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3 years ago

Which equations correctly represent a line that has a slope of -2/3 and passes through the points (–2, 8) and (1, 6)?

Mathematics

2 answers:

OlgaM077 [116]3 years ago

6 0

Answer:

2x + 3y = 20

Step-by-step explanation:

Slope of the line is -2/3 . We can use any of the given points to find the equation of the line. Lets use (1, 6)

The general point-slope form of a line is:

$y-y_{1} =m(x-x_{1} )$

Here m is the slope which is -2/3

x1 and y1 are the coordinates of the point. So x1 = 1 and y1 = 6

Using these values, we get:

$y-6=-\frac{2}{3} (x-1)\\\\ 3(y-6)=-2(x-1)\\\\ 3y-18=-2x+2\\\\ 2x+3y=20$

Nataly_w [17]3 years ago

3 0

Answer:

2x + 3y = 20

Step-by-step explanation:

We are given two points: (–2, 8) and (1, 6) and the slope (m) of the line and we are to find the equation of this line.

We know that the standard equation of a line is:

$y=mx+c$

So we will plug in the given values in the above equation to find the y intercept.

$6=-\frac{2}{3} (1)+c$

$c=\frac{20}{3}$

So the equation of this line will be:

$y=-\frac{2}{3} x+\frac{20}{3}$

2x + 3y = 20

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Answer:

5 * 2 is 10 + 5 and then 15 * 2 + 15 45 * 2 + 45

Step-by-step explanation:

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3 years ago

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Triangle ABC is a right triangle, and angles A and C are equal but not right angles. What is the measure of angle B ?

Dmitry [639]

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Step-by-step explanation:

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3 years ago

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Riverside Elementary School is holding a school-wide election to choose a school color. Five-eighths of the votes were for blue,

Mnenie [13.5K]

Answer:

Step-by-step explanation:

Let the total number of votes to choose a color = x

Number of votes for blue = $\frac{5}{8}\times x$

Remaining votes = x - $\frac{5}{8}\times x$

= $\frac{8x-5x}{8}\times x$

= $\frac{3}{8}\times x$

Votes for green = $\frac{5}{9}\times (\text{Remaining votes})}$

= $\frac{5}{9}\times \frac{3x}{8}$

= $\frac{5}{24}\times x$

Finally remaining votes = $\frac{3x}{8}-\frac{5x}{24}$

= $\frac{9x-5x}{24}$

= $\frac{4x}{24}$

= $\frac{x}{6}$

Since these votes are for red therefore,

$\frac{x}{6}$ = 48

x = 48×6

= 288

a) Votes for blue are $\frac{5x}{8}$

Therefore, exact number for blue votes = $\frac{5\times 288}{8}$

= 5×36

= 180

b). Votes for green = $\frac{5x}{24}$

= $\frac{5\times 288}{24}$

= 60

c). Since 25 students were absent on that day of the vote, number of students at Riverside Elementary School = 288 + 25

= 313

d). Since seven tenths of the votes for blue were made by the girls.

Therefore, number of girls voted for blue = $\frac{7}{10}\times 180$

= 7×18

= 126

Since total votes made = 288

Therefore, half of the votes made = $\frac{288}{2}$

= 144

Now it's clear that number of votes made by girls is less than half of all the votes.

e). 126 girls voted for blue.

5 0

3 years ago

On the dietitians beverage tray are 16 filled six ounce glasses. Four glasses contain prune juice and two glasses contain apple

zubka84 [21]

Answer:

$\frac{5}{8}$

Step-by-step explanation:

Given:

Total number of glasses = 16

Number of glasses containing prune juice = 4

Number of glasses containing apple juice = 2

To find: fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice

Solution:

A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.

Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10

Total number of glasses = 16

So,

Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = $\frac{10}{16}=\frac{5}{8}$

8 0

3 years ago

If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey re

Nikolay [14]

Answer:

The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].

Step-by-step explanation:

The sample drawn is of size, n = 5046.

As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean $\hat p$ and standard deviation $\sqrt{\frac{\hat p (1-\hat p)}{n} }$ .

The mean is: $\hat p=0.31$

The confidence level (CL) = 98%

The confidence interval for single proportion is:

$CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]$

Here $z_{(\alpha /2)}$ = critical value and α = significance level.

Compute the value of α as follows:

$\alpha =1-CL\\=1-0.98\\=0.02$

For α = 0.02 the critical value can be computed from the z table.

Then the value of $z_{(\alpha /2)}$ is ± 2.33.

The 98% confidence interval for population proportion is:

$CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33]$

Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.

7 0

3 years ago