0.63789 ; 1.38211 )

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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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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:

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 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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Answer:

16 inches

Step-by-step explanation:

Multiply 120 by 2 to start reversing the triangle area equation.

120*2 = 240.

Now divide by 15

240/15=

16

The length is 16 inches

Answer:

A. 52 is your answer

Step-by-step explanation:

Explained below

Answer:

Ans is a

First you solve the inside of the bracket u will get 4(13)

which will give u 52

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

Answer:

8

Step-by-step explanation:

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

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

|7| = 7

7

The plants which are growing at the same rate are Plant 1 and Plant 4.

Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.

If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.

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Answer:

B. 1 and 4

Step-by-step explanation:

Edge 2023

As Deanna is sitting farther from the center she is travelling at a faster rate.

Circumference of a circle is the distance around the circle.

We know that merry-go-round covers distance in form of circles and we also know that circumference of a circle is 2πr.

As Deanna sits on a horse on the outer edge of the merry-go-round, 10 feet from the center of the ride it can thought of as the radius.

∴ In one rotation Denna will cover (2πr) feet which is

= (2π×10 feet.

= 62.8 feet in 15 seconds.

Now if we do the previous calculation for Raquel with r taken as 8 she will cover:

= 50.24 feet in 15 seconds.

Therefore Deanna is spinning at a faster speed.

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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:

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

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:

5

Step-by-step explanation:

Every number from the absolute sign will be positive.

Step-by-step explanation:

the point is (2, -5).

the origin is (0, 0).

the distance between 2 points is calculated via Pythagoras due right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.

the direct distance is the Hypotenuse, and the x coordinate and y coordinate differences are the legs.

so,

distance² = (2 - 0)² + (-5 - 0)² = 2² + (-5)² = 4 + 25 = 29

distance = sqrt(29) = 5.385164807...

so, the second answer option is correct.

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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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

we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

we have to solve the following sentence

[tex]\sqrt{17}[/tex] --- 4     ( insert <,>, = to make the following sentence true)

what is square root ?

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is  [tex]\sqrt{}[/tex] .

we know that

square root of 17 is 4.12310563

which is 4+ 0.12310563

that is if we add 4+0.12310563 we get 4.12310563

therefore square root of 17 is greater than 4

that is [tex]\sqrt{17}[/tex] > 4  

since 4.12310563 > 4

hence,   we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4

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

The total number of students chosen is 4, 13, 22, and 31.

To determine the students who will be going to the board:

Now, using the following term formula, a + d (n - 1).

The second student is up next.

The third student will:

The fourth student will:

Therefore, the total number of students chosen is 4, 13, 22, and 31.

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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: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

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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