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Arlecino [84]
3 years ago
9

Which expression can be substituted for y in the top equation of the

Mathematics
1 answer:
maria [59]3 years ago
6 0

Answer:

Y=7+3x, x=-3, y=-2

Step-by-step explanation:

3x-5y=1. Equation 1

3x-y=-7. Equation 2

-y=-7-3x isolate for y in equation 2

y=7+3x multiplied by -1 to get positive y

3x-5(7+3x)=1 substitute y value of equation 2 (7+3x) into equation 1

3x-35-15x=1

-12x=36

x=-3

solve for y.

3x-5y=1

3(-3)-5y=1

-9-5y=1

-5y=10

y=-2

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A radiator contains 10 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure anti
prohojiy [21]

ANSWER

Find out the how much fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .

To proof

let us assume that the fluid should be drained and replaced with pure antifreeze be x .

As given

A radiator contains 10 quarts of fluid, 30% of which is antifreeze.

Now write 30% in the decimal form

= \frac{30}{100}

Now write 60% in the decimal form

= \frac{60}{100}

After  drained and replaced the fluid with pure antifreeze than the quantity becomes = ( 10 - x )

The quantity of  antifreeze is

= \frac{30\times (10 - x)}{100}

The fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .

than the equation becomes

= x + \frac{30\times ( 10 - x )}{100} = \frac{60\times10}{100}

solyving

100x +300 - 30x = 600

70x = 300

x = \frac{300}{70}

x = 4.28 quarts (approx)

Hence 4.28 quarts (approx) fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .

Therefore the option (c.) is correct .

3 0
4 years ago
Read 2 more answers
Find the probability that the senator was in the Democratic party, given that the senator was returning to office.
shutvik [7]

Answer:

The probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

Step-by-step explanation:

The complete question is:

Sophia made the following two-way table categorizing the US senators in 2015 by their political party and whether or not it was their first term in the senate.

                   Democratic         Republican         Independent        Total

First Term           11                          28                        11                     50

Returning           33                         26                        11                     70

Total                   44                         54                        22                  120

Find the probability that the senator was in the Democratic party, given that the senator was returning to office.

Solution:

The conditional probability of an event <em>A</em> given that another event <em>X</em> has already occurred is given by:

P(A|X)=\frac{P(A\cap X)}{P(X)}

The probability of an event <em>E</em> is given by the ratio of the number of favorable outcomes to the total number of outcomes.

P(E)=\frac{n(E)}{N}

Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:

P(D\cap R)=\frac{33}{120}=0.275

Compute the probability of selecting an US senator who was returning to office as follows:

P(R)=\frac{70}{120}=0.5833

Compute the conditional probability, P (D | R) as follows:

P(D|R)=\frac{P(D\cap R)}{P(R)}

            =\frac{0.275}{0.5833}\\\\=0.4714555\\\\\approx 0.4715

Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

4 0
3 years ago
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BlackZzzverrR [31]
The answer is true because they both have the 90 degree box and a mark in the line indicating they are the same length.
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Which of the following circles have their centers on the x-axis? Check all that apply.
Alexeev081 [22]

Answer: Option A and Option D

Step-by-step explanation:

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(h, 0)

Therefore all the circles that have their centers on the x axis will have a value of k = 0.

Identify among the options all those equations that have a value of k = 0

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Rewrite the expression as an algebraic expression in x. <br> cos(tan−1 x)
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