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3 years ago

What is the solution to the system of equations? Use the substitution method. {y=−2x+5 3x−4y=2

2 answers:

5 0

We have that
<span>y=−2x+5 --------> equation 1
3x−4y=2---------> equation 2
</span><span>substituting 1 in 2
</span>3x-4*(-2x+5)=2--------> 3x+8x-20=2--------> 11x=22-----> x=2
y=-2x+5-----> -2*2+5-----> y=1

the solution is
x=2
y=1

dimulka [17.4K]3 years ago

3 0

$LINEAR \: \: EQUATIONS \: \: IN \: \: TWO \: \: \\ VARIABLES \\ \\ \\\\Given \: \: - \\ \\ y \: = - 2x + 5 \: \: \: - - - eq.(1) \\ \\ \: 3x - 4y = 2 \: \: \: \: - - - eq.(2) \\ \\ Using \: \: substitution \: \: method \: , \: \\ Putting \: \: \: eq.(1) \: \: in \: \: eq.(2) \\ \\ 3x - 4 \: ( - 2x + 5) = 2 \\ \\ 3x + 8x - 20 = 2 \\ \\ 11x \: - 20 \: \: = \: \: 2 \\ \\ 11x \: \: = \: \: 22 \: \: \\ \\ x \: \: = \: \: \frac{22}{11} \: \: = \: \: 2 \: \: \: - - - eq.(3) \\ \\ Putting \: \: eq.(3) \: \: in \: \: eq.(1) \: \\ \\ We \: get \: \: - \\ \\ y = - 2(2) + 5 = 5 - 4 = 1 \\ \\ \\ Hence \: \\ \\ \: || \: \: x = 2 \: \: || \: \: \: \: and \: \: \: || \: \: y = 1 \: \: || \: \: \: \: \: \: \: \: Ans.$

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Monica [59]

Answer:

The student will have to reimburse 2,991.03 two years later.

Step-by-step explanation:

This is a compound interest problem:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

A is the amount the student will have to reimburse two years later.

P is his loan. so $P = 2,500$

The bank loans this money at a rate of 9 % capitalized monthly. This means that $r = 0.09$ and $n = 12$ , since the money is compounded monthly, this means, 12 times in a year.

He will have to reimburse two years later, so $t = 2$

$A = P(1 + \frac{r}{n})^{nt}$

$A = 2,500(1 + \frac{0.09}{12})^{24}$

$A = 2,991.03$

The student will have to reimburse 2,991.03 two years later.

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3 years ago

Which relationships have the same constant of proportionality between y and x as in the equation y=1/2x Choose 3 answers:

Andrew [12]

Answer:

A and B has the same constant of proportionality

Step-by-step explanation:

$y \propto x$

$y = kx ----1$

Where k is the constant of proportionality

We are supposed to find Which relationships have the same constant of proportionality between y and x as in the equation $y=\frac{1}{2}x$

On comparing with 1

$k = \frac{1}{2}$

A)6y = 3x

$y = \frac{3}{6}x\\y = \frac{1}{2}x$

So, this equation has the same constant of proportionality

B) $(x_1,y_1)=(2,1)\\(x_2,y_2)=(4,2)$

To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, $y - 1=\frac{2-1}{4-2}(x-2)\\y-1=\frac{1}{2}(x-2)\\y-1=\frac{1}{2}x-1\\y=\frac{1}{2}x$

So, this equation has the same constant of proportionality

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To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, $y - 2=\frac{4-2}{2-1}(x-1)\\y - 2=2(x-1)\\y - 2=2x-2\\y=2x$

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To find the equation :

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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So, this equation do not has the same constant of proportionality

Hence A and B has the same constant of proportionality

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3 years ago

Read 2 more answers

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Answer:

Step-by-step explanation:

Easy! You plug in 3 for n! H(3) = 3^3 - 2

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3 years ago

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scZoUnD [109]

Answer:

The percentage of people that scored less than Calvin is 38.21 %

Step-by-step explanation:

In this question, we are concerned with calculating the percentage of exam scores lesser than what Calvin scores.

To calculate this, we first need to calculate the standard score or the z-score of Calvin result.

Mathematically;

z = (x - mean)/SD

from the question, x = 78, mean = 81 and SD = 10

Substituting this, we have

z = (78 -81)/10 = -3/10 = -0.3

So we proceed to calculate the probability.

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We make use of the standard table to get this probability

P(z< - 0.3) = 0.38209

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