What is the intermediate step in the form (x + a)2 = b as a result of completing the
square for the following equation?
5x2 – 168 = -60x + 12

Answers

Answer 1

Answer:

5x2 – 168 = -60x + 12

5x*2 – 156 = -60x

-55x*2=156

55x=-78

x=-1.41818181818

also know as 18/7 or 1 4/7

Answer 2

Answer:

[tex](x+6)^{2}[/tex] = 51

Step-by-step explanation:

5x2 – 168 = -60x + 12

5x2  + 60 x – 180 = 0

[tex]x^{2}[/tex]  + 12 x – 15 = 0

[tex]x^{2}[/tex]  + 12 x   = 15

        + 36      + 36

[tex]x^{2}[/tex]  + 12 x  + 36  =  51

[tex](x+6)^{2}[/tex] = 51

[tex]\sqrt{(x+6)^{2} }[/tex] = [tex]\sqrt{51}[/tex]

x + 6 =  [tex]\sqrt{51}[/tex]

x   = -6 ± [tex]\sqrt{51}[/tex]


Related Questions

how do u factor..
x^2 + 10× - 2400 = 0 ​

Answers

Answer:

[tex]{ \bf{ {x}^{2} + 10x - 2400 = 0}} \\ { \bf{ \red{it \: has \: no \: rational \: factors}}} \\ x = - 54.2 \: \: and \: \: 44.2[/tex]

x^2+10•-2400=0
x^2-24000=0
x^2=24000
take the square root of 24000

show the solution 3×(2÷3)^3+(2÷3)^2−20×2÷3+12​

Answers

Answer with Step-by-step explanation:

We are given that

[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]

[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]

[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]

[tex]\frac{4-40}{3}+12[/tex]

[tex]-\frac{36}{3}+12[/tex]

[tex]-12+12[/tex]

[tex]=0[/tex]

(x+1)^2 . (x^2+1) = 0

Answers

Answer:

[tex]x^4+2x^3+2x^2+2x+1[/tex]

Step-by-step explanation:

Given that,

[tex](x+1)^2 . (x^2+1) = 0[/tex]

We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]

So,

[tex](x+1)^2=x^2+1+2x[/tex]

So,

[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]

So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]

The average of 7 numbers is 45.If the last two numbers are 27 and 43 what is the average of the first five

Answers

Answer:

49

Step-by-step explanation:

The average is calculated as

average = [tex]\frac{sum}{count}[/tex] Given the average of 7 numbers is 45 , then

[tex]\frac{sum}{7}[/tex] = 45 ( multiply both sides by 7 )

sum of 7 numbers = 315

Subtract 27, 43 from the sum to obtain the sum of first 5 numbers

315 - (27 + 43) = 315 - 70 = 245 , then

average of first 5 numbers = [tex]\frac{245}{5}[/tex] = 49

The product of two integers is (-112).
If one of them is (-8), find the other.​

Answers

[tex]\huge\bold{Given :}[/tex]

Product of two integers = - 112

One of the integer = -8

[tex]\huge\bold{To\:find :}[/tex]

The other integer.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\blue{The \:other \:integer\:is\: 14.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Let the other integer be [tex]x[/tex].

As per the question, we have

[tex]Product \: \: of \: \: two \: \: integers = - 112[/tex]

➼ [tex] \: - 8 \times x = - 112[/tex]

➼ [tex] \: x = \frac{ - 112}{ - 8} [/tex]

➼ [tex] \: x = 14[/tex]

[tex]\sf\purple{Therefore,\:the\:other\:integer\:x\:is\:14.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex] - 8 \times 14 = - 112[/tex]

➺ [tex] \: - 112 = - 112[/tex]

➺ L. H. S. = R. H. S

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

If the product of two integers is -112 and one of them is -8, that means the value of the second integer would be 14.

Step-by-step explanation:

The product of two integers equals -112 means that there are two numbers that, when multiplied, were equivalent to -112. Since you know one of the integers is -8, you can infer that the second integer is both a positive number AND the remainder of [tex]\frac{-112}{-8}[/tex] or 14.

Select all the correct answers.
Which expressions are equivalent to the given expression?

Answers

Answer:

6√7=15.874507866387543=√252

Step-by-step explanation:

hope this is helpful

The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.

How to find equivalent expression?

Applying the surd rule,

√a = [tex]a^{\frac{1}{2} }[/tex]

Hence,

[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]

using surd rule, we can also decompose √252

Therefore,

√252 = √36 × 7 = 6√7

Hence, the equivalent expression of √252 are as follows:

[tex]252^{\frac{1}{2} }[/tex]6√7

learn more on expression here: https://brainly.com/question/27768447

#SPJ2

Select the fraction greater than 7/9. a)4/5 b)2/3 c)13/18 d)3/5

Answers

Answer:

A)4/5

Step-by-step explanation:

7/9=0.778

so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.

a)4/5=0.8

b)2/3=0.667

c)13/18=0.722

d)3/5=0.6

The decimal that's greater than 0.778 is A=0.8 so that's the answer.

6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.

Answers

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]

Then

[tex]a_n = a_1q^{n-1}[/tex]

[tex]a_n = 17.5(0.7)^{n-1}[/tex]

First 5 terms:

[tex]a_1 = 17.5[/tex]

[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]

[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]

[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]

[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]

Find the total distance the ball has travelled after it hits the ground the 5th time.

[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Which of the following is true of the discriminant for the graph below

Answers

Answer:

Step-by-step explanation:

The discriminant is used to determine the number and nature of the zeros of a quadratic. If the discriminant is positive and a perfect square, there are 2 rational zeros; if the discriminant is positive and not a perfect square, there are 2 rational complex zeros; if the discriminant is 0, there is 1 rational root; if the discriminant is negative, there are no real roots.

The roots/solutions/zeros of a quadratic are where the graph goes through the x axis. Those are the real zeros, even if they don't fall exactly on a number like 1 or 2 or 3; they can fall on 1.32, 4.35, etc. They are still real. If the graph doesn't go through the x-axis at all, the zeros are imaginary because the discriminant was negative and you can't take the square root of a negative number. As you can see on our graph, the parabola never goes through the x-axis. Therefore, the zeros are imaginary because the discriminant was negative. Choice C.  Get familiar with your discriminants and the nature of quadratic solutions. Your life will be much easier!

Given: x+y=10

If x= -21, what is y?
Type a numerical answer in the space provided. Do not type spaces in your answer

Answers

Answer:31

Step-by-step explanation:

Answer:

y=31

Step-by-step explanation:

-21 + y= 10

-21 + y + 21 =10 + 21

y = 10+21

y = 31

HOPE THIS ANSWER HELPS YOU :)))

Mary is making a recipe that calls for 3/4 teaspoon of cinnamon. Her only
measuring spoon holds 4/8 teaspoon. How many times will she need to fill
her measuring spoon to get enough cinnamon for the recipe?

Answers

Answer:

She will need to fill her spoon twice, once adding in the full amount, and the second adding half the amount.

3/4  ÷ 4/8

=3/4 * 2/1

=6/4

=1.5

So, that much amount would be needed o be added to the recipe during the two times

17. Find the area of a triangle whose base is 6 cm and height is 8 cm.
48 square cm
24 square cm
48 cm
24 cm

Answers

Answer:

24 square cm

Step-by-step explanation:

Answer:

48cm

Step-by-step explanation:

Because 6 times 8= 48cm

what is the distance from the origin to point A graphed on the complex plane below

Answers

Answer:

√13

Step-by-step explanation:

d² = (-3)² + (-2)²

d² = 9 + 4

d² = 13

d = √13

(5+6b^3)^2 expand and combine like terms

Answers

Answer:

[tex]( 5 + 6b^3)^2 = 36b^6 + 60b^3 + 25[/tex]

Step-by-step explanation:

[tex](a + b)^2 = a^2 + b^2 + 2ab[/tex]

So,

        [tex](5 + 6b^3)^2 = (5)^2 + (6b^3)^2 + 2 (5)(6b^3)[/tex]

                       [tex]= 25 + 36b^6 + 60b^3[/tex]

What is the average rate of change of f
over the interval (-5,0]?
Give an exact number.

Answers

Answer:

Average rate of change = 0.6

Step-by-step explanation:

Average rate of change of a function between x = a and x = b is given by,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

From the graph attached,

f(-5) = 0

f(0) = 3

Average rate of change of the graph between x = -5 and x = 0,

Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]

                                        = [tex]\frac{3}{5}[/tex]

                                        = 0.6

Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.

Solve for X
I’ll give BRAINLIEST to the correct answer

Answers

Answer: x = 19

Hi! I was studying for the NYC SHSAT when this exact problem came up a year ago. I will do my best to try to answer it correctly!

Step-by-step explanation:

To start, we have to notice the similar properties of the angles. They are alternate exterior angles (?). Therefore, I think that you just have to put the angles on opposite sides of the equation!

(6x + 6) = 120

-6              -6

6x/6 = 114/6

x = 19

Mr. Brown has a gate that measures 65 ft by 72 ft. He needs to reinforce the gate by placing a strip of wood on the diagonal of the fence. How long will the strip of wood need to be? ​

Answers

97ft
Please mark brainliest!

given that x^2+y^2=9 and xy=5, find the value of (x - y)^2. ​

Answers

Answer:

[tex](x -y)^2 = -1[/tex]

Step-by-step explanation:

[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]

           [tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]

Solution:

The binomial expansion of (x - y)² is

(x - y)² = x² - 2xy + y²

Substitute the given values to the equation

(x - y)² = x² - 2xy + y²

(x - y)² = x² + y² - 2xy

(x - y)² = 9 - 2(5)

(x - y)² = 9 - 10

(x - y)² = -1

Therefore the value of (x - y)² is -1.

#ILoveMath

#ILoveYouShaina

Line CD passes through points C(1,3) and D(4,-3). What is the equation of line CD in standard form?

Answers

(1,3) means x1 = 1 and y1 = 3
(4,-3) means x2 = 4 and y2 = -3

To find slope:
(y2-y1) / (x2-x1)
(-3-3) / (4-1)
-6 / 3
Slope is -2

To find intercept:

y-y1 = m(x - x1)
y - 3 = -2(x - 1)
y - 3 = -2x + 2
y = -2x + 5 :)

Answer:

2x + y = 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = C (1, 3) and (x₂, y₂ ) = D (4, - 3)

m = [tex]\frac{-3-3}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 3 )

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = - 2x + 5 ← equation in slope- intercept form

Add 2x to both sides

2x + y = 5 ← equation in standard form

How many quarters are there in 5 3/4?

Answers

Answer:

One quarter= 1/4

5 3/4= 23/4

Number of quarters in 5 3/4= 23/4 divided by 1/4

23/4 ÷ 1/4

= 23/4 × 4

=23

I hope this helps!

Answer:

23

Step-by-step explanation:

5x4 + 3

5 x 4 = 20

20 + 3 (3 Is the fraction part)

3
2
In the diagram above, Z3 = 40°.
Find the measure of Z2.
L2 = [?]°

Answers

40, by alternate interior angles

I don't really understand it's due soon can someone please help me​

Answers

Answer:

60

Step-by-step explanation:

Given: 1/2a + 2/3b =50

(Since b is equal to 30 we will automatically replace b with 30)

Step 1: Simplify both sides of the equation.

1/2a+20=50

Step 2: Subtract 20 from both sides.

1/2a=50-20

1/2a=30

Step 3: Multiply both sides by 2.

2(1/2a) 2(30)

a=60

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

a = 15

Step-by-step explanation:

1/2(a) + (2/3 x 30) = 50

2/3 x 30 = 20

1/2(a) + 20 = 50

Rearrange > 20 to -20

-20 + 50 = 30

1/2(a) = 30

Rearrange 1/2 to 2

2 > 30/2

30/2 = 15

a = 15

Hope this helps, and please let me know if it is correct or isn't.

Have a nice day

Find the solutions to 8x2 + 56x = 0. Check all that apply.

A. X = 8

B. x = 0

C. X = -7

D. X = 7​

Answers

Answer:

B and C

Step-by-step explanation:

fjdjjsngbsnsjf x

HELP? I WILL MARK BRAINIEST!!! Yuson must complete 15 hours of community service. She does 3 hours each day. Which linear equation represents the hours Yuson still has to work after x days?
Answer: y = 3x – 15
For the graph of the equation you wrote in Part A, what does the y-intercept represent?
A. Hours of community service completed each day
B. Hours of community service still to complete
C. Total hours of community service that must be completed
D. Days it takes to complete 15 hours of community service

Answers

Answer: C

Step-by-step explanation:

Can somebody pls help !!

Answers

$26.84

Hope this helps!!

Answer:

$26.84

Step-by-step explanation:

We have to find 10% of 268.40. To do that, we multiply it by 0.10:

268.40 * 0.1 = 26.840, or $26.84

doe anyone know this

Answers

The answer is blue if you spin 30 times

What is the difference of the rational expressions below? 4/x^3 - 2x-1/3x

Answers

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{4}{x^3}[/tex] - [tex]\frac{2x-1}{3x}[/tex]

Multiplying the numerator/ denominator of the first fraction by 3 and the numerator/denominator of the second fraction by x² will ensure that the fractions have a common denominator.

= [tex]\frac{3(4)}{3x^3}[/tex] - [tex]\frac{x^2(2x-1)}{3x^3}[/tex]

= [tex]\frac{12}{3x^3}[/tex] - [tex]\frac{2x^3-x^2}{3x^3}[/tex] ← combine terms on numerator

= [tex]\frac{12-2x^3+x^2}{3x^3}[/tex]

= [tex]\frac{-2x^3+x^2+12}{3x^3}[/tex] → C

In order for the parallelogram to be a
rhombus, x = [?].
(5x - 8°
(2x + 16)°

Answers

Answer:

8

Step-by-step explanation:

5x-8 = 2x+16

Move 2x to the left side and you get 3x-8 = 16

Move -8 to the right side and you get 3x = 24

Divide 3 on both sides and you get x = 8

If f(1) = 2 and f(n) = f(n − 1)2 + 3 then find the value of f(3).

Answers

Answer:

52

Step-by-step explanation:

f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into

f(n-1)²+3 to get

f(1)²+3 = 2²+3 = 4+3=7

Thus, f(2) =7. Similarly,

f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52

What they mean by 1/2? I mean I do know that 1/2 means half, but what they mean?​

Answers

Step-by-step explanation:

See you know the area of rectangle that is base x perpendicular

When you cut half the area of rectangle, it becomes a triangle

That is why the formula is 1/2 x base x perpendicular

Other Questions
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