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3 years ago

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Christine went shopping and bought each of her eight nephews a gift, either a video costing $14.95 or a CD costing $16.88. She s

pent $131.18 on the gifts. How many
videos and how many CDs did she buy?

1 answer:

VikaD [51]3 years ago

4 0

Answer:

Step-by-step explanation:

Define number of videos purchased as "n" and number of CD's purchased as "c" then we can equation the total purchases and the costs by:

8 nephews:

n + c = 8

Spent $121.53

14.95*n + 16.88*c = 121.53

Substitute one variable as a function of the other. Preference the simpler equation (n + c = 8)

n = 8 - c

=>

14.95*(8-c) + 16.88c = 121.53

119.60 + 1.93c = 121.53

1.93c = 1.93

c = 1

=>

n = 7

*Check:

14.95*(7) + 16.88*(1) = 121.53

im so sorry if this is wrong :/

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3 years ago

Solve by graphing <br><br> u=v and 6u=2v-24

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Answer:

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Step-by-step explanation:

In this exercise, we have two equations, namely:

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And we are asked to solve this problem by graphing. In this way, we can write a system of linear equations in two variables, but first of all, let's rewrite:

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Then:

$\left\{ \begin{array}{c}y=x\\6y=2x-24\end{array}\right.$

So here we have two lines.

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The second one is:

$6y=2x-24 \\ \\ \therefore y=\frac{2x-24}{6} \\ \\ \therefore \boxed{y=\frac{1}{3}x-4}$

This line has a slope $m=\frac{1}{3}$ and cuts the y-axis at $b=-4$

By using graph tools, we get the graph shown below, then:

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3 years ago

A garden table and a bench cost $653 combined. The garden table cost $97 less than the bench. what is the cost of the bench?

SIZIF [17.4K]

T is the cost of the table. B is the cost of a bench.

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3 years ago

A shade of yellow light with a wavelength of 5.8×10-7 m and a frequency of 5.17 × 10-14 Hz

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We have,

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Frequency of yellow light, $f=5.17\times 10^{-14}\ Hz$

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The speed of a wave is given in terms of wavelength and frequency as :

$v=f\lambda\\\\v=5.17\times 10^{-14}\times 5.8\times 10^{-7}\\\\v=2.99\times 10^{-20}\ m/s$

So, the speed of light in a shade of yellow light is $2.99\times 10^{-20}\ m/s$ .

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3 years ago

Given the quadratic function f(x) = 4x^2 - 4x + 3, determine all possible solutions for f(x) = 0

solong [7]

Answer:

The solutions to the quadratic function are:

$x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}$

Step-by-step explanation:

Given the function

$f\left(x\right)\:=\:4x^2\:-\:4x\:+\:3$

Let us determine all possible solutions for f(x) = 0

$0=4x^2-4x+3$

switch both sides

$4x^2-4x+3=0$

subtract 3 from both sides

$4x^2-4x+3-3=0-3$

simplify

$4x^2-4x=-3$

Divide both sides by 4

$\frac{4x^2-4x}{4}=\frac{-3}{4}$

$x^2-x=-\frac{3}{4}$

Add (-1/2)² to both sides

$x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{3}{4}+\left(-\frac{1}{2}\right)^2$

$x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{1}{2}$

$\left(x-\frac{1}{2}\right)^2=-\frac{1}{2}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{1}{2}=\sqrt{-\frac{1}{2}}$

$x-\frac{1}{2}=\sqrt{-1}\sqrt{\frac{1}{2}}$ ∵ $\sqrt{-\frac{1}{2}}=\sqrt{-1}\sqrt{\frac{1}{2}}$

as

$\sqrt{-1}=i$

so

$x-\frac{1}{2}=i\sqrt{\frac{1}{2}}$

Add 1/2 to both sides

$x-\frac{1}{2}+\frac{1}{2}=i\sqrt{\frac{1}{2}}+\frac{1}{2}$

$x=i\sqrt{\frac{1}{2}}+\frac{1}{2}$

also solving

$x-\frac{1}{2}=-\sqrt{-\frac{1}{2}}$

$x-\frac{1}{2}=-i\sqrt{\frac{1}{2}}$

Add 1/2 to both sides

$x-\frac{1}{2}+\frac{1}{2}=-i\sqrt{\frac{1}{2}}+\frac{1}{2}$

$x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}$

Therefore, the solutions to the quadratic function are:

$x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}$

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3 years ago