Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x

Answers

Answer 1
x^2 - 6x = -5

To complete the square we are going to rewrite the equation to a quadratic equation in the form:

ax² + bx + c

To do this we are going to transpose.

x² - 6x = -5
x² - 6x + 5 = 0

Now we are going to rewrite the new equation in the form


a(x + h)² + k

Where a = 1
h = 6x
k = 5


1(x² - 6x) + 5 = 0
1(x² - 6x/2 + 3²) + 5 = 0, to find h, divide it by 2 then square the quotient and add it to the equation.

1(x² - 3x + 9) + 5 - 9 = 0, to find k, subtract the square rooted quotient after multiplying it by a.

1(x - 3)²- 4 = 0

Now we solve.

1(x - 3)² - 4 = 0
1(x - 3)² = 4
±√1(x - 3)² = ±√4
(x - 3) = √4 or (x - 3) = -√4
x = 5 or x = 1





Related Questions

what is 300+45-9x2+22-1+2

Answers

Answer:

350

Step-by-step explanation:

Use PEMDAS.

[tex]300+45-9*2+22-1+2[/tex]

300+45-18+22-1+2

345-18+22-1+2

327+22-1+2

349-1+2

348+2

350

The camping group has 24 ppl in all 21 out of 24 would like a s’more it takes 1 min and 30 sec to make each one if two ppl are making them at the same time how long will it take to make one for each person

Answers

Answer:

16 minute 30 seconds

Step-by-step explanation:

1 minute 30 seconds = 1.5 minutes

1.5 x 21 = 31.5 minutes

One person will make 10, one person makes 11.

11

11× 1.5 = 16.5

10× 1.5 = 15

16.5 is the answer

16.5 is the number that would be the correct answer to your question

What is the radius of a circular swimming pool with a diameter of 20 feet?

Answers

Answer:

10 feet

Step-by-step explanation:

The half of 20 is 10. So, hence it is 10 feet.

The radius of a circular swimming pool with a diameter of 20 feet will be 10 feet.

What is a circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Assume 'r' is the radius of the circle and 'd' is the diameter of the circle.

The radius of the circle is half of the diameter of the circle. Then the equation is given as,

r = d / 2

The diameter of the swimming pool is 20 feet. Then the radius of the swimming pool is given as,

r = 20 / 2

r = 10 feet

The radius of a roundabout pool with a measurement of 20 feet will be 10 feet.

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ2

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In the diagram below of triangle MNO, P is the midpoint of MO and Q is the
midpoint of NO.If PQ = 49 – 8x, and MN = 41 + 3x, what is the measure of
MN?
O
N
P
M M

Answers

Answer:

MN = 50

Step-by-step explanation:

Given:

PQ = 49 – 8x

MN = 41 + 3x

Required:

Measure of MN

Solution:

PQ = ½(MN) => Mid-segment theorem of a triangle

Substitute

49 - 8x = ½(41 + 3x)

Multiply both sides by 2

2(49 - 8x) = 41 + 3x

98 - 16x = 41 + 3x

Collect like terms

98 - 41 = 16x + 3x

57 = 19x

57/19 = 19x/19

3 = x

x = 3

Find MN:

MN = 41 + 3x

Plug in the value of x

MN = 41 + 3(3) = 41 + 9

MN = 50

who is the president of Uganda​

Answers

Who is the president of Uganda?

Answer: Yoweri Museveni

☆彡Hanna
Yoweri Museveni is the president of Uganda

which term in the quotient of this expression contains an error?

Answers

Answer:

The + 78 :-  it should be + 60.

Step-by-step explanation:

Long division:-

x - 3 )4x^4 - 6x^3 + 0x^2 + 6x + 3 ( 4x^3 + 6x^2 + 18x + 60 <--- Quotient.

         4x^4 - 12x^3

                      6x^3 + 0x^2

                       6x^2 - 18x^2

                                   18x^2 + 6x

                                    18x^2 - 54x

                                                 60x + 3

                                                  60x - 180

                                                              183

What is the value of log √10?

Answers

Answer:

0.5

Step-by-step explanation:

Answer:

.5

Step-by-step explanation:

calculator

Work out the equation of the line which passes through the point (-1,2)
and is parallel to the line y = x + 4.

Answers

Answer:

m = 1 (since the gradient of parallel lines is the same)

Then substitute point (-1;2)

C = 3

y = x+3

Could I get help with this? Thank you

Answers

Answer:

Equation: [tex]y=-\frac{5}{4} x[/tex]

Slope: [tex]-\frac{5}{4}[/tex]

Point: [tex](-4,5)[/tex]

Step-by-step explanation:

To find the slope, you need two points [tex](-4,5)[/tex] and [tex](0,0)[/tex].

Then use the Slope Formula to Identify the slope.

M = Slope

M = [tex]\frac{y2-y1}{x2-x1}[/tex]         Second y being subtracted by the first y / the second x being subtracted by the first x.

M = [tex]\frac{0-5}{0--4}[/tex]          Plot the x and y values (In order) Then subtract

M = [tex]\frac{-5}{4}[/tex]             Move the negative sign

M = [tex]-\frac{5}{4}[/tex]

Slope = [tex]-\frac{5}{4}[/tex]

Then the Equation has to be written in Slope-Intercept Form (y=mx+b)

y = [tex]-\frac{5}{4} x[/tex]

As shown in the diagram below, AABC - A DEF, AB=14, BC=4, DE=7, and EF = X
D
14
B
4
С
E
X
F
What is the length of EF?
А
28
B
14
2
4

Answers

Answer:

EF=4

Step-by-step explanation:

vì diện tích bằng nhau và bằng 28 áp dụng công thức tính diện tích

PLEASE HELP!!!! WHOEVER GETS IT RIGHT GETS BRAINLIEST !!!!

FIND THE VALUE OF X

Answers

Answer:16 degree is the answer.

Since r and m are parallel:

10x-3=7x+45

3x=48

x=16

What is an equation that represents the line that passes through the points (1, 1) and (-2, 7)?

Answers

Answer:
Not sure if this is correct but I hope this helps :)

Find y if the distance between
points P and R is 25 and point R
is located in the first quadrant.
p= (3,-18) r=(10,y)

Answers

Answer:

y = 6

Step-by-step explanation:

[tex]\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\[/tex]

y^2 + 36y - 252 = 0

(y-6)(y+42) = 0

y = 6 (accettable)

y = -42 (not accettable)

Use the expression below to answer the question.

6n(19−8)÷3=22
In describing the expression, which term would not be used?



a.difference

c.product

b.sum

d.quotient

Answers

Answer:

b sum

Step-by-step explanation:

Translate to an algebraic expression.

The difference of five times a number and two

Answers

Algebraic expression: 5n-2

The school newspaper surveyed 100 commuter students and asked three questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. And third, they were asked their heights. Identify the type of random variable being measured by each.

Answers

Answer:

The number of courses they were currently enrolled in is a discrete random variable.

The time it took them to drive to campus is a continuous random variable.

Their heights is a continuous random variable.

Step-by-step explanation:

Random variables:

Random variables can be classified as continuous or discrete.

Discrete variables are countable numbers(0,1,2,...), while continuous variables can assume decimal values.

First, students were asked how many courses they were currently enrolled in.

Can be 0,1,2,... that is, has to be a countable number, so the number of courses they were currently enrolled in is a discrete random variable.

Second, the commuter students were asked to estimate how long it took them to drive to campus.

Can be for example, 10.5 minutes, half an hour, that is, can be represented by decimal values, and thus the time it took them to drive to campus is a continuous random variable.

And third, they were asked their heights.

Can also be decimal numbers, so continuous.

TERCER TRIMESTRE SEGUNDO GRADO
DEL 7 DE JUNIO AL 18 DE JUNIO
4- Calcular la media, la mediana y la moda de la siguiente serie de numeros: 5, 3, 6, 5, 4, 5, 2, 8, 6,5,4,8,3,4,5,4,8,2
5.4.

Answers

Answer:

MEDIA: 4.8

MEDIANA: 5

MODA: 5

espero que te ayude :)

The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.

Which is an equivalent equation solved for t?

Answers

Answer:

(f-v)/a = t

Step-by-step explanation:

f = v + at

Subtract v from each side

f-v = v-v + at

f-v = at

Divide each side by a

(f-v)/a = at/a

(f-v)/a = t

Answer:

f - v =  a

 t

Step-by-step explanation:

Equation:

f =  v + at

subtract -v on both sides

f - v = at

divide t on both sides of the equation

f - v = a

  t

Joan is a babysitter. She earns $8.50 per hour. Joan wants to buy a new phone that costs $161.50 with the tax included. Write an equation relating the number of hours she needs to babysit to the amount of money she earns. Find out how many hours Joan must babysit to buy the phone. Use h to represent the number of hours Joan babysits.

Answers

Answer:

8.5=161.50;h= 19 hours

Step-by-step explanation:

So its pretty easy all you have to do is multiply 8.5 x 19

A flower store has an inventory of 25 roses, 15 lilies, 30 tulips, 20 gladiola, and 10 daisies. A customer picks one of the flowers at random.

What is the probability that the flower is not a rose?

Answers

Answer: 75/100

Step-by-step explanation:

the total number of flowers= 25+15+30+20+10

                                             = 100

so probability that the flower is not a rose is= 75/100

Note: i got 75 by subtracting 100 by 25                                          

       

expand 3e(e+4)
Hhhhhhh

Answers

Answer:

[tex]3e^{2} + 12e[/tex]

Step-by-step explanation:

[tex]3ee+3e4[/tex]

[tex]3ee+3 * 4e[/tex]

[tex]3e^{2} + 12e\\[/tex]

[tex]3 \: {e}^{2} + 12 \: e[/tex] ✅

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

[tex]3 \: e \: ( \: e + 4 \: ) \\ \\ = 3 \: e \times \: e + 3 \: e \times 4 \\ \\ = 3 \: {e}^{2} + 12 \: e[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Will mark Brainlest Help pls​

Answers

g(-1) = -1, g(2) + g(1) = 7

Step-by-step explanation:

Given: g(x) = x³ + x² - x - 2

g(-1) ==> x = -1

g(-1) = (-1)³ + (-1)² - (-1) - 2

g(-1) = -1 + 1 + 1 - 2

g(-1) = -1

g(2) ==> x = 2

g(2) = (2)³ + (2)² - (2) - 2

g(2) = 8 + 4 - 2 - 2

g(2) = 8

g(1) ==> x = 1

g(1) = (1)³ + (1)² - (1) - 2

g(1) = 1 + 1 - 1 - 2

g(1) = -1

g(2) + g(1) = 8 + (-1) = 7

please help i will mark you brainliest... A number - _________= the previous number

Answers

Answer:

1

Step-by-step explanation:

When 1 substract from any number then will get previous number.

Example:

Let any number that is 5

5-1=4

4 is the just previous number of 5

Therefore, number -1 = the previous number

Answer will be 1

The angles shown below are supplementary:

what is the value of x

Answers

Answer:

[tex]x=12[/tex]

Step-by-step explanation:

By definition, supplementary angles add up to 180 degrees. Therefore, we can set up the follow equation to solve for [tex]x[/tex]:

[tex]10x+60=180,\\10x=120,\\x=\boxed{12}[/tex]

Answer:

x=12

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

10x+60=180

Subtract 60 from both sides:

10x=120

Divide 10 to both sides:

x=12

hi I need help on this

Answers

Answer: Volume=120yd^3

Explanation:
A of the base= (1/2)(10•3)
A of the base= 15

V of triangular prism= 15•8=120

Find the
surface area of the
prism.

Answers

Answer:

D.  972 ft^2

Step-by-step explanation:

SA = 2B + PH

where SA = total surface area of the prism,

B = area of a base

P = perimeter of the base

H = height of the prism

SA = 2 * bh/2 + (15 ft + 12 ft + 9 ft)(24 ft)

SA = (9 ft)(12 ft) + (15 ft + 12 ft + 9 ft)(24 ft)

SA = 972 ft^2

If a triangle has angles of X+2, 2x, and 55. What are the three angle
measurements?

Answers

Answer:

41, 43 and 82

Step-by-step explanation:

hope it may help you

ang
Name two vertical angles, two supplementary
angles in the diagram below.

Answers

Answer:

5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.

Solve the inequality.
|6p+3|>15
A p<2 or p>−3
B p>−2 or p<3
C p<−2 or p>3
D p>2 or p<−3

Answers

Step-by-step explanation:

|6p + 3| > 15

6p = 15 - 3

6p = 12

divide both sides by 6

6p÷6 = 12 ÷ 6

p = 2

hence, p >2 or p < - 3

Armando works in a research institute and they have collected the following data on a random sample of 500 students,
Gender
GRE score before and after participation in a GRE prep course (GRE is a test you take for entering graduate school)
Armando wants to answer questions the following questions:
1: After taking the GRE preparation course, did women show more improvement on the GRE score or men?
2: After the GRE preparation course, did more women get admitted to the graduate program or men?
3: What statistical method should he use?
a. He should use the one-sample test of the mean to answer question one and the one-sample test of proportion to answer question b.
b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.
c. He should use the two-sample test of proportion to answer question one and the two-sample test of the mean to answer question b.
d. He should use the paired-sample of the mean to answer question one and two sample test of the mean to answer question two.

Answers

Answer:

b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.

Step-by-step explanation:

Here we have two independent groups, Men and Women, therefore, to show if it is the Men or Women who performed better, this can be determined based the mean scores of each group. Therefore, use the two sample test of mean which is used to test whether the unknown mean of two independent population are equal or not.

In other to determine those who have the greater number of admissions between the two groups, this is determined by comparing the proportion of each group admitted. Hence, rather Than testing for the mean, we compare the proportion. Hence, we use the two sample test of proportion.

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