The perimeter of a rectangular pool is 312 m.
If the width of the pool is 68 m, what is its length?
Length of the pool:
m

Answer:

(A)[tex]x + 3= x^2 + 2x-4[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = x + 3\\y= x^2 + 2x-4[/tex]

Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.

Substitution of y into [tex]y=x^2 + 2x-4[/tex] gives us:

[tex]x + 3= x^2 + 2x-4[/tex]

The correct option is A.

Answer:

10 inches

Step-by-step explanation:

Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?

Hence, L1/L2 = W1/W2

∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches

Answer: [tex]2(xy )^{2}[/tex]  the same thing as 2([tex]x^{2} y^{2}[/tex])

Step-by-step explanation:

You multiply 2 by x times y squared.

Answer:

The center  is (-8/3,0) and the radius is 1

Step-by-step explanation:

(x+8/3)^2 + y^2 = 1

We know the equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

Rewriting

(x- -8/3)^2 + (y-0)^2 = 1^2

The center  is (-8/3,0) and the radius is 1

hope it will be helpful.......

Answer:

  120

Step-by-step explanation:

n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.

n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.

The least common multiple of 6 and 40 is 120.

The smallest positive integer n is 120.

_____

Check

120^2/18 = 800

120^3/640 = 2700

Answer: 2077

There are 31 terms.

S₃₁ = 31(a₁+a₃₁)/2 = 31(7+127)/2 = 2077

Answer:

Ok, the first step to see the behavior of this data is doing a graph of it,

So we can see that it looks like an reversed V. (at the bottom of the answer you can see the graph)

Then, we can model this with a piecewise function like:

For the first part we can take the two pairs:

if 11 am is our t = 0h

(0, 85) and (6, 93)

then the linear equation

y = a*t + b

a = (93 - 85)/(6 -0) = 8/6.

and b = 85.

then the linear equation is:

y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

The second part of this equation can be modeled with the points

(6, 93) and (11, 84)

then we have:

y = s*t + c

s = (84 - 93)/(11 - 6) = -7/5

and we can find the value of c as:

93 = (-7/5)*6 + c

93 + (7/5)*6 = 101.4

then this second part is:

y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

then, in conclusion we have:

         y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

f(x) =

         y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

Answer:

y=7.496sin(0.3243x+0.315)+73.489

Step-by-step explanation:

simply put the data into a graph and graph each equation to see if its matched

Answer:

2

Step-by-step explanation:

The question, is basically asking for the order of rotational symmetry for the parallelogram. This is 2, which means while spinning the parallelogram around its centre point 360 degrees, it looks exactly the same, or matches with its original at 2 points

Answer:

No

Step-by-step explanation:

2 = 3 inches

2x5=10

10 = 3x5 of 15 inches

so no and it would take 8 minutes to fill up the tub

Answer:

4

Step-by-step explanation:

perimeter=4a

8/4=a

a=2

area=a square

=2*2

=4

hope so this will help you

Step-by-step explanation:

given,

perimeter (p)=8cm

or, 4 l =8cm

or, l =8/4

therefore l =2cm

now area of square =l^2

=(2cm)^2

therefore l= 4 cm^2.....is ans wer..

Answer:

Terri’s speed can be calculated like this:

her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h

Step-by-step explanation:

Answer:10

Step-by-step explanation:

8/80=1/10*100=10

I’m guessing number 32 is true, since it asks you to round to the nearest integer.

To solve this problem, use the Pythagorean Theorem, which is a^2 + b^2 = c^2, where c is the hypotenuse. The hypotenuse of the triangle is always the longest side, meaning the hypotenuse would be 15.23.

To ensure these measurements can be used in order to make a right triangle, substitute the numbers into the Pythagorean Theorem.

6^2 + 14^2 = 15.23^2.

36 + 196 = 231.9529

232 = 231.9529

Because we were asked to round, that makes the equation 232 = 232, meaning the answer is true.

Answer:

d

Step-by-step explanation:

google

Answer:

(x, y) = (2, -1.5)

Step-by-step explanation:

x + 2y = -1

5x - 4y = 16

<=>

(2)x + (2)2y = (2)(-1)

5x - 4y = 16

<=>

2x + 4y = -2

5x - 4y = 16

<=>

7x = 14

<=>

x = 2

(*)x + 2y = -1

=> 2 + 2y = -1

=> 2y = -3

=> y = -1.5

=> (x, y) = (2, -1.5)

Answer:

solution,

[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]

Use negative power rule:

[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]

[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]

Simplify:

[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]

Use this rule:

[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]

[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]

Since, 4*4=16 ,the square root of 16 is 4

[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]

Simplify:

[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

see below

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 9 and the height is 20

V = pi  ( 9)^2 ( 20)

V = 1620 pi

If we approximate pi by 3.14

V =5086.80 cm^3

If we approximate pi by pi button

V =5089.3800099 cm^3

Answer:

V=5089.380099cm^3

Step-by-step explanation:

V=πr^2h

V=π(9)^2(20)

V=π(9)^2(20)

V=5089.380099cm^3

Answer:

$42.88

Step-by-step explanation:

Let's create a proportion using the following setup:

cost/pounds=cost/pounds

We know that it costs $20.42 for a 10 pound turkey.

$20.42/10 pounds= cost/pounds

We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.

$20.42/ 10 pounds= $x/ 21 pounds

20.42/10=x/21

We want to find x, by getting x by itself.

x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.

21*(20.42/10)=(x/21)*21

21* 20.42/10=x

21*2.042=x

42.882=x

Round to the nearest cent, or hundredth.

42.88=x

x= $42.88

A 21 pound turkey costs $42.88

Answer: A

Step-by-step explanation: 2(−3k−5) = (2)(−3k+−5) = (2)(−3k)+(2)(−5) = −6k−10

Answer:

4 (20) + 6(6) = 120

4(20) + 4 (6) = 100

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

Build time (hours) = 4c + 6a = 120

Test time (hours) = 4c + 4 a = 100

Where c represents the number of child bikes and a represents adult bikes.

So, for 20 child bikes and 6 adult bikes:

4 (20) + 6(6) = 120

4(20) + 4 (6) = 100

Feel free to ask for more if needed or if you did not understand something.

Answer:

I think it is C

Step-by-step explanation:

Answer:

The correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

A function defines an output given an input and the set of all the possible inputs to a function is the domain of a function such that there is an output, such that the domain is the set of x values which are points on the curve of the function

The set of outputs that are produced from a given input is the range of a function

The given function is f(x) = (x + 2)(x + 6)

From the curve we see that the minimum y-coordinate, f(x), value is at -4, which is the lower bound of the range, while the x-coordinate values, the domain can be seen extending past the graph sheet which from the expression for the function also (f(x) = (x + 2)(x + 6)) indicates that the x values is the set of all real numbers (on the number line)

Therefore, the correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4.

Answer:

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

Equal steps mean each number is the same distance from the previous one

From -2 to 28 is 28 units

There are 4 spaces between the numbers

28/4 = 7

Each number is in increase of 7

-2 + 7 = 5

5+7 = 12

12+7 = 19

19+7 = 26

The third number would be 12

Hey there! :)

Answer:

y + 32 = 3(x + 8)

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of the points into the equation:

[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]

Simplify:

[tex]m = \frac{33}{11}[/tex]

m = 3.

Point-slope form is:

y-y₁=m(x-x₁)

Plug in the coordinates of the first point, as well as the slope:

y - (-32) = 3(x - (-8)

y + 32 = 3(x + 8)

Answer:    y+32=3(x+8)

Step-by-step explanation:

First  you need to find the slope.The slope is the change in y divided by the change in x values.

-32 - 1 = -33

-8 - 3 =    -11  

-33/-11 = 3   the slope is 3  

and in point-slope form is  like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.

it could be like   y-1=3(x-3) or y+32= 3(x+8)

Answer:

1(a)1,030,000+0.13x

(b)$1,030,026

2. (a)Base and Index

(b)See Explanation

Ste-by-Step Explanation

(a)Total Amount to be paid to the four actors

=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)

Collect like terms

=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x

[tex]\text{Total Amount Paid= }1,030,000+0.13x[/tex]

(b)When x=200

[tex]\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026[/tex]

Question 2

(a)The two parts of a power are the base and index.

Take, for example, the expression: [tex]a^b\\[/tex]

[tex]a$ is the base\\b is the index[/tex]

Another example using numbers is: [tex]10^3[/tex]

In this case:

[tex]10$ is the base\\3 is the index[/tex]

(b)Like terms are terms that have the same letter/variable attached to them.

For example, the following pairs are like terms

These, however, are not like terms

Answer:

0.471

Step-by-step explanation:

Calculation for the probability that they spend less than $2,000 per year on insurance per year

First step is to find the base

Base =$2,000-$400

=$1,600

Second step is to find the probability using this formula

P=1/b+a×base

Where,

b represents $3,800

a represents $400

base represents $1,600

Let plug in the formula

P=1/$3,800-$400×$1,600

Hence,

P=1×$1,600/$3,800-$400

P=$1,600/$3,400

P=0.471

Therefore the probability that they spend less than $2,000 per year on insurance per year will be 0.471

Answer:what are you solving it by

Step-by-step explanation:

Answer:

Correct option: E

Step-by-step explanation:

The group must have 1 man and 1 woman.

So, for the woman slot, we have 4 possible choices, because we have 4 women and 1 slot to occupy.

For the man slot, we have 2 possible choices, because we have 2 men and 1 slot to occupy.

So the number of different groups we can make is the product of the number of possibilities for each slot:

Number of groups = 4 * 2 = 8

Correct option: E

Answer:

$280 dollars

Step-by-step explanation:

When they were leaving

[tex]\$1 \approx \frac{7}{10}$ Euro\\Therefore:\\\$1000 \approx \dfrac{7}{10}\times 1000 =700$ Euro[/tex]

When they returned home, they brought 196 Euros.

[tex]If\:\:\$1 \approx \frac{7}{10}$ Euro\\Then: 1 Euro $=\$ \dfrac{10}{7}\\\\$Therefore:\\\\196 Euros = \$ 196 \times \dfrac{10}{7} =\$280[/tex]

They brought back $280 dollars to the United States.

Answer:

They brought back 280 dollars.

Step-by-step explanation:

From the question, one United States dollar was worth about $\frac{7}{10}$ of a euro implies that:

$1 = 7/10 euro, or 0.70 euro. That is, the exchange rate is $1:0.70 euro.

The equivalence of the exchange $1:0.70 euro can also be obtained by dividing both sides by 0.70 as follows:

$1 / 0.7 = 0.7 / 0.7 => $1.43:1 euro. That is, $1.43 is equal to one euro.

Since they returned with 196 euros and $1.43 is equal to one euro, we will simply multiply 196 euros by $1.43 to obtain the amount of dollars they brought back as follows:

Amount of dollars they brought back = $1.43 * 196 = $280 to the nearest dollar.

Therefore, they brought back 280 dollars.