Find the range of values of k for which the equation 4x² + 12x + k = 0 has no real roots.

Answers

Answer 1

Hello there!

Answer:

[tex](9, +\infty)[/tex]

Step-by-step explanation:

It has no real roots only if

[tex] \sqrt{b {}^{2} - 4ac } [/tex]

has no roots. That means that b² - 4ac is smaller than 0:

[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]

Answer 2

we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]


Related Questions

8. Using the formula C= id, find the circumference of a circle with a
diameter of 9 cm.
A. 28.26 cm B. 28.26 m C. 29.26 cm D. 29.26 m​

Answers

Answer:

Circumference of a circle, C

                 [tex]C=\pi d= \pi 9=28.26cm\\Option \ A[/tex]

Identify and write down the keywords in the word problem. (1.) Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3. Evaluate the expression 2g + 3a when g = 4 and a = 8 to find the cost of buying 4 cartons of grape juice and 8 cartons of apple juice. What is the difference in price Missy and Jared paid? Show your work.

Answers

The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.

The cost of 4 grapes and 8 apples will be,

Cost = 2g + 3a

Cost = ( 2 x 4 ) + ( 3 x 8 )

Cost = 8 + 24

Cost = $32

The difference in the price  Missy and Jared paid is,

Difference = $32 - $ 20

Difference = $12

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Which set of lengths CAN form a triangle?
6, 9, 12
3, 3 ,7
1, 2, 3
6, 9, 15

Answers

the first one can be a triangle and the last one 6 9 12

A recipe for punch requires 20 grams of drink mix for 5 liters.

How many grams of drink mix are needed per liter of water?

Answers

4 grams of drink mix is needed per liter of water

Do you know how to do this

Answers

Answer:

B

C

E

Step-by-step explanation:

2.9 and 3.8 are .9 apart

Select all answers with a .9 difference

39➗(2+1) - 2x (4+1)
5/7 - Exit Ticket

Answers

Answer:

13 - 10x

= -3x

hope it helps

6029-5817 is the correct answer 45

Answers

the answer is 212 .... not sure where 45 came from

Billy is creating a circular garden divided into 8 equal sections. The diameter of the garden is 12 feet.

Billy noticed that several of his carrots had been eaten by some mischievous rabbits. Billy wants to build a fence around his circular garden to keep the rabbits out. How much fence would Billy need? Explain how you determined your answer. Show all your work.

Billy decides that next year he will make his garden a raised-bed garden. He plans to make a short wall of paving bricks all the way around the garden, then fill the space inside with fresh soil. If he makes the wall 1 foot high, what volume of soil will he have to purchase in order to fill the circle to the top of the bricks?

Answers

Answer:

Step-by-step explanation:

area=πr^2

so we need to find the area then divide by 8

so

we know that diameter=2radius or diameter/2=radius so

12=diameter

12/2=radius=6

subsitute

area=π(6)^2

area=36π

divide 36π by 8

36π/8=18π/4=9π/2π=4.5π

area of one section is 4.5π square feet or if we aprox pito 3.14159 then we get

4.5(3.14159)=area=14.1372 square feet or 14.14 square feet

Find the length of a using the Pythagorean theorem

Answers

Answer:

a = 12

Step-by-step explanation:

a² + 9² = 15²

a² = 15² - 9²

a² = 225 - 81

a² = 144

take the square root of both sides

a = 12

Answer:

[tex] {a }^{2} + {9}^{2} = {15}^{2} \\ {a}^{2} = - 81 + 225 \\ {a}^{2} = 144 \\ a = \sqrt{144 \: } \\ a = 12[/tex]

The solid below is made of eight rectangular prisms, each with dimensions of 14 inches (in.) by 9 inches by 10 inches.
What is the volume, in cubic inches, of the object?

DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest.

Answers

Answer:

D

Step-by-step explanation:

Volume of one prism

V = base x width x height = 14 x 9 x 10 = 1260 in^3

Volume of the solid

V = volume of one prims x 8 = 1260 x 8 = 10,080 in^3

Let ​x^2+10x=6.
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x^2+10x+___=___

Answers

Answer:

x² + 10x + 25 = 31

Step-by-step explanation:

To complete the square use half the x coefficent (10/2 = 5)

and square it (5² = 25)

Then add it to both sides

x² + 10x + 25 = 6 + 25

x² + 10x + 25 = 31

Answer:

x^2 + 10x + 25 = 31

Step-by-step explanation:

x^2 + 10x + (10/2)^2 = 6 + 25

x^2 + 10x + 25 = 6 + 25

x^2 + 10x + 25 = 31

The first step requires a bit of explanation. The way to complete the square is to take 1/2 the linear term (10x) and square it

1/2 10 = 5

5 squared = 25

That number must be added to the right side to maintain equality.

Chau will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $44 and costs an
additional $0.11 per mile driven. The second plan has an initial fee of $49 and costs an additional $0.07 per mile driven.

for what amount of driving to the two plans cost the same amount?

What is the cost when the two plans cost the same?

Answers

Answer:

I don't know

Step-by-step explanation:

i don't know

A new business borrows $320,000 at a yearly simple interest rate of 7%.
The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!

Answers

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]

explain step by step please thank you! Paco drives an average of 55 miles per hour. Their destination is 274 miles away. wants to arrive at 4:00 p.m. and allow an extra hour for stops. What time should he go out?​

Answers

Answer:

11:01 am

Step-by-step explanation:

If paco drives 55 miles per hour you must divide 274 by 55 to find the amount of time it will take for him to reach his destination:

274÷55=4.981818...

Now we have 4 hours plus 0.981818.. hours which the latter we multiply by 60 to find out how many minutes are 0.981818 hours:

60×0.981818...=58.9090...

which I will round to 59 as clocks show an hour and a minute so rounding it so it's accurate to the second is unnecassary, this means it will take him 4 hours 59 minutes to reach his destination so we subtract this from 4:00 pm:

4:00 pm-4 hours 59 minutes= 11:01 am

So our answer is 11:01 am

whats 2+2 pls i have a test tomorrow i need to pass it

Answers

4. Some other ways to get 4 are 2^2, 4/1, 2x2, 5-1, and 1+3.
Factors include:
1, 2, and 4. As a result, it’s not a prime number.
the answer to this question is 4

The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.

Answers

The density of the material is 1533.3 grams per quarts.

What is density?

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.

Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.

The formula to find the density is Density=Mass/Volume

Density =6900/4.5

Density= 1533.3 grams per quarts

Therefore, the density of the material is 1533.3 grams per quarts.

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a(n)=6+(n-1)(-2) what its the fourth sixth and thirteenth terms

Answers

Answer:

4th term = 0

6th term = -4

13th term = -18

Step-by-step explanation:

a(n) = 6 + -2(n-1)

a(4) = 6 + (-2)(3) which is 6-6

a(6) = 6 + (-2)(5) which is 6-10

a(13) = 6 + (-2)(12) which is 6-24

rewrite the rectangular equation x^2+y^2-8y=0 as a polar equation

Answers

Answer:

We'll use the following identities:

r = √(x2 + y2), from which we also have r2 = x2 + y2

y = r*sinθ

First, let's re-write your equation:

r = 8*sin(θ).  Multiply both sides by r:

r2 = 8r sin(θ)

Now, we'll use substitute using the identities:

x2 + y2 = 8y

Re-arrange and complete the square:

x2 + y2 - 8y = 0

x2 + (y-4)2 - 16 = 0

x2 + (y-4)2 = 16

This represents a circle with center (0,4), and radius 4.

Step-by-step explanation:

sorry if it wrong

Is (2, 3) a solution for the equation 2x + 3y = 6?

Answers

Answer:

No

Step-by-step explanation:

Input the values and see if the equation is true.

2x + 3y = 6

(2, 3) x = 2, y = 3

2(2) + 3(3) = 6

4 + 9 = 6

13 ≠ 6

NEED HELP LOL

if i have an 80% in a class for the first semester and a 90% in a class for the second semester, what is my grade for the year?

Answers

80+90/2=85
Your answer is 85%

For the geometric sequence, the common ratio is 2 and the 12th term is a12 =6144. What is the first term?

A. a1=2

B.a1=3

C.a1=4

D.a1=5

Answers

Answer:

B. a1 = 3

Step-by-step explanation:

Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:

[tex]6144 /2/2/2/2/2/2/2/2/2/2/2 = 3[/tex]

For a better understanding of the question, let's use the formula for geometric equations:

a(r)^(n-1)

1. Let's plug in the values we know

r = common ratio = 2 n = 12

a(2)^(12-1)

2. Set equation equal to 6144 (Since we use n = 12) and solve for a

a = 6144/ (2^11) a = 3

To confirm this, let's use the formula for geometric equations again:

a(r)^(n-1)

a = first term = 3

r = common ratio = 2

3(2)^(12-1) = 6144

Therefore, a1 = 3

which expressions are equivalent to 2(-6c + 3) + 4c
A. -8c + 6
B. 3(-4c + 2)+4c
C. None of the Above​

Answers

Answer:

A and B

Step-by-step explanation:

2(-6c + 3) + 4c

According to PEMDAS, we should evaluate the parentheses first.

However, the parentheses are already simplified completely.

Now we look for exponents. However, there are no exponents.

Next is multiplication. We can see there is a 2 directly outside of the parentheses. Distribute the 2 across each term in the parentheses.

-12c + 6 + 4c

Now combine like terms with addition.

-8c + 6

We can see that A. -8c + 6 is an answer choice.

Let's look at B. 3(-4c + 2) + 4c

Following the same steps, we will move on to multiplication.

-12c + 6 + 4c

Combine like terms with addition.

-8c + 6

This is also an answer choice.

Hope this helps!

Find the equation of the exponential function represented by the table below: 1 4 16 64

Answers

Only given 1 4 16 and 64 it seems to be y = 4^x assuming that f(0)=1 and f(1)=4 and so on

multiply the sum by the difference of 19 and 57​

Answers

Answer:2009#73

Step-by-step explanation:

3939+373

Ie,ek

A woman bought a number of items for $24. She realized that if she had bought 4 more items for
the same money, she would have pald $8 less per Item. How many Items did she buy?

Answers

Answer:

The woman bought 2 items at $12 each.

Step-by-step explanation:

Given that a woman bought a number of items for $ 24, and she realized that if she had bought 4 more items for the same money, she would have paid $ 8 less per item, to determine how many Items did she buy the following calculation must be done:

X = 24

X + 4 = 24

24/2 = 12

24/6 = 4

12 - 4 = 8

Therefore, the woman bought 2 items.

PLEASE help test due tonight !!!Use the two-way frequency table to answer questions #14-19

Answers

Answer:

14. 1/13

15. 14/15

16. 1/13

17. 15/30=1/2

18. 12/13

19. 12/15

If you are happy with my answers, please give brainliest <3

The Barker family just left the local pet store with Lucky, their new family dog. The pet store owner told the Barker family that for the next 6 months, Lucky would grow at an average rate of 9 pounds per month. Currently, Lucky is 2 months old and weighs 3 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 3 at 2 months old Part A: Complete the given table that represents Lucky's current weight, in pounds, as a function of his age, in months. Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Lucky's current weight, in pounds, as a function of his age, in months. Part D: If Lucky continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Lucky weigh by the time he is one year old?

Answers

The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.

Answers

A linear equation that models the situation is 1.4p + 2n = 40.

This equation represents the total daily revenue from the pens (1.4p) and notebooks (2n) and sets it equal to the target revenue of $40. The variables p and n represent the number of pens and notebooks sold, respectively. This equation can be used to determine the number of pens and notebooks that need to be sold in order to reach the target revenue of $40.

Answer:

1.40p+2n=40

Step-by-step explanation:

Two sides of a parallelogram are 500 feet and 790 feet. The measure of the angle
between these sides is 33°. Find the area of the parallelogram to the nearest square
foot

Answers

Answer:

215117 ft²

Step-by-step explanation:

Assumed the base is the longer side.

The height of the parallelogram is:

h/500 = sin 33° h = 500 sin 33° h =  272.3 ft

The area is:

A = bh A = 790*272.3 = 215117 ft²

Answer:

215132

Step-by-step explanation:

deltamath

A survey where political groups try to collect information about what voters think is called a * Ballot initiative Public opinion poll Electoral College Acondidate is chosen to run for office is called​

Answers

Answer:

Step-by-step explanation:

A person selected by others to run for office is the nominee.

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