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3 years ago

Solve this system of equations using substitution.

Mathematics

2 answers:

trapecia [35]3 years ago

8 0

Answer:

y = 30, x = 10

Step-by-step explanation:

y = 3x...eqn i

x = -2y + 70...eqn ii

Now,

Substituting eqn i in eqn ii,

x = -2y + 70

or, x = -2(3x) + 70

or, x = -6x + 70

or, x + 6x = 70

or, 7x = 70

so, x = 10

Now,

y = 3x = 3 * 10 = 30

KIM [24]3 years ago

3 0

Answer:

y=3x

x=-2y+70

x=-2(3x)+70

x=-6x+70

collect like terms

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3 years ago

Read 2 more answers

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample

adelina 88 [10]

Answer:

$\sigma = 12.5$ ---- sample standard deviation

$\sigma^2 = 157.2$ ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

$x_1 = \frac{56 + 64}{2} = 60$

$x_2 = \frac{65 + 73}{2} = 69$

And so on

So, the table becomes:

$\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}$

Calculate the mean

$\bar x = \frac{\sum fx}{\sum f}$

$\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}$

$\bar x = \frac{4191}{55}$

$\bar x = 76.2$

The variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}$

$\sigma^2 = \frac{8488.8}{54}$

$\sigma^2 = 157.2$

The sample standard deviation is:

$\sigma = \sqrt{\sigma^2$

$\sigma = \sqrt{157.2$

$\sigma = 12.5$

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

$\sigma^2 = 157.2$

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3 years ago

Write an equation and solve round to the nearest hundredth when necessary 19 is what percent of 40

german

Answer:

Final answer is 47.5%.

Step-by-step explanation:

Let the missing percent is x.

Then x percent of 40 can be written as: $40\cdot\frac{x}{100}$ .

Given that resulting percent value is 19.

So we can set both equal.

$40\cdot\frac{x}{100}=19$

$40x=19\cdot100$

$40x=1900$

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$x=47.5$

So the final answer is 47.5%.

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