What is the simplified form of the expression x^2-4x-21 over 4(x-7)

Answers

Answer 1

The simplified form of the expression (x² - 4x -21)/4(x-7) is (x + 3)/4

How to determine the simplified form of the expression

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

x²-4x-21 over 4(x-7)

Express properly

So, we have

(x² - 4x -21)/4(x-7)

Factor the numerator

This gives

(x + 3)(x - 7)/4(x-7)

Cancel out the common factors

This gives

(x + 3)/4

Hence, the simplified form of the expression is (x + 3)/4

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Related Questions

Solve for m
-7+4m+10=15-2m−7+4m+10=15−2mminus, 7, plus, 4, m, plus, 10, equals, 15, minus, 2, m
m=

Answers

The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2

Algebra

-7 + 4m + 10 = 15 - 2m

collect like terms

4m + 2m = 15 + 7 - 10

6m = 12

divide both sides by 6

m = 12/6

m = 2

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Juan needs to rewrite this difference as one expression. First he factored the denominators. What step should Juan take next when subtracting these expressions

Answers

The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).

Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).

An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

The given expression is (3x/(x²-7x+10))-(2x/(3x-15))

Firstly, we will factored the denominator as

(3x/(x-2)(x-5))-(2x/3(x-5)).

Now, we will multiply and divide the second fraction by (x-2), we get

(3x/(x-2)(x-5))-((2x(x-2))/3(x-5)(x-2)).

Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).

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Assuming a normal distribution, families spends an average of $500 on their monthly cell phone bills with a standard deviation of $75. What is the probability a random families' bill is between $350 and $400

Answers

There is a 0.02275 to 0.0968 chance that a random family's bill will be between $350 and $400.

Calculating the probability

Provided that,

Mean of the population = 500

The standard deviation(S.D) of the population = 75

Assume,the variable in normal distribution = X

Z= (x- mean)/ S.D

Provided , x = $350 - $400

Z= 350-500/75 = -2(when x=$350)

Z= 400-500/75 = -1.3 (taken x= $400)

The probability that a household will spend between $350 and $400 monthly

P(350>X<400) = P( -2>Z<-1.3)

                        = 0.02275 to 0.0968 (from probability table)

Therefore, the final answer is 0.02275 to 0.0968.

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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4

Answers

The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

2.3p – 10.1 = 6.49p – 4 and230p – 1010 = 650p – 400 – p

Which equations have the same solution as the given equation?

It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.

The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.

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Answer:

B & C

Step-by-step explanation:

edge 2023

Look at the image below.
Find the area of the parallelogram.

Answers

Answer: 80 square units

Step-by-step explanation:

[tex]A=(8)(10)=80[/tex]

A data value is considered​ _______ if its​ z-score is less than 2 or greater than 2.

Answers

A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.

What does a standard deviation of 2 mean?

Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

If 7.2 and 7.9 are two points on a number line , find the number in the middle of the points​

Answers

Answer:

7.55

Step-by-step explanation:

A midpoint can be found by doing 7.2 + 7.9 then dividing by the number of points (in this case 2).

x/2 + 11 = 19
solve this equation

Answers

Answer:

x/2 = 19-11

x/2 = 8

x = 8×2

x= 16

Answer:

x=16

Step-by-step explanation:

x/2 + 11 = 19

*2     *2    *2    Multiply 2 on both sides to make x stand by itself

x+22 = 38

  -22   -22

x=16

Check

Plug in 16 instead of x.

16/2 + 11 = 19

8+11=19

19=19

Hope it helps:)

N
Mason is creating a design using a straightedge and compass. He wants to construct a segment FG, which is congruent to segment BE in the
given figure.
A. the distance from B to E
To what width should Mason set his compass when constructing segment FG?
OB.
O C.
O D.
the distance from D to F
The distance from F to c
A
the distance from A to C
F
A
D

Answers

The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.

Width

FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.

Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.

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Answer:

b to e

Step-by-step explanation:

plato

Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC

Answers

The theorem that would be included in the proof is: CPCTC theorem.

What is the CPCTC Theorem?

CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.

To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:

1. angle D ≅ angle F [given]

2. angle DBE ≅ angle ECF [given]

3. side DE ≅ side EF [given]

4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]

5. DB ≅ FC [by the CPCTC theorem]

With the given proof, we can state that side DB is congruent to side FC.

Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.

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3 m
8 m
12 m
9m
6 m
Find the total surface area of the trapezoidal prism in the figure.

Answers

The total surface area of the trapezoidal prism is 180m². Option C

Total surface area of a trapezoidal prism

The formula for the total surface area of a trapezoidal prism is;

Total surface area = h (b + d) + l (a + b + c + d)

Where

b and d are parallel sides = 3, 9

h is the distance = 8

l is the length of the trapezoidal prism. = 12

Substitute into the formula

Total surface area = [tex]8(3 + 6) + 12(3 + 6)[/tex]

Total surface area = 72 + 108

Total surface area = 180 m²

Thus, the total surface area of the trapezoidal prism is 180m². Option C

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Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the descriptions.

Answers

The tiles to match the descriptions are;

Hull house - Neighbourhood assistance.

Muckrakers - Investigative journalists.

Protestants - Temperance movement.

Women's suffrage - Nineteenth amendment.

What is Progressive time period?

The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.

Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.

Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.

Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.

Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.

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The complete question is-

Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the

descriptions                        

Tiles;

Hull House

Muckrakers

Protestants

Women's Suffrage

Pairs;

Investigative journalists

Temperance Movement

Neighbourhood assistance

Nineteenth Amendment

What value, written as a decimal, should lena use as the common ratio? 1.0 1.5 2.5 2.0

Answers

The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0

According to the question,

1.0  1.5  2.5  2.0

a = 1.0

r = 1.5/1 = 1.5

r = 2.5/1.5 = 1.6667

r = 2/2.5 = 0.8

common ratio is different, so given sequence is not geometric sequence.

Hence,  the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.

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In total, 2 baseballs and 3 footballs cost $67. a football is $4 more than 3 times the cost of a baseball. find the cost of a baseball

Answers

The cost of the Baseball is $5.

Lets take football cost as "x"

And taking baseball cost as "y"

According to given conditions,

2y + 3x = 67

x= 3y + 4

Lets put the values of x in equation (1):

2y + 3 (3y+4) = 67

=> 2y + 9y + 12 = 67

=> 11y = 55

y = 5

x = 3(5) + 4

x = 19

Hence the cost of the Baseball is $5.

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What is the recursive formula for the geometric sequence with this explicit
formula?

a^n=9(-1/3)^(n-1)

Answers

The answer of this equation is a^n=9(-1/4) (n+ 1)

f(x)=x^2-x-56=0 what are the zeros in the function?
please help!!!

Answers

Answer:

-7, 8.

Step-by-step explanation:

x^2 - x - 56 = 0

Let's see if we can factor this function:

We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).

They are  -8 and 7 , so the factors are:

(x - 8)(x + 7) = 0

x - 8 = 0 giving x =  8 and

x + 7 = 0 giving x = -7.

The zeros are -7, 8

The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.

Answers

The area of the logo is 136. 14 cm²

Determining the area

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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The number of marriage licenses issued by Clark County Nevada, the county where Las Vegas is located, has been decreasing since the year 2000. Using the table, how many marriage licenses were issued in 2008? 2010 Year 105,000 2001 2003 2006 Marriage Licenses 141,000 133,000 121,000 A. 113,000 B. 121,000 C. 118,000 10 Points D. 102,000​

Answers

If the marriage licenses  issued in 2001,2003,2006,2010 were 141000,133000,121000,141000 then by solving arithmetic progression we will get that the marriage licenses issued in 2008 were 113000.

Given that the marriage licenses issued in 2001,2003,2006,2010 were 141000,133000,121000,141000.

We are required to find how many marriage licenses were issued in 2008.

Average difference between licenses issued from 2001 to 2003=

=133000-141000)/2

=-4000

Average difference between licenses issued from 2003 to 2006=

=(121000-133000)/3

=-12000/3

=-4000

Average difference between licenses issued from 2006 to 2010=

=(105000-121000)/4

=-16000/4

=-4000

It is an arithmetic progression because the difference between marriage issued from one year to another is equal.

An arithmetic progression is a sequence in which each terms are having equal difference between them.

Nth term=a+(n-1)d

8th term=141000+(8-1)*(-4000)

=141000+7*(-4000)

=141000-28000

=113000

Hence the marriage licenses issued in 2008 were 113000 which is

option A.

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which relation is a function

Answers

B

a function is a relationship between inputs where each input is related to exactly one output.

The relation in option B is a function.

What is Function?

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are 4 relations, A, B, C, D.

From the definition of function, it is clear that, no input value have more than one output value.

A : The value of x = -2 is mapping to 2, 1, 0, -1.

That is, an input value is having more than one output values.

So this is not a function.

B : Here the input values, 0, 1, 2 and 3 maps to -2.

Here the input values are distinct. No input values are mapping to more than one output value.

So this is a function.

C : Here 1 is mapping to -2 and 3. So not a function.

D : For x = 0, there are two y values, 3 and -3.

So this is not a function.

Hence option B is a function.

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Find the volume of a pyramid with a square base, where the side length of the base is
18.7 ft and the height of the pyramid is 8.8 ft.

Answers

Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

Which choice is equivalent to the quotient below? √16 OA. A OB. N/హ / OC. 2 D. √√2​

Answers

Answer:

C

Step-by-step explanation:

Please refer to the attached photo for step by step solutions.

Note: Square roots and squares will always cancel out each other.

This question is down below. Please solve in detail if you know how to solve.

Answers

Answer:

8.4 meters tall   ( one decimal place)

Step-by-step explanation:

See diagram below:

find distance 'd'   as     tan 68 = opp / adj = d/6

   then   d = 6 tan 68       =  14.85 m

Then find   h   as   tan 9  = h / d

                               d tan 9 = h

                              14.85  tan 9 = h = 2.35 m tall

                                      add the 6 m height of the house    8.4  m tall

What is the measure of angle ABC

Answers

Answer: A

Step-by-step explanation:

[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.

EXTRA POINTS, AND ILL GIVE YOU BRAINLIEST
1 x/3 - 3/4 = 5/12 solve for x!

Answers

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

What is an equation?

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

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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can someone please help me

Answers

Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.

How to determine angles in a unit circle

Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).

To solve this problem, we must take these tips into account:

Angles in the first quadrant are within 0 < θ < π/2.Angles in the second quadrant are within π/2 < θ < π.Angles in the third quadrant are within π < θ < 3π/2.Angles in the fourth quadrant are within 3π/2 < θ < 2π.

Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.

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Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a $1$, then he rolls again. In a non-leap year, what is the expected value of the difference between the number of days Bob eats unsweetened cereal and the number of days he eats sweetened cereal

Answers

Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

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Find the product of X^2 (4x - 3).

A. 5x^3

B. 5x^3 - 3x^3

C. 4x^3 - 3x^2

D. X^2 + 4x - 3

Answers

x² ( 4x - 3)

Apply the multiplicative law of distribution.

x² × 4x - x² × 3

Multiply the monomial

4x³ - x² × 3

Multiply the monomial

4x³ - 3x² ==> Answer

Therefore, the correct option is "C".

Statement
The wastes from
nuclear power plants
are very toxic.
Nuclear power plants
produce less air
pollution than power
plants that use fossil
fuels.
Nuclear power plants
are safe.
The benefits of nuclear
power outweigh the
risks.
How my answer changed
Part of the lesson or other evidence that
changed my mind supported my original
answer
H

Answers

The new statement will be:

The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that  from powerplants that make use of fossil fuels.Power plants that are Nuclear  are regarded as safe.The risks of nuclear power is much more lower than the benefits.

What changed my mind in the above?

Nuclear energy is known to be one that produce a lot of radioactive waste and this tends to pose a threat to  human health and the environment.

Hence, The new statement will be:

The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that  from powerplants that make use of fossil fuels.Power plants that are Nuclear  are regarded as safe.The risks of nuclear power is much more lower than the benefits.

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Describe the following expressions in words: x+4 ​

Answers

Four added to a number

Hope this helped :)

Which of the following equations will produce the graph shown below?

Answers

The equation that will produce the given graph is; 6x² + 6y² = 144

What is the equation of the Circle?

The standard equation of a circle can be expressed as:

(x + a)² + (y - b)² = r²

where;

(a, b) is the center of the circle

r is the radius of the circle.

From the diagram, we can see that the radius of the circle is between 4 and 5.  Thus, the correct equation must have a radius between these values.

From the option, we can see that the only equation that will have a radius between 4 and 5 is;

6x² + 6y² = 144

Divide through by 6 to get;

x² + y² = 24

x² + y² = √24

Thus r = √24 which is greater than 5

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If the interview questions are not restricted but do provide an indication as to the direction of the interview, what type of interview is being conducted A wave on a string is described by D(x,t)=(4.0cm) sin[2(x/(2.4m)+t/(0.26s)+1)], where x is in m and t is in s.1. What is the wave speed?2. What is the frequency?3. What is the wave number?4.At t=.65s, what is the displacement of the string at x=2.6m? nitrosamines, polycyclic aromatic hydrocarbons, and radiation-emitting polonium are among the powerful carcinogens in which tobacco product? Julius Caesar. How does this scene heighten the suspense in the play? Act 2 scene 4 A company is manufacturing models of the EiffelTower to sell in gift shops. If the model needs tofit in a 1-foot tall box, and the actual height of thetower is 984 feet, which scale is best? Due to an error in computing depreciation expense, Crote Corporation understated accumulated depreciation by $64 million as of December 31, 2021. Crote has a tax rate of 25%.Crote's retained earnings as of December 31, 2021, would be:a. overstated by $48.00 million.b. overstated by $64.00 million.c. understated by $48.00 million.d. understated by $64.00 million. Complete the ground-state electron configuration for these ions using the noble gas abbreviation and identify the charge on the ion. indium(III) ion electron configuration: ___indium(III) ion charge: __thallium(III) ion electronic configuration: __thallium(III) ion charge: ___ problem 5: an analog accelerometer outputs -5 v to + 5 v in three different pins as the acceleration in what is the second stepwise equilibrium constant expression for phosphoric acid h3po4? ann was surprised to find that she experiences depression differently than her friend fred. what is the difference between men and women with depressive disorder? a crime in which a stolen vehicle assumes the identity of a legally owned, or nonstolen, vehicle of a similar make and model is called: a person standing a certain distance from eleven identical loudspeakers is hearing a sound level intensity of 112 db. what sound level intensity would this person hear if two are turned off? in dB people usually make a clean break after breaking up, especially if they were in a long-term relationship and had a shared social network.T/F In a Harris survey, adults were asked how often they typically travel on commercial flights, and it was found that P(N) = 0.33, where N denotes a response of "never." What does the following expression represent and what is its value? P(N) fitb. when psychologists make judgments about prisoners, mental hospital patients, or children in terms of their mental health, they are making ______ judgments. miryam and louis, both in 10th grade, are in a relationship. which of the following terms are they least likely to use to refer to their arrangement?Which of the following terms are they least likely to use to refer to their arrangement? a. going with each other b. dating each other c. seeing each other This story "rock" uses first person narrative. Explain how the narrative influences our perception of the events in the story, and how this contributes to the story's meaning determine whether the statement below is true or false. justify the answer. the vector is in rn v . v = v2 Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.y = ex2, y = 0, x = 4, x = 4(a) About the x-axis(b) About y = 12. Find the volume V of the described solid S.The base of S is the region enclosed by the parabola y = 4 2x2 and the xaxis. Cross-sections perpendicular to the yaxis are squares. how much h2 would be produced by the complete reaction of the iron bar?