X^2 - 10x - 20 = 0, which number would have to be added to "complete the square"?

Answers

Answer 1

Answer:

45

Step-by-step explanation:

When you're completing the square you're adding (b/2)^2 which in this case is (-5)^2 or 25. This is because when you rewrite it as a square binomial you write it in the form (x+(b/2))^2 which is going to result in x^2+b+(b/2)^2. Since you need to reach 25 you need to add 45 since the last value is at -20.

Answer 2

Answer:

25 to both sides

Step-by-step explanation:

Group x² and x terms

(x² - 10x ) - 20

complete the square

(x² - 10x +25 ) -20 -25

(x-5)² -45


Related Questions

Which of the following rational functions is graphed below?
-10
A. F(x)=
(x-1)(x+1)
X+1
B. F(x)=xx-1)
10
C. F(X) = XX+1)
x-1
x(x+1)
D. F(x) = (x+1)(x − 1)
X

Answers

In order to answer your question you need to add the graph so we know what you are looking at

Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, In the graph,

we can see that we have a vertical asymptote at x = -1.

Hence, This means that the denominator of the rational equation becomes zero when x = -1.

So the equation must be:

⇒ y = 1 / (x + 1)

Here, The denominator is x + 1, and as expected, it becomes zero when, x = -1.

Then, we conclude that the correct option is C.

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′. The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5).
The slope of is

Answers

The coordinates of point N are (3, 5).2 the answer is 2/1 but just write 2.

We have given that,

Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′.

What is the coordinate?

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

The coordinates of point M are (2, 4), and the coordinates of point N are (3, 5)

Therefore we get,

2 the answer is 2/1 but just write 2.

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In triangle PQR, find the measure of angle Q.
P= 64 degrees
Q= X
R= 2x

Answers

Answer:

38.667°

Step-by-step explanation:

the total sum of 3 angles in a triangle is 180

in triangle PQR this means:

P+Q+R = 180

so:

64+x+2x=180

64+3x=180

3x=116

x=116/3=38.667

So Q=X=38.667

Solve for x (12x-7)/4=(5x+18)/3

Answers

Answer:

Step-by-step explanation:do i know u

Answer:

x= 5.8125

Step-by-step explanation:

Given: [tex]\frac{12x-7}{4} =\frac{5x+18}{3}[/tex]

Since we have one fraction equal to another fraction, we can cross multiply.

(12x -7)(3)= 4(5x +18)

Expand:

36x -21= 20x +72

Bring all the x terms to one side, constant to the other:

36x -20x= 72 +21

Simplify:

16x= 93

Divide both sides by 16:

[tex]x= \frac{93}{16}[/tex]

x= 5.8125

Additional:

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Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left? (Round your answer to the nearest tenth)

Answers

Answer: 2.4 hours

===================================================

Explanation:

She has already ran 8 miles, so she has 26-8 = 18 miles left to go.

She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.

I used the equation distance = rate*time, and solved for time to get time = distance/rate.

--------------------

Another approach:

Here's how you can use algebra.

x = time she has left in hours

7.5x = distance covered in those x hours

7.5x+8 = total distance

7.5x+8 = 26

7.5x = 26-8

7.5x = 18

x = 18/(7.5)

x = 2.4

4, 2.5, 1, -0.5, -2, , ,
which number is after -2

Answers

Answer:

The number after - 2 is - 3.5.

Step-by-step explanation:

Follow the pattern

Let the number be  after -2

as in the question after 4 we have 2.5 then 1 and so on.

if we subtract 4 from 2.5 we get

2.5 - 4 = -1.5

similarly:  1 - 2.5 = -1.5

-0.5 - 1 = -1.5

and now

x -(-2) = - 1.5

x = - 1.5 -2

x = - 3.5

so the number after - 2 is - 3.5.

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Name the relationship between x and y:

Answers

Answer:

They are the same angle.

Step-by-step explanation:

We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.

Option 2: Corresponding angles.

Hope this helps!

If not, I am sorry.

Sam and Joe are working to solve 6 divided 1/4 Sam thinks the answer is 24. Joe thinks the answer is . Explain who is correct. Use a model to help explain your thinking.

Answers

Answer:

Sam is correct

Step-by-step explanation:

6 divided by 1/4.

This is asking how many times can 1/4 go into 6?  This might be a calculation needed if Sam brought 6 pies to the party of 24 people.  How should Sam cut the pies so that each person gets an equal share, and there is none left over.  This is a serious issue because Sam only knows how to cut pies into quarters.  He always gets confused when having to split a pie into 5, 6, 7, 8 or even 9 equal pieces.  Sam decided that if he cuts the pies into quarters, that he'll have exactly 24 pieces of pie, all equal in size, and exactly enough to feed everyone.

Sam says 24 is wrong.  I don't see the figure that Sam has in mind, but it apparently is not 24.

When a pie is cut into quarters, it will serve 4 people.  If one has 6 pies, and everyone takes only one slice, then there would be 4 x 6 or 24 pieces of pie, exactly what is needed:  one for each person.

Which equation represents a side that is perpendicular to side d? O y = 2x+5 Oy=-2x+5 NG 0 Y=2x-5/2 OY--12-12 = Which equation represents a side that is perpendicular to side d ? O y = 2x + 5 Oy = -2x + 5 NG 0 Y = 2x - 5 / 2 OY -- 12-12 =​

Answers

The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

What is the slope?

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

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Find the length of side xx in simplest radical form with a rational denominator.

Answers

Answer:

the answer pf x its 15

by adding the middle sum to 90 degreess and by dividing 6 and 90 you get 15

The graph of g(x) is the result of translating the graph of f(x) = 3 ^ x six units to the rightWhat is the equation of g(x)

Answers

Answer: [tex]g(x) = 3^{x-6}[/tex]

Step-by-step explanation:

Think about it like doing

x - 6 = 0

x = 6

That is how you know that it will be shifted 6 units right (how you can tell the difference between right and left shift)

PLEASE HELP 15 POINTS

Answers

Answer:

B

Step-by-step explanation:

Used elimination method.

first plugged in (0,0)which remove A,D

than saw the line is not solid so chose B

Draw a line representing the “rise” and a line representing the “run” of the line. State the slope of the line in simplest form.

Answers

The slope of the line in its simplest form is 3.

The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].

We need to find the slope of the line in its simplest form.

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.

Select any two points on the line like A and B.

From the below figure it is clear that

Rise = Change in y = -2-(-5) = 3

Run = Change in x = 9-0 = 9

Now, [tex]\frac{9}{3} =3[/tex]

Therefore, the slope of the line in simplest form is 3.

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Please please help! translate the phrase into a variable expression. use the letter p to name the variable. if necessary, use the asterisk (*) for multiplication and the slash (/) for division

... the total number of parrots in the jungle and the 2 parrots your neighbor owns ...

Answers

The expression p+2 will denote the statement given

What is a Variable ?

A variable is a unknown quantity in an equation , which is used to denote the parameter that needs to be determined.

It is given that

the total number of parrots in the jungle and the 2 parrots your neighbor owns

Let p be the total parrots in the jungle

p+2 will denote the statement given

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What should be done to both sides to solve the equation?

Solve x-2=10

Answers

Answer:

add 2 to each side of the equation

Step-by-step explanation:

x-2=10

To solve for x, we need to add 2 to each side of the equation

x-2+2 = 10+2

x = 12

Please help me with my math

Answers

The value of z is 119° and the value of y is 28°.

What is corresponding angles?

When two parallel lines meet any other line, comparable angles are generated in matching corners or corresponding corners with the transversal, these angles are called corresponding angles.

If the given diagram is modified a bit it will look as shown below, the two angles will be 61° because the two angles are corresponding angles.

Now, since 61° and x lie on the same side of the line, therefore, the sum of the two angles will be,

61° + x = 180°

x = 119°

Also, the angles measured at 61° and (3y-23)° lie on the same side of the transversal, therefore, these two angles are corresponding angles. Thus,

61° = (3y-23)°

61 = 3y - 23

y = 28

Hence, the value of z is 119° and the value of y is 28°.

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The composition Do,0.75(x,y). Do,2(x,y) is applied to LMN to create L”M”N”

Answers

Transformation involves changing the position and size of a shape.

The true statements are:

∠m≅∠m'Δlmn≅Δl'm'n'The coordinates of n" are .N''(3,-1.5)

The complete question is as follows:-

The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).

What is translation?

The process of changing the location of the image on the coordinate system will be known as the translation.

The coordinates of the triangle are:

L =(-1,2)

M = (-1,-1)

N = ( 2,-1)

The transformation rule is given as:

do 0.75 (x,y) 2 (x,y)

The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.

Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:

∠l≅∠l''

∠m≅∠m''

∠n≅∠n''

Δlmn⇒Δl'm'n'

The above highlights mean that:

The angles of both triangles are congruent

The triangles are similar

Next, we apply the rule on the coordinates of the triangle

L'' = 0.75 x 2 x (-1,2)

L'' = ( -1.5,3)

M'' = 0.75 x 2 x (-1,-1)

M'' = ( -1.5 , -1.5)

N'' = 0.75 x 2 x (2,-1)

N'' = (3 , -1.5)

Hence, the true statements are: The coordinates of n" are.

∠m≅∠m'Δlmn≅Δl'm'n'The coordinates of n" are . N''(3,-1.5)

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a man is 18 years older than his son. 3 years ago he was 4 times as old as his son how old is the man now​

Answers

Answer:

The man is 27 years old.

Step-by-step explanation:

You can create a system of equations.
Let x = the age of the man
Let y = the age of his son
You can create the following equations based on what was given in the problem:
1. x = y + 18
2. (x - 3) = 4(y - 3)
You can simplify the second equation:
x - 3 = 4y - 12
x = 4y - 9
Then, solve the system of equations:
x = y + 18
-
x = 4y - 9
____________
0 = -3x + 27
The son's age is 9, therefore the father is 27 years old.

Hi can I have help on this question with a simple explanation as I find things difficult to understand. Thank you :)

Answers

Step-by-step explanation:

Line L → 2x - 3y = 6

Where a = 2 and b = -3

• So, we can use this formula to find the gradient of Line L.

m = -a/b

m = -2/-3

m = 2/3 IS THE ANSWER

Answer:

gradient = 2/3

Step-by-step explanation:

Here is another way....manipulate the equation to y = mx+ b form

  where m = slope ( gradient)

2x - 3y = 6          add 3 y to both sides

6 + 3y = 2x         subtract 6 from both sides

3y = 2x - 6          divide by 3

y = 2/3 x - 2        gradient = 2/3

Find the slope of every line that is parallel to line on the graph (0,-3) (5,-4)

Answers

The slope of the line parallel to the line on the graph (0,-3) (5,-4) is - 1 / 5

How to find the slope of a parallel lines?

Parallel lines have the same slope.

Therefore,

slope = m = y₂ - y₁ / x₂ - x₁

Therefore,

x₁ = 0

x₂ = 5

y₁ = -3

y₂ = -4

Therefore,

slope = -4 - (-3)  / 5 - 0

slope = -4 + 3 / 5

slope = - 1 / 5

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Which point on the y-axis is on the line that passes through point R and is parallel to line PQ?

(0, Two-thirds)
(0, 4)
(Two-thirds, 0)
(4, 0)

Answers

Answer:

The answer would be (0, 2/3) or (0, Two-thirds)

Answer:

0, 2/3

Step-by-step explanation:

If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml?

Answers

7.7278 g/ml is the most accurate density of the substance.

What is density?

It is define as the quantity per unit volume, unit area, or unit length.

i.e. the mass of a substance per unit volume.

Mathematically,

[tex]\rho =\frac{m}{v}[/tex]       ----- equation  (1)

Where,

p is the density

m is the mass

v is the volume

According to the question,

Mass = 27.82 grams  

Volume = 3.6 ml

By substituting the Value of m and v in equation 1.

[tex]\rho =\frac{27.82}{3.6}[/tex]

[tex]\rho = 7.7277777 g/ml[/tex]

Therefore,

The most accurate density of the substance in g/ml is  7.7277777 g/ml.

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Which quadrilateral has exactly one pair of parallel sides?

a) rhombus
b) kite
c) trapezoid
d) parallelogram

Answers

Answer:

trapezoid

the horizontal side lengths wont touch each other if you extend them out

The polynomial p(x)=1-2x^2-3x^3+4x has what order?

Answers

This polynomial has an ascending order

determine whether the given graph is a function or not.

Answers

Answer:

Function

Step-by-step explanation:

Yes, the graph is a function. For each x value, there is a unique y value that corresponds with it.

A graph can also be tested as a function by using the popular "vertical-line test".

Question 7 of 25
If f(x)=6x²,-4 and g(x)=2x+2, find (f- g)(x).
OA. 2x-5x2-2
OB. 6x²-2x-6
OC. 4x²-6
O D. 6x²2-2x-2

Answers

Answer:

x2

Step-by-step explanation:

x2

Which are true about the pyramid? Check all that apply.
The base of the pyramid is a square with four sides, each measuring 756 feet.
The slant height of the pyramid is 612 feet.
The slant height of the pyramid is 756 feet.
All four triangular faces are congruent.
All four triangular faces are not congruent.
The pyramid has four lateral faces.

Answers

The statements that are true about the pyramid are

The base of the pyramid is a square with four sides, each measuring 756 feet.The slant height of the pyramid is 612 feet.All four triangular faces are congruent.The pyramid has four lateral faces.

Properties of a Square pyramid

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

The length of a side of its base is 756 ft

and

The height / altitude of a triangular face is 612 ft

Since the pyramid is a square pyramid,

Then, the base must be a square with each side measuring 756 feet

∴ The first statement is true

Since the height of a triangular face is 612 ft,

Then,

∴ The slant height of the pyramid is 612 feet

NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face

Thus, the second statement is true

Since the triangular faces each have a base of 756ft and a height of 612 ft,

Then,

All four triangular faces are congruent

∴ The fourth statement is true

NOTE: Lateral sides of a solid are the faces on the sides of the shape

The pyramid has four lateral faces which are each a triangle

∴ The last statement is true

Hence, the statements that are true about the pyramid are

The base of the pyramid is a square with four sides, each measuring 756 feet.The slant height of the pyramid is 612 feet.All four triangular faces are congruent.The pyramid has four lateral faces.

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A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14. A hiker in Africa discovers a skull that contains 72 % of its original amount of C 14 .

Answers

If the 72% of its original amount of C-14. Then the number of years will be 3285.

The complete question is attached below.

What is an exponent?

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.

Then the function is given below.

[tex]\rm N= N_0 \ e^{-kt}[/tex]

Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.

[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]

We have N = 0.72N₀, the time will be

[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]

Take log on both side, then we have

ln 0.72 = -0.001 × t × ln e

  -0.33 = -0.001 × t

         t = 3285 years

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Consider the ordered pairs (1, 4), (–1, 2), and (0, 3). Which of the four equations below could have been used to generate these three ordered pairs? A. y = x + 3 B. y = –x – 6 C. y = – x + 3 D. y = – x – 3

Answers

The equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3

How to determine the equation?

The ordered pairs are given as:

(1, 4), (–1, 2), and (0, 3)

From the above ordered pairs, we can see that the difference between the x and y values is 3.

This means that:

y - x = 3

Add 3 to both sides

y = x + 3

Hence, the equation of the ordered pairs (1, 4), (–1, 2), and (0, 3) is y = x + 3

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What is the cosiner fade when the sign of fada equals 2/5

Answers

The value of cosine theta (cosθ) for the given triangle is determined as 4.58/5.

Complete side lengths of the triangle

For a given sine value of a triangle, the remaining side length of the triangle can be calculated as follows;

sinθ = opp/hypo = 2/5

opposite side = 2hypotenuse side = 5Adjacent side of the triangle

b² = 5² - 2²

b² = 21

b = 4.58

Value of cosine θ

Cosθ = adj/hypo

Cosθ = 4.58/5

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Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price Assuming that Hamids revenue is found by multiplying the book price by the number of copies sold, create an equation (in standard form) to model his revenue. This year Rafael has 60 regular customers which is 150 percent of the 40 regular customers he had last year. Which quadratic equation is equivalent to (x-4)2-(x-4) - 6 = 0? Which sentence contains a linking verb?Ulysses S. Grant, the Union general, helped the North win the Civil War.The battle of Antietam changed Union policy regarding participation in the war.Abraham Lincoln, a famous president during the Civil War, held a consistent view of an undivided Union.As the war progressed, General Robert E. Lee became increasingly concerned about invading the North. Suppose you just purchased a digital music player and put 6 tracks on it. After listening to it you decide you only like 2 songs. With the random feature on the player, each of the 6 songs is played once in random order. Find the probability that among the first 2 songs played A. You like both of themB. You like neither of themC. You like exactly 1 PLSSS HELP ITS DUE TODAY!!!Read the following passage from To Kill a Mockingbird, and then answer the question below:Before bedtime I was in Jems room trying to borrow a book, when Atticus knocked and entered. He sat on the side of Jems bed, looked at us soberly, then he grinned. Erhrm, he said. He was beginning to preface some things he said with a throaty noise, and I thought he must at last be getting old, but he looked the same. I dont exactly know how to say this, he began. Well, just say it, said Jem. Have we done something? Our father was actually fidgeting. No, I just want to explain to you thatyour Aunt Alexandra asked me... son, you know youre a Finch, dont you? Thats what Ive been told. Jem looked out of the corners of his eyes. His voice rose uncontrollably, Atticus, whats the matter? Atticus crossed his knees and folded his arms. Im trying to tell you the facts of life. Jems disgust deepened. I know all that stuff, he said. Atticus suddenly grew serious. In his lawyers voice, without a shade of inflection, he said: Your aunt has asked me to try and impress upon you and Jean Louise that you are not from run-of-themill people, that you are the product of several generations gentle breeding Atticus paused, watching me locate an elusive redbug on my leg. Gentle breeding, he continued, when I had found and scratched it, and that you should try to live up to your name Atticus persevered in spite of us: She asked me to tell you you must try to behave like the little lady and gentleman that you are. She wants to talk to you about the family and what its meant to Maycomb County through the years, so youll have some idea of who you are, so you might be moved to behave accordingly, he concluded at a gallop. Stunned, Jem and I looked at each other, then at Atticus, whose collar seemed to worry him. We did not speak to him. Presently I picked up a comb from Jems dresser and ran its teeth along the edge. Stop that noise, Atticus said. His curtness stung me. The comb was midway in its journey, and I banged it down.Question:Jem and Scout are not seen as living up to their status of a little lady and a young gentleman. Provide a piece of explicit evidence and a piece of implicit evidence to support this idea. Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5Which statements are true about a histogram with one-minute increments representing the data? Select three options.A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes.The histogram will have a shape that is left-skewed.The histogram will show that the mean time is greater than the median time of 7.4 minutes.The shape of the histogram can be approximated with a normal curve.The histogram will show that most of the data is centered between 6 minutes and 9 minutes.