"all real numbers that are greater than -6 and less than -2."

If we let t be the number of seconds since you started backing away and we let r(t) be the radius of the spot of light in centimeters.

r(t) =5 + 7t

If we let a(r(t)) to be the area of the spot,

where A = a(r(t)) and r= 5 + 7t

a(r(t)) = π (5+7t)²

a(r(t)) = π (49t² + 70t +25)

For t=4s

a(r(4)) = π[49(4)²+70(4)+25]

=1089π cm²

For t=7s

a(r(7)) = π[49(7)²+70(7)+25]

=2916 π cm²

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

The slope is undefined.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-1)/(-4-(-4))

m=-8/(-4+4)

m=-8/0

undefined

Answer:

Parts of the expression:

b: a variable representing a quantity that can vary or change.

12: a constant representing a fixed value.

r: a variable representing a quantity that can vary or change.

Word expression:

"Add twelve times the quantity of r to b."

Step-by-step explanation:

Answer:

y = -13/10x + 2/5

Hope this helps!

Answer:

75 books

Step-by-step explanation:

30=(2/5)x

x=75 total books

Answer: Its an enlargement

Enlargement - Getting bigger

Reduction - getting smaller

Answer:

5x+12+x'

_______

2x'-2x-4

'=2

There are 1048576 different telephone numbers in city A have 774 as the first three digits.

Permutation with repetition is used to calculate all of the possible combinations of telephone numbers.

For the N different types and we have to choose (a) of the different types, the number of possible combinations would be :

\(P = N^(i)\)

From the given problem, we have

The total number = 7 digits

The constant number = 3 digits

Thus, i = 7 - 3 = 4 digits

Now the characters = {0,1, 2, 3, 4, 5, 6, 7, 8, 9}

N = 10

Substituting the parameter, we can find the number of possible combinations of a telephone number in the city a which is;

P = 4¹⁰

P = 1048576

Hence, there are 1048576 different telephone numbers in city A have 774 as the first three digits.

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

Answer:

x = 30

Step-by-step explanation:

x/2 = 12 + 3

x = 2(12+3)

x = 30

The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

We have to given that,

All the numbers are,

⇒ 5⁰

⇒ |2|

⇒ (- 1/2)²

⇒ 5/8

⇒ 30%

Now, We can simplify each as,

⇒ 5⁰

⇒ 1

⇒ |2|

⇒ 2

⇒ (- 1/2)²

⇒ 1/4

⇒ 0.25

⇒ 5/8

⇒ 0.625

⇒ 30%

⇒ 30/100

⇒ 0.3

Hence, Ascending order is,

0.25, 0.3, 0.625, 1 , 2

Or,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

Thus, The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

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Here is my solution, I hope it is helpful.

Answer:

x = 15

Step-by-step explanation:

Answer:

0,8,5

Step-by-step explanation:

x+22 <32

Subtract 22 from each side

x+22-22 <32-22

x <10

The choices that fit

0,8,5

Answer:

Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.

Step-by-step explanation:

x + 22 < 32

This problem is fairly simple! All we need to do is substitute each number given for x and compute to find out if the equation will be true! First what we need to do is plug in each number given into our variable x. Our numbers are: 0, 10, 8, 71, 15, and 5

x = 0

0 + 22 < 32

22 < 32

Is 22 less than 32? It is! So it belongs to the solution set.

x = 10

10 + 22 < 32

32 < 32

32 is equal to 32, not less than 32. A number cannot be itself and less than itself, thus x = 10 does not belong to the solution set.

x = 8

8 + 22 < 32

30 < 32

Is 30 less than 32? Yes! Since the inequality is true (that's what these kinds of equations are called) it  belongs to the solution set.

x = 71

71 + 22 < 32

94 < 32

Is 94 less than 32? No. 71 does not belong to this solution set.

x = 15

15 + 22 < 32

37 < 32

37 is not less than 32. Therefore it doesn't belong to the solution set.

x = 5

5 + 22 < 32

27 < 32

Is 27 less than 32? Yes. Therefore, it belongs to the solution set.

Therefore, our applicable set is: 0, 8, and 5. All of these numbers make the inequality true.

Done :) Refer to the photo taken. Let me know if this is what you where looking for. Sorry for the sideways image.

Answer:

\(0.75 \: \: \: \: or \: \frac{15}{2} \)

Step-by-step explanation:

\(10x > 120 - 45 |collect \: like \: terms| \\ 10x > 75 |simplify \: | \\ \frac{10x}{10} > \frac{75}{10} |divide \: both \: side \: by \: 10 | \\ x > 0.75 \: or \: \frac{15}{2} \)

Answer:

2y

Step-by-step explanation:

Since 17y and 15y both have a y, you can combine it. You can subtract 17-15 to get 2, so the answer is 2y.

Answer:

The train would travel 30km in 30 minutes.

Step-by-step explanation:

Speed of train = 60km/hr

30 minutes = I hour ÷ 2

If 30 minutes is equal to half an hour, and it takes an hour for the train to travel 60 km, then you would have to half 60 km to find the length travelled in 30 minutes.

Equation: 60km ÷ 2 = 30km

Answer:

The right answer is 16m

Step-by-step explanation:

4*4=16

Answer:

16 m

Step-by-step explanation:

→ Remember how sides a square has

4

→ Multiply that by the side length of 4

4 × 4 = 16

Answer:

4.3

Step-by-step explanation:

12.1-7.8= 4.3

Hope this helps! :) Is correct pls mark brainliest!

Answer:

4.3

Step-by-step explanation:

Answer:

a = 1

b = 5

Step-by-step explanation:

a + 2b = 11

(a - b = -4) × 2

2a - 2b = -8

------------------------

a + 2b = 11

2a - 2b = -8

-------------------

3a = 3

÷3   ÷3

-----------

a = 1

----------------------------------------------------------------------------------------------------------

a - b = -4

1 - b = -4

-1         -1

---------------

-b = -5

÷-1   ÷-1

-------------

b = 5

I hope this helps!

The third ordered pair that satisfy the given equation is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

\(a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}\)

The radius of the circle is calculated as;

\(r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96\)

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

\(b < r\\\\b < 388.96\)

\(a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)\)

Thus, the third ordered pair that satisfy the given equation is (123, 369).

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Answer:

25/4.1 or 6 and 2/5

Step-by-step explanation:

I can simplify both 100 and 16.4 by 4, so: 100/16.4=25/4.1

Because this is an improper fraction, I simplify it to: 6 and 2/5

Answer:

x=3 in equation ;5x=15 and in equation C.

Answer:

A

Step-by-step explanation:

The SSS is the side-side-side way to prove the triangles are congruent, so each side needs to have a match between triangle 1 and triangle 2. Since AC and BC are congruent to sides, that leaves AC. Hope this helps :)

To prove that both triangles are congruent, the additional information needed is: A. AB ≅ PQ.

Two triangles with three pairs of corresponding congruent sides can be proven to be congruent to each other based on the SSS congruence theorem.

We are already given that two pairs of corresponding sides of the two triangles are congruent. To prove that triangles ABC and PQR are congruent by SSS, the additional information needed is: A. AB ≅ PQ.

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The base of the function given 2(4)ˣ+5 is 4ˣ

The base of an exponential function. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. Base 1. If f(x) is an exponential function whose base equals 1 – that is if f(x)=1x.

Given is a function, 2(4)ˣ+5, we need to find the base of the function,

With the multiplication of 4ˣ with 2, the rate at which f(x) changes is 2 times larger. Now it is added by 5, by adding 5 the value of f(x) is always 5 greater than the value of f(x).

This reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 8 times that of the original function.

Hence, the base of the function given 2(4)ˣ+5 is 4ˣ

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