Use the long division method to find the result when 9x³ +30x² + 10x - 24 is
divided by 3x + 8. If there is a remainder, express the result in the form
q(x)+7(2).

Answer:

2a + b = 180
 a + b = 118

a = 64, b = 56

Step-by-step explanation:

If you look at the triangle on the top right of the diagonal, there are 3 angles a, a and b. Since the 3 angles of a triangle add up to 180°

      a + a + b = 180

=>   2a + b = 180.......(1)

We are given that the largest angle is 118°

The largest angle of the parallelogram is a + b. Remember that opposite angles of a parallelogram are equal and the sum of the angles add up to 360

Therefore a + b = 118 ....(2)

Given equations (1) and (2), subtract (1) from (2):

Eq (1) - Eq(2) :

2a + b - (a + b) = 180 - 118

a = 62

Substitute for a in equation (2) to get

a + b = 118

62 + b = 118

b = 118 - 62 = 56

So the two angles are a = 64° and b = 56°

Answer:

a = 62, b = 56

Step-by-step explanation:

given the largest angle is 118° , then

a + b = 118 ( subtract b from both sides )

a = 118 - b → (1)

the sum of the interior angles of a quadrilateral = 360°

the angle adjacent to a is b ( alternate angles ) , then

a + b + a + a + b + a = 360

4a + 2b = 360 → (2)

substitute a = 118 - b into (2)

4(118 - b) + 2b = 360

472 - 4b + 2b = 360

472 - 2b = 360 ( subtract 472 from both sides )

- 2b = - 112 ( divide both sides by - 2 )

b = 56

substitute b = 56 into (1)

a = 118 - 56 = 62

a = 62 and b = 56

Answer: Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Answer: a transformation, which is used to resize the object

Step-by-step explanation:

the shape changes size but not shape

The elk population in 2014 will be 19,700 ,A population is an identified grouping of objects with the purpose of analysis and data collection.

A population is an identified grouping of objects with the purpose of analysis and data collection. Examples include people and animals. It comprises of a related collection of species that live in a specific area and have the ability to interbreed.

The population increased by 12,700-12,000 = 700 between the two measures, however, it did so over a period of 1 year, from 2004 to 2003. Divide 700 elk by 1

The elk population in 2014 will be 19,700We must first establish the method

2014=700 should add 10 times then we will get the 2014th year population.

so the population of 2014th will 19700

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hello

to solve this question, we just have to find the expression that is equal to 4b

option A

option a is incorrect

let's look at option B

option B is correct

and finally option C

option C is correct

from the calculations above, option B and C are the right answers

The correct option is option B that is "The graph of f(x) is shifted 17 units up". It is shifted 17 units up. By adding 17 to the equation, y increases by 17. If y increases by 17, the graph shifts up by 17.

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.

The process of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the modification of algebraic equations, it is a typical kind of algebraic problem.

It is shifted 17 units up.

By adding 17 to the equation, y increases by 17.

If y increases by 17, the graph shifts up by 17.

Option B, "The graph of f(x) is shifted 17 units up," is the answer. It is moved upward 17 units. Adding 17 to the formula causes y to rise by 17. The graph moves up 17 units if y rises by 17.

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Answer:

x = 16

Step-by-step explanation:

The Sarah's path and Marcus path will intersect at the point  (5,4) .

In the question ,

it is given that

the park is modeled by the equation y = x − 1  .

On comparing with the slope intercept form ,

we get

the slope as 1 .

Since both the paths are perpendicular ,

the slope for Marcus path is -1 .

hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c

9 = (-1)0 + c

9 = c

so equation is y = (-1)x + 9

So to find the point of intersection , we solve both the equations .

Substituting y = x − 1 in y = (-1)x + 9 ,

we get

x − 1 = (-1)x + 9

x - 1 = -x + 9

x + x = 9 + 1

2x = 10

x = 5

So, y = 5 - 1 = 4

the point of intersection is (5,4) .

Therefore , The Sarah's path and Marcus path will intersect at the point  (5,4) .

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Given a rectangular peice of paper

Length = 34 cm

Width = 16 cm

So, the area of the rectangle = 34 x 16 = 544 cm²

Two semicircles cut out of it

The diameter of the circle = d = 16 cm

So, the radius of the circle = r = d/2 = 8 cm

The area of the two semicircles = area of the complete circle

so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²

So, the area of the remaining paper = area of the rectangle - area of the circle

= 544 - 200.96 = 343.04 cm²

So, the answer will be Area = 343.04 cm²

Two lines are parallel if they hay the same slope.

The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

From the graph, line m passes through the points (0, 1) and (3,3), then its slope is:

Equation of a line in slope-intercept form

where m is the slope and (x1, y2) is a point on the line.

The new line has to pass through point P(1, -2). Substituting with this point and m = 2/3 into the general formula:

Answer:

an=7/2

Step-by-step explanation:

an=a(n-1)+15

given a1=8

multiply; a(n-1)

a(n-1)=an-a1

enter an-a1 in the equation

an=an-8+15

an=an+7

collect like terms;

an-an=(-7)

divide by negative both side

an-an/(-)=(-(-7)

2an=7

divide by 2 both side

2an/2=7/2

therefore the answer is an=7/2

Answer:

the answer for your question is option A

Answer:b

Step-by-step explanation:

The minimum that could be earned is $150. The required inequalities are solved below:

What is an inequality?

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: The symbol a b indicates that an is smaller than b. The symbol a > b indicates that an is more than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed.

(a) The minimum that could be earned is $150.

(b) The required inequality is given as 150+20x≥630

or, 20x≥630-150

or, x≥480/20

or, x≥24

(c) The required inequality is given as 150+20x≥750

or, 20x≥750-150

or, x≥600/20

or, x≥30

(d) The required inequality is given as 150+20x≤950

or, 20x≤950-150

or, x≤800/20

or, x≤40

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predicted value of the slope , A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable.

When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable, and multiple linear regression is used when there are numerous variables.

A regression model called simple linear regression uses a straight line to calculate the association between one independent variable and one dependent variable. Both variables ought to have numerical values.

When the parameters are linear, a regression equation (or function) is said to be linear in statistics. Although the predictor variables can be transformed in ways that result in curvature, the equation must be linear in the parameters.

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in linear regression, the fitted value is the:  predicted value of the dependent variable

When you enter the values of the predictors, factor levels, and other inputs into a statistical model, the predicted mean response value is known as the fitted value.

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Explanation

We are asked to determine if the question is a continuous or discrete data set

The discrete data set is a data set that can be counted

Continuous data set are data that can be measured

For the given question, the answer will be option A

Answer:373248

Step-by-step explanation:

Answer:

Step-by-step explanation:

12*6=72

72^3=373248

Answer:

30

Explanation:

To know the output value of the function, we need to replace x by -5 and calculated f(x). So:

Therefore, if the input x is -5, the output f(x) is 30

So, the answer is 30.

Answer:

There was a 48% increase from last year.

Step-by-step explanation:

Last year the debate club had 25 members. This year there are 37 members in the club. Estimate the percent change in the number of club members.

= (37 - 25) / 25

= -12 / 25

= 0.48 or 48%

There was a 48% increase from last year.

check:

25 * 1.48 = 37

Two yellow marbles are added to the bag to make the probability of choosing a yellow marble 1/3 .

There is a bag containing five green marbles, three red marbles, and four blue marbles and four yellow marbles.

The probability that a given event will happen is expressed as a number between 0 and 1 where 0 means there is no chance of the event occurring and 1 means that the outcome is certain.

There are a total of 16 marbles in the bag (5 + 3+ 4+4 = 16). This means that the probability of drawing a marble of a particular color is the number of marbles of that color divided by the total number of marbles in the bag.

Let ‘x’ number of additional yellow marbles be added to the bag.

Then, the required probability will be

(4 + x )/ (16+x ) = 1/3

=> 3(4+x) =16 +x

=> 12+3x = 16+x

=> 2x =4

=> x= 2

Hence, the required number of marbles is 2.

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The equations that have No solution are2t + 1 = 1 + 2t ,  2t + 1 = 2t and  2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .

In the question ,

equations are given ,

we have to find which equation have NO Solution .

So,

(a) First equation is given as

2t + 1 = 1 + 2t

On rewriting the terms , we get

2t - 2t = 1 - 1

0 = 1-1 ,

we cannot find the solution of x .

hence this equation has No solution .

(b) equation is

2t + 1 = 2t

On rewriting the terms , we get

2t -2t = -1

0 = -1

hence ,this equation have No Solution .

(c) equation is 2(t+1) = 2t + 1

2t + 2 = 2t + 1

2t - 2t = 1 - 2

0 = -1

hence , this equation have No Solution .

(d) equation is 2t+t=2t+1

3t = 2t + 1

3t - 2t = 1

t = 1

hence , this equation have Unique Solution .

(e) equation is 2t = 1

So, t = 1/2

hence , this equation have Unique Solution .

Therefore , The equations that have No solution are 2t + 1 = 2t and  2(t+1) = 2t + 1 , the correct options are (a) , (b) and (c) .

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Answer: 8.4cm

Step-by-step explanation:

sin cos tan

SOH CAH TOA

It is cos because CAH does not have opposite (o) in it and we want to find the opposite.

O is opposite (opposite angle)

A is adjacent (next to angle)

H is hypotenuse (opposite right angle)

This is how I remember it

Cos(61)*17.4=8.435

8.4cm

-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

Two or more expressions with an Equal sign is called as Equation.

Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

4357/21 - 4200

Take LCM as 21.

4357-88200/21

-83843/21

=-3992.5

Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

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The height of the flagpole is 27 feet.

Given,

If two triangles are similar, sides of these triangles will be proportional.

Height of the flagpole  = h feet

Shadow castes by the flagpole  = 72 feet

Height of the person  = 6 feet

Shadow casted by the person = 16 feet

By using the property of similar triangles,

Hence, h/6 = 72/16

h = (6×72)/ 16

h = 27 feet

Therefore, The height of the flagpole is 27 feet.

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Using the stated transformation, the graph of g(2x) is given at the end of the answer.

An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:

g(x) = f(ax).

The definition of stretch or compression depends on the value of the constant a, as follows:

In this problem, the rule is:

f(x) = g(2x).

Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:

That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.

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The coordinates of (6, -4) after a reflection in the line x = 2 are:

(-4, -4)

If we have a point (x, y) and we do a reflection in the line x = a, the new coordinates of the point will be:

(a - x, y)

In this case, we have (6, -4) and the line of reflection is x = 2, then the coordinates after the reflection are:

(2 - 6, -4) = (-4, -4)

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Answer:

11

Step-by-step explanation:

How to find the arithmetic mean:

Add all numbers together, and divide by the amount of numbers.

Ans: 15 + 7 = 22

22 ÷ by amount of numbers =

22 ÷ 2 =

11

Ans = 11

Answer:

C (4,5)

Step-by-step explanation:

See the attached image.

Answer:

Step-by-step explanation:

Area of rectangle formula:

Find the width by substituting the given values:

Answer:

23,180 pieces

Explanation:

The number of white paper used = 13,480 pieces

Since they used 7,880 fewer pieces of blue paper than white paper

The number of blue paper used = 13,480 - 7880 =5,600 pieces

They also used 1,500 fewer pieces of yellow paper than blue paper.

The number of yellow paper used = 5,600-1500 =4100 pieces

Therefore. the total number of pieces of paper

=13,480 + 5,600 + 4100

=23,180 pieces

[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]

IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.

GOODLUCK!!