A used book store also started selling used CDs and videos. In the first week, the store sold a combin
ation of 40 CDs and videos. They charged $4 per CD and $6 per video
and the total sales were $180. Determine the total number of CDs and videos sold
Set up two equations, one for number of CD's and videos sold and one for amount of money
made. Then solve for each variable by graphing in Desmos. Clearly state your answers in a
sentence.

Answer:

$1856.47

Step-by-step explanation:

500 x 1.3^5=1856.465

Answer:

Your answer is 16.05

Step-by-step explanation:

15.75 + 0.3 = 16.05

16.05 - 0.3 = 15.75

Answer:

every other term is negative, so it would be -64

Step-by-step explanation:

hope it helps!

Given:

The two points on a coordinate plane are C(-5,-1) and D(0,3).

To find:

The distance between C and D.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, the distance between C(-5,-1) and D(0,3) is

[tex]CD=\sqrt{(0-(-5))^2+(3-(-1))^2}[/tex]

[tex]CD=\sqrt{(0+5)^2+(3+1)^2}[/tex]

[tex]CD=\sqrt{(5)^2+(4)^2}[/tex]

[tex]CD=\sqrt{25+16}[/tex]

On further simplification, we get

[tex]CD=\sqrt{41}[/tex]

[tex]CD=6.40312424[/tex]

[tex]CD\approx 6.40[/tex]

Therefore, the distance between C and D is 6.40 units.

Answer:

y=3/2x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

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Answer:

a

Step-by-step explanation:

On the number line, negative numbers are less than zero. positive numbers are larger than zero.

Answer:

=177

Step-by-step explanation:

The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (10³⁶ + 26/18)

The sum of the digits in the expansion is given as,

⇒ 1 + 0 + 2 + 6 + 1 + 8

⇒ 18

The sum of the digits in the expansion (10³⁶ + 26/18) will be 18.

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Answer:

D

Step-by-step explanation:

Sin(x)=25/35=5/7

=> x = 45.6

Answer:

Total surface area of the prism = 920 cm²

Step-by-step explanation:

Given prism has 2 similar triangular surfaces and 3 rectangular surfaces of different dimensions.

Area of one triangular side = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

Area of 2 similar sides = Base × Height

                                     = 8 × 15

                                     = 120 cm²

Area of rectangular side with dimensions 17cm × 20cm

Area of the side = 17 × 20 = 340 cm²

Area of the second rectangular side with dimensions 8cm × 20cm

Area of the side = 8 × 20 = 160 cm²

Area of third rectangular side with dimensions 20cm × 15cm

Area of the side = 20 × 15 = 300 cm²

Total surface area of the given triangular prism = 120 + 340 + 160 + 300

                                                                               = 920 cm²

Answer:

See attached.

Step-by-step explanation:

The table is as shown

White paints {cups}   Red paints{cups}

4                                       3

2                                       1

1                                       0

5                                      4

5                                      4

The white paint mixes with the red paint is the ratio of 4 is to 3 in that every 4 cups of white paints is mixed with 3 cups of red paints.

Answer:

Hi! Your answer is m = 19

Step-by-step explanation:

~use the slope formula to find the average rate of change~

Answer:

- 1

Step-by-step explanation:

[tex]\frac{1}{\cot ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cos \left(x\right)}=\sec \left(x\right),\\\frac{1}{\cot ^2\left(x\right)}-\sec ^2\left(x\right)\\\\\mathrm{Use\:the\:basic\:trigonometric\:identity}:\quad \frac{1}{\cot \left(x\right)}=\tan \left(x\right),\\\tan ^2\left(x\right)-\sec ^2\left(x\right)\\\\=> \frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}-\frac{1}{\cos ^2\left(x\right)}\\[/tex]

[tex]=> \frac{\sin ^2\left(x\right)-1}{\cos ^2\left(x\right)}\\\\=> -\frac{\cos ^2\left(x\right)}{\cos ^2\left(x\right)}\\=> - 1[/tex]

Hope  that  helps!

By using trigonometric identities,  [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1

"Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain."

Given expression

[tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex]

We know the trigonometric identity

[tex]{cot^{2}(x) } =( \frac{sinx}{cosx})^{2}[/tex]

= [tex]\frac{1}{(\frac{cosx}{sinx} )^{2} } -\frac{1}{cos^{2}(x) }[/tex]                    

= [tex]\frac{sin^{2} (x)}{cos^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex]

= [tex]\frac{sin^{2}(x)-1}{cos^{2}x }[/tex]

= [tex]\frac{-(1- sin^{2}(x))}{cos^{2}x }[/tex]

We know the trigonometric identity

[tex]sin^{2}(x) +cos^{2}(x) = 1[/tex]

= [tex]\frac{-(cos^{2}x)}{cos^{2}x }[/tex]

= -1

Hence, [tex]\frac{1}{cot^{2}(x) } -\frac{1}{cos^{2}(x) }[/tex] = -1

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Answer:

16 cm

Step-by-step explanation:

Circumference is equal to 2 pi r.

Isolating r gives us C/2pi = r

50.26/2pi = 8, exactly.

Diameter is equal to 2r, so the diameter is 16 cm.

Answer:

r≈8

Step-by-step explanation:

Answer:

965

Step-by-step explanation:

Answer:

x = [tex]\frac{b-7}{a-2}[/tex]

Step-by-step explanation:

Given

ax + 7 = 2x + b ( subtract 2x from both sides )

ax - 2x + 7 = b ( subtract 7 from both sides )

ax - 2x = b - 7 ← factor out x from each term on the left side

x(a - 2) = b - 7 ← divide both sides by (a - 2)

x = [tex]\frac{b-7}{a-2}[/tex]

Answer:

180-165= 15

(They tried to throw you off with the second line)

Answer is 15 degrees

Answer:

1/3, 2/6, 3/9, 4/12..are equivalent fractions. Equivalent fraction of a given fraction is got by multiplying or dividing its numerator and denominator by the same whole number. For example, if we multiply the numerator and denominator of 2/3 by 4 we get.

Step-by-step explanation:

The equivalent fractions of  the given fraction [tex]\dfrac{2}{6}[/tex] are [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex] .

The fractions which have the same value but can  have different numerators or denominators when either multiplying , dividing or converting it into the lowest form is called equivalent fractions

The upper part of a fraction or part of a whole is called numerator and the lower part of a fraction or the whole is called denominator.

Equivalent fraction can be obtained by multiplying  numerator and denominator with the same number .

Example : equivalent fraction of  [tex]\dfrac{5}{8}[/tex] is

[tex]\dfrac{5}{8} = \dfrac{5 \times 1 }{8 \times 1} =\dfrac{5\times2}{8\times2} ........=\dfrac{5}{8}[/tex]

According to the data provided in the problem

[tex]\dfrac{2}{6} = \dfrac{2 \times 1 }{6 \times 1} =\dfrac{2\times2}{6\times2} ........=\dfrac{2}{6}[/tex]

Thus the equivalent fractions of [tex]\dfrac{2}{6}[/tex] are  [tex]\dfrac{4}{12} ,\dfrac{6}{18} ,\dfrac{8}{24}[/tex]

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Answer:

I dont know

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in right triangle ABC

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + AC² = BC² , substitute values

5² + AC² = 13²

25 + AC² = 169 ( subtract 25 from both sides )

AC² = 144 ( take the square root of both sides )

AC = [tex]\sqrt{144}[/tex] = 12

Since the triangles are congruent then corresponding sides are congruent, then

DE = AC = 12 inches → B

Answer:

2/3

Step-by-step explanation:

You first multiply 4x1/3 which equals 4/3. Now you do -2/3+4/3=2/3. Hope this helps!

Answer:

2/3

Step-by-step explanation:

[tex]\frac{-2}{3}+4*\frac{1}{3}=\frac{-2}{3}+\frac{4}{3}\\\\=\frac{(-2) + 4}{3}\\\\\\= \frac{2}{3}[/tex]

Answer:

What?

Step-by-step explanation:

Answer:

negative

1

4,6

Step-by-step explanation:

Answer:

A&C

Step-by-step explanation:

Answer:

The operation is commutative

Step-by-step explanation:

Operations

The * operation is defined on the set of real numbers R by

[tex]a * b=a^3+b^3-3ab[/tex]

For the operation to be commutative a*b should be equal to b*a.

Computing b*a:

[tex]b * a=b^3+a^3-3ba[/tex]

Rearranging:

[tex]b * a=a^3+b^3-3ab[/tex]

It's apparent that a*b=b*a, thus the operation is commutative

you have to find a number they are both divisible by to get it to simplest form. 18:225.

divide both by 3. 6:75.

you can divide it by 3 again.

answer: 2:25

The ratio of two quantities can be obtained by writing them as a fraction. The ratio in the form of  1 : n is given as 225 / 18.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The number of staff in the school = 18

And, the number of students in the school = 225

Since, the ratio of two numbers a and b is given as a : b = a / b.

In the form of 1 : n it can be written as, a : b = 1 / (b / a).

Similarly, the ratio of staff and students n the form of 1 : n can be written as,

Staff : Students = 18 : 225

=> Staff : Students = 1 / (18 / 225)

=> Staff : Students = 225 / 18.

Hence, the ratio Staff : Students can be written in the form 1 : n as 225 / 18.

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Answer:

= 0.2 pound per day

Step-by-step explanation:

This is a fraction equal to

1 pound ÷ 5 days

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 5

1 pound ÷ 5

5 days ÷ 5

=  

0.2 pound

1 day

=  

0.2 pound

day

= 0.2 pound per day