When 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, what is the value of q? Show your work please.

Answers

Answer 1

Answer:

  q = 10

Step-by-step explanation:

The desired form is a rearrangement of the given equation, divided by the leading coefficient.

Monic polynomial

A monic polynomial is one with a leading coefficient of 1. The desired form requires that we start from that condition. In order to avoid fractions, we can begin by subtracting the constant term on the left.

  2x^2 -20x +49 = 19 . . . . . . given

  2x^2 -20x = -30 . . . . . . . . subtract 49

  x^2 -10x = -15 . . . . . . . . . divide by 2

Completing the square

The square of the binomial a+b is given by ...

  (x +b)^2 = x^2 +2bx +b^2

That is the constant term on the right is the square of half the coefficient of x. To achieve this perfect square trinomial in our equation, we need to add the square of half of -10.

  x^2 -10x +25 = -15 +25 . . . . . . add (-10/2)^2 = 25 to both sides

  (x -5)^2 = 10 . . . . . . . . . . . write in the desired form

The value of q in the form ...

  (x -p)^2 = q

is 10.


Related Questions

Use the diagram to answer the question

Line m is parallel to line p. M angle HEF IS 39 degrees. And m IGF is 13 degrees. Find the m EFG. Explain in detail how you know you are correct. I WILL MARK THE BRAINLIEST

Answers

Answer:

[tex]m\angle EFG=52^{o}[/tex]

Step-by-step explanation:

We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]

Upon substituting our given values we will get,

[tex]m\angle EFG=13^{o}+39^{o}[/tex]

[tex]m\angle EFG=52^{o}[/tex]

Therefore, measure of angle EFG is 52 degrees.

First twelve mulitples of 4

Answers

Answer:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

Step-by-step explanation:

4*1 = 4

4*2 = 8

4*3 = 12

and so on...

Answer:

4,8,12,16,20,24,28,32,36,40,44, and 48

Step-by-step explanation:

4*1=44*2=84*3=124*4=164*5=204*6=244*7=284*8=324*9=364*10=404*11=444*12=48

p(x)=x^2-x-6 q(x)=x-3 What is p(x)-q(x)

Answers

Answer:

[tex]x^{2} -2x-3 or the factored form (x+1)(x-3)[/tex]

Step-by-step explanation:

p(x) -q(x)=

[tex]x^{2} -x-6-x+3\\=x^{2} -2x-3[/tex]



6a. Suppose you need to find a box that you can fit your cube-shaped gift into. You know that you will need to find a box that is 4 inches longer than the cube’s length, 3 inches wider than the cube’s width, and 7 inches taller than the cube’s height. Create a polynomial that represents the gift box’s volume in terms of the cube’s length/width/height, in factored and standard form

Answers

Answer:

( l + 4) * ( w + 3 ) * ( h + 7)

let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.

Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.

( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )

6 * 5 * 9 = 270

(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)

Answer:

V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84

Step-by-step explanation:

Let x = the side of the cube

Then the dimensions of the gift box are

l   = x + 4

w = x + 3

h = x+ 7

V = lwh

V = (x+ 4)(x + 3)(x + 7)     Multiply the first two terms

V = (x² + 7x + 12)(x+ 7)     Remove parentheses

V = x³ + 14x² + 61x + 84

Question 3(Multiple Choice Worth 5 points) (06.08A) Simplify negative 15.5 divided by 5 .. −3.1 3.1 −3.3 3.3

Answers

A negative divided by a positive gives a negative result

So the answer is -3.1

Hope this helps!

Answer: -3.1

this was correct on my test, hope it helps! ;)

(Brainliest would help a lot btw)

Wells college Aurora New York Was previously an all girls college.In 2005 the college began to allow boys to enroll.By 2012 The ratio of boys to girls was 3 to 7. If there were 200 more girls than boys in 2012 how many boys in enrolled that year

Answers

Answer:

150

Step-by-step explanation:

The ratio of boys to girls is 3 to 7.

We don't know the number of boys or girls. The number of boys and the number of girls are multiples of 3 and 7, respectively. Since they are in the ratio of 3 to 7, then by multiplying both 3 and 7 by the same number, you will get the number of boys and the number of girls. We need to find that number. Call that number x.

The ratio of boys to girls is:

3x to 7x

There are 3x boys and 7x girls.

The number of girls is 200 more than the number of boys.

7x = 3x + 200

Subtract 3x from both sides.

4x = 200

Divide both sides by 4.

x = 50

The number of boys is 3x, so

3x = 3(50) = 150

150 boys and 350 girls were enrolled that year.

Since a college was previously an all girls college, and then it began to allow boys to enroll, and by 2012 the ratio of boys to girls was 3 to 7, to determine, if there were 200 more girls than boys in 2012, how many boys were enrolled that year, the following cross multiplication calculation must be performed:

7 - 3 = 200 3 = X 4 = 200 3 = X 3 x 200/4 = X 600/4 = X 150 = X 150/3 = 50 (150 + 200) / 3 = 50

Therefore, 150 boys and 350 girls were enrolled that year.

Learn more in https://brainly.com/question/13904768

Which expressions are equivalent to -6n+(-12)+4n

Answers

Answer:

-2n - 12

Step-by-step explanation:

Combine like terms. Note that each term has one variable (n). Also note  that one negative sign and one positive sign results in a negative sign.

-6n + (-12) + 4n = -6n  + 4n - 12 = -2n - 12

-2n - 12 is your answer

~

Answer:

A

Step-by-step explanation:

4(n-3)-6n

Jane moved from a house with 58 square feet of closet space to an apartment with 29.58 square feet of closet space. What is the percentage decrease of Jane's closet space? A. 96% B. 39% C. 49% D. 51% R

Answers

You would take the answer of 29.58 divided by 58 to get 51%. 51% is how much of the new closet space of the old one. you would then subtract 51% from 100% to find your answer. your answer would be (C) a 49% decrease.

Three times the sum of a number and 2 is the same as the number minus 4

Answers

Answer:

3* ( n+2) = n-4

n=-5

Step-by-step explanation:

Three times the sum of a number and 2 is the same as the number minus 4

3* ( n+2) = n-4

Distribute

3n +6 = n-4

Subtract n from each side.

3n-n +6 =n-n-4

2n +6 = -4

Subtract 6 from each side.

2n +6-6 = -4-6

2n = -10

Divide by 2 on each side.

2n/2 = -10/2

n = -5

The perimeter of a rectangle is 34 units. Its width is 6.5 units. Write an equation to determine the length of the rectangle.

Answers

Answer:

The length for a rectangle with a perimeter of 34 units and a width of 6.5 units would be 10.5 units.

Step-by-step explanation:

To find the length, you can use the equation [34 - (6.5 x 2) ÷ 2 = the length]. So, 6.5 x 2 = 13, then 34 - 13 = 21, finally, 21 ÷ 2 = 10.5 . So the length of the rectangle is 10.5 . To double check, (6.5 x 2) + (10.5 x 2) (=) 34. So this answer is correct.

20 Points!! Will give Brainliest!!! Need Help ASAP!!! PLzz!!

Ray knows that the m<3 = m<6.

Which of the following conclusions can Ray make based on the given information?
A. Lines l and m are parallel because alternate interior angles are equal.
B. Lines l and m are parallel because alternate exterior angles are equal.
C. Lines l and m are parallel because corresponding angles are equal.
D. No conclusion can be made about the lines.

Answers

Answer:

The answer is B

Step-by-step explanation:

3 and 6 are alternate exterior angles which make lines l and m parallel.

Answer: c

Step-by-step explanation:

A shopper wants to ensure he has enough cash to purchase a $59 coffee table, so he asks a clerk what the total will be with the sales tax included. The clerk tells him the total will be $61.36. What is the sales tax percentage?

Answers

Answer:


Step-by-step explanation:

First you have to subtract 59$ from 61.36 which will give you 2.36.Then you have to multiply 0.02 to 59 which equals 1.18.Then you multiply 0.04 by 59 which will give you the answer.Hope this helps!!!Your answer should be 0.04!!!Please Mark brainliest!!!!!

Final answer:

To find out the sales tax percentage, first find the amount paid in taxes by subtracting the original price from the total price. Then divide this tax amount by the original price and multiply by 100 to get the percentage, which is 4% in this case.

Explanation:

To determine the sales tax percentage charged on the coffee table, we first calculate the total amount of sales tax paid. We subtract the original price of the table ($59) from the total amount paid with tax ($61.36) to find the amount of tax paid.

$61.36 - $59.00 = $2.36

Now, we'll convert the sales tax into a percentage of the original price. We do this by dividing the sales tax amount by the original price and then multiplying by 100 to get the percentage.

$2.36 ÷ $59 = 0.04 (rounded to two decimal places)

0.04 × 100 = 4%

Therefore, the sales tax percentage on the coffee table is 4%.

Learn more about Sales Tax Calculation here:

https://brainly.com/question/18375545

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30 points!!! Plzz help!!! Will give Brainliest!!!! Need help ASAP!!!!

Using the diagram shown, select all that apply to the pair of angles, 1 and 2.
A. acute
B. right
C. obtuse
D. adjacent
E. vertical
F. complementary
G. supplementary

Answers

B. Right (they are 90° angles)
D. Adjacent (they share sides)
G. Supplementary (the total of the 2 angles is 180°)

Answers for m1 m2 m3

Answers

Answer:

<1 = 30

<2= 41

<3 = 96

Step-by-step explanation:

 Angle 1  ,66 and 84 form a triangle and triangles add to 180 degrees

<1 + 66 + 84 = 180

Combine like terms

<1 +150 = 180

Subtract 150 from each side

<1 + 150 -150 = 180-150

<1 = 30


Angle 3 and 84 form a straight line.  A straight line is 180 degrees.

<3 + 84  =180

Subtract 84 from each side

<3 +84-84 = 180 - 84

<3 = 96



<2 , <3 and 43 form a triangle which adds to 180 degrees,

<2 + <3 + 43 = 180

We have already found <3 to equal 96 degrees

<2 + 96+43 = 180

Combine like terms

<2 +139=180

Subtract 139 from each side.

<2 +130-139 = 180-139

<2 = 41

which property is used to simplify the expression 5+(6+-6)=5+0

additive inverse property

additive identity property

associative property of addition

commutative property of addition

Answers

Answer:

additive inverse property

Step-by-step explanation:

which property is used to simplify the expression 5+(6+-6)=5+0

additive inverse property

x+-x = 0

additive identity property

0+8=8

associative property of addition  

a+(b+c) = (a+b)+c

commutative property of addition

a+b=b+a

Answer: additive inverse property

Step-by-step explanation: i looked it up lol

solve this please PLZ PLZ PLZ ITS REALLY EASY!!!

Answers

Answer: 169.56

Step-by-step explanation:

A = r²θ

r = 6θ = 270° = [tex]\frac{3\pi}{2}[/tex]

A = (6)²[tex](\frac{3\pi}{2})[/tex]

   = 36[tex](\frac{3\pi}{2})[/tex]

   = 18(3π)

   = 54π

   ≈ 169.56

solve for x -3x+6=2x-24

-30

-6

6

30

Answers

-3x + 6 = 2x - 24.

Add 3x to both sides.

6 = 5x - 24.

Add 24 to both sides.

30 = 5x.

Divide it all by 5.

x = 6.

Which tables represent constant functions?

Answers

A function is a law that tells you how to associate inputs (x values) and outputs (y values).

In the case of constant functions, it doesn't matter which input you choose, the ouput must always be the same.

So, a constant function has always the same output (y values) for every input (x values) you feed.

Answer:

Third and last choices represent constant functions.

Step-by-step explanation:

A constant function refers to those functions that only have one variable, which is constant. For example, x=2, y=4, x=-1, are constant function, because they don't variate.

From the given tables, the third and last choices are constant function, because you can observe that one variable doesn't variate. The third function has y=3 as the constant value, and the last table has y=-1 is the constant function.

Therefore, the right choices are third and last table.

Aria walked down a trail into a valley. V(d) models Aria's vertical distance from the top of the valley (in kilometers) after walking d kilometers along the trail. What does the statement V(3)<3 mean?

Answers

Answer:

When Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3 km

Step-by-step explanation:

Remember that V(d) denotes Aria's vertical distance from the top of the valley V after she has walked d kilometers along the trail.

This means that V(3) is Aria's vertical distance from the top of the valley after she has walked 3km.

Therefore, V(3)<3 means that Aria's vertical distance from the top of the valley after she has walked 3km, is less than 3km

In other words, the statement means that when Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3km

V(3) < 3 means Aria's vertical distance from the top of the valley is less than 3 kilometers after walking 3 kilometers along the trail. It shows her descent into the valley is not more than 3 kilometers vertically at that point.

The inequality V(3) < 3 means that after Aria has walked 3 kilometers along the trail, her vertical distance from the top of the valley is less than 3 kilometers. In other words, Aria has descended into the valley, but her descent after 3 kilometers along the trail is not greater than 3 kilometers vertically. This provides a way to understand her position relative to the top of the valley based on the distance she has walked.

You can spend at most $10 at the mall. You want to buy a book that costs $6.75 and a cold drink. Write and solve an inequality to represent the amount of money you can spend on your cold drink.


Plzz Hellp me!!!;(

Answers

Answer:

the amount of money you can spend on the drink is no more than 3.25

Step-by-step explanation

total is greater than/equal to cost of book plus cost of drink

10>/=6.75+x (x represents the drink)

x</=3.25

Answer: 10.00-6.75=find out yourself, EASY


Step-by-step explanation:

Since you have 10 dollars and you find a book and a cold drink for all 6.75

you will need to subtract the numbers to find your answer



Which lines are parallel if m angle 1= m angle 2 ?

Answers

Heya!!!


Answer to your question:

A) line m is parallel to line n;by the converse of corresponding angles postulate.


Hope it helps *_*
Yes that’s it your doing good

how do the graphs of the function f(x)=(3/2)x and g(x)=(2/3)x compare

Answers

Answer:

f is a line through 0 and (2,3)

g is a line through 0 and (3,2)

Step-by-step explanation:

f and g are proportional linear functions. They each have the form y=mx+b where b=0 and m is a fraction. The m or slope tell us the form the function takes on the graph. It is a straight line through 0 with steepness m.

[tex]f(x)=\frac{3}{2} x[/tex] has steepness 3/2. Starting at (0,0) or the origin, move up three grid lines on the y-axis and then over 2 grid lines. Mark your point at (2,3). Then connect and draw arrows on the end.


[tex]g(x)=\frac{2}{3}x[/tex] has steepness 2/3. Starting at (0,0) or the origin, move up two grid lines on the y-axis and over 3 grid lines. Mark your point at (3,2). Then connect and draw he arrows on the end.

Answer:

The graphs are reflections of each other over the y-axis. The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth.

Step-by-step explanation:

what is another way to write the expression P x (10 - 2)

A. 10 x 2 - P
B. (10 x 2) x P
C. (P x 10) - (P x 2)
D. (10 x 2) - P

Answers

C is the answer because if you distributed the P separately to each term (10 and -2) you would get 10P and -2P

The complement of an angle is 53 degrees. What is the measure of an angle?

Answers

37. complementary angles always add up to 90. just subtract 57 from 90 and you get 37.

which property is used below?

Distributive property
multiplication property of inequality
Subtraction property of inequality
Associative property of multiplication

Answers

Answer:

multiplication property of inequality

Step-by-step explanation:

-1/3 x - 2/3 ≥ 7x+3

We can multiply by 3 on each side to clear the fraction by the Multiplication property of inequality

Since c>0

and a≥b

ac ≥ bc


(WILL GIVE BRAINLIEST)Find the polynomial function with real coefficients that has zeros 1, 1 , 2+ i sqrt 3

Answers

Answer:

[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]

Step-by-step explanation:

We have given that this polynomial has the given zeroes of 1, 1, and [tex]2+i\sqrt{3}[/tex], we can express the polynomial in a factored form where each zero has the form x-a (where a is our zero):

polynomial= [tex](x-1) (x-1) (2+i\sqrt{3})[/tex]

                  =[tex](x^2+1-2x) (2+i\sqrt{3})[/tex]

                   =[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]

Find the slope of:2y+8x=6

Answers

Answer:

-4

Step-by-step explanation:


The slope of the line given by the equation 2y + 8x = 6 is -4. This was found by converting the equation into slope-intercept form, y = mx + b.

To find the slope of the equation 2y + 8x = 6, we first need to convert it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Start with the given equation: 2y + 8x = 6Isolate y by subtracting 8x from both sides: 2y = -8x + 6Divide everything by 2 to solve for y: y = -4x + 3In the slope-intercept form y = -4x + 3, the coefficient of x is the slope -4.

Therefore, the slope of the line is -4.

Nathan took his car in for service and repairs. He had a coupon for 10% off. Original Prices • Labor $218.97 • Parts $303.47 • Other $77.78 Which amount is closest to Nathan's total costs after the 10% discount and including 6% sales tax? [Assume tax is applied after the discount is applied.] A. $573 B. $508 C. $540 D. $504

Answers

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

218.97 + 303.47 + 77.78 = $600.22

600.22 x .10 = 60.02 (amount of discount)

600.22 - 60.02 = $540.20 (amount he owes)

Answer is C

Answer:The answer should be D


Step-by-step explanation:


The length of a rectangular garden is represented by 3x-4 and the width is represented by 2x-5. Which of the following represents the total area of the garden

Answers


Both of them.

(3x-4) × (2x-5)
6x^2-15x-8x-20
6x^2 - 23x - 20 = area

The options are

a.) 5x - 9

b.) 6x + 20

c.) 6x²- 23x + 20

d.) 6x²-14x - 9

Answer:

c.) 6x²- 23x + 20

Step-by-step explanation:

Rectangle area can be computed as length × width . The garden is a rectangle so the area can be computed by multiplying the length and the width.

Area= L × W

Length = 3x - 4

width = 2x - 5

Area = (3x - 4)(2x - 5)

Area = 3x(2x) + 3x(-5) -4(2x) -4(-5)

Note : - × - = +

Area = 6x² -15x - 8x + 20

Area = 6x² - 23x + 20

Gary ordered 30 pizzas for a party. 60% of the pizzas have 12 slices each. The remaining 40% of the pizzas have 10 slices each. Complete the model. Then complete the statements to find the total number of slices of pizza.

Answers

Answer:

60% of 30 is 18 and 40% of 30 is 12

18 x 12 = 216

12 x 10 = 120

216 + 120 = 336

Step-by-step explanation:


Answer: IN ORDER: 18,12,216,120,336

Step-by-step explanation: Got it right on TTM

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