Mr. Russo had 6.25 cubic feet of potting soil in his raised garden bed. Then he took a bag of soil and poured in enough to completely fill the 9-cubic-foot bed. Let x represent how much soil was in the bag. Which inequality describes the problem?

The inverse of a function may or may not be a function

The function g(x) is given as:

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

(a) Inverse function g^-1(x)

We have:

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

Replace g(x) with y

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

Swap the positions of x and y

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

Add 3 to both sides

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

Divide both sides by 2

[tex]\frac{x + 3}2 = (y - 1)^2[/tex]

Take square roots of both sides

[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]

Add 1 to both sides

[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]

Rewrite as:

[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]

Express as inverse function of g

[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

(b) The domain, and the range of g(x) and g^-1(x)

Function g(x)

The function g(x) is a quadratic function.

So, the domain is:

The range is:

Function g^-1(x)

The function g^-1(x) is a square root function.

So, the domain is:

The range is:

The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).

(c) The graph

See attachment for the graph

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Answer:

120 yd²

Step-by-step explanation:

The floor consists of a square and a triangle

area of square = 10² = 100 yd²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 4 and h = 10 , then

area = [tex]\frac{1}{2}[/tex] × 4 × 10 = 2 × 10 = 20 yd²

company needs 100 + 20 = 120 yd²

Answer:

y = 15d + 25 or y = 15x + 25

Answer:

5 because 20 percent in a fraction is 1/5 so you would just divide 25 by 5. Or you could do 25 times .2 and your answer is still 5.

Step-by-step explanation:

20% of 25 is 5

25 Percentages

1% = 0.25

5% = 1.25

10% = 2.5

15% = 3.75

20% = 5

Answer:the answer is a

Step-by-step explanation:

Answer:

38.4[litres].

Step-by-step explanation:

[tex]1. \ the \ rule \ \frac{470.7[km]}{52.3[l]} =\frac{345.6[km]}{x};[/tex]

[tex]2. \ x=\frac{345.6*52.3}{470.7}=38.4[l].[/tex]

Step-by-step explanation:

Ratio 9:2, therefore total number of shares is 11.

because 9+2 = 11

total cards = 8,250

8,250/11 = 750

This is the value for one of the shares.

As the ratio is 9:2 we can find:

9 X 750 : 2 X 750

To see what everyone has won.

T-shirts : 2 X 750 = 1,500.

Hope you understand how it's done, if not leave a comment and I'll try to be more thorough

Answer:

Yes

Step-by-step explanation:

1 hour = 60 min

25 hours = 60 x 25 min

Answer:

14

Step-by-step explanation:

There are 168 black cubes in the arranagement.

A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.

To get the number of black cubes in the arrangement, we will use the equation below;

Hence there are 168 black cubes in the arrangement.

Learn more about cubes at https://brainly.com/question/1972490

Answer:

Not Similar because they don't have equivalent angles.

Step-by-step explanation:

First one is D

Second one is A

The Triangle XYZ is Congruent to PQR by ASA congruence, the Triangle XYZ is Congruent to MNO by SSS congruence, the Triangle XYZ is Congruent to STU by SAS congruence

A triangle is a polygon with three sides, they are classified as acute angle triangle, right angle triangle, obtuse angle triangle on the basis of angles subtended by the vertices.

The triangles PQR, MNO, XYZ, STU can be seen in the figure

Triangles PQR, MNO, and STU, which have resulted from rotating, reflecting, and translating triangle XYZ.

The Triangle XYZ is Congruent to PQR by ASA congruence

From the image

XY = PQ  

∠YXZ= ∠QPR

∠YZX = ∠PQR

The Triangle XYZ is Congruent to MNO by SSS congruence

From the image

XY= MN

YZ=ON

ZX=OM

The Triangle XYZ is Congruent to STU by SAS congruence

XY = ST

∠YXZ=∠TSU

XZ= SU

To know more about Triangle

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#SPJ2

Answer:

111.101, 110.111, 101.121, 101.112

Step-by-step explanation:

Descending order means values starting with big ones and ending with the small ones.

So, in this case,

Hope it helps :)

Answer:

the slope is 8

Step-by-step explanation:

since , x = 8 is a vertical line ,so the slope is undefined

Answer:

s =$10, l = 15, together they are $25

Step-by-step explanation:

Alberto: 1s + 1l = 25

Kali: 3s + 9l = 165

Multiply Alberto x 3: 3s + 3l = 75

Subtract from Kali:

 3s + 9l = 165

- 3s + 3l = 75

         6l = 90

l = 15, Large = $15.

Substitute into one of the equations: s + l = 25

s + 15 = 25

s = 10

Answer:

1. A

2. C

Step-by-step explanation:

If they are corresponding, so their angle measures are the same. Hope this helps. :)

Answer:

1) 1 and 6

2) 110. these are corresponding angles so they are congruent

Step-by-step explanation:

Answer:

-8/3

Step-by-step explanation:

rise/run

rise: -8

run: 3

-8/3

The question is an illustration of parallel lines, and equivalent ratios

The length of pt is 11.7 cm

Given that:

[tex]pr = 7cm[/tex]

[tex]ts =3cm[/tex]

[tex]tq = 5cm[/tex]

This means that:

[tex]pr : ts = pt : tq[/tex]

Substitute values for pr, ts and tq

[tex]7cm : 3cm =pt : 5cm[/tex]

Express the ratios as fractions

[tex]\frac{7cm }{ 3cm }= \frac{pt}{5cm }[/tex]

Cancel out the common units

[tex]\frac{7}{ 3}= \frac{pt}{5cm }[/tex]

Cross multiply

[tex]3pt = 35cm[/tex]

Divide both sides by 3

[tex]pt = 11.7cm[/tex]

Hence, the length of pt is 11.7 cm

Read more about equivalent ratios at:

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Answer:

b = (a/16) - 4

Step-by-step explanation:

a = 16(b + 4)

a = 16b + 64

16b + 64 = a

16b = a - 64

16b/16 = (a/16) - 64/16

b = (a/16) - 4

Answer:

b = a/16 - 4.

Step-by-step explanation:

a=16(b+4)

b+4 = a/16

b = a/16 - 4.

Answer: Properties of Multiplication. You can use the properties of multiplication to evaluate expressions. Commutative Property. Changing the order of factors does not change their product. Example: a x b = b x a. 4 x 20 = 20 x 4. Associative Property. Changing the grouping of factors does not change their product.

Answer:

1

Step-by-step explanation:

Using similarity

8/4 = 2/y

2 = 2/y

2y = 2

y = 2/2

y = 1

- #4 -

y = 12

[] First we will solve for x. Our angles with x are vertical angles, so they can be set equal to each other

8x - 61 = 6x - 13

8x - 48 = 6x

-48 = -2x

24 = x

[] Then, we will plug it into one of the angles (with x) and solve:

8x - 61

8(24) - 61

192 - 61 = 131

[] Last, these are supplementary angles so we can add them together and set it equal to 180:

131 + 3y + 1 = 180

132 + 2y = 180

2y = 48

y = 12

- #6 -

y = 22

[] First we will solve for x. These angles are vertial angles, so we can do the following:

9x + 42 = 15x

42 = 6x

7 = x -> x = 7

[] Then, we will plug it into one of the angles (with x) and solve:

15x = 15(7) = 105

[] Last, we will solve for y. These are supplementary angles so we can add them together and set it equal to 180:

4y - 13 + 105 = 180

4y + 92 = 180

4y = 88

y = 22

- #7 -

y = 9

[] First we will solve for x. They are supplementary angles so we can add them together and set it equal to 180:

x + 21 + 3x + 11 = 180

4x + 32 = 180

4x = 148

x = 37

[] Then, we will plug it into one of the angles (with x) and solve:

3x + 11 = 3(37) + 11 = 111 + 11 = 122

[] Last, we will solve for y. These are vertical angles, so they can be set equal to solve:

122 = 14y - 4

126 = 14y

9 = y

- See attached for where I pulled numbers from -

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

m<2 + m<3 = 180°

Step-by-step explanation:

Lines intersected by a transversal are parallel if same-side interior angles are supplementary.

Answer: m<2 + m<3 = 180°

Answer:

36 And 59

Step-by-step explanation:

Answer:

i believe its -4 and -2

Step-by-step explanation:

hope tha work

Answer:

A={a,b,c}

B={1,2}

A×B={(a,1),(a,2),(b,1),(b,2),(c,1),(c,2)

Answer:

x = 20

Step-by-step explanation:

(2x+10) = 180 - 130

2x + 10 = 50

2x= 40

x = 20

hope this helps! :)

The amount of money  he could have in savings after two more years is:c. $1,315. 06.

First step is to calculate the 12 month saving

Saving= 12 month × $103.19

Saving = $1238.28

Second step is to calculate the interest earned

Interest = Prt

Interest= $1238.28×·0.031×1

Interest= $38.39

Third step is to calculate the balance after 2 years

Saving= $1238.28 +(2 years × $38.39)

Saving= $1238.28 +$76.78

Saving= $1315.06

Inconclusion the amount of money  he could have in savings after two more years is:c. $1,315. 06.

Learn more about interest here:

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Answer:

12

Step-by-step explanation:

So there is 3:5 right, so 20 divided by 5 equals 4, there are four 5's in 20.  Then 4 multiplied by 3 equals 12. So there are 12 students that has BROWN EYES.

Hope I Helped You :)

Answer:

0.05 or 5%

Step-by-step explanation:

The formula for simple interest is as follows:

A = P(1+rt), with A representing the final amount, P representing the initial amount, r being the rate, and t being time. Plugging our values in, we have

5610 = 4400(1+5.5r). We know that 5 years and 6 months is 5.5 because 6 months = 0.5 years

5610 = 4400(1+5.5r)

expand

5610 = 4400 + 24200r

subtract 4400 from both sides to isolate the variable and its coefficient

1210 = 24200r

divide both sides by 24200 to isolate the variable

r = 0.05 or 5% as 0.05 * 100 = 5

Answer:

m = 5

Step-by-step explanation:

Since the triangles are similar in the way shown, then

6/10 = 3/m

6m = 10 × 3

m = 5