what is the slope of the line that passes through the points (-2,7) and (2,-5)? Write your answer in simplest form.

1. Angle AOF has what measurement according to the protractor? A. 40 B. 140 C. 60 D. 120

fredd [130]

Answer:

140 degrees

Step-by-step explanation:

Just measure from point A to point F giving you 140 degrees.

7 0

3 years ago

Which theorem, term, or corollary is represented by the picture?

Over [174]

The triangle is an Corollary 1 to the isosceles triangle theorem.

Given that,

In the picture we have a triangle,

We have to find which triangle is it.

From the triangle,

The 2 sides are equal and the 2 angles are also equal.

So, The triangle is an Corollary 1 to the isosceles triangle theorem.

According to the isosceles triangle theorem, if two triangle sides are congruent, then the angles across from those sides are likewise congruent.

An isosceles triangle is one with two sides that are the same size and a third side that is a different size.

Therefore, The triangle is an Corollary 1 to the isosceles triangle theorem.

To learn more about triangle visit: brainly.com/question/2773823

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8 0

1 year ago

The table shows a person’s annual salary y (in thousands of dollars) after x years of education beyond high school. What is the

kolezko [41]

Answer:

A. The annual salary of the person after 8 years of education beyond high school will be $76,000.

C. The annual salary of the person after 30 years of education beyond high school will be $208,000.

The given situation does not make sense in real world.

Step-by-step explanation:

We have been given a table of values, which shows a person’s annual salary y (in thousands of dollars) after x years of education beyond high school.

A. First of all we will find the equation of the line form our given values.

We can see that our function is increasing at a constant rate as each next term is 12 more than the last term:

$40-28=12$

$52-40=12$

Let us find the slope of our given line using points (0,28) and (10,88) in slope formula.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where,

$y_2-y_1$ = Change in two y-coordinates.

$x_2-x_1$ = Change in same x-coordinates of two y-coordinates.

Upon substituting coordinates of our given points in slope formula we will get,

$\text{Slope}=\frac{88-28}{10-0}$

$\text{Slope}=\frac{60}{10}$

$\text{Slope}=6$

Since we know that slope-intercept form of an equation is: $y=mx+b$ , where,

m = Slope of the line,

b = y-intercept or initial value.

We can see from our table that at x equals zero, y equals 28, so our y-intercept will be 28.

Upon substituting m=6 and b=28 in slope-intercept form of equation we will get,

$y=6x+28$

Therefore, the equation $y=6x+28$ represents the annual salary in thousands of dollars after x years of education beyond high school.

To find the salary of a person after 8 years of education beyond high school, let us substitute x=8 in our equation.

$y=6*8+28$

$y=48+28$

$y=76$

As the equation gives annual salary of a person in thousand dollars, therefore, the annual salary of the person after 8 years of education beyond high school will be $76,000.

C. To find the salary of a person with 30 years of education, we will substitute x=30 in our equation.

$y=6*30+28$

$y=180+28$

$y=208$

Therefore, the annual salary of the person after 30 years of education beyond high school will be $208,000.

Since a person does not study 30 years beyond high school, therefore, this situation does not make sense in real word.

3 0

3 years ago

Sara has 20 sweets.

nalin [4]

Answer:

The probability that the two sweet will not be same type is $\frac{111}{190}$

Step-by-step explanation:

P(two sweets not same) = 1 - P( two sweets will be same)

There are 3 possible outcomes where two sweets will be same.

1. it can be two liquor-ice, 2. it can be 2 mint and 3. it can be two humbug

P(two liquor-ice) $=\frac{12}{20} \times\frac{11}{19}= \frac{33}{95}$

P(two mint) $=\frac{5}{20} \times \frac{4}{19} =\frac{1}{19}$

P(tow humbug) $=\frac{3}{20} \times\frac{2}{19} =\frac{3}{190}$

Now we have:

P(two sweets not same) = 1 - P( two sweets will be same)

$=1- \left(\frac{33}{95}+ \frac{1}{19}+ \frac{3}{190} \right)$

$1-\frac{79}{190}$

$=\frac{111}{190}$

Therefore, the probability that the two sweet will not be same type is $\frac{111}{190}$

3 0

3 years ago

The sum of three consecutive integers is 177. What are the integers

Lady bird [3.3K]

Answer:

57, 59, 61

Step-by-step explanation:

5 0

3 years ago