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3 years ago

A- 10 b- 70 c- 110 d- 170

Mathematics

1 answer:

mylen [45]3 years ago

3 0

Step-by-step explanation:

step 1. 2x + 50 and 7x are vertical angles

step 2. vertical angles are equal

step 3. 2x + 50 = 7x

step 4. 5x = 50, x= 10

step 5. <AEB = 2x + 50 = 2(10) + 50 = 70.

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What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y

Gekata [30.6K]

Answer:

$y=\displaystyle-\frac{4}{3}x+22$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept
Parallel lines always have the same slope (m)

Determine the slope (m):

$y=\displaystyle-\frac{4}{3}x -1$

The slope of the given line is $\displaystyle-\frac{4}{3}$ , since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be $\displaystyle-\frac{4}{3}$ . Plug this into y=mx+b:

$y=\displaystyle-\frac{4}{3}x+b$

Determine the y-intercept (b):

$y=\displaystyle-\frac{4}{3}x+b$

To find the y-intercept, plug in the given point (6,14) and solve for b:

$14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22$

Therefore, the y-intercept of the line is 22. Plug this back into $y=\displaystyle-\frac{4}{3}x+b$ :

$y=\displaystyle-\frac{4}{3}x+22$

I hope this helps!

5 0

3 years ago

9. Stephanie swam 5/8 of a lap in the morning and

sweet-ann [11.9K]

Answer:

7/24

Step-by-step explanation:

5/8 is equal to 15/24

1/3 is equal to 8/24

15/24 minus 8/24 equals 7/24

4 0

4 years ago

Calculate the variance and the standard deviation of the data below 23. 19, 22, 30, 28

Alina [70]

To get the variance, start with finding the mean of your data points:

(23 + 19 + 22 + 30 + 28) / 5 = 24.4

Now take each data point and subtract the mean from it, then square that value:

23 - 24.4 = -1.4 * -1.4 = 1.96

19 - 24.4 = -5.4 * -5.4 = 29.16

22 - 24.4 = -2.4 * -2.4 = 5.76

30 - 24.4 = 5.6 * 5.6 = 31.36

28 - 24.4 = 3.6 * 3.6 = 12.96

Now get the average of those new numbers. That is your variance:

(1.96 + 29.16 + 5.76 + 31.36 + 12.96) / 5 = 16.24

The standard deviation will be the square root of the variance:

√(16.24) = 4.0299 (rounded to 4DP)

7 0

3 years ago

12-2(7x-3)=3(1-2x)-5x

vfiekz [6]

12 - 2(7x - 3) = 3(1-2x) - 5x
12 - 14x + 6 = 3 - 6x - 5x
-14x + 6x + 5x = 3 - 12 - 6
-3x = -15
x = -15/-3
x = 5

6 0

3 years ago

Use the following information to answer the question. Bellei Extravecchio Balsamico Tradizionale is a very expensive brand of ba

DaniilM [7]

Answer:

The observed value of the chi-square statistic is 34.71

Step-by-step explanation:

Given the data in the question';

Calculate the observed value of the chi-square statistic

The chi-square statistic will be;

∑ $_{i}$ [ ( O $_{i}$ - E $_{i}$ )² / E $_{i}$ ]

here O $_{i}$ is observed frequency of $_{i}$ th class

E $_{i}$ is expected frequency of $_{i}$ th class

$_{i}$ = 1, 2 which denote the class of food experts who guess correctly and who didn't guess correctly

∈ $_{i}$ = n × probability of not guessing correctly = 168 × 2/3 = 112

∈1 = n × probability of guessing correctly 168 × 1/3 = 56

∑ $_{i}$ [ ( O $_{i}$ - E $_{i}$ )² / E $_{i}$ ] = [ ( 92 - 56)² / 56 ] + [ ( 76 - 112)² / 112 ]

= 1296/56 + 1296/112

= 23.14 + 11.57

= 34.71

Therefore, the observed value of the chi-square statistic is 34.71

4 0

3 years ago