Mathematics College

Identify one example of each angle pair in the diagram to the right.

Answers

Answer 1

Alternate exterior angles are ∠9 and (∠1 + ∠2)

Consecutive interior angles are ∠7 and ∠4

Consecutive exterior angles are ∠9 and ∠∠3

Vertical angles are ∠2 and ∠5

Linear pairs are ∠7 and ∠8

We have,

Alternate exterior angles: Pairs of angles on opposite sides of a transversal line, formed by two parallel lines, and located outside the intersected lines.

Consecutive interior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located between the intersected lines.

Consecutive exterior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located outside the intersected lines.

Vertical angles: Pairs of non-adjacent angles formed by the intersection of two lines, sharing the same vertex and having equal measures.

Linear pair: A pair of adjacent angles formed by the intersection of two lines, sharing a common side, and whose measures add up to 180 degrees.

So,

Alternate exterior angles

= ∠9 and (∠1 + ∠2)

Consecutive interior angles

= ∠7 and ∠4

Consecutive exterior angles

= ∠9 and ∠∠3

Vertical angles

= ∠2 and ∠5

Linear pair

= ∠7 and ∠∠8

Thus,

Alternate exterior angles are ∠9 and (∠1 + ∠2)

Consecutive interior angles are ∠7 and ∠4

Consecutive exterior angles are ∠9 and ∠∠3

Vertical angles are ∠2 and ∠5

Linear pairs are ∠7 and ∠8

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Related Questions

a x = ±5
b. x = ±5i
C. x = ±3√√5
d. x = ±3√3
e. x = ±3i√√3
f. x= ±3i√√5

1. x^2+45=0
2. x^2=-25
3. x^2-25=0
4. x^2-45=0
5. x^2=27
6. x^2+27=0

Match the items

Answers

Answer:

1f, 2b, 3a, 4c, 5d, 6e

see image

Step-by-step explanation:

Solve the equations by getting x all by itself on one side. Then, square root to get rid of the exponent.

Any problem where you square root a negative will give you an i in the answer. This is because sqrt(-1) is i. Because i^2 = -1

Also, when you are simplifying square roots for your final answer, look for a perfect square number inside of the radical. Like Sqrt45 can be broken down to

Sqrt9•sqrt5

And because 9 is a perfect square, sqrt9 simplifies to just 3. See image.

1. F (-45 = -9 * 5)
2. B
3. A
4. C
5. D
6. E

Whenever you take the square root of a negative number, we create a complex number i

Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8

Answers

Using the elimination method, the value of x in the system of equations is calculated as: 8.

How to Solve a System of Equations by Elimination?

To solve a system of equations given using the elimination method, do the following:

Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:

4x - 10y = 2 --> eqn. 1

-15x + 10y = -90 --> eqn. 2

Add

-11x = -88

Divide both sides by -11

x = 8

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A cylindrical container has a radius of 17 inches and a height of 63 inches, how many gallons will it hold?

Answers

Answer:

=57198.98

Step-by-step explanation:

Volume of Cylinder = pi x radius^2 x height

= pi x 17^2 x 63

=57198.9774439

=57198.98

t
Use the table to the right, which shows the age distribution of those who earned less than
minimum wage in a recent year. If a worker is randomly selected from those surveyed, what
y is the probability that the person is younger than 65?
na
Ci
20
ar
The probability that the person is younger than 65 is
(Type a decimal rounded to three decimal places as needed.)
CID
Age
16-19
20-24
25-34
35-44
45-54
55-64
65 and older
Working Below Minimum
Wage (thousands)
350
412
318
200
107
51
49

Answers

The probability that a person chosen at random is younger than 65 is 0.967.

What is the probability?

Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.

The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)

(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)

1438 / 1487 = 0.967

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Translate this phrase into an algebraic expression.
64 decreased by twice Matt's savings
Use the variable m to represent Matt's savings.
10

Answers

64 decrease by twice the number then the algebraic expression be

64 - 2m.

What is algebraic expression?

The algebraic expression exists acquired by a finite number of the fundamental functions of algebra upon characters expressing numbers. Algebraic expressions contain at least one variable and at least one operation (addition, subtraction, multiplication, division).

From the given information, we get

Let, Matt's savings be denoted by the variable m.

Twice the number be 2m.

64 decrease by twice the digit then the algebraic expression be 64-2w.

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Maths-4
What is the smallest number that is divisible by each of the numbers given below
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
5040
3780
1260
2520
None of the above

Answers

Answer:

5040 is the right answer

Step-by-step explanation:

5040/1=5040

5040/2=2520

5040/3=1680

5040/4=1260

5040/5=1008

5040/6=840

5040/7=720

5040/8=630

5040/9=560

5040/10=504

Factor:
y(a−b)-(a−b)

Answers

Answer: [tex](a-b)(y-1)[/tex]

Step-by-step explanation:

Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].

Which of the following similarity statements about the triangles in the figure is true?

Right triangle P Q R has angle Q marked as a right angle. A segment is drawn from point Q to side P R. The point where the segment intersects side PR is point S. Angle P S Q is marked as a right angle.

A. Triangle P Q R is similar to triangle P S Q, which is similar to triangle Q S R.
B. Triangle R Q P is similar to triangle S Q P, which is similar to triangle R S Q.
C. Triangle Q R P is similar to triangle Q S P, which is similar to triangle Q S R.
D. Triangle P R Q is similar to triangle Q P S, which is similar to triangle R Q S.

Answers

Answer:

Answer B is correct

If (one month) I make a total of 10 hours of calls at Standard hours , how much more or less will I pay for basic contact than for premium

Answers

The amount of money that you would pay less for basic contact is $15 while the amount you will pay more for premium =$465.

Calculation of the call rate per hour

From the given table in the diagram, the cost of calls made for 10 hours at Standard time=

$6 × 10 = $60

The amount of calls done for basic contact is 3 hours per month for $15 . Total cost per month = 3×15= $45

The amount of calls done for premium contact is 15 hours per month for $35 . Total cost per month = 15× 35=$525

Ordinarily, you per $60 for standard call hours. This means that,

$60 - 45 = $15 less for basic contact and

$525 - $60 = $465 more for premium.

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A brave knight traveled on his horse from one kingdom to another in 2 days. The first day he rode at a speed of 10 mph, and the

Answers

It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let us assume that he travelled at 20 mph on the second day. If he traveled exactly the same amount of time each day and went 300 miles, find how many hours it took the knight to travel from one kingdom to another.

Let t represent the time in hours travelled each day.

Total distance travelled in day one = 10t

Total distance travelled in day one = 20t

Hence:

10t + 20t = 300

t = 10 hours

Total time = 10 + 10 = 20 hours

It would take the brave night 20 hours on his horse from one kingdom to another in 2 days.

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Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)

Answers

The rule that describes the transformation is (x, y) - (-y, -x).

What is transformation?Transformation is the process of using rules to transform some graphics into something else.When a shape is either reflected, rotated, or translated, the coordinates of the vertices that make up the shape change.The four different forms of transformations—Translation, Reflection, Rotation, and Enlargement—are depicted in the following illustrations.The underlying coordinate system remains fixed while an object transformation modifies the coordinates of each point on the object in accordance with some rule. • A coordinate transformation expresses each point of the object in the new coordinate system by defining it in terms of the old one.

The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.

The rule that describes the transformation is (x, y) - (-y, -x).

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what is the slope of a line that is parallel to the line whose equation is y=4/5x-3

Answers

Answer: 4/5

Step-by-step explanation: For a line to be parallel to another line there must be two conditions true.

Condition 1: Both lines must have the same slope (i.e the same x in the form y = mx + b)

Condition 2: Both lines must have different y-intercepts (i.e different b in the form y = mx + b)

Thus, if you are looking for the slope of the line parallel to y = 4/5x - 3, we can look at condition 1, and see that the slope should also be 4/5 for the other line.

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. (-3, 1)

Answers

The information given illustrates that the graph of the function decreasing.

How to illustrate the information?

We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.

Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.

So according to the given graph on the interval (-3, 1) the graph is decreasing.

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Mariana and her best friend are attending a concert in a large auditorium. They just climbed up 125 steps. The number of steps they climbed can be represented by

zero
positive
negative

Answers

The number of steps they climbed can be represented by positive

How to represent the number of steps?

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

Answers

Answer:

Median is 83

Range: 61

Step-by-step explanation:

The median is the number in the middle. The range is the max. number subtracted from the min number.

HELP ASAP

Question
Garret studies number of hours sleep per night among students who have a grade point average of 3.0–4.0 versus students who have a grade point average of 2.0–3.0.

His theory is that students who get more sleep will have a higher grade point average than students who get less sleep because they are more rested and, therefore, better able to concentrate.

In his samples, the mean number of hours of sleep students with a grade point average of 3.0–4.0 received each night was 6.8. The mean number of hours of sleep students with a grade point average of 2.0–3.0 received each night was 6.4.

Assuming there are no outliers or skew, do the results support Garret's theory?

Select from the drop-down menus to correctly complete the statements.

Since the samples were large and randomly chosen, we can use the samples to understand the populations.

Because the sample mean for students with a grade point average of 3.0–4.0 is
Choose...
a. less than
b. about the same
c.greater than
the sample mean for students with a grade point average of 2.0–3.0, the results
Choose...
a. tend to
b. do not tend to

Answers

The sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0, the results tend to

How to interpret Garret studies?

From the question, we have the following highlights

The sample size is large enoughThe sample is at randomStudents who have a grade point average of 3.0 - 4.0 sleep for an average of 6.8 hoursStudents who have a grade point average of 2.0–3.0 sleep for an average of 6.4 hoursThere are no outliers

From the above highlights, the sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0

This is because 6.8 is greater than 6.4

This means that Garret's theory about the hours of sleep is correct

Answers

Based on the given horizontal and vertical sides of a rectangle and its perimeter, the value of x in the expression is 6

Perimeter of rectangle

Perimeter of rectangle = 2(length + width)

Perimeter of the rectangle = 34 ft

Length of the rectangle = 3(x - 2) ft

= 3x - 6

Width of the rectangle = 4x - 7 + (-2x)

= 4x - 7 - 2x

= 2x - 7

Perimeter of rectangle = 2(length + width)

34 = 2{(3x - 6) + (2x - 7)}

34 = 2(3x - 6 + 2x - 7)

34 = 2(5x - 13)

34 = 10x - 26

34 + 26 = 10x

60 = 10x

x = 60/10

x = 6

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Please help to solve these 3 questions

Answers

Based on the number of goals scored in the football matches, the mode is 4 goals. The median is 3 goals and the mean goals scored is 2.6 goals.

What are the statistics from the football matches?

The mode is the number of goals that was scored in the most matches. This number is 4 goals as this was scored in 6 matches.

To find the median, order the numbers:

0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6

The median is:

= (3 + 3) / 2

= 3

The mean is:

= (0 + 0 + 0 + 0 + 1 + 1 + 2 +2 +2 + 3 + 3 + 3 + 4 + 4+ 4 + 4 +4 + 4 + 5 + 6) / 20

= 2.6 goals

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Evaluate 4s^2 for s = 1/4. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.

Answers

Answer:

1/4

Step-by-step explanation:

Given [tex]\displaystyle{s=\dfrac{1}{4}}[/tex] and we have to evaluate [tex]\displaystyle{4s^2}[/tex]. We can do by substituting the given value s = 1/4 in 4s² term:

[tex]\displaystyle{4\cdot \left(\dfrac{1}{4}\right)^2}\\\\\displaystyle{4\cdot \dfrac{1}{16}}\\\\\displaystyle{\dfrac{1}{4}}[/tex]

Therefore the value is 1/4

POINTS, AND BRAINLIEST

Answers

The identification of parts A,B andC is illustrated below with their various reasons given.

What is an equilateral triangle?

An equilateral triangle is the triangle that has all its sides equal in length and each angle is made up of angle 60°.

Part A = The similar triangle are RGE and PBE

Part B = The triangles selected are similar because it was formed by an interception of the parallel lines of the rectangle GCPR.

Part C= All the sides of the equilateral triangle are the same therefore the distance from B to E and from P to E is the same with BP which is 225ft.

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1) Can we predict the calories in a fast-food product if we know the amount of protein in that
product? Several fast-food products were examined and the number of calories and amount of
protein (in grams) were recorded. In the sample, the smallest and largest amounts of protein
were 4 grams and 22 grams, respectively. Analyzing the data resulted in the following
information:
Correlation of Protein and Calories = r = -0.87
The regression equation is Calories=302.5 -0.51 (Protein)
Interpret the correlation coefficient. There is a:
O strong negative linear relationship between protein amount and calories.
O weak negative linear relationship between protein amount and calories.
O strong positive linear relationship between protein amount and calories.
O weak positive linear relationship between protein amount and calories.

Answers

The correct option regarding the correlation coefficient is given as follows:

strong negative linear relationship between protein amount and calories.

What is a correlation coefficient?

It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

In this problem, the coefficient is of -0.87, which is a negative value with absolute value greater than 0.6, hence the relationship is strong is the correct option is given as follows:

strong negative linear relationship between protein amount and calories.

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A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r* ) is 2.75%. The average inflation premium is 2.05%, and the maturity risk premium is estimated to be 0.1 3 (t 2 1)%, where t 5 number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds

Answers

Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%

How is the default risk premium found?

The default risk premium can be found as:

=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium

Solving gives:

= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)

= 0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)

= 1.2%

The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.

This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.

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Evaulate u^2-4u+2 when u=-2

Answers

You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.

find a whole number between 3.75 and the square root of 36

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt{36}=6[/tex]

A whole number between 3.75 and 6 is 5.

could also be 4. 4 is between 3.75 and srt of 36

Can u guys please give me the correct answer

Answers

Answer:

Step-by-step explanation:

angle on a straight line is 180

angle of 1 = 180 -110

=70

25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure

Answers

based on the number of mice that took part in the experiment, the total number of mice that had at least one effect is 20 mice.

how many mice had a health effect?

15 mice had at least 1 tumor while 4 mice had both a tumor and respiratory failure.

the number of mice with just a tumor is:

= 15 - 4

= 11 mice

the number of mice with respiratory failure alone is:

= 9 - 4

= 5 mice

the mice that had at least one symptom is:

= 11 + 5 + 4 mice with both

= 20 mice

question is:

what are the number of mice with at least one effect?

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Would this expression:
[tex](x^{2} -16)^{2}[/tex]

be classified as a difference of squares? Or a perfect square trinomial?

Why?

Answers

The given expression is a perfect square trinomial.

How to classify the given expression?

Here we have the expression:

[tex](x^2 - 16)^2[/tex]

Notice that we can rewrite it as:

[tex](x^2 - 4^2)^2[/tex]

Then we can see that inside the parenthesis we have a difference of squares, but it is squared, so if we define:

[tex]x^2 = a\\4^2 = b[/tex]

We will have:

[tex](a - b)^2 = a^2 + -2ab + b^2 = (x^2)^2 - 2*(4^2)*(x^2) + (4^2)^2[/tex]

Which is in fact, a perfect square trinomial.

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What number represents the smallest value? .3 or .33

Answers

Answer:

Step-by-step explanation:

.33 is .03 greater than .3

The number which represents the smallest value between 0.3 and 0.33 is the number 0.3.

Given are two decimal numbers.

0.3 and 0.33

It is required to find the number which is the smallest between these two.

The number 0.3 can be written as 0.30.

And the other number is 0.33.

In order to find the smallest number, check the digits from left to right.

The first digit after the decimal point of both numbers is 3.

The second digit after the decimal point is 0 for 0.30 and 3 for 0.33.

Here 0 is smaller than 3.

So, 0.30 is smaller than 0.33.

Hence, the smallest value is 0.3.

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slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.

Answers

The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

How to find sides of a right triangle?

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15 = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36 = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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Given the following values, evaluate the logarithmic function. log2≈0.301, log3≈0.447, log4≈0.602, log5≈0.699, 2log(2/square root of 5)

Answers

The expression of the given logarithmic function 2log(2/√5) is; D: -0.097

How to solve Logarithmic Functions?

From logarithmic Identities, we know that;

log (x/y) = log x - log y

log (x * y) = log x + log y

Thus;

2log(2/√5) = 2[log 2 - log √5)

Now, log √5 can also be expressed as;

log √5 = ¹/₂log 5

Thus;

2log(2/√5) = 2[log 2 - ¹/₂log 5]

⇒ 2 log 2 - log 5

We are given the values;

log2≈0.301, log3≈0.447, log4≈0.602, log5≈0.699

Thus;

2log(2/√5) = 2 log 2 - log 5 = 2(0.301) - 0.699

⇒ -0.097

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