Given that for all values of x,
f(x) = 3x + p
g(x) = px + 4
and fg(x) = 6x + 9
where p and q are constants.
Work out the values of p and q.

To get the answer to this question we would have to calculate how much each DVD costs in each scenario.

To do this we will divide each cost by the total number of CDS:

[tex]\frac{2.30}{10} = .23[/tex]

[tex]\frac{10.50}{50} = .21[/tex]

For the pack of 10 CDS each CD costs 23 cents. On the contrary, for the pack of 50 CDs each CD costs 21 cents. Therefore to get a better deal, you would want to go with the 50 CDs.

Hope this helps!

- Kay

The cost per CD is lower when buying the package of 50 CDs, it is the better buy. You would save money by purchasing the package of 50 CDs for $10.50.

To determine which is the better buy, we need to compare the cost per CD in both scenarios.

Let's first calculate the cost per CD when buying 10 CDs:

Cost for 10 CDs = $2.30

Cost per CD = $2.30 / 10 CDs = $0.23 per CD

Now, let's calculate the cost per CD when buying a package of 50 CDs:

Cost for 50 CDs = $10.50

Cost per CD = $10.50 / 50 CDs = $0.21 per CD

Comparing the two options:

- Buying 10 CDs individually costs $0.23 per CD.

- Buying a package of 50 CDs costs $0.21 per CD.

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Answer: 6 miles

Step-by-step explanation: 1/3 hour = 2

1 hour = 6 (2x3=6)

Answer:

6 miles

Step-by-step explanation:

Answer:

Option (D)

Step-by-step explanation:

Formula to calculate the final amount after 't' years is,

A = [tex]P(1+\frac{r}{n})^{nt}[/tex]

Here P = Initial amount

r = rate of interest

n = number of times compounding done

t = duration of investment

For A = $8000

r = 0.06

t = 10 years

n = 12 (compounded monthly in a year)

Therefore, final amount = [tex]8000(1+\frac{0.06}{12})^{12\times 10}[/tex]

                                        = [tex]8000(1+0.005)^{120}[/tex]

                                        = [tex]8000(1.005)^{120}[/tex]

                                        = 8000(1.8194)

                                        = $14555.17

Therefore, Option (D) will be the answer.

Answer:

the answer is d

Step-by-step explanation:

$14,555.17

Notice that the denominator is a multiplied by 2 for each fraction.

1/1•2 = 1/2

1 /2•2 = 1/4

1/4•2 = 1/8

1/8•2 = 1/16

1/16•2 =1/32

The next size is 1/32.

Answer for #5:

7 friends

Step-by-step explanation:

convert fraction into 4ths:

1/4, 2/4, 3/4, 1/4

add together:

7/4ths

if each friend ate 1/4 of the pizzas, then there are 7 friends

Answer:

Step-by-step explanation:

AD = DC and BE=EC ⇒

DE = 1/2AB

DE = 4*9 + 1 = 36 + 1 = 37

AD = DC

BE = EC

It gives that 2(DE) = AB

The length of DE.

According to the question,

2(DE) = AB

By putting the respected values, we get

2( 4x + 1 ) = 11x - 25

or, 8x + 2 = 11x - 25

or, 25 + 2 = 11x - 8x ( transposition method )

or, 27 = 3x

or, x = 27/3 = 9

The value of x is 9.

DE = 4(9) + 1 = 36 + 1 = 37

DE = 37

Answer:

I believe it should be the second answer

Answer:

The answer is 127.6

Step-by-step explanation:

To find the volume of something, you multiply.

So:5.5 times 3.2 times 7.25 is equal to 127.6

HOPE THIS HELPS YOU!!!!    :)

Answer:

127.60 square inches

Step-by-step explanation:

Multiply the diameters all together to get your answers.

5.5 x 3.2 x 7.25

Multiply

5.5 x 3.2 = 17.6

Multiply some more

17.6 x 7.25 = 127.6

You can also just multiply like this:

5.5 x 3.2 x 7.25 = 127.6

Hope this helped :)

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Answer:

-8 and 3

Step-by-step explanation:

The asked numbers are -8 and 3.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, two numbers multiply to -24 and add up to -5

Let the two numbers be x and y

x+y = -5...(i)

xy = -24

x = -24/y...(ii)

Put eq (ii) in eq (i)

-24/y + y = -5

-24 + y² = -5y

y²+5y-24 = 0

Factorizing,

y = 8 and 3

Taking y = 3, put it in eq(ii)

x = -24/3

x = -8

Hence, the asked numbers are -8 and 3.

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Answer:

8

Step-by-step explanation:

I hope this helps you out!

Answer:

8

Step-by-step explanation:

...

Given :

A morning truck can carry no more than 1480 pounds of cargo.

Brian loaded 640 pounds into the truck already.

He is loading boxes that weigh 70 pounds.

To Find :

How many boxes can he out into the truck.

Solution :

Weight left for carrying cargo, W = 4180 - 640 pounds

W = 3540 pounds

Number of boxes of 70 pounds cargo he can carry in truck is :

[tex]n =\dfrac{3540}{70}\\\\n = 50.57[/tex] ≈ 50 .

Therefore, number of box they can carry is 50.

Hence, this is the required solution.

Answer:

rise : atmospheric pressure increases

fall : atmospheric pressure decreases

Step-by-step explanation:

In the context, it is given that a weather forecaster takes the help of the barometer to check the air pressure and predicts the weather. The column of mercury level in the barometer shows a rise or fall in the glass tube as the weight of the atmosphere falling on the mercury surface changes.

Here it is given that the mercury rises for 0.02 in, then it falls 0.09 in,  it then rises by 0.07 in and then again falls by 0.18 in. The word "rise" here shows that the weight of the atmosphere is more. In other words, increase in atmospheric pressure increases the level of mercury in the glass tube and the decrease in or "fall" in the mercury level shows the drop in atmospheric pressure.

3 is 13 more than 10, and 3 is 30% of 10, so 30% im pretty sure

Answer:

130%

Step-by-step explanation:

It's 130% because 10*130% is 13.

Answer:

Step-by-step explanation:

h=V/lw

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y  grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\[/tex]

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)[/tex]  [as x+y=14]

[tex]\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\[/tex]

[tex]\Rightarrow x =(25 \times 14)/32=10.9375[/tex] grams

and [tex]y = 14-x= 14-10.9375=3.0625[/tex] grams.

Hence, 10.9375 grams of 82% gold and 3.0625  grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y  grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

[tex]\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\[/tex]

[tex]\Rightarrow x =(50 \times 14)/57=12.28[/tex] grams

and [tex]y = 14-x= 14-12.28=1.72[/tex] grams.

Hence, 12.28 grams of 82% gold and 1.72  grams of 50% gold added to make 14 grams of 75% gold.

Answer:

202 miles per day

Step-by-step explanation:

Answer:

165

Step-by-step explanation:

A 2-column table with 3 rows. Column 1 is labeled Days, x with entries 3, 4, 5. Column 2 is labeled Miles, y with entries 771, 973, 1,175.

The Bodens drove for awhile before they made a plan to drive a set number of miles each day. Days 3, 4, and 5 are displayed in the table. Assume the relationship is linear.

Determine the initial number of miles that the Boden family drove before they made their plan.

771 miles

367 miles

165 miles

135 miles

This is your correct answer 165, oops this is the wrong question sorry

Answer:

7

Step-by-step explanation:

7 is not a factor of 48, since 7 can not be multiplied by another whole number to get 48. (48 divided by 7 is 6.8)

Answer:

7

Step-by-step explanation:

Answer:

z=kx/y

zy=kx

zy/x=kx/x ( divided both side by x. to find k)

k=zy/x

k=6×4/3(z=6,y=4,x=3)

k=24/3

k=8

so z=kx/y

z=8×5/2(replace the numbers in the place of variables,k=8,x=5,y=2)

z=40/2

z=20

Answer:

[tex]101 * 102 = 10302[/tex]

Step-by-step explanation:

Given

[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]

Required

Find 101 * 102

[tex]101 * 102 =[/tex]

Express as a sum of 100

[tex](100 + 1) * (100 + 2)[/tex]

Compare this to [tex](x + a)(x + b)[/tex]

We have that:

[tex]x = 100[/tex]

[tex]a = 1[/tex]

[tex]b = 2[/tex]

Recall that:

[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]

Substitute 100 for x, 1 for a and 2 for b

[tex](100 + 1) * (100 + 2) = 100^2 + (1 + 2) * 100 + 1 * 2[/tex]

[tex](100 + 1) * (100 + 2) = 100^2 + 3 * 100 + 2[/tex]

[tex](100 + 1) * (100 + 2) = 10000 + 300 + 2[/tex]

[tex](100 + 1) * (100 + 2) = 10302[/tex]

Hence:

[tex]101 * 102 = 10302[/tex]

Answer:

42.5

Step-by-step explanation:

x                      15

_                       _

85                   100

15x85=1275

1275/100=127.5

127.5-85=42.5

Answer:

v=5

Step-by-step explanation:

you are trying to make 4v into v right ?

so simply divide it by 4 - the same if it was 4a or 7a or 9k, always start by dividing by the number

then you need to balance the two sides - so whatever number you divide the letter by (which is the 4 in this case) , you do the same with the other side , so whatever number is after the equal sign , divide it by 4

PART ONE                                      ↓ 4v  =   20  

           DIVIDE BY 4                       →  v   =    20

PART TWO                                          v   =   20 ↓

                                                            v   =     5 ←           DIVIDE BY 4

Answer:

it is D.... PERIODT

Step-by-step explanation:

Answer:

-8,1 mabey I don't really know

Answer:

-2

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

Answer:

0.00462962962

Step-by-step explanation:

Answer:

The equation of the line in the slope-point form is y - 7 = 10(x + 6)

The equation of the line in the slope-intercept form is y = 10x + 67

Step-by-step explanation:

The slope-point form of the linear equation is y - y1 = m(x - x1), where

The slope-intercept form of the linear equation is y = m x + b, where

∵ The slope of the line is 10

∴ m = 10

∵ The line passes through the point (-6, 7)

∴ x1 = -6 and y = 7

→ Substitute them in the slope-point form above

∵ y - 7 = 10(x - -6)

∵ (-)(-) = (+)

∴ y - 7 = 10(x + 6)

∴ The equation of the line in the slope-point form is y - 7 = 10(x + 6)

→ Substitute m in the slope-intercept form

∵ y = 10x + b

→ To find b substitute x by -6 and y by 7 in the equation

∵ 7 = 10(-6) + b

∴ 7 = -60 + b

→ Add 60 to both sides to find b

∴ 67 = b

→ Substitute the value of b in the equation

∴ y = 10x + 67

∴ The equation of the line in the slope-intercept form is y = 10x + 67