A fountain sprays water into a pool as part of the filtration system. The projected path of water is modeled by the function given in the table, where x represents the time in seconds since the water left the fountain and f(x) represents the height in feet above the pool’s water line.



How many seconds does the water travel through the air?

–6
1.5
3
5

The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.

Total distance if Pete walks from A to B to C:

= 15 + 25 = 40 yards

As we know in the triangle the sum of the two sides is greater than the third side.

25 + 15 > AC

40 > AC

or

AC < 40

The direct distance from A to C is more than 10(25-15) yards.

The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.

Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

Answer:

40, 10, 30
see picture

Step-by-step explanation:

The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.

The complete question is attached below.

Suppose that the given function is

f: X → Y

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

 f⁻¹: Y → X

It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'

The function is given below.

f(x) = (1/4)x – 12

Then the inverse function of the function f(x) will be

(1/4)f⁻¹(x) - 12 = x

            f⁻¹(x) = 4x + 48

Then the correct option is D.

Learn more about inverse function here:

https://brainly.com/question/19425567

#SPJ1

Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.

So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!

So your final answer is 3/4.


Brainliest and heart if this helped you out
#Learnwithbrainly

-11, -6, -7 and -6.1 are the answers

The inequality is r lesser than or equal to -6

Answer:

12 Vanilla Frosted Cupcakes

Step-by-step explanation:

30 Cupcakes.

1/5 Of 30 is 6.

30 - 6 = 24.

24/2 = 12.

[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]

Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [

PLEASE GIVE BRAINLIEST

Answer:

10

Step-by-step explanation:

By the geometric mean theorem,

Work Shown:

[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]

Therefore,

[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]

There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then

[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]

It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let

[tex]x = \dfrac7{11}[/tex]

Multiply the numerator and denominator by 9,

[tex]x = \dfrac{63}{99}[/tex]

It follows that

[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]

The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.

Answer:

90

Step-by-step explanation:

Using long division, we find that  Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90

The square root contains two same numbers and the cubic root contains three same numbers.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The square root contains two same numbers and the cubic root contains three same numbers.

For an example:-

√9 = [tex]\sqrt{3\times 3}[/tex] =  3 as we can see in the example the value of the square root of 9 is 3 it consists of two threes in the roots.

∛27 = [tex]\sqrt[3]{3\times 3\times 3}[/tex] = 3 here we have found that 27 contains 3 times 3 so the cube root of 27 will be equal to 3.

Therefore square root contains two same numbers and the cubic root contains three same numbers.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

Answer:

[tex]\fbox {tan A = 0.5333}[/tex]

Step-by-step explanation:

tan A = opposite side of ∠A / hypotenuse

tan A = 8 / 15

tan A = 0.5333

Answer:

tan A = perpendicular/ base

tan A = 8/15

tan A=0.5333

Step-by-step explanation:

please mark me as brainlest

Answer:

y = 1.5x + 1

Step-by-step explanation:

→ Choose 2 points

( 2 , 4 ) ( -2 , -2 )

→ Find the gradient

-6 ÷ -4 = 1.5

→ Write into format

y = 1.5x + c

→ Substitute in ( 2 , 4 )

4 = 3 + c

→ Minus 3 from both sides

1 = c

y = 1.5x + 1

The average rate of change in h(t) is 6.

It is a measure of how much the function changed per unit, on average, over that interval.

h(t) = 3 + 70t - 16t²

Average rate of change

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2

h(1) = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2

h(3) = 69

Average rate of change = Δh / Δt

=[h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6.

Hence, the rate of change is 6.

Learn more about this concept here:

https://brainly.com/question/18090092

#SPJ1

Answer:

[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]

Explanation:

Foil method: (a + b)(c + d) = ac + ad + bc + bd

Solving steps:

[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]

[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]

[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]

[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]

[tex]1 +2\sqrt{7}[/tex]

option b) 1 + 2√7

Foil property method :-

[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]

then, on substituting the values,

[tex]\sf⇒ \:  \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]

[tex]\sf⇒ \:  \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]

Answer:

This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

What is the equation for this situation?

It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:

y = x + 5.5

The possible values are

x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

Learn more about equation in:

brainly.com/question/10413253

Step-by-step explanation:

This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

For the given expression

y = x + 5.5

The possible values are

x = It is expected x is equal to 0 or greater to it

since the minimum amount of white flour that can be added is 0.

y = It is expected y is equal than 5.5 or greater to it since even if no

white flour is added the minimum total is 5.5.

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ1

Answer:

A

Step-by-step explanation:

The parabola opens to the left, so this eliminates C and D.

Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.

The circumference of this circle with a radius of 7 cm is equal to 44 cm.

Given the following data:

Mathematically, the circumference of a circle can be calculated by using this formula:

Circumference = 2πr

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

Circumference = 2 × 3.14 × 7

Circumference = 43.96 ≈ 44 cm.

Read more on circumference here: brainly.com/question/14478195

#SPJ1

Answer:

2 pi : 1

Step-by-step explanation:

for every one unit of radius, there are two pi units in the circumference!

Answer:

9. 15b + 4

10. 4y + 6

11. 15r+72

12. 130n + 20

Step-by-step explanation:

9. Combine Like terms

10. Combine Like terms

11. Distribute the 8 into (r + 9) then combine like terms

12. Distribute 10 into (3n + 2 + 10n) then combine like terms

Answer:

[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]

Step-by-step explanation:

[tex]\textsf {Question 9}[/tex]

[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]

[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]

[tex]\mathsf {15b + 4}[/tex]

[tex]\textsf {Question 10}[/tex]

[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]

[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]

[tex]\mathsf {4y + 6}[/tex]

[tex]\textsf {Question 11}[/tex]

[tex]\mathsf {8(r + 9) + 7r}[/tex]

[tex]\mathsf {8r + 8(9) + 7r}[/tex]

[tex]\mathsf {8r + 7r + 72}[/tex]

[tex]\mathsf {15r + 72}[/tex]

[tex]\textsf {Question 12}[/tex]

[tex]\mathsf {10(3n + 2 + 10n)}[/tex]

[tex]\mathsf {10(13n + 2)}[/tex]

[tex]\mathsf {10(13n) + 10(2)}[/tex]

[tex]\mathsf {130n + 20}[/tex]

Answer:

$189

Step-by-step explanation:

35% of 140 = 49

140 + 149 = 189

Tom's total saving this year is $189.

It is a 35 percent increased saving from last year's $140.

Percentages are fractional values where the denominator is fixed to be 100.

To convert percentage into number, we multiply by 100.

In the question, we are informed that Tom was able to save 35% more this year than he did last year.

We are asked if he saved $140 last year, then how much did he save this year.

The increase in Tom's savings = 35% of last year's savings,

or, the increase = 35/100 * 140 (To convert percentage into quantity, we divide by 100).

or, the increase = $49.

Therefore, Tom's total savings this year = Last year's savings + Increase,

or, Tom's total saving this year = $140 + $49 = $189.

Learn more about percentages at

https://brainly.com/question/843074

#SPJ2

In insurance, in a 100/300 policy, it should be noted that up to $100,000 bodily injury per single person injured in the accident will be covered.

An insurance coverage simply means the amount of risk or liability for an individual.

In this case, in a 100/300 policy, up to $100,000 bodily injury per single person injured in the accident will be covered.

Also,an amount up to $300,000 in total will be for bodily injuries per accident. Finally, there's a $100,000 for damages to the property of others.

Learn more about insurance on:

brainly.com/question/25855858

#SPJ1

Using the point-slope equation, the equations that represent the data are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).

Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):

Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25

Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):

y - 6 = -1.25(x - (-2))

y - 6 = -1.25(x + 2)

This cam be rewritten as:

y - 6 = -1.25x - 2.5

y - 6 + 2.5 = -1.25x

y -3.5 = -1.25x

The equations that represent the data in the table are:

y - 6 = -1.25(x + 2)

y -3.5 = -1.25x

Learn more about the point-slope equation on:

https://brainly.com/question/11472166

#SPJ1

Answer:

See below

Step-by-step explanation:

The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .

a = adult tickets         cost = 15 a

c = children's tickets    <=== this is equal to 20 - a    

                  cost for children's tickets equals   10(20 - a)

15 a + 10c   =   225           rememeber c = 20 -a <===put that in

15 a      + 10 ( 20 -a)   = 225    solve for a

15a + 200 - 10 a = 225

5 a = 25

a = 5   tix                 then     c = 20 - a =  15   tix

The area of the surface of the pool is 7322.64 m².

The area of rectangle is product of length and its breadth.

i.e., length * breadth

Given: Length = 100 m, Width = 52 m and Diameter = 52 m

Area of rectangle,

= 100 × 52

= 5200 m²

Now,

Area of semicircle = 1/2 × πr²

=1/2 × 3.14 × 26²

= 1061.32 m²

Hence, area of the surface of the pool is

= 1061.32 + 1061.32 + 5200

= 7322.64 m²

Learn more about this concept here:

https://brainly.com/question/15461609

#SPJ1

5200 square meters, 1061, 7322

The attached graph represents the graph of f(x) = (x - 1)^2 - 2

The equation is given as:

f(x) = (x - 1)^2 - 2

Next, we set x to -2, -1, 0, 1 and 2.

So, we have:

f(-2) = (-2 - 1)^2 - 2 = 7

f(-1) = (-1 - 1)^2 - 2 = 2

f(0) = (0 - 1)^2 - 2 = -1

f(1) = (1 - 1)^2 - 2 = -2

f(2) = (2 - 1)^2 - 2 = -1

This means that the table of values is

x      f(x)

-2    7

-1    2

0    -1

1     -2

2    -1

Next, we plot the above points and connect them.

See attachment for the graph of f(x) = (x - 1)^2 - 2

Read more about graphs and functions at:

https://brainly.com/question/4025726

#SPJ1

LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)

The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.

It is given that

lim x->2 for f(x)

[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]

f(x) = 2x+1 x ≤2

f(x)= x² , x >2

When both the function tends to 2

Left Hand Limit

f(x) = 2 *2 +1

f(x) = 5

Right Hand Limit

f(x) = x² ,

f(x) = 4

LHL in not equal to RHL , Therefore the limit does not exists.

To know more about Limit of a Function

https://brainly.com/question/7446469

#SPJ1

Answer: 6 ft

Step-by-step explanation:

[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]