Find k so that 9x^2-48x+k is the square of a binomial.

Answers

Answer 1

Answer:

Step-by-step explanation:

The discriminant must be zero.

Discriminant = (-48)^2 - 4*9k = 2304 - 36K

36k = 2304

k = 64

Answer 2

Using the square of a subtraction, it is found that k = 64.

What is a square of a subtraction?

It is a notable product, given by:

[tex](ax - b)^2 = a^2x^2 - 2abx + b^2[/tex]

In this problem, the expression is:

[tex]9x^2 - 48x + k[/tex]

We want it to be the square of a binomial, hence:

[tex]a^2x^2 - 2abx + b^2 = 9x^2 - 48x + k[/tex]

Then, comparing both sides, first the value of a is found:

[tex]a^2 = 9[/tex]

[tex]a = \sqrt{9}[/tex]

[tex]a = 3[/tex]

Then, with the second term, the value of b is found.

[tex]2ab = 48[/tex]

[tex]6b = 48[/tex]

[tex]b = \frac{48}{6}[/tex]

[tex]b = 8[/tex]

Finally, the value of k is found.

[tex]k = b^2 = 8^2 = 64[/tex]

You can learn more about the square of a subtraction at https://brainly.com/question/9239489


Related Questions

A professor holds office hours during final exam week and discovers much to his dismay that his sudden popularity affords him little time to engage in his favorite activity, watching cat videos. Fifteen students per hour arrive at his office and he patiently answers questions, averaging three minutes per student. On average, how many students are waiting to ask questions?

Answers

Answer:

There are no student waiting to ask questions

Step-by-step explanation:

The number of students that arre

The arrival rate of the student, λ = 15/hr

The number of minutes spent per student, W = 3 minutes

The number of students waiting to ask questions, 'L', is given by Little's law as follows;

L = λ·W

Where;

L = The number of students in the system

λ = The arrival rate = 15 students/hour

W = The average time spent in the system = 3 minutes = 1/20 hour

∴ L = 15 student/hour × (1/20) hour = 3/4 Students

Given that the number of students waiting to ask questions is a fraction, less than 1, we round down, and there are therefore no student waiting to ask questions

A friend owes $10,000 on his credit card. He plans to stop making charges and pay off the balance. The card has a minimum payment of 5%. He figures correctly that 5% of $10,000 is $500. From that he concludes that he needs to make the 5% minimum payment for only 20 months Is your friend right? If not, explain the error in his reasoning.

Answers

Answer:

yes he is correct

Step-by-step explanation:

10000x0.05=500 so thats correct

he will pay 500 for 20 month= 10,000

7 x 4 - 20
Answer this 2 mins later (timer on math probs)

Answers

Answer:

I think answer is 8.....

Plzzs helppppppppppppp

Answers

Answer:

3/24 and 35/63

Step-by-step explanation:

3 / 6 of 1 / 4 = 3 x 1 / 6 x 4 = 3 / 24

7 / 9 of 5 / 7 = 7 x 5 / 9 x 7 = 35/63

Answer:

3            1               1

_     X    _      =       _  

6            4              8

7            5              5

_     X     _   =        _

9            7              9

Hope this helped :)

THE TEACHER WONT HELP ☺️ pls

Answers

answer:

2/5=0.4

2/5=40%

step-by-step explanation:

to get 2/5 as a decimal you can simply just divide 2÷5 which is 0.4

and from there you can use 0.4 to find the percentage multiply 0.4 x 100 which is 40

good luck :)

hopefully, this helps

have a great day !!

HELP WHOEVER ANSWERS CORRECTLY GETS BRAINLIEST ANSWER

5x+7y+12.5+6y+1x+5

Answers

Answer: 6x + 13y + 17.5

Step-by-step explanation:

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min. P(51.5 < X < 51.7)

Answers

Answer:

0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.

This means that [tex]a = 50, b = 52[/tex]

If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min.

[tex]P(51.5 \leq X \leq 51.7) = \frac{51.7 - 51.5}{52 - 50} = \frac{0.2}{2} = 0.1[/tex]

0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.

How many feet are in half a mile?

Answers

Answer:

answer below:)

Step-by-step explanation:

There are 5280 feet in one mile. So, half a mile is equal to 0.5 x 5280 = 2640 feet.

5280 looked it up on safari

a) work out the size of angle x
b) give reasons for your answer

Answers

Answer:

angle B=100 degrees

vertically opposite angle

angle B +x= 180 degree

100-180=x

80 degree =x

Answer:

x = 80°

Step-by-step explanation:

GIVEN :-

AD ║ EHCG as transversal∠CBD = 100°∠EFB = x°

TO FIND :-

The measure of x°

PROCEDURE :-

∠CBD + ∠FBD = 180°      (∵ ∠CBD & ∠FBD form a linear pair )

⇒ ∠FBD = 180° - 100° = 80°

Also,

∠FBD = ∠EFB       (∵ Alternative Interior Angles are equal )

⇒ x = 80°


Martina is currently 18 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey . Use this information to answer the following questions.
If you let x represent Joey's current age, what expression can you use to represent Martina's? PLEASE HELP
current age?

Answers

Answer:

The age of Joey is 4 years  and

The age of Martina is 22 years .

Step-by-step explanation:

Given as :

Martina is 18 years older than her Joey

In 5 years, Martina will be three times older than Joey

Let The age of Martina = M years

And The age of Joey = J years

Now, According to questions

M = J + 18          ........1

(M+5) = 3 × (J+5)

Or, M + 5 = 3 J + 15

Or, M - 3 J = 15 - 5

∴ M - 3 J = 10                ..........2

Solving eq 1 and 2

Put the value of M from eq 1 into eq 2

So, (J + 18) - 3 J = 10

Or, J - 3 J = 10 - 18

Or, - 2 J = - 8

∴ J =

i.e J = 4 years

So, The age of Joey = J = 4 years

Now, Put the value of J in eq 1

So, M = J + 18

Or, M = 4 + 18

∴ M = 22 years

So, The age of Martina = M = 22 years

Hence,The age of Joey is 4 years  and The age of Martina is 22 years . Answer

Plz help it’s missing




....................

Answers

Answer:

6. the number placed in thousand place 95,184 is 1

7. the cube of 2 and 3 is 27-8is 19

8. The divisor is 4

9. 25

10. the prime number is 13

Answer:

6. 95,000

7. I can't read it

8. I cant read that either

9. 5 pounds

10. 14

Step-by-step explanation:

[tex]12.5=n-1.5[/tex]

Answers

Answer:

n=14

Step-by-step explanation:

12.5=n-1.5

-n=-1.5-12.5

-n=-14

n=14

potrzebuję na teraz pls

Answers

Answer:

sywuwyqiqjkasa

Step-by-step explanation:

Yueyeiwwiwieiei2i2i2i

Jennifer is attending a school orchestra concert.She sees her math teacher seated 4.5 meters ahead of her and her science teacher seated 1.1 metes to her right.how far apart are the two teachers?

Answers

Answer:

j

Step-by-step explanation:

jj

Which example models a negative integer A.Students in a classroom B. The age of a parent C. Money lost from a pocket D. the height of a tree

Answers

Answer:

C- Money lost from a pocket

Step-by-step explanation:

It would be C because something is decreasing ( now a negative) from what they did have.

7. Bella scored 8 points in the second round. This
made her total score 39. How many points did she
score in the first round?

Answers

I I think Bella scored 31 points in the first round


Find the equation of the line through (-5,4) which is parallel to the line y=-x+6.
Give your answer in the form y=mx+b

Answers

Answer:

[tex]y = -x -1[/tex]

Step-by-step explanation:

Given

Passed through (-5,4)

Parallel to: y=-x + 6

Required

Determine the line equation

If it is parallel to: y=-x + 6, then it means that they have the same slope.

A linear equation y = mx + b has the slope m.

So, by comparison of y = mx + b  to y = -x + 6

[tex]m = -1[/tex]

The line equation is then calculated as:

[tex]y=m(x - x_1) + y_1[/tex]

Where

[tex]m = -1[/tex]

[tex](x_1,y_1) = (-5,4)[/tex]

So:

[tex]y = -1(x - (-5)) + 4[/tex]

[tex]y = -1(x +5) + 4[/tex]

[tex]y = -x -5 + 4[/tex]

[tex]y = -x -1[/tex]


What is the sum (2 – 3i) + (-4-2i) ?

Answers

-2-5i is the correct answer

The sum of the complex numbers (2 – 3i) and (-4-2i) is -2 - 5i.

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation [tex]i^2[/tex] = -1. The real part of a complex number is denoted by Re(z) = a, and the imaginary part is denoted by Im(z) = b.

Complex numbers can be added, subtracted, multiplied, and divided in a similar way to real numbers. The addition and subtraction of complex numbers is done by adding or subtracting the real and imaginary parts separately.

To find the sum of complex numbers, we add their real parts and their imaginary parts separately. Let's calculate the sum of the given complex numbers:

(2 - 3i) + (-4 - 2i)

Real part: 2 + (-4) = -2

Imaginary part: (-3i) + (-2i) = -5i

Therefore, the sum of (2 - 3i) + (-4 - 2i) is -2 - 5i.

Learn more about Complex numbers here:

https://brainly.com/question/20566728

#SPJ6

Jeff had $20. He spent 18 of his money on lunch and 25 of his money at the movies.
How much money does Jeff have left?
A. $5.50
B. $7.00
C. $8.25
D. $9.50

Answers

C 8.25 is the correct answer it is the most reasonable to aswell
C. $8.25 because 20+18=43 and 43% of 20 is about 8.6

Find the value of, x/2 + x/3 + x/6

Answers

x/2+x/3+x/6
3x/3•2+2x/2•3+x/6
3x/6+2x/6+x/6
3x+2x+x6
—————-
6
6x/6
SOLUTION x

What is the equation of the line, in slope-intercept form, that passes through the
points (-2, -2) and
and (4, — 3)?

Answers

Answer:

y = [tex]\frac{-1}{6}[/tex]x - [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

1. Find the slope -3- -2 / 4 - -2  so -3+2/4+2, -1/6 so m = -1/6

2.  Find y intercept (b)   y = mx + b so -2 = -1/6(-2) + b, -2 = 1/3 + b

b = -2-1/3, b = -6/3 - 1/3, so b = -7/3

3.  Put it all together y = mx + b so y = -1/6x -7/3

BRAINLIEST STARS

7)
You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. What is the probability of NOT picking a
green marble out of the bag randomly?
A)
0
B)
1/2
C) 1/5
D)4/5

Answers

Answer:

that should be D

Step-by-step explanation:

Its D because there are to many other colors

ANSWER QUICK PLEASE
The city of Eastville has 32,000 people and the city of Lakeside has 56,000 people. Eatsville is gaining 600 people each year. Lakeside is losing 1000 people each year. How many years will it take for both cities to have the same amount of residents?

Answers

Answer:

15 years

Step-by-step explanation:

Create an equation where x is the number of years

32,000 + 600x = 56,000 - 1000x

Solve for x:

600x = 24,000 - 1000x

1600x = 24,000

x = 15

So, it will take 15 years for both cities to have the same number of residents

Answer: answer is x=15

Step-by-step explanation:

A bookstore has 45 copies of a bestseller available on Saturday morning. Twenty-one customers purchase the book that day. On Monday, a shipment of 25 books arrives and 14 copies are sold. Which statements are correct?

Answers

Answer:

Need to see the statements

Step-by-step explanation:

There are no statements

so what would the answer be to 2/3 x 6/7

Answers

Answer:

4/7

Step-by-step explanation:

Given function:

2/3·6/7

Cross multiply:

6=2 and 3=1

Rename:

2/1·2/7

Multiply the terms:

2/1·2/7=4/7

Therefore, 2/3·6/7 is 4/7..

Answer:

4/7

Step-by-step explanation:

1. you multiply

2/3 x 6/7 equals 2 x 6 and 3 x 7 equals 12/21

Multiply the denominator and numerator

2. simplify

12/21 equals 4/7

If the sum of two numbers is 10 and the diffference is 6, find the numbers​

Answers

8 and 2
8+2 = 10
8-2 = 6

X + y = 10

Rewrite as y = 10-x

Y - x = 6

Replace y

10-x -x = 6

Simplify:

10-2x = 6

Subtract 10 from both sides:

-2x = -4

Divide both sides by -2:

X = 2

Now replace x in the first equation:

2 + y = 10

Subtract 2 from both sides:

Y = 8

The two numbers are 8 and 2

Write the following expression in exponential form: 4.5 × 4.5 × 4.5 × 4.5 × 4.5 × 4.5 × 4.5

Answers

Answer:

[tex]4.5^{7}[/tex]

Step-by-step explanation:

Just count how many 4.5 there are.

4.5^7

jwnnd  jwdjndw jnfjwnjj fjnwjnfs cn jjwj wmc sknkw c mssc kskwc

The shorter leg of a right triangle is 10 meters. the hypotenuse is 2 meters longer than the longer leg. Find all three sides

Answers

Answer:

the shorter leg is 10 meters, longer leg is 24 meters and the hypotenuse is 26 meters

Select the Ratio that is not equivalent to the rest.
25 points
12:25
6:15
14:35
2:5

Answers

12:25 is not equivalent to the rest

A parallogram is ______________ a rectangle.

a
sometimes
b
always
c
never

Answers

Answer:

sometimes a square could be a parallelogram too and a rhombus and a normal parallelogram

Step-by-step explanation:

it has two parallel pairs

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