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antiseptic1488 [7]

3 years ago

13

Rosana used linear combination to solve the system of equations shown. She did so by multiplying the second equation by a certai

n number to eliminate the y-terms. What number did Rosana multiply the second equation by? $\left \{ {{x - y = 16} \atop {0.5x + 0.2y = 25}} \right.$

1 answer:

jasenka [17]3 years ago

6 0

She multiplied it by 5, because that would make the equation:

2.5 + y = 125

So when we add -y and y cancel out

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Plot point C(2,7). If M is the midpoint of CD , what are the coordinates of D?

Y_Kistochka [10]

Answer:

The coordinates of D is (-4,-9)

Step-by-step explanation:

Given

C = (2,7)

<em>M=(-1,-1) ----- Missing part of question</em>

Required

Determine the coordinates of D

<em>Let the coordinates of D be (x₂,y₂)</em>

<em>We'll solve this question using mid point formula;</em>

<em></em> $M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ <em></em>

<em>Where</em>

$C(x_1,y_1) = (2,7)$ and $M(x,y) = (-1,-1)$

Put these values in the formula

$(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})$

By comparison;

$-1 = \frac{2+x_2}{2}$ and $-1 = \frac{7+y_2}{2}$

$-1 = \frac{2+x_2}{2}$

Multiply both sides by 2

$-2 = 2 + x_2$

Subtract 2 from both sides

$-2 -2 = x_2$

$x_2 = -4$

$-1 = \frac{7+y_2}{2}$

Multiply both sides by 2

$-2 = 7 + y_2$

Subtract 7 from both sides

$-2 - 7 = y_2$

$y_2 = -9$

<em>Hence, the coordinates of D is (-4,-9)</em>

4 0

4 years ago

If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?

sergey [27]

Sin θ = 2 / 7
tan θ > 0
cos θ = ?

sin θ = opposite / hypotenuse
tan θ = opposite / adjacent
cos θ = adjacent / hypotenuse

short leg = opposite = 2
hypotenuse = 7
long leg = adjacent = ?

adjacent = √(7² - 2²)
adjacent = √(49 - 4)
adjacent = √45
adjacent = √9 * 5
adjacent = 3 √5

cos θ = adjacent / hypotenuse
cos θ = 3√5 / 7

6 0

3 years ago

Write the algebraic expression that matches each graph ...y = ___

Dvinal [7]

Answer:

"absolute value function," y = |x|

Step-by-step explanation:

This is the graph of the "absolute value function," y = |x|.

7 0

3 years ago

Several years ago, 38% of parents who had children in grades K-12 were satisfied with the quality of education the students r

Colt1911 [192]

Answer:

$0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995$

$0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564$

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

For this case we are interesting in the parameter of the true proportion of people satisfied with the quality of education the students receive

The confidence level is given 95%, the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical values are:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The estimated proportion of people satisfied with the quality of education the students receive is given by:

$\hat p =\frac{499}{1165}= 0.428$

The confidence interval for the proportion if interest is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And replacing the info given we got:

$0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995$

$0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564$

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

8 0

4 years ago

Victoria has 2.50 pounds of bell peppers and the cost is $1.25. What is the price for 1 pound of bell peppers?

AleksAgata [21]

Answer:

The price of one pound of bell peppers is $0.6.

Step-by-step explanation:

This problem is equivalent to the following:

<em>"if 10 oranges cost $20, how much does 1 orange cost? "</em>

and the answer to that question is:

price of 1 orange = $20/ 10 oranges = $2 per orange.

Put simply, we divided the total price by the total number of items, and we shall do the same thing for the case of bell peppers:

price of 1 pound = $1.25/ 2.5 pounds = $0.5/ pound.

The price for 1 pound of bell peppers is $0.5.

8 0

4 years ago