he table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.

Answers

Answer 1

The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

What is the slope?

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have given a table:

Time     height

2                8

4               12

6                16

8               20

10              24

The slope of the line = (12-8)/(4-2) = 4/2 = 2

The value of the slope is positive we can say,  the height of water increases as time passes.

Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

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Answer 2

the answer is A: The height of the water increases 2 inches per minute.

hope this helped :)


Related Questions

A 7 x 8 array is 7 rows of ____

Answers

Answer:

8

Step-by-step explanation:

It's 7 rows of 8 items

Which theorem can be used to prove ABC ~ EDC ? ​

Answers

Answer: SAS

Step-by-step explanation:

Since [tex]\frac{BC}{CD}=\frac{AC}{CE}=\frac{1}{2}[/tex], and [tex]\angle ACB \cong \angle DCE[/tex] because they are vertical angles, the triangles are similar by SAS

Sianna bought 3 pens, 4 notebooks, and a calculator. The calculator cost $25. If x represents the cost of each pen and y represents the cost of each notebook, which expression represents the amount of change Sianna should receive from $50?

3x + 4y +25

50 – (3x + 4y)
50 – (3x + 4y + 25)
3x + 4y + 25 + 50

Answers

Answer:

50 – (3x + 4y + 25)

Step-by-step explanation:

To see how much change she is gonna receive we need to find how much she spent on the items and add them all up:

The calculator was $25

The price of pens and notebooks are unknown so they are represented with x and y respectively.

With given information we can write the following equation to see the change she will receive:

50 – (3x + 4y + 25)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f(4)= -1 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

If a point point (x , y) satifys a function, then it can be written as :

[tex]\qquad \tt \rightarrow \: f(x) = y[/tex]

Here, point (x , y) is replaced by (4 , -1)

[tex]\qquad \tt \rightarrow \: f(4) = - 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

simplify 12 + 15 ÷ 3 × 6 – 4

Answers

Answer: 40 (Simplify)

solve the compound inequality -5<4x+3<=8

Answers

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a<  b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

We are given

-5 < 4x+3 ≤ 8

⇒ (add -3 to all sides to get ) -5+(-3) < 4x+3+(-3) ≤8+(-3)

⇒-8 < 4x ≤ 5

⇒[tex]\frac{-8}{4} < x \leq \frac{5}{4}[/tex]

⇒-2<x<5/4

Hence, the solution is -2<x<5/4.

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2x+3y=9 -2x+2y=6 The y cordinate

Answers

Answer:

y = 3

Step-by-step explanation:

2x + 3y = 9

-2x + 2y = 6

We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.

PLEASE HELP

In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.

So far I know that the equation is
x² + x² = c²
But i dont know how to simplify that

Answers

The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2

Given that the softball diamond is square in shape.

Let the side of the square i.e. distance between consecutive bases is x

The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.  

Using the Pythagorean theorem we have:

x² +x²= c²,

where c is the distance from the 1st base to the 3rd base.

Combining similar terms gives us

2x²=c²

Taking the square root of both sides we have

√2x²= √c²

⇒x√2=c

⇒c=x√2

This is the expression for the distance from the 1st base to the 3rd base in terms of side length.

Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.

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a + b = c
a + b + c =36

Given that a and b have the same value, work out the values of a,b and c

Answers

Answer:

a=9

b=9

c=18

Step-by-step explanation:

c(a+b)+a+b=36

2a+2b=36

a+b=18

c=18

A rectangle has a side length of three and two sevenths centimeters and a side width of 4 centimeters. What is the area of the rectangle?ten and six sevenths cm2
thirteen and one seventh cm2
thirteen and five sevenths cm2
fifteen and one seventh cm2

Answers

The area of the rectangle is thirteen and one seventh cm2

What is the area of the rectangle?

A rectangle is a four-sided object that has two widths and two lengths. The sum of angles in a rectangle is 360 degrees.

Area of a rectangle = length x width

3 2/7 x 4

23/7 x 4 = 92 / 7 =  13 1/7 cm²

We conclude that the area of the rectangle is (13 + 1/7) cm²

How to get the area of the rectangle?

For a rectangle of length L and width W, the area is:

A = L*W

Here we know that:

L = (3 + 2/7)cm

W = 4cm

Then the area is:

A = (3 + 2/7)cm*4cm = (12 + 8/7)cm² = (13 + 1/7) cm²

We conclude that the area of the rectangle is (13 + 1/7) cm²

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NEED HELP!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The third answer

Step-by-step explanation:

if p is equivalent to q then q must be equivalent to p. I’m not 100% sure but that’s my best guess. I hope this helps :)

What is the domain of the linear parent function?

Answers

Answer:

The parent function of linear functions is y=x and it passes through the origin.The domain and range of all linear functions are all real numbers.



Step-by-step explanation:

Which is the graph of f(x) = √x?

Answers

Look at the attached image.

Make d the subject of the formula h=d/3+2

Answers

Answer: D=3(h-2)

Explanation —>

Suppose line g is the line with the equation y = x. Given A (7,-3) , B (6,3), and C (-2,-7), what are the coordinates of the vertices of a’b’c’ for the reflection

Answers

Answer: A'(-3, 7), B'(3, 6), C'(-7, -2)

Step-by-step explanation:

Reflecting over y = x maps (x,y) onto (y,x).

Which function has a restricted domain?

Answers

Greeting to you! My name is Cecille and I’m here to answer that question

For more explanation, please see the attachment

Gertrude has a life insurance policy that will pay her family $97,000 per year I she dies. If interest rates are at 1.4% when the insurance company has to pay, what is the amount of the lump sum that the insurance company must put into a bank account? A. $692,857,142.90 B. $6,928,571.43 c. $692,857.14 D. $69,285,714.29​

Answers

The amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

Gertrude has a life insurance policy that will pay her family $97,000 per year.

If interest rates are at 1.4% when the insurance company has to pay

r = 1.4%

or

r = 0.014

The amount of the lump sum that the insurance company must put into a bank account:

= 97,000/0.014

= 6928571.429 ≈ $6,928,571.43

Thus, the amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

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What are the zeroes of the function? Round to the nearest hundredth. 0 2.05 8.33 14.61

Answers

The zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61

The complete question is given below:-

Y=-6x²+100x-180 What are the zeroes of the function? Round to the nearest hundredth.

What is a quadratic equation?

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Use the quadratic formula to solve it:

Y= -6x² +100x -180

a= -6

b= 100

c= -180

x =[tex]\dfrac{ -b \pm \sqrt{(b^2 - 4ac)} }{ 2a}[/tex]

x =[tex]\dfrac{-100 \pm \sqrt {(10,000 -4*-6*-180)}}{ -12}[/tex]

x1 =[tex]\dfrac{ (-100 + 75.3658 )} { -12}[/tex]

x1 = 24.6342 / -12

x1 = -2.05285

x2 =[tex]\dfrac{ (-100 - 75.3658 )} { -12}[/tex]

x2 = (- 175.3658 ) / -12

x 2 = 14.6138

Therefore the zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61

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Answer:

D..   last one
If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Step-by-step explanation:

Find the acute x given that tan x=2sinx

Answers

The measure of the acute angle is 60 degrees

Trigonometry identity

Given the following trigonometry equation

tan x=2sinx

This can also be written as;

sinx/cosx=2sinx

Simplify to have:

1/cosx =2

2cosx = 1

cosx = 1/2

x = arccos(1/2)

x = 60 degrees

Hence the measure of the acute angle is 60 degrees

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Giving a test to a group of students, the grades and gender are summarized below

A B C Total
Male 20 13 7 40
Female 9 2 8 19
Total 29 15 15 59


If one student is chosen at random,

Find the probability that the student got an A.

20
29


29
59


20
59

Answers

The grades and gender is 29/59

What is probability?

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

              A              B             C              Total

Male       20            13            7                 40

Female    9               2            8                 19

Total        29            15            15               59

Total candidates who have A grade = 20+9 = 29

So, the probability that the student got an A

= 29/59

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write a quadratic function in standard form with zeros -5 and 0

Answers

Answer:

(x^2+5x)

Step-by-step explanation:

Please check out the attached photo

Find the longer and shorter lengths and hypotenuses

Answers

Answer:

Short leg: 9 in

Long leg: 40 in

Hypotenuse: 41 in

Step-by-step explanation:

This problem involves the Pythagorean Theorem, solving a system of equations, and solving a quadratic equation.

The Pythagorean Theorem applies because the question states this is a right triangle.  That is one equation.  

Two more equations come from descriptive relationships between various sides of the triangle.

Solving the system is done here with the Substitution Method, and solving the quadratic equation is done with factoring and the zero product property.  Other methods could be used, but there is a character limit, so we can't dive into every way to solve this.

The Pythagorean Theorem

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex] where "c" is the hypotenuse of the right triangle.

"c" must be hypotenuse.

It doesn't matter which of the two legs' lengths is used for "a" & "b".  However, because of other parts of the question, we'll need to know which one is which.

The question refers back multiple times to one specific leg (the short one).  So, when we refer back to that leg in our equations, we need to make sure we're using the same leg each time.

Keeping track of which leg is which

Let's use "a" for the smaller leg, and "b" for the longer leg.

"c", as always, is the hypotenuse.

Setting up the relationships between the sides

Next, the question gives two statements relating the side lengths of the triangle to each other.

For the first statement, "the length of the longer leg of a right triangle" (that's "b") "...is 13 inches more than three times the length of the shorter leg ("a").

Translating the first sentence into math:

"the length of the longer leg of a right triangle"  means  "b""...is..."  means  "=""...13 inches more than..."  means " +13 " (start with what's coming next, and then do the adding)"...three times..."  means " 3* ""... the length of the shorter leg."  means "a".

[tex]b=3a+13[/tex]

Similarly from the second statement, we get:  [tex]c=3a+14[/tex]

Combining this with the Pythagorean Theorem, we have a system of 3 equations, and 3 unknowns.

[tex]b=3a+13[/tex]

[tex]c=3a+14[/tex]

[tex]a^2+b^2=c^2[/tex]

Solving a system of equations

To solve a system of equations, there are two main methods:  

The substitution methodThe elimination method

Either method can be used, but the substitution method is the most intuitive.

Substitution method

To solve a system with the substitution method, isolate variable in an equation, written in terms of the other variables, and substitute them in to try to get a single equation with a single unknown.

Looking at our system, the first two equations already have "b" and "c" isolated in terms of "a".  If we substitute both of these into the third equation, we'll have a single equation in terms of a, and can attempt to solve it.

[tex]b=3a+13[/tex]

[tex]c=3a+14[/tex]

[tex]a^2+b^2=c^2[/tex]

Substituting...

[tex]a^2+(3a+13)^2=(3a+14)^2[/tex]

Rewrite the square binomials as a product...

[tex]a^2+(3a+13)(3a+13)=(3a+14)(3a+14)[/tex]

Apply FOIL (a combination of the distributive property, the commutative properties of multiplication, and combining like terms)...

[tex]a^2+(9a^2+39a+39a+169)=(9a^2+42a+42a+196)\\a^2+(9a^2+78a+169)=(9a^2+84a+196)\\[/tex]

Observe that the equation is a degree-2 polynomial (polynomial with highest power of 2; aka quadratic).  Move all terms to one side to get the equation equal to zero in preparation for solving:

[tex]a^2+(9a^2+78a+169)=(9a^2+84a+196)\\a^2+9a^2+78a+169-(9a^2+84a+196)=0\\a^2-6a-27=0\\[/tex]

There are a few ways to solve this, including the quadratic formula.  However, factoring the polynomial and using the zero product property is quite efficient here:

Factoring to solve a Quadratic

Since the leading coefficient is 1, we can use the shortcut and find factors of -27 that add to make -6.

-27 has factor pairs of:

1 and -273 and -99 and -327 and -1

3 and -9 add to make -6, so factoring the polynomial is

[tex]a^2-6a-27=0\\(a+3)(a-9)=0[/tex]

Applying the zero product property...

[tex](a+3)=0[/tex] or [tex](a-9)=0[/tex]

So a=-3 or a=9.  Given that this represents a length in a triangle, we discard the negative solution.  So a=9.

Finding the other two unknowns

To finish up, substitute the "a" back into the two equations for "b" and "c".

[tex]b=3a+13\\b=3(9)+13\\b=27+13\\b=40[/tex]

[tex]c=3a+14\\c=3(9)+14\\c=27+14\\c=41[/tex]

The original problem set up our measurements in inches, so all three values are measured in inches.

Remember which length was which

"a": short leg

"b": longer leg

"c": hypotenuse

Short leg: 9 in

Long leg: 40 in

Hypotenuse: 41 in.

1

2.

3

5 5

6

8

9

12

13

10-

8

6

909

NS

2

-6 -5 -4 -3 -2 -1 1 2 3 4

1 2 3 4 5 6 X

f

-6

-8

-10

-12-

-141

1 1 1

NO

w

f(4) = g(4)

Of(4) = g(-2)

O f2) = g(-2)

Of(-2) = g(-2)

Mark this and return

Answers

Answer: f(-3)=g(-3)

Step-by-step explanation:

The graphs intersect at x = -3.

The correct option is f(-3) = g(-3).

What is function?

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that two lines are intersecting at point (-3, -4)

Therefore the system of equations of these two have a solution at (-3, -4)

So, if taking the lines as function,

We have f(x) and g(x),

so both of them are intersecting at (-3, -4) so the range when the domain is -3 will be equal.

Hence the correct option is f(-3) = g(-3).

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What is the slope of the line shown below (3,-2) (2,4)?
A. -2
B. -1/2
C. 1/2
D. 2

Answers

Answer:

D. 2

Step-by-step explanation:

rise / run = slope

rise = 2

run = 1

2/1 = 2

slope = 2

Answer:

2 (Answer D)

Step-by-step explanation:

The green line has a positive slope, so we can immediately reject Answers A and B.

A line with a slope of +2 rises steeply as we move from left to right, whereas a line with slope +1/2 rises much less steeply.  Also, it's quite clear, visually, that the slope of the given line is greater than 1.  Thus, the slope of the given line is +2 (Answer D).

A paint mix uses red and white paintin a ratio of 1:12.
a) How much white paint will be needed to mix with 1.4
litres of red paint ?
b) Ifatotalof15.5litresofpaintismixed,calculate
the amount of white paint and the amount of red paint used. Give your answers to the nearest 0.1 litre.

Answers

Answer:

(a).16.8 litres

(b).red-1.2 litres

white-14.3 litres

I need all of these please

Answers

Answer:

second answer is 120

firsr answer is 25

Detailed Answers:

1) (625/5) * 0.2

= (625/5) * 0.2
= 125 * 0.2
=> 25

2) 83 + (-85)

= 83 + (-85)
= 83 + -85
=> -2

3) 150/-5 * (-4)

= 150/-5 * (-4)
= -30 * -4
=> 120

4) (-34) + (-255)

= (-34) + (-255)
= -34 + -255
=> -289

5) 80 - (-22)

= 80 - (-22)
= 80 + 22
=> 102

6) 28 - (-65)

= 28 - (-65)
= 28 + 65
=> 93

7) -555/-5 * (-6)

= -555/-5 * (-6)
= 111 * -6
=> -666

8) 28 - (-26)

= 28 - (-26)
= 28 + 26
=> 54

9) -3 * 5

= -3 * 5
= -(3 * 5)
=> -15

10) [-19 - (-20) - (-34)] / (-6)

= [-19 - (-20) - (-34)] / (-6)
= [-19 + 20 + 34] / (-6)
= [1 + 34] / -6
= 35/-6
=> 5.83

11) -424/4

= -424/4
=> -106

12) [-18 - (-66) - 22] * 2

= [-18 - (-66) - 22] * 2
= [-18 + 66 - 22] * 2
= 26 * 2
=> 52

13) 19 - 23

= 19 - 23
=> -4

14) -61 - (-21)

= -61 - (-21)
= -61 + 21
=> -40

15) (-72/9) + (-64/8) + (-44/11)

= (-72/9) + (-64/8) + (-44/11)
= -8 + -8 + -4
= -16 + -4
=> -20

16) (16 - 21 + 34) / (-8)

= (16 - 21 + 34) / (-8)
= (29) / (-8)
= 29/-8
=> 3.625

The perimeter of a triangle is 73 inches if two sides are of equal length and the third side is 7 inches longer than the others find the length of three sides

Answers

Answer:

22,22,29 in

Step-by-step explanation:

x + x     +    x+7 = 73

3x = 66

x = 22      then lengths = 22, 22, 29 in

can someone please help mee

Answers

Answer:

[tex]f(z) = z^2-3z+2[/tex]

[tex]f(x+1) = x^2-x[/tex]

[tex]f(\sqrt{2}+1) = 2-\sqrt{2}[/tex]

Step-by-step explanation:

[tex]f(x+1) = x^2+2x+1-3x-3+2[/tex]

[tex]f(\sqrt{2}+1) = 2+2\sqrt{2}+1-3\sqrt{2}-3+2[/tex]

A soccer field (football pitch) has a length of 101.0 m and a
width of 70.2 m. Find the total area of the field in square
meters (m²) and convert this measurement to square yards
(yd2). Use the fact that 1 yard = 0.9144 m. Round your answer
to the nearest whole number.

Answers

Answer:

7754

Step-by-step explanation:

give brainiest, please. <3

Answer:

about 7,754 m

Step-by-step explanation:

101 * 70.2 = 7,090.2

7,090.2/0.9144 = 7,753.9

Bella wants to know how long her dog is. She measure its body and finds that it is 54 cm long. Then she measures the tail and find it is 34 cm long. How long is Bella's dog from body to tail?

Answers

Answer:

88 cm

Step-by-step explanation:

body to tail = length of body + length of tail

body to tail = 54 cm + 34 cm

body to tail = 88 cm

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