Please help ASAP

Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values.

3x^2 + kx - 8

Answers

Answer 1

Answer:

Any value of k

Step-by-step explanation:

The quadratic expression can be factored into two binomials if it has two real roots.

Two real roots possible with non-negative discriminant:

D ≥ 0

As D = b² - 4ac, we get the following inequality

k² - 4(3)(-8) ≥ 0k² + 96 ≥ 0k² ≥ - 96

This is true for any value of k

k ∈ (- ∞, + ∞)
Answer 2

Answer:

(-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]

Step-by-step explanation:

Binomial:  two terms connected by a plus or minus sign.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If a quadratic expression factors into two binomials, it will have two real roots.  Therefore, the discriminant will be greater than zero.

Given quadratic expression:

  [tex]3x^2+kx-8[/tex]

[tex]\implies a=3, \quad b=k, \quad c=-8[/tex]

Substitute the values of a, b and c into the discriminant, set it to > 0:

[tex]\implies k^2-4(3)(-8) > 0[/tex]

[tex]\implies k^2+96 > 0[/tex]

As k² ≥ 0 for all real numbers,

[tex]\implies k^2+96 \geq 96[/tex]

Therefore, the values of k are (-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]


Related Questions

Which of the objects below best holds 1 gallon? A. bathtub B. milk jug C. measuring cup O D. glass of water​

Answers

Answer: B: milk jug

Step-by-step explanation:

A gallon is equivalent to 128 oz and a glass of water would not be able to hold that capacity, neither can a bathtub because a bathtub would need more than 1 gallon of water to fill it up. A measuring cup is usually used for cooking etc... and usually the measurements aren't measured by gallons. So the only realistic answer it would be is a milk jug.

A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 10cm, and the base has a radius of 4.5. The cooler has 16956cmCubed of water in it. How many cups can be filled from the cooler?
Use 3.14 for [tex]\pi[/tex] , and do not round your answer.

Answers

Answer: the answer is 150 :)

Step-by-step explanation: Volume of a cone is

V = 1/3 pi * r^2 *h

The volume of one cone is

pi = 3.14

r = d/2 = 6/2 =3

h=9

Substitute what we know

V = 1/3 * (3.14) * (3^2) * (9)

  = 27* 3.14

  = 84.78  cm^3

The water cooler has 12717 cm^3 water

Divide the water by the volume of the paper cup cone  and we will know how many paper cup cones we can fill, assuming we fill them completely.

12717/ 84.78 = 150

We can fill 150 paper cup cones. have a great day!

What is 28x²y + 38xy - 6y factored?

Answers

Answer:

(2y)(7x-1)(2x+3)

Step-by-step explanation:

first, all the terms have a 2 and a y in common. you can take that out of every term. then i just used the quadratic x factor method, you can find out what it is via the internet, its the fastest option to factor if possible :)

Answer:

[tex]=2y (7x-1) (2x+3)[/tex]

Step-by-step explanation:

[tex]28x^{2}y + 38xy - 6y[/tex]

[tex]=2y(14x^{2} +19-3)[/tex]

[tex]=(7x-1) (2x+3)[/tex]

[tex]=2y(7x-1) (2x+3)[/tex]

Please help I'm stuck​

Answers

Answer:

C, those who vote FOR the Ballet Measure tend to be from District 2.

Step-by-step explanation:

Look carefully, read the questions! Okay! Cya!

Those who vote for the ballot measure tend to be from District 2. The correct option is C.

How to calculate the relative frequency of the data?

To calculate the relative frequency, we need to divide each cell value by the total number of people who voted. This will give us the proportion of people in each category.

District 1:

For: 13/75 ≈ 0.1733

Against: 12/75 ≈ 0.16

District 2:

For: 15/75 ≈ 0.2

Against: 10/75 ≈ 0.1333

District 3:

For: 9/75 ≈ 0.12

Against: 16/75 ≈ 0.2133

Based on the relative frequencies, we can see that the highest proportion of people who voted for the ballot measure is from District 2 (0.2),

While the highest proportion of people who voted against the ballot measure is from District 3 (0.2133). Therefore, the association that the two-way table suggests is:

The correct option is C.

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Can anyone please solve this? I need it to be right.

Answers

Answer:

65

Step-by-step explanation:

[tex]\frac{3(2^5)-13(-2)+2^3}{-2^2+3^2-3} =\frac{3(32)+26+(8)}{(-4)+(9)-3} =\frac{96+34}{2} =\frac{130}{2}=65[/tex]

What is the best estimate of the area of the figure on the grid if each square has a side length of 1 inch?
12 square inches
O 20 square inches
25 square inches
O 33 square inches

Answers

Answer:12 i think

Step-by-step explanation:

a) Factorise
x2 - 422

Answers

Answer:

(x + 42)(x - 42)

Step-by-step explanation:

Keep this in mind :

a² - b² = (a + b)(a - b)

In this case,

a = xb = 42

So, by factorizing,

x² - 42² = (x + 42)(x - 42)

★a²-b²=(a+b)(a-b)

So

x²-42²

a=x ,b=42

(x+42)(x-42)

Done!

14.
8 builders can finish a house in 20 days.
Each of the builders works at the same rate.
6 of the builders stop working after 14 days.
The other builders continue building the house at the same rate until it is
finished,
How long does it take to build the house?

Answers

Answer:

it took the remaining two builders five days to finish

It takes 38 days to build the house for the remaining workers. Since it is said that the total working days for building a house with 8 workers is 20 and 6 workers left after 14 days and each worker is working at the same rate.

Given data:

8 builders can finish a house in 20 days

Each builder works at the same rate

After 14 days 6 builders left.

Calculating the required days:

When 6 builders left after 14 days, 2 builders have remained

Then, we can write

1 builder can finish the work that these 6 builders did in those 14 days is

6×14=84 days

Since it takes 20 days for 8 builders to finish a house, then for 1 builder it takes

1 builder = 20×8=160 days

Then the remaining left for 1 builder to finish the house is 160-84=76 days

Then the remaining 2 builders will build the house in 76/2 days

That is 38 days.

Therefore, the remaining builders build the house in 38 days at the same rate.

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WILL GIVE BRAINLIEST, THANKS, AND 5 STARS!
PLEASE HELP AND EXPLAIN!

The Cosmic Pool company is building a pool in Mary’s back yard. The pool is to be 8ft longer than it is wide and cover 240 square feet of the back yard. Determine both dimensions of the pool and the perimeter.
Group of answer choices

(A) Dimensions: width = 20ft & length = 12ft
Perimeter: 32ft

(B) Dimensions: width = 20ft & length = 12ft
Perimeter: 64ft

(C) Dimensions: width = 12ft & length = 20ft
Perimeter: 32ft

(D) Dimensions: width = 12ft & length = 20ft
Perimeter: 64ft

Answers

Answer:

(D) Dimensions: width = 12ft & length = 20ft / Perimeter: 64ft

Step-by-step explanation:

Let the length be x and width be y.

We have:

x = y + 8Area = 240 ft²

Set equation and solve

xy = 240y(y + 8) = 240y² + 8y = 240y² + 8y + 16 = 256(y + 4)² = 16²y + 4 = 16y = 12 ft

The length is:

x = 12 + 8 = 20 ft

The perimeter is:

P = 2(x + y) = 2(20 + 12) = 2(32) = 64 ft

Correct choice is D

Let they be l and b

l=b+8l-b=8--(1)

And

lb=240

So

(l+b)^2=(l-b)^2+4b=(8)^2+4(240)=64+960=1024l+b=32--(2)

From both equations

2l=40l=20

And.

b=20-8=12ft

Option D

Two brothers decided to bike to visit their grandma who lived 12 miles away. One of them biked at speed 8 mph and then he waited for his brother for 30 minutes. What was the speed of the second brother?

Answers

Answer:

6 m/hr

Step-by-step explanation:

The first brother took   12/8 = 1.5 hr

the second brother took  1.5 + .5 = 2hours

  12 miles / 2 hrs =

Jon owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.
He sells shorts for $14 and T-shirts for $6 each. Jon can work 12 hours a day,
at most. It takes him 15 minutes to design a T-shirt and an hour to design a
pair of shorts. He must design at least 12 items each day, but he cannot
design more than 20 items in one day. Which set of inequalities below
represents this scenario?
A. S 2 12-tss 20 - ts 12 -0.25t, s 2 0; t2 0
B. s2 12-t, ss 20-t, ss 12 -0.25t, s 0;t20
O C. s2 12-t s2 20-t ss 12 -0.25t, s 2 0;t2 0
D. s2 12+ tss 20 + tss 12 -0.25t, s 0,20

Answers

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The set of inequalities below represents this scenario s ≥ 12 - t,

s ≤ 30 - t, s ≤ 24 - 0.66·t

We have given that,

at most. It takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts. He must design at least 12 items each day, but he cannot design more than 20 items in one day.

What is inequality?

A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

lets t=times

s=shorts

We have to determine the correct inequality so that we will get,

The correct option is;

s ≥ 12 - t,

s ≤ 30 - t,

s ≤ 24 - 0.66·t

Therefore option B is correct.

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In a right triangle, cosine a = 0.352 and sine a = 0.936. what is the approximate value of tangent a? 0.329 0.376 1.288 2.659

Answers

The value of tangent a in the right triangle in which , cosine a = 0.352 and sine a = 0.936 is 2.659.

What are the trigonometric ratios?

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle. The value of tangent of angle is equal to the ratio of sine of that angle to the cosine of that angle.

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}[/tex]

Here, θ is the angle.

The value of angle given in the problem are,

Cosine a = 0.352 Sine a = 0.936.

Put these values in the above fromula as,

[tex]\tan (a)=\dfrac{\sin(a)}{\cos(a)}\\\tan (a)=\dfrac{0.936}{0.352}\\\tan(a)=2.659[/tex]

Hence, the value of tangent a in the right triangle in which , cosine a = 0.352 and sine a = 0.936 is 2.659.

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Answer:

D(2.659)

Step-by-step explanation:

got it right on edg

lat a = the length of a car in meters. Let b = the length of the same car in centimeters. which number is greater, a or b? Answer for 100 points.

Answers

Answer:

B

Step-by-step explanation:

Centimeters are 100 times bigger than meters, so if you had 1 meter, it would be 100 centimeters. Therefore, centimeters are greater than meters.

B is the answer I’ve had this question on one of my tests and I got a 93 average

pls answer its important

Answers

Answer:

i dunno'

Step-by-step explanatio i dont know how to explain diss this

An airplane flies with a constant speed
of 820 miles per hour. How far can it
travel in 3 1/2 hours?

Answers

2870 miles

D= s x t

= 820 x 3.5

=2870

Hope this helps!

Jake drew the sketch below of a kite that he wants to make.
A kite with height equal to the sum of 10 centimeters and 50 centimeters and the width equal to the sum of 20 centimeters and 20 centimeters.
Part A
Which of the following expressions can be used to find the area of the kite? Select all that apply.
2 (12 × 20 × 50) + 2(12 × 20 × 10)
2 (12 × 20 × 60)
2 (20 × 50) + 2(20 × 10)
12 (20 × 50) + 12(20 × 10)
12(40 × 60)
Part B
What is the area of Jake's kite? Enter your answer in the box.

area =
cm2

Answers

Answer:

Part A: 2 (20 × 50) + 2(20 × 10)

Part B: 1200 cm²

Step-by-step explanation:

Part A:

2 (20 × 50) + 2(20 × 10)

= 2(1000) + 2(200)

= 2000 + 400

= 2400

Part B:

Divide the answer by 2.

= 2400/2

= 1200 cm²

Because the formula to find the area of a kite is

1/2 x (p x q), where p is the sum of a diagonal and d is the sum of a diagonal.

A suit is on sale for $414 , which is 28% less than the regular price.
What is the regular price?

Answers

Answer:

.72x=414

Step-by-step explanation:

Two drums have their radii in the ratio of 2:3, if the height of the first drum is 1.5m, what is the height of the second drum, if the two contain same amount of water?​

Answers

Answer:

0.6

Step-by-step explanation:

apply the volume of cylinder and equal both of them because both contain same amount of water.

see the picture for full solution

The table shows the possible outcomes of spinning the given
spinner and tossing a fair coin. find the probability of spinning a 1 and tossing a
head.
5
3
4
1 2 3 4 5
h1,
h2,h 3, 4, 5,h
t 1, 2, 3, t4, t5,t
the probability of spinning a 1 and tossing a head is

Answers

Spinning the spinner and tossing the coin is an illustration of probability

The probability of spinning a 1 and tossing a head is 0.10

How to determine the probability?

From the table, we have the following parameters:

Total outcomes, n = 10

A 1 and a head, n(H1) = 1

So, the probability of spinning a 1 and tossing a head is:

P(H1) = n(H1)/n

Substitute known values

P(H1) = 1/10

Evaluate the quotient

P(H1) = 0.10

Hence, the probability of spinning a 1 and tossing a head is 0.10

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a fence is shown on a blueprint and has sides of length 17 cm, 18 cm, 15 cm, and 19 cm. If the scale on the blueprint is 2 cm:7 m, what is the total length of the fence? show ur work pls

Answers

Answer:

241.5

Step-by-step explanation:

First add all your numbers togather

17 + 18 + 15 + 19

= 69

THEN..

Multiply by 7

= 69 × 7

= 483

After that divide it by 2..

483 ÷ 2

= 241.5

How much paper is needed to make a cone with a radius of 6cm, a height of 8cm, and a slant height of 10cm?

Answers

[tex]\sf\large\underline{\star Given:-}[/tex]

[tex]\rightarrow[/tex] Radius(r) of cone = [tex]\sf\pink{6cm.}[/tex]

[tex]\rightarrow[/tex] Height(h) of Cone = [tex]\sf\pink{8cm.}[/tex]

[tex]\rightarrow[/tex] Slant height(l) of cone = [tex]\sf\pink{10cm}[/tex]

[tex]\sf\large\underline{\star To \: Find:-}[/tex]

[tex]\rightarrow[/tex] Length of paper needed to make a cone with above given dimensions (i.e, curved surface area of cone).

[tex]\sf\large\underline{\star Solution:-}[/tex]

[tex]\rightarrow[/tex] As we know that,

Curved surface area of cone = [tex]\sf\blue{πrl}[/tex]

On substituting the value of radius(r) and slant height(l) in this formula we get,

[tex]\rightarrow[/tex] [tex]\sf{=\: \frac{22}{7}×6×10}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\: \frac{22}{7}×60}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\: \frac{1320}{7}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\: 188.57 cm^2.}[/tex]

Therefore, [tex]\sf\purple{188.57cm^2}[/tex] paper is needed to make a cone of given dimensions.

_____________________________

Hope it helps:)

Step-by-step explanation:

Given:-

Radius of cone :- 6cmHeight of cone :- 8cmSlant height of cone :- 10 cm

To find :-

How much paper is needed to make a cone

Concept :-

We need to find the Curved surface area of cone to find the amount of paper needed to make the cone of given dimensions.

Solution :-

As we know ,

the formula for finding the curved surface area of cone :- πrl

putting the known values ,

CSA :- 3.14 × 6 × 10 cm²

CSA of cone :- 188.4 cm²

Answer is 1, I just need the working. Thank you

Answers

there are three pictures with every step

good luck writing that on the paper bro lol

What is the area of this figure? 4 cm 5 cm 5 cm​

Answers

Answer:

100

Step-by-step explanation:

5*5*4=100

Tell which value of the variable is the solution of the equation.

30 = 6w​

w = 3​, 5​, 6​, 8

Answers

Answer:

w = 5

Step-by-step explanation:

6w/6 = 30/6

= 5

30. The surface area of a rectangular prism is
450 m2. What will be the new surface area if
all the dimensions are doubled?
A. 675 m2
B. 900 m2
C. 1,800 m2
D. 3,600 cm
hevolume of a

Answers

Answer:

1800 m²

Step-by-step explanation:

The surface area of a prism is the sum of the areas of its faces.

⇒ Surface area of rectangle prism = 2(LH) + 2(BH) + 2(LB)

⇒ Surface area of rectangle prism = 2(LH) + 2(BH) + 2(LB) = 450 m²

⇒ 2(LH + BH + LB) = 450 m²

Finding the surface area if the dimensions are doubled:

⇒ 2[(2L × 2H) + (2B × 2H) + (2L × 2B)]

⇒ 2[(4LH) + (4BH) + (4LB)]

⇒ 2[4LH + 4BH + 4LB]

⇒ 2[4(LH + BH + LB)]

⇒ 2[2 × 2(LH + BH + LB)]

⇒ 2[2(450)]                                                           [2(LH + BH + LB) = 450 m²]

⇒ 2[900]

1800 m² (Option C)

Karla’s recipe for brownies serves 10 people. She needs to feed 40 people. The ingredients for the original recipe says that she needs 1 3/4 cups of sugar. How many cups of sugar will she need to serve 40 people?

Answers

Answer:

7 cups

Step-by-step explanation:

1 3/4 x 4 = 7

Karla will need 7 cups of sugar to serve 40 people.

Jamie and Linda are having a contest to see whose photo will get more "likes" on social media.

Jamie's photo got 75 likes by the end of the first day and is getting 36 more likes each day.

Linda's likes can be modeled by the function f(x)=18(2)x.
Which statements are true? Select all that apply.

Hint: Use a table or graph to compare the number of likes that Jamie and Linda get. Remember that the value of the function at x=1 represents number of likes at the end of the first day.

Answers

Answer:

2) Jamie's photo gets more likes within the first three days than Linda's photo.

Whats the area of a circle that has a 8mm dimeter using 3.14 of pi

Answers

Answer:

50.24

Step-by-step explanation:

8/2 = 4

3.14 x 4^2 = 50.24

Which value represents |26|?
OA) -26
OB) O
OC) 26
OD) 126

Answers

The answer of the question is OC)26 :)

Larry has a bag of candy that weighs 12 pounds. He wants to divide the candy into 5 equal groups. How much will each group weigh​

Answers

Answer:

2.4 pounds

Step-by-step explanation:

12/5=2.4

To get 5 equal parts of 12, you have to do 12 divided by 5.

Other Questions
Which of the objects below best holds 1 quart? A. gas tank pitcher C. coffee mug D. pool What is the best summary of the passage?a.a boy has been looking forward to his grandmothers visit, but when her car ends up in the shop, she cant make the trip. he feels disappointed until his mother suggests that he and his sister take the train to his grandmothers house. he is hopeful that a four-leaf clover he found will give him good luck on the visit. several obstacles arise that make him worry that the visit will not happen. the boy thinks about his luck with each change of circumstance. ultimately, the boy has good luck, and the visit happens.b.a boy rides the train to visit his grandmother. he prefers riding the train because cars make him feel sick, so he considers getting to ride the train to be good luck. he thinks the good luck comes from a four-leaf clover he found in the park. even when the train stops briefly, the boy feels lucky because it starts moving again quickly and gets him to his grandmother safely.c.a boy wants to visit his grandmother. he picks a four-leaf clover in hopes that it will give him good luck and make the visit happen. his mother tells him that his grandmother cannot come to pick him up, but that turns out to be good luck because it means he gets to ride a train. the boy gets to his grandmothers house and feels lucky.d.a boy and his sister visit their grandmother together. they take the train and are pleased to find out that their grandmother has made cookies. this is a welcome discovery because along the way, they encounter several obstacles that make them worry that the visit will be either cancelled or delayed. State Newton's law of motion. Express each of the following rational numbers in power notation (i) -1/125 how is the level of thyroxine controlled gsce Bob shoots off a small rocket from the balcony of his apartment. The balcony is 30 ft above the ground and the rocket travels at 40 ft/second. When does it reach the highest point? What is the highest point? When does it hit the ground (seconds)? what are difference between graphite and diamond ASAP I GOT 5 MORE MINUTESS HELPPPPPPP Choose the correct answer: A: How often do you eat sushi? B: ____________.a) A while in onceb) Once a in Whilec) Once in a Whiled) In a while once Which group believed that only a powerful government could save card liberty federalist or anti-federalist A dress shop has a markup rate of 200%. find the selling price of a dress that cost the store owner $80.pls help Andy is blowing up a spherically shaped balloon. If he is able to blow 81 cm^3 of air with every breath, it takes him 12 breaths to fully inflate the balloon. What rights do states not have under the Constitution? HISTORY At a concession stand, three hot dog(s) and two hamburger(s) cost $7.50, two hot dog(s) and three hamburger(s) cost $8.75. Find the cost of one hot dog and the cost of one hamburger What are some skills and knowledge of hunter-gatherer? felttheir grievanceswere notaddressed. As aresult, theirdesire tobecomeindependentfrom GreatBritain wasgrowingstronger.A. People in theAmerican coloniesB. Many of the BritishcitizensC. Many of the RedCoats pls help with number 27 to find the area 20 points for awnser and thank you brainly people for helping me so much! Please help me with this question An atom has the amount of 50 electrons, what is the value of the principal quantum number Which results are more likely for someone without personal finance skills? Select three options.larger long-term credit or loan costsless preparation for emergenciesfewer utility expensessimple long-term investment strategiesincreased long-term challengesMark this and returnNeytSubmiteconomics