100 POINTS!!!!! PLEASE HELP!

100 POINTS!!!!! PLEASE HELP!

Answers

Answer 1

Answer:

[tex]a^{12} b^{4}[/tex]

Step-by-step explanation:

To simplify we will have to use the negative exponent rule and the power rule along with some algebra.

Negative Exponent Rule

[tex]a^{-b} =\frac{1}{a^b}[/tex]

Power Rule

[tex](a^b)^{c} =a^{bc}[/tex]

Given

[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]a^{-4}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]

Rewrite [tex]b^{-1}[/tex] using negative exponent rule.

[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]

Simplify

[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]

Rewrite the base as its reciprocal.

[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]

Apply the power rule.

[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]

Cancel the common factor of [tex]c^2[/tex].

[tex]a^8b^2 a^4b^2[/tex]

Apply the power rule.

[tex]a^{12} b^{4}[/tex]

Answer 2

Answer:

[tex]a^{12}\:b^{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]

Simplify:

[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]

Collect like terms:

[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]

Simplify:

[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies a^{12}\:b^{4}(1)[/tex]

[tex]\implies a^{12}\:b^{4}[/tex]


Related Questions

The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.

During the first 24 hours, at what times does the water depth reach a maximum?

Answers

Answer:

Below

Step-by-step explanation:

f(t) = 4.1 (sin pi/6 t  - pi/3) + 19.7    <===will be a maximum when the sin portion is equal to 1

   so    sin ( pi/6 t - pi/3) = 1     given that sin is equal to one   at 0 and pi and 2 pi  and 3 pi    and 4 pi   etc

              pi/6 t - pi/3 =  0  or pi , 2 pi, 3 pi  , 4 pi

                  then t = 2 and 8 and 14   and 20 hrs  ( every 6 hrs starting with t = 2)

Question 5(Multiple Choice Worth 2 points)
(Sample Spaces LC)

A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.

A s= (1, 2, 3, 4, 5, 6

B s=(purple, pink, red, blue, green, orange, yellow}

C s=(g. r, b. y. o, p)

D s= (green, blue, yellow, orange, purple, red)

Answers

The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}

What is sample space?

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.

A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.

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Math- algebra 1 - please help

Answers

For both pizzas A and B to cost the same, there must be 5 toppings. Equations can be categorized as identities or conditional equations.

what is equation ?

The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two equilateral triangles and an equivalent sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear model is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables.

given

number of toppings be x

number of toppings for pizza A = $10 + x*$1.5

number of toppings for pizza B = $12.5 + x*$1

10 +1.5x = 12.5 + x

10 -12.5 = x- 1.5x

-2.5 = - 0.5x

x = 5

For both pizzas A and B to cost the same, there must be 5 toppings.

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Find the value of x.
30°
105°
xo

Answers

Exterior angle of triangle x has a value of 135 in this sentence.

What is the simplest technique to measure angles?

A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.

What exactly is the triangle rule?

According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.

By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.

Practice. Triangle Angle Measurement

via the triangle's external angle characteristic, x = 105 + 30 = 135.

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Determine which two numbers come next in the sequence 5,5,10,15,25, __, __

Answers

The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.

How can the  two numbers that come next in the sequence be calculated?

To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.

5 + 5 = 10

(5 + 10) = 15

(10 + 15) = 25

(15 + 25) = 40

(25 + 40) = 65

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Combine the like terms to create an equivalent expression.

4r + 14 - r - 6 =​

Answers

[tex]4r + 14 - r - 6[/tex]

Combine Like Terms:

[tex](4r-r)+(14-6)[/tex]

[tex]=\fbox{3r + 8}[/tex]

Barrett is comparing the membership fees for two museums. The art museum charges a one-time fee of $8.25 plus $2.25 per month. The science museum charges a one-time fee of $10.75 plus $3.50 per month. How much does Barrett save by joining the art museum instead of the science museum? Enter your answers in the boxes.

(blank) $ + (blank) $ m put answers in blanks

Answers

Barrett saves by joining the art museum instead of science museum is $2.50 plus $1.25 per month.

What is concept of savings?

Saving money is one of the essential aspects of building wealth and having a secure financial future. Saving money gives you a way out of the uncertainties of life and provides you with an opportunity to enjoy a quality life.Savings represents an individual's unspent earnings. It is the amount that remains after meeting the household expenses.

What are benefits of membership?

Member benefits are the perks, services, and access that members receive as part of their membership. In other words they are what members get in exchange for joining the organization and if applicable, paying member dues.

Now we have

Fee charged by science museum= $10.75

Fee charged by art  museum         =$8.25

Now by subtracting he saves       =$2.50

Again

he saves =amount charged by science - amount charged by arts

              = $3.50 -$2.25

              = $1.25

In the results he saves $2.50 +$1.25 per month.

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What are the domain and range of f(x) = x - 3| +6?
O Domain: {x|x is all real numbers}
Range: {yly ≥ 6}
O Domain: {x|x≥ 3}
Range: {y ly ≥ 6}
O Domain: {x|x is all real numbers}
Range: {yly 2-6}
O Domain: {x|x≥ 3}
Range: {yly 2-6}

Answers

The domain and range of the absolute value function are the ones in the first option.

Domain: {x|x is all real numbers}Range: {yly ≥ 6}

What are the domain an range of the absolute value function?

Here we have the absolute value function:

f(x) = |x - 3| + 6

The domain for all absolute value functions is the set of all real numbers, as there are no input that generates a problem with the function.

And the range, the set of the inputs, has a minimum at the vertex.

Remember that if the vertex is (h, k), then we can write the function as:

f(x) = |x - h| + k

Then in this case:

f(x) = |x - 3| + 6

The vertex is at (3, 6)

Then the range is the set of all real values equal to or larger than 6, or:

y ≥ 6

Then the correct option is the first one:

Domain: {x|x is all real numbers}

Range: {yly ≥ 6}

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A traffic radar records the speed of cars driving through an intersection. It records these statistics:

Mean=36.2 mph
Median=28.5 mph
Mode=30.0 mph

What is the most common speed of a car driving through the intersection?
a. 31.6
b. 36.2
c. 30.0
d. 28.5

Answers

The most common speed of a car driving through the intersection is 30.0 mph which is indicated by the Mode.

What is the mode of data?

A mode of data is defined as an observation with the highest frequency among the values that appear most frequently in the given data.

In the case of ungrouped data, all that is required is to find the observation that happens most frequently.

A traffic radar records the speed of cars driving through an intersection. It records these statistics:

Mean = 36.2 mph

Median = 28.5 mph

Mode = 30.0 mph

As per the question, a car driving through the intersection at 30.0 mph is the most common speed.

This is indicated by the Mode which is the value that appears most frequently in a data set.

Hence, the correct answer would be an option (C).

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What does (AM) represent to segment [BC]? Justify. ​

Answers

AM is a perpendicular bisector of BC.

What is a bisector example?

A ray that divides an angle into two equal parts is known as an angle bisector or the bisector of an angle. For instance, each measurement will be equal to 30 degrees if ray AX divides an angle of 60 degrees into two equal parts. There is an angle bisector for each angle.

A line's bisector is defined.

To divide a segment or an angle into two congruent parts is to bisect it. The midpoint of a line segment will be traversed by its bisector. A line segment's perpendicular bisector is parallel to the line segment and passes through its midpoint.

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The volume of
a refrigerator, in cubic centimeters, is given
by the function V(x) = (x)(x + 1)(x – 2). Write a
new function for the volume of the refrigerator
in cubic millimeters if x is in centimeters.

Answers

The newly rewritten function expression of V(x) is V(x) = (x)(x + 1)(x – 2)/1000

How to rewrite the function expression?

From the question, we have the following parameters that can be used in our computation:

A function expression

The function expression is given as

V(x) = (x)(x + 1)(x – 2)

Where if x is in centimeters and V(x) is in cubic centimeters

The new function for the volume of the refrigerator is stated to be in cubic millimeters

Using the above as a guide, we have the following:

1 cubic centimeters = 1000 cubic millimeters

So, we have

V(x) = (x)(x + 1)(x – 2)

1 cubic centimeters = 1000 cubic millimeters

Cross multiply

V(x) * 1000 = 1* (x)(x + 1)(x – 2)

Divide both sides by 1000

V(x) = (x)(x + 1)(x – 2)/1000

Hence, the function is V(x) = (x)(x + 1)(x – 2)/1000

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Ashanti cashed her paycheck at Cash-n-Go. The fee at Cash-n-Go is 7.5% of the amount of the check. Her paycheck was $670. How much was the fee for Ashanti to cash her paycheck?​

Answers

Answer:

$50.25

Step-by-step explanation:

7.5% as a decimal is 0.075.

So, the fee is [tex](0.075)(670)=\$50.25[/tex].

Find the 8th term of the geometric sequence whose common ratio is 3/2 and whose first term is 6.

Answers

Answer:

A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is always the same. This ratio is called the common ratio of the sequence.

In this case, the common ratio is 3/2 and the first term is 6. The nth term of a geometric sequence can be found using the formula:

a_n = a_1 * r^(n-1)

where a_n is the nth term, a_1 is the first term, and r is the common ratio.

Substituting the given values, we have:

a_8 = 6 * (3/2)^(8-1) = 6 * (3/2)^7

Calculating, we find that the 8th term is:

a_8 = 6 * (3/2)^7 = 6 * (9/2) = 27

Therefore, the 8th term is 27.

Step-by-step explanation:

Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?​

Answers

To determine how much it will cost Aftab to buy enough concrete slabs to make the patio, you will need to know the size of the patio and how many slabs are needed to cover it. Once you have this information, you can multiply the number of slabs by the cost per slab to find the total cost. For example, if the patio is 10 square meters and requires 20 concrete slabs to cover it, the total cost would be 3.10 * 20 = £62.

If g(x) = x³ - 2x, find the value of g(2+h)-g(2)dividebyh answer is h square plus six h plus ten

Answers

Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.

The difference quotient is defined as:

[g(2+h) - g(2)] / h

So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:

lim h→0 [g(2+h) - g(2)] / h

Substituting the value of x in the function g(x), we get:

lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h

This simplifies to:

lim h→0 [8+6h+h²-2h - 4] / h

Which simplifies to:

lim h→0 [h²+6h+4] / h

And, finally:

lim h→0 [h(h+6)] / h

The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:

h+6

So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.

Therefore, the value of g(2+h)-g(2) divided by h is:

(h+6) - 6 / h

Which simplifies to:

h / h

Which is equal to:

1

So, the final answer is 1.

Step-by-step explanation:

Help me I'm stuck with this one, HELP!!!!!

Answers

Answer:

b= 106 or b= -58

Step-by-step explanation:

word sentence

82= b-24

solution b equals 106

or

word sentence 82= 24-b

solution b equals -58

Which of the following best describes X on the scatter plot below?

Answers

The option that best describes X on the scatterplot is;

C: Outlier

How to Interpret a scatterplot?

Let us first define the terms in the given options before we analyze the scatterplot.

1) Negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.

2) A nonlinear relationship is also referred to as nonlinear association, and it exists when a constant change in the independent variable does not result in a constant change in the dependent variable.

3) An outlier is defined as a data point that differs significantly from other observations.

4) Clusters are small populations that a wider population is divided into.

Now, from the scatter plot, we see that X is isolated from the plotted points which tells us that it differs greatly from the other points and as such it fits the definition of an outlier.

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The missing options are;

A. negative correlation

B. nonlinear association

C. outlier

D. cluster

Compare.
2.2O 14/4
A. <
B. >
C. =

Answers

Answer:≤ sorry if it's wrong I'm not a fan of math

Step-by-step explanation:

Write the following expression in expanded form:9 to power of 3× 7to the power of 4

Answers

Exponential Expressions into Expanded Form into Answer:

[tex]9^{3}[/tex] = 9⋅9⋅9 = 729

[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401

I hope this helps, have a good day!

Answer:


= 9⋅9⋅9 = 729

= 7⋅7⋅7⋅7 = 2401

Step-by-step explanation:

Complete this division sentence.
5884÷94 =
R

Answers

The remainder of the given division 5884/ 94 is 56 and hence the complete sentence is 5884/94 = 62 + 56/94.

What is remainder and how to find a remainder?

The amount that remains after division is complete is known as a remnant. Simply divide the number by another number that is one of its multiples to obtain the remainder.

The division of any number can be written as follows:

a/n = q + r/n

where, a is the dividend, n is the divisor, r is the remainder and q is the quotient.

When we divide the number 5884 by 94 using the long division method the quotient is 62 and the remainder is 56.

Hence, the complete sentence is 5884/94 = 62 + 56/94.

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Trace triangle JKL and point P.

Draw the dilation of AJKL

using scale factor 3 and P

as the center of dilation,

Answers

The dilation of triangle JKL, with point P at the origin and scale factor of 3, is graphed on the image shown at the end of the answer.

What is a dilation?

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The coordinates of the vertices of the original triangle JKL for this problem are attributed as follows:

J(1,1).K(1,5).L(4,1).

The scale factor of the dilation is given as follows:

k = 3.

Meaning that each coordinate of each vertex of the triangle will be multiplied by 3, thus obtaining the coordinates of the vertices of the image of triangle JKL after the dilation, as follows:

J'(3,3).K'(3,15).L'(12,3).

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Rewrite the following expression using the Distributive Property. 5(2x -8)

A. -30x
B. 10x -40
C. 10x + 40
D. 10x -8

I think it is either B or C but I'm not sure.

Answers

Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

B is right just distribute them and you’ll see the negative sign appearing in the answer

Given the example below, determine the property displayed.

7+3=3+7

Answers

Answer:

commutative property of addition

Step-by-step explanation:

commutative property of addition

The commutative property of addition allows you to change the order of the numbers in an addition.

For example, 1 + 2 = 2 + 1

let there be 800 people at school. prove that 3 of them do share a birthday. how can we prove it according to the pigeonhole principle?

Answers

According to the Pigeonhole Principle, if you have more objects than available spaces, then at least two of the objects must occupy the same space. In this case, we have 800 people at school, and only 365 days in a year. This means that at least three of the people must share the same birthday, since there are not enough days in the year for each person to have a unique birthday.

Simplify the following rational expression. Be sure to state the condition.

Answers

The simplified form of the rational expression (x²+5x+6)/(3x+6) is (x+3)/2.

And we used factorization to find the simplified form.

What is factorization?

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

Given:

The rational expression,

(x²+5x+6)/(3x+6).

Simplifying,

the expression using factorization method.

First, (x²+5x+6),

= x²+2x+3x+6

= x(x+2)+3(x+2)

= (x+2) (x+3)

And 3x+6 = 3(x+2)

Substituting the simplified values to the given expression,

(x²+5x+6)/(3x+6),

= (x+2) (x+3) / {3(x+2)}

Factor out the common factor,

= (x+3)/2

Therefore, the simplified form is (x+3)/2.

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Solve for x

Select the correct response:
A: 14
B: 19.25
C: 10
D: 6.5

Answers

The value of the x is 10.

What is the exterior angle theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

We have given,

angles of the triangle:

Interior angles :

∠D = 2x + 7,

∠E = 26°,

Exterior angle:

∠C = 6x - 7

To find x = ?

few common properties about the angles of a triangle:

A triangle has 3 internal angles which always sum up to 180 degrees.

It has 6 exterior angles and this theorem gets applied to each of the exterior angles.

Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.

So,

∠C  = ∠D + ∠E

6x - 7 = 2x + 7 + 26,

6x - 7 - 2x - 7 = 26,

4x - 14 = 26,

4x = 40

x = 40/4

x = 10,

Hence, the value of the x is 10.

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3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10

Answers

-1 on the left x-axis and 4 on the right y-axis.

Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.

step 1: ascend the y-axis six times.

Step 2: Use 4/1 to increase from the y-4 axis's by 1  to the right

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Lena had 149 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.

Answers

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

Define Expression .

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Here,

Given :  Lena has $149

she spends k amount of money

The money left be x

=> 149-k =x

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

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In Exercises 13-15, use f(x) = x² and g(x) = 4x - 6 to find h(x).

13. h(x) = f(x) - g(x)

14. h(x) = f(g(x))

15. h(x) is the inverse of g(x)

Answers

The value of the function h(x) is x² -  4x +6 and 4-6 x².

What is a formula for a function?

Any function's x-intercept, y-intercept, and slope can be calculated using function formulas. You could also determine a quadratic function's vertex. Additionally, the function can be graphed for various x values.

Simply adding the values of the functions f(x) and g will yield the value of the function f(x) and g(x).

Therefore, we get

f(x) = x² and  we have g(x) = 4x - 6

h(x) = f(x) - g(x)

h(x) =   x² -  4x +6

h(x) = f(g(x))

     =  x²( 4x - 6)

     = 4-6 x²

h(x) is the inverse of g(x)

   = inverse of 4x - 6

   = 1/ 4x - 6

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the slope to (9, -10), (0, 8) with the work shown please.

Answers

Answer:

-2

Step-by-step explanation:

To find the slope, subtract y1 - y2, then divide by x1-x2

The y numbers in this set is -10 & 8

The x numbers in this set is 9 & 0

-10-8= -18

9-0 = 9

-18/9 = -2

The slope would be -2

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What is an example of goods brainly? Why does Walter lie about visiting new york How do you describe rational and irrational? 4x-5(2x+1)=6x+1. how many solution will this have? is this right when might the BAC of a dead body be misleading or unhelpful If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram. What conditions pushed people to rebel against governments during the Age of Revolutions? You must include the name of a specific country and WHY they rebelled. when assessing a countrys economic market potential, examine all of the following exceptO government lawsO consumption patternsO populationO GDP What did Alexander do for history that made him Great?Or was he great at all? Buffalo grass is a species of plant found on the grazing prairie of Wyoming. It is a tough grass that has silicates (compounds containing oxygen and silicon) that reinforce its leaves. This variation has allowed this type of grass to survive for many years in an adverse environment. This is an example of which mechanism of evolution? O Mutation O Natural Selection O Gene Flow Genetic Drift Please help with this question Im confused on it PLEASE HELPP The endpoints of a line segment AB are (1, -6) and (5, -6). The equation of a line BC is y=x-11. Is triangle ABC a right triangle? Justify your answer. Because milk tea is flourishing in their town, Mathilda decided to sell Wintermelon milk tea (WMT) powder at Php 1 per gram and Okinawa milk tea (OMT) powder at Php 2 per gram. To increase her profit, she plans to mix the two milk tea powders. How much OMT should she mix with 300 grams of WMT so that she can sell the resulting mixture at Php 1.80 per gram? Which of the following will increase planned investment spending on the part of firms?A. A lower real interest rateB. Increased optimism about future demand for its productC. Increases in the corporate income taxD. All of the aboveE. A and B only Communication which occurs via staff meeting would fall under whichcategory?A. horizontalC. verticalB. a synchronousD. Synchronous Many screening measures can be considered diagnostic since they provide extremely detailed data about a students skills in particular literacy domains. T/F How do you find the 3rd side of a triangle? The control of offenders in the community under strict conditions, by means of frequent reporting to a probation officer whose caseload is generally limited to 30 offenders, is called ________. Crestive17. Match the definition with the correct word.compliant; manageabletractablecanvassbeatificplacid Thematic Essay Political Systems:Several empires and nations throughout global history have been ruled by strong leaders who have followed policies of absolutism.Task: - Define the term absolutism and identify the characteristics of absolutist rule.- Select a nation or empire like the Incan empire, the Byzantine empire, the Ming empire in China, the Ottoman empire of Suleiman the Great that was ruled according to the principles of absolutism Identify the specific characteristics of absolutist government that existed in this nation or empire.- Discuss the major positive and/or negative effects that absolutism had on this empire or nation. 4 to 5 paragraphs- Introduction- 2 to 3 Bodies- Conclusion