Given −7 is one of the roots of the quadratic equation
(x + k)2 = 16, where k is a constant, find the values of k.

Answers

Answer 1

Answer:

  k = {3, 11}

Step-by-step explanation:

Taking the square root of the given equation, we find ...

  x +k = ±4

For x = -7, this is ...

  -7 +k = ±4

  k = 7 ±4 = {3, 11}

Possible values of k are 3 and 11.

Answer 2

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

Taking square root on the both sides of equation (x + k)² = 16 we get,

[tex]\implies\rm{( {x + k)}^{2} } = 16[/tex]

[tex]\implies\rm{x + k = ± 4}[/tex]

Making two conditions for ± 4 i.e

1) x + k = 4

[tex]\implies\rm{ - 7 + k = 4}[/tex]

[tex]\implies\rm{k = 4 + 7}[/tex]

[tex]\implies\rm{k = 11}[/tex]

2) x + k = -4

[tex]\implies\rm{ - 7 + k = - 4}[/tex]

[tex]\implies\rm{k = - 4 + 7}[/tex]

[tex]\implies\rm{k = 3}[/tex]

Thus the values of k can be either 11 or 3.

Related Questions

Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 68 km/h faster than the other. If the two planes are 5052 kilometers apart after 3 hours, what is the rate of each plane?

Answers

Step-by-step explanation:

the slower plane travels x km in 3 hours.

the faster plane travels x + 3×68 = x + 204 km in 3 hours.

x + x + 204 = 5052 km

2x = 4848 km

x = 2424 km (in 3 hours).

so, the slower plane's speed is 808 km/h.

the faster plane's speed is 808 + 68 = 876 km/h.

Solve for m.

35m>−30


m>−50

m<−50

m>−18

m<−18

Answers

[tex]35m>-30\\\\\implies \dfrac{35m}{35}>-\dfrac{30}{35}\\\\\implies m>-\dfrac{6}{7}[/tex]

How to solve the function problem for this one?

Answers

Answer:

a. f(12) = - 1

b. x = 27 when f(x) = 4

Step-by-step explanation:

We are given that [tex]f(x)=\frac{1}{3} x-5[/tex] and we want to find f(12) and f(x) = 4

To find f(12) we simply plug in 12 into x and evaluate it

[tex]f(x)=\frac{1}{3} x-5[/tex]

plug in 12

[tex]f(12)=\frac{1}{3} (12)-5[/tex]

multiply 12 and 1/3 to get 4

[tex]f(12)=4-5[/tex]

subtract 5 from 4 to get -1

[tex]f(12)=-1[/tex]

Now we want to find the value of x when f(x) = 4

To do this we substitute 4 for f(x) and solve for x

[tex]f(x)=\frac{1}{3} x-5[/tex]

substitute 4 for f(x) and solve for x

[tex]4=\frac{1}{3}x -5[/tex]

add 5 to both sides

[tex]9=\frac{1}{3} x[/tex]

multiply both sides by 3

27 = x

And we are done.

So f(12) = -1 and x = 27 when f(x) = 4

For a plug in 12 for x:

f(12) = 1/3(12)-5

f(12) = 4-5

f(12) = -1

For b plug in 4 for x:

f(4) = 1/3(4)-5

f(4) = 4/3 -5

f(4) = 0.75-5

f(4)= -4.25

How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!

Answers

Answer:

It is the first one.

What type of number is ?
Choose all answers that apply:
A
Whole number
00
B
Integer
С
Rational
D
Irrational

Answers

Answer:

Irrational Number

Step-by-step explanation:

Mark as brainliest if correct

Select the equation that contains the points (-1, -8) and (3, 4).

Answers

show us the equations
show us the equation

A drilling team detected water 38 feet below the ground. If it took workers 8 days to be able to dig and pull up the water, how much did they dig each day on average? Form an equation

Answers

Answer: 38 divided by 8 which would equal 4.75 or 4 3/4 feet each day.

Step-by-step explanation: You divide the amount of total feet by the amount of days it took.

True or False. If true, give a convincing argument. If false, explain why it is false. Be sure to use mathematical language in your explanation.

As an airplane flies toward you, its angle of elevation increases.

Answers

Answer:

True.

Step-by-step explanation:

We assume that the plane is flying at a constant height above the ground.

The angle of elevation is the angle made between the plane, you and the point on  the ground directly below the plane. As the plane approaches you the distance between you and the point on the ground decreases and therefore the angle of elevation increases.

Solve for x.
-8 =X/4

Answers

x = −32

lllllllllllllllllllllllllllllllllllllllllll

It would be appreciated if there could be an explanation along the answer

Answers

Answer:

i think probably 80°

Step-by-step explanation:

PQ = RS

2x+3 = 4x-3

x = 3

PTQ = RTS

9y-3x-1 = 5x+7y-5

2y-8x = -4

y-4x = -2

y-4(3) = -2

y-12 = -2

y = -2+12

y = 10

so PTQ = 9y-3x-1

9(10)-3(3)-1

90-9-1

80°

If 5/3 liters of water is enough to water ⅕ of your yard, 5 3 how much water is needed to water the entire yard?

Answers

Answer:

8 1/3 liters

Step-by-step explanation:

create a proportion from water : yard

let 'y' = water for entire yard

5/3 ÷ 1/5 = y ÷ 5/5

5/3 · 5/1 = y/1

25/3 = y/1

3y = 25

y = 8 1/3

Is this the right question

Answers

Answer:

no, ssa is the incorrect one

no it’s not A is correct i think

if x is reduced by 25%. the result will be

Answers

[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer♡}}[/tex]

[tex]a \: number \: x \: is \: reduced \: by \: 25\%[/tex]

[tex]25\% \: of \: x \: means \: ( \frac{25}{100} )(x) = 0.25x \\ \\=> x - 0.25x \\ = > 0.75x[/tex]

hope helpful~

The reduced quantity if x is reduced by 25% is 0.75x.

What is percentage?

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

x is reduced by 25%,

Calculate the 25% of x as shown below,

25 / 100 × x

0.25x

Calculate the reduced quantity,

Reduced quantity = x - 0.25x

Reduced quantity = x(1 - 0.25)

Reduced quantity = 0.75x

To know more about percentages:

brainly.com/question/20818421

#SPJ2

549.5 to 1 decimal place

Answers

Answer:

It is still 549.5

Step-by-step explanation:

Rounding to 1 decimal place is just rounding by the tenth place

So it is still 549.5

Hope this helps!

549.5 (still the same answer)

pls help this a math question. image below

Answers

Answer:

D

Step-by-step explanation:

Same X, but different Y value, it is five apart in D

The answer is d your welcome

6 O
Which function is graphed on the coordinate plane below?
Ty
x
f(x) = 2x - 6
Of(x) = 2x + 6
f(x) = -2x + 6
Mark this and retum
Save and Exit
Next
Submit

Answers

Step-by-step explanation:

we don't see all possible answer options.

but it does not matter.

the line is clearly

y = 2x - 6

why ?

the slope is always the factor of x.

and the slope is defined as ratio of "y coordinate change / x coordinate change".

and we can clearly see, for every change in x by +1, y changes by +2. zu, the slope is 2/1 = 2.

and when x = 0, the graph shows us the y-intercept with y = -6.

hence the above mentioned equation.

The Function is graphed on the coordinate plane is y= 2x- 6.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have points from the graph as (3, 0) and (0, -6).

So, the slope of line is

slope= (-6 -0)/ (0-3)

slope = -6/ (-3)

slope= 2

Now, using the slope intercept form

y= mx + b

y= 2x + b

Now, put x= 3 and y= 0 we get

0= 6 + b

b = -6

So, the required function is

y= 2x - 6.

Learn more about Slope here:

https://brainly.com/question/3605446

#SPJ7

This is a function?

O True
O False

Answers

Answer:

true

Step-by-step explanation:im not really sure

What is the approximate value of b?

Answers

The answer is 7.6

Using the Pythagoras theorem, we can work out that b must be equal to the square root of 58, which is approximately 7.6

Anthony is gathering workout clothes. There are 4 pairs of running shoes and 10 workout shirts to choose from. How many different workout outfits can Anthony make?

Answers

Answer:

40

Step-by-step explanation:

But he doesn’t have pants so 0 but yeah 40 sounds right

In a relation y = 2t + 1, what is the value of y if t = 7

Answers

Answer:

If t = 7, y = 16

Step-by-step explanation:

y = 2t + 1

y = 2(7) + 1

y = 14 + 1

y = 15

Find the value of x.

Answers

Answer:

x = 12

Step-by-step explanation:

Angle Bisector Theorem:  PS / PQ = RS / QR

24/14 = x/7

cross-multiply:

14x = 168

x = 12

simplify the quotient. Write the answer in sn.

Answers

Answer:

2.4*10^4

Step-by-step explanation:

write in scientific notation

first i would simplify the 3.6/1.5

=2.4

then you get (2.4*10^7)/10^3

formula: (m^x)/(m^y)= m^(x-y)

(2.4*10^7)/10^3

=2.4*10^(7-3)/1

=2.4*10^4

help pls will give brainliest

Answers

Answer:

$100-5(15) aka $25 still owed

The areas of two similar
squares are 16 m2 and 49 m2.
What is the scale factor of
their side lengths?
[?]:[ ]

Answers

4:7

Take the square root of each square to get the side lengths

4*4=16
7*7=49

Answer:

4:7

Step-by-step explanation:

We know that

Area of square = s²

For square 1

16 = s²

√16 = s

4 = s

For square 2

49 = s²

√49 = s

7 = s

Scale factor = 4:7

the given cube has a mass of 173 grams, what is it’s density

Answers

Answer:

I think the density is 4cm.

Hope that helps you.

Step-by-step explanation:

Plz help me with this

Answers

Answer:

sorry cant see the question

Step-by-step explanation:

In Need of help please Help :c

Answers

Answer:

proportional: A, B, D, G, Inon-proportional: C, E, F, H

Step-by-step explanation:

Any relation with a non-zero initial value or y-intercept is non-proportional. Any relation that has a constant ratio between output and input is proportional.

  C has an initial value of 7

  E has a y-intercept of -3

  F has an initial value of 2.00

  H has an initial value of 5

All of these are non-proportional. The remainder are proportional.

A triangle has two sides of length 6 and 18. What is the smallest possible whole-number length for the third side?

Answers

Answer:

Step-by-step explanation:

A triangle has two sides of length 14 and 5. What is the largest possible whole-number length for the third side?

Answer:

11 units

Step-by-step explanation:

Between 18-8 = 10 and 18+8 = 26, the smallest integer number INSIDE this interval is 11.

Please Help Me please

Answers

Answer:

the 3 one

Step-by-step explanation:

If b = the number of boys, which algebraic expression represents the phrase
below?
the sum of the number of boys and 15 girls
A. b + 15
B. b. 15
C. b - 15
D.
b
15

Answers

Answer:

A. b + 15

Step-by-step explanation:

b = the number of boys, substitute below:

The sum of the number of boys and 15 girls → The sum of b and 15 → b + 15

Correct choice is A

Other Questions
Factor: 3x4y3 48y3 Fred is 5 inches shorter than the quotient of Ricks height and 4. let r represent Ricks height. Write an expression that represents Freds height The price of a bicycle is $108.00 plus 7% sales tax. What is the sales tax on this bicycle in dollars and cents? how do i get the answer for this problem. 2x+2x+2=4x+2 DOES ANYONE KNOW THE AWNSER PLEASE HELP What channel is the kennedy center honors on tonight? PLEASE!!!! Which option identifies the satellite technology best utilized in the following scenario?A forest management company that is not concerned about time-sensitive problems uses a standardizedinternet satellite mapping system to get a rough sense of the status of wooded areas that are normallyinaccessible to all but skilled hikers. water vapor present in air support water cycle reciprocal of 2 3/11 Consider the following force:A horse is pulling forward on a wagon with a force of 200 N.According to Newton's third law, what other force must be happening?The horse is pushing backward on the wagon with a force of 200 N.The ground is pushing backward on the horse with a force of 200 N.The wagon is pulling backward on the horse with a force of 200 N. Meg visited her Aunt Clare for lunch. After they ate, Aunt Clare made tea. She put the same amount of black tea and milk in both their cups, but Meg decided to add some extra milk to hers. Which cup of tea was darker after they had finished adding milk? One possible theme of call of the wild could be that only the strongest survive. Explain how this relates to darwins theory of natural selection and the survival of the fittest. Do you agree or disagree with this idea? Is there one aspect in which you agree but another with which u do not? please help i only have a few days- untill schools over If 3.31 moles of argon gas occupies a volume of 100 L what volume does 13.15 moles of argon occupy under the same temperature and pressure Can someone please give me the (Answers) to this? ... please ... Will give 10 points.Why does an atom have a neutral charge?A It has equal numbers of electrons and protons.B. The number of neutrons equals the number of protons andelectrons in the atom.C. It has equal numbers of electrons and neutrons.D. It has equal numbers of neutrons and protons. please answer , thank you in advance to whoever does !!!! What type of evidence does Machiavelli use to support his claim that a prince should have no aim other than war and its rules and discipline? logical evidence anecdotal evidence empirical evidence both logical and anecdotal evidence. Read the following passages.Passage 1As the sun began to set, Joanna and her team began to build their snow fortress. Joanna assigned Tucker, Billy, and the other classmates tasks. She announced to the team that she would be the spy. When she made this declaration, Billy rolled his eyes. It seemed as though he disagreed with Joanna taking on the role of leader and spy, but he just got to work. The Hillside team was busy working together to make their fort, which was very large and made of ice and snow. When Joanna saw the enemy's impressive structure, she turned to her team but got a distressed look on her face."Stop! None of you are following my instructions," Joanna cried. "Billy just pushed the walls together, and now there are cracks. If you don't work together and build the fort in the correct way, the whole thing will fall apart.""Don't worry," Tucker replied. "Everything will turn out okay."Tucker looked over at Billy and gave him a gentle smile. Then, Tucker made some holes that could be used for covert operations.Passage 2As the sun began to set, my team and I began to build our snow fortress. I had imagined a simple design that would withstand any attack from the enemy. As the leader, I assigned each individual a task and made myself a spy. Hillside created a massive fort wall made of ice and snow. I turned to my teammates to share my concerns, only to realize that they had failed to follow my instructions. Each person was building a part of the wall in a different manner. Their lack of teamwork and inability to follow directions would make the entire structure fall apart! When I expressed my concerns, Tucker claimed that everything would turn out well. Billy pushed the walls together. Sure enough, fractures formed in the walls. But, Tucker saved the day by creating holes that could be used for covert operations.What is a similarity in the way the authors use point of view in each passage? help What city is the capital of Texas?A)Austin. B)Dallas. C)Santa Fe. D)Sacramento Given that P=x+y.Find P when:x=3 and y=11