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2 years ago

Solve this system of equations by using the substitution method. y=2x-5 6x+7=y

Mathematics

2 answers:

gogolik [260]2 years ago

7 0

Answer:

$x = - 3 \: and \: y = - 11$

Step-by-step explanation:

$since \: y = 2x - 5(equation \: 1) \: \\$

$substitute \: for \: y \: in \: equation \: 2 \: (6x + 7 = y)$

$6x + 7 = y \\ 6x + 7 = 2x - 5 \\ collect \: like \: terms \\ 6x - 2x = - 5 - 7 \\ 4x = - 12 \\ x = \frac{ - 12}{4} \\ x = - 3$

$substitute \: for \: x in \: equation \: 1$

$y = 2x - 5 \\ y = 2( - 3) - 5 \\ y = - 6 - 5 \\ y = - 11$

Ludmilka [50]2 years ago

4 0

Answer:

$y = 2.x = \frac{1}{11}$

<h3>Step-by-step explanation:</h3>

$\binom{x - 56x + 7 = y}{y = 2}$

_______________________

1. Substitute y = 2 :

$(x - 56x + 7 = 2)$

<h3 />

2. Simplify :

$( - 55x + 7 = 2)$

3. Isolate x for $( - 55x + 7 = 2) : x = \frac{1}{11}$

<h3 />

4. The solution of the system of equations are :

$y = 2.x = \frac{1}{11}$

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An art history professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below

madam [21]

Answer:

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.

This means that $\mu = 79.7, \sigma = 8.4$

B: Scores below the top 13% and above the bottom 56%

So between the 56th percentile and the 100 - 13 = 87th percentile.

56th percentile:

X when Z has a p-value of 0.56, so X when Z = 0.15. Then

$Z = \frac{X - \mu}{\sigma}$

$0.15 = \frac{X - 79.7}{8.4}$

$X - 79.7 = 0.15*8.4$

$X = 81$

87th percentile:

X when Z has a p-value of 0.87, so X when Z = 1.13.

$Z = \frac{X - \mu}{\sigma}$

$1.13 = \frac{X - 79.7}{8.4}$

$X - 79.7 = 1.13*8.4$

$X = 89$

The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.

4 0

3 years ago

A single story house is to be built on a rectangular lot 70 feet wide by 100 feet deep. The shorter side of the lot is along the

dedylja [7]

Answer:

250 sq ft

Step-by-step explanation:

Since the shorter side is along the street and the setback is 10ft from each side, the house is 50 ft wide

and 100 -20 -30 = 50 ft long

50 x 50 = 250 sq ft

3 0

3 years ago

Solve each prportion. (2/y-4)=(y+3/4)

vampirchik [111]

Answer:

y = 5, -4

Step-by-step explanation:

To solve proportions you cross-multiply.

$\frac{2}{y-4} =\frac{y+3}{4} \rightarrow 2\times4 = (y-4)\times(y+3) \rightarrow 8=y^2-y-12$

Now that we have 8 = y^2 - y - 12, we must make the entire trinomial equal to 0 by subtracting 8 from both sides.

y^2 - y - 20 = 0

Factor the trinomial.

(y - 5)(y + 4) = 0

Make both factors equal to 0 to solve for both values of y.

y - 5 = 0 --> y = 5
y + 4 = 0 --> y = -4

y = 5, -4

4 0

3 years ago

A system of equations is given below:

My name is Ann [436]

Solving by substitution:

y = 4x - 3

2x + 7y = 41

Let us substitute the first equation y = 4x - 3 into the second.

2x + 7y = 41

2x + 7(y = 4x -3) = 41

2x + 7(4x -3) = 41

So that's the third option.

I hope this helps.

4 0

3 years ago

Read 2 more answers

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and

Luda [366]

Answer:

C. 45 and 141 seconds

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 93 seconds

Standard deviation = 16 seconds

99.7% of running times are approximately between:

By the Empirical rule, within 3 standard deviations of the mean, so between 3 standard deviations below the mean and 3 standard deviations above the mean

3 stnadard deviations below the mean

93 - 3*16 = 45 seconds

3 standard deviations above the mean

93 + 3*16 = 141 seconds

The correct answer is:

C. 45 and 141 seconds

3 0

3 years ago