A CD costs £12 and a T-shirt costs £15, I have £60 to spend. I buy x number of CDs and y number of T-shirts. Write;

A) An expression for the amount of money I spend.

B) An inequality showing the amount of money I spend has to be less than or the same as what I have.

-Can you plot your inequality on a pair of axis?

-Can you use the graph to find the different numbers of CDs and T-shirts I can buy?

Worth 20 points!

Answer: 909.03

Step-by-step explanation:

We know that the equation is an exponential function, it can be written as y=ab^x

[tex]100 &=a b^{6.5} \dots \mathrm{Equation \ 1} \\11 &= a b^{1} \\[/tex]

[tex]\Rightarrow ab^1=11[/tex]

[tex]\Rightarrow \frac{ab^1}{b}=\frac{11}{b};\quad \:b\ne \:0[/tex]

[tex]\Rightarrow a=\frac{11}{b}[/tex]

a = 11/b, substitute it in equation 1

[tex]100 &=a b^{6.5}[/tex]

[tex]\Rightarrow 100=\left(\frac{11}{b}\right)b^{6.5}[/tex]

[tex]\Rightarrow 100b=11b^\frac{11}{2}[/tex]

[tex]\Rightarrow 11\sqrt{b^{11} } =100b[/tex]

[tex]\Rightarrow \sqrt{b^{11} } =\frac{100}{11}}[/tex]

[tex]\Rightarrow \sqrt{b^{11} } =\frac{100}{11}}[/tex]

[tex]\Rightarrow {b^{11} } =\frac{10000}{121}}[/tex]

[tex]\Rightarrow {b} =\frac{\sqrt[11]{10000 \cdot 11^9} }{11}[/tex]

[tex]\Rightarrow {b} = 1.49379[/tex]

a = 11/b

a = 11/(1.49379)

a = 7.36382

Equation: y = (7.36382)(1.49379)^x

Now plug in 12 for x:
[tex]\Rightarrow { \left(7.36382\right)\left(1.49379\right)^{12}[/tex]

[tex]\Rightarrow 7.36382\cdot \:1.49379^{12}[/tex]

[tex]\Rightarrow 7.36382\cdot \:123.44530\dots[/tex]

[tex]\Rightarrow 909.03[/tex]

Therefore, f(12) = 909.03 for the exponential function

2) Find the area of a parallelogram with a height of 8 inches and a base of 14 inches.

A=bh=14·8=112in²

3) Find the surface Area of the rectangular prism with a length of 15 cm, height of 7 cm, and width of 5 cm.

A=2(wl+hl+hw)=2·(5·15+7·15+7·5)=430cm²

4) Find the volume of the following figure:

[tex]V=\frac{lwh}{3} =\frac{16*8*9}{3} =384[/tex]

5) You are wrapping a cube shape present that is 9 inches tall. How much wrapping paper will you need to wrap the entire present.

SA = [tex]l*w*h[/tex] = 9x9x9 = 729in²

6) A truck has a trailer that has a length of 13ft, a width of 6ft, and a height of 8ft. What is the volume of the trailer?

[tex]V=whl=6*8*13=624[/tex]

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Step-by-step explanation:

Find the area of a parallelogram then the surface Area of the rectangular prism

THAT IS=

A=2(wl+hl+hw)=2·(5·15+7·15+7·5)=430cm sq. Find the volume of the following figure: then the amount of paper for the present. A =  = 9x9x9 = 729in sq.  then

Volume of truck: Volume=widthxhieghtxlength=6x8x13=624

If this was helpful please give a thank you and a brainliest

Answer:

angle 3 is 70

ANGLE :> 3

IS.

70

Answer :D

8 [tex]\frac{2}{3}[/tex] (8 2/3)

Question explanation:

5 [tex]\frac{3}{4}[/tex] +  2 [tex]\frac{11}{12}[/tex] = [tex]\frac{26}{3}[/tex] = 8 [tex]\frac{2}{3}[/tex]

(5 3/4) + (2 11/12) = (26/3) = (8 2/3)

(5 + 2) + ( [tex]\frac{3}{4}[/tex] + [tex]\frac{11}{12}[/tex] )

(5 + 2) + (3/4 + 11/12)

7 + 3 x 3 + [tex]\frac{11}{12}[/tex]

   (4 x 3)  (11/12)

7 + [tex]\frac{9}{12}[/tex] + [tex]\frac{11}{12}[/tex]

(9/12) + (11/12)

7 + 9 + 11

      (12)

7 + [tex]\frac{20}{12}[/tex]

(7 + 20/12)

7 + (20 ÷ 4)

     (12 ÷ 4)

7 + [tex]\frac{5}{3}[/tex]

(5/3)

7 + 1 [tex]\frac{2}{3}[/tex]  

( 1 2/3)

= 8 [tex]\frac{2}{3}[/tex]

 (8 2/3)

8 [tex]\frac{2}{3}[/tex] = [tex]\frac{26}{3}[/tex] = 8 [tex]\frac{2}{3}[/tex]

(8 2/3) (26/3) (8 2/3)

I hope this finds you well - Answered by Lilo

Hello !

[tex]\huge \pmb {\boxed {\frak{Proof \: is \: shown \: below :}}}[/tex]

Your answer is B.

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Dollixna ~

The given inequality y < -4 is shown in the attached graph. The correct answer would be an option (B).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Inequalities with "< or > "symbols are shown with a dashed line to indicate that the line is not inside the area. Inequalities involving symbols are depicted with a solid line to indicate that the line is included in the region.

We have been the given inequality y < -4

Rearrange the equation such that "y" is on the left and all other variables are on the right.

Plot the "y=" line (a solid line for y or y, and a dashed line for y or y>). The shade above the line for a "greater than" (y> or y), or below the line for a "less than" (y or y).

Hence, the given inequality y < -4 is have shown in the attached graph.

Learn more about the inequalities here:

brainly.com/question/20383699

#SPJ2

Answer:

96 bricks

Step-by-step explanation:

Alan does 1/5 of the job in an hour. Gavin does 1/7 of the job in an hour

Together, 12/35 of the job should be done in an hour. In [tex]2 \frac{11}{12}[/tex] hours, the work should be done.

rate at 4 hours=[tex]2 \frac{11}{12}[/tex]*(normal speed-26)

To clarify, x=the normal rate

4 hours(normal rate-26)=[tex]2 \frac{11}{12}[/tex](normal rate)

4(x-26)=[tex]2 \frac{11}{12}[/tex]x

x=96

Answer:

First, set up equations for total cost for both Happy Paws and Woof Watchers.

x= number of hours

y= total cost

Happy Paws

y=3.50x +16

Woof Watchers

y=4.75x+11

4.75x+11=3.50x+16

x=4

You can check your answer by doing the following:

Happy Paws: (3.50)(4)+16= 30

Woof Watchers: (4.75)(4)+11= 30

Step-by-step explanation:

Answer:

that is 100

Step-by-step explanation:

5 to the power of 5 is 1oo

0 0 0

2 3 1

4 6 2

6 9 3

the lines should be straight tho

Answer:

The top right one with the measurements 8mm x 8mm for the base and 10 mm for the slant height

Step-by-step explanation:

The net has a square base so that means the net forms a square based pyramid
Hope this helps :)

Answer:

The answer is the second figure on the top of the page.

Step-by-step explanation:

That's because the square is 8mm x 8mm

so the figure that has a square and 8mm x 8mm is the second one in the first row.

Answer:

40 degrees

100-60=40

Step-by-step explanation:

The angle x is in another angle that looks like 100 and 100 minus 60 is 40.

Hope this helps and if it is correct.

Answer:

Step-by-step explanation:

Remark

x + 60 together make up an angle that is vertically opposite the 100 degree angle.

Vertically opposite angles are equal.

Equation

x + 60 = 100

Solution and Answer

x + 60 = 100                    Subtract 60 from both sides.

x + 60-60 = 100 - 60      Combine

Answer: x = 40

Answer: 235 cm^2

Explanation: you can cut the shape into two smaller ones and then solve for each smaller shapes area. to find out the length of the top piece with 11 as length you can subtract nine from fourteen. from their you calculate the area of the top shape (11x5=55) and then the bottom shape (9x20=180). from their just add the two areas to get 235.

Answer:

246 cm squared

Step-by-step explanation:

u hv to break up the big shape into little shapes so you would do 20x9 and 20-14 which is 6 and do 6x11 and then add them up

Answer:

2

Step-by-step explanation:

5 has 2 siblings it's number 5

Answer:

12

Step-by-step explanation:

if we know we want a profit of at least 114, we need to solve for x.

if we put 12 for x we get the answer 117 and when we put 11 for x we get less than 114.

-0.5(12)^2 + 25(12)-111 = 117

Answer:

do 60 times 5 puls540 and 12

Step-by-step explanation:

i think i am wrong but i am right i think

Answer:

-14/15 - 1/3v

Step-by-step explanation:

combine like terms -6/5 = -18/15 + 4/15 = -14/15

-2/3 + 1/3 = -1/3

Answer:

X Values: Years After 1985

Y Values: Cell Phone Subscriptions

I am not sure of this answer, but please ask whoever assigned you it.

We're given:

Let a represent the number of children who swam.

Let b represent the number of adults who swam.

Because we've set two variables, we need two equations to be able to find the answers.

One of the equations will regard price while the other will regard the number of people, as those are the two things given in the question.

Number of people:

[tex]a+b=478[/tex]

Price:

[tex]1.75a+2.25b=975[/tex]

We can solve this question using substitution, where we plug one equation into the other.

Isolate a in the first equation:

[tex]a+b=478\\a=478-b[/tex]

Plug the first equation into the second equation by replacing a:

[tex]1.75a+2.25b=975\\1.75(478-b)+2.25b=975[/tex]

Solve for b:

[tex]1.75(478-b)+2.25b=975[/tex]

⇒ Open up the parentheses:

[tex]836.5-1.75b+2.25b=975\\836.5-0.5b=975[/tex]

⇒ Subtract 836.5 from both sides to isolate b:

[tex]-0.5b=138.5[/tex]

⇒ Divide both sides by -0.5:

[tex]b=277[/tex]

Solve for a:

[tex]a+b=478[/tex]

⇒ Replace b with 277:

[tex]a+277=478\\a=201[/tex]

There were 201 children and 277 children at the pool that day.

Answer:

c) (-3s) - 9

Step-by-step explanation:

(-5s) + 2s - 9

-5s + 2s - 9 <== combine like terms

-3s - 9

Therefore, our answer is c.

Hope this helps!

Answer:

the answer is C.

Step-by-step explanation:

Start by combining like terms (-5s) and 2s= (-3s)

You can't subtract 9 from this because they aren't like terms.

(-3s) -9

Answer:

Yah no way man your gonna fail

Step-by-step explanation:

Answer:

1.2 cm

Step-by-step explanation:

3/5, in decimal form, is 0.6.

You find the diameter by multiplying the radius by 2.

0.6 * 2 = 1.2

Answer:

1 1/5 or 1.2

Step-by-step explanation:

You multiply the radius (the number in the picture) by two, because the diameter is twice the radius

hope that helps

Answer:

About 25%

Step-by-step explanation:

If there are 8 selections the there are two spins

the 2 is divided by eight giving you 0.25 convert that into 25 and add the percentile so 25%.

Sorry if this is wrong. If this is right pls give brainlest.