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 Thanks anyone for help :)))

Answer:

The answer is option 1.

Step-by-step explanation:

In order to find the equation, you have to apply Discriminant Law, D = b² - 4ac. When D < 0, the equation has no real roots (no x-intercept). When D = 0, it has 2 and equal roots (1 x-intercept). When D > 0, it has 2 distinct roots (2 x-intercept).

Option 1,

[tex]y = 3 {x}^{2} - 2x + 1[/tex]

[tex]D = {( - 2)}^{2} - 4(3)(1)[/tex]

[tex]D = - 8[/tex]

[tex]D < 0[/tex]

Option 2,

[tex]y = 3 {x}^{2} - 6x + 3[/tex]

[tex]D = {( - 6)}^{2} - 4(3)(3)[/tex]

[tex]D = 0[/tex]

Option 3,

[tex]y = 3 {x}^{2} - 7x + 1[/tex]

[tex]D = {( - 7)}^{2} - 4(3)(1)[/tex]

[tex]D = 37[/tex]

[tex]D > 0[/tex]

Option 4,

[tex]y = 3 {x}^{2} - 4x - 2[/tex]

[tex]D = {( - 4)}^{2} - 4(3)( - 2)[/tex]

[tex]D = 40[/tex]

[tex]D > 0[/tex]

As you look at the graph, the curve does not meet x-axis so the discriminant must be less than 0.

The given curve in the graph is generated by the equation y =3x² - 2x +1. The correct option is A.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

In order to find the equation, you have to apply Discriminant Law, D = b² - 4ac. When D < 0, the equation has no real roots (no x-intercept). When D = 0, it has 2 and equal roots (1 x-intercept). When D > 0, it has 2 distinct roots (2 x-intercepts).

Option 1,

y =3x² - 2x +1

D = b² - 4ac

D = ( -2 )² - ( 4 x 3 x 1 )

D = 4 - 12

D = -6

D < 0

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Answer:

16.66 years

Step-by-step explanation:

100(the percentage that it needs to increase) divided by 6 (the percentage of intrest) You could do 1.0/0.06 but i find it eaiser to do it this way

It will take 33.33 years to double his money.

We have roger who inherited $5000 from his father who invested the money in an account bearing 6% annual interest.

We have to find out how long it would take for this inheritance to double in value.

The formula to calculate the Simple Interest on a given amount of principal money (x) at the rate of (r%) for a given amount of time (t) is -

[tex]SI =\frac{x \times r \times t}{100}[/tex]

In the question given : Simple Interest = 2 x Principal = 2[tex]x[/tex]

Hence, the equation becomes -

[tex]2x =\frac{x\times r\times t}{100} \\\\t = \frac{200}{r} \\\\t = \frac{200}{6} \\[/tex]

t = 33.33 years

Hence, it will take 33.33 years to double his money.

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Answer:170

Step-by-step explanation:

The measure of angle LNP is 275 degrees.

The inscribed angle theorem says that an inscribed angle is half the intercepted arc measure.

In the circle below, O is the center, MP is the diameter, and mangle POL = 85º.

The measure of angle  LNP is determined in the following steps given below.

[tex]\rm \angle LNP=360-\angle POL\\\\ \angle LNP=360-85\\\\ \angle LNP=275[/tex]

Hence, the measure of angle LNP is 275 degrees.

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Answer:

D= {-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6}

R={-6,-5,-4,-3,-2,-1,1,2,5)

Step-by-step explanation:

Step-by-step explanation:

Hi there!!

Here, the thing is we should add them first yaa.

so, let's add them

[tex] = - 2 \frac{1}{6} + \frac{7}{3} [/tex]

by taking lcm we get their lcm is 6 and let's do it according to that,

[tex] = \frac{ - 12 \times 1}{6} + \frac{7 \times 2}{6} [/tex]

now, let's simplify them ok..

[tex] = \frac{ - 12 + 14}{6} [/tex]

so, we get 2/6 (i.e 1/3)

now, the number line must be greator than 1 and less than 1.

Hope it helps...

Answer:

1/25

Step-by-step explanation:

[tex]\frac{5^{4} }{5^{6} } =\frac{1}{5^{2} } =\frac{1}{25}[/tex]

Answer:

see explanation

Step-by-step explanation:

GC = 11B + 1D

WS = 9B + 2D

Linear equations will point downward

Western Sizzlin is the best deal per person because in total it would be $11 and Golden Corral would be $12.

Answer:

Also, there seem to be many typos in this question, I am trying my best to decipher them all :) next time maybe double check the wording thx!

Step-by-step explanation:

the question doesn't make sense because if you were to pay $1120 per month, for 2 years, you would go over the amount that you bought. I also am not sure what a dews payment is. Try wording it differently/check you spelling.

Answer:

120

Step-by-step explanation:

expand and calculate

10x9x8x7!/(10-3)!x3!

10x9x8x7!/7!x3!

reduce

10x9x8x7!/7!x3!

10x9x8/3!

Calculate the product

10x9x8/3!

Now Cacluate the factorial

720/3!

720/6

reduce

120

Answer: 120

Step-by-step explanation:

Answer:

y=4x-5

Step-by-step explanation:

y=mx+b,

You can identify that the y-intercept is -5.

Using rise/run, there is a rise of +4 and a run of +1, 4/1=4.

Slope = 4

Y-intercept=-5

Slope-intercept form of equation of line is, y = mx + c

Equation of line L is,  y = 5x - 5

From given figure, it is observed that line L is passing through point (0, -5) and (1, 0).

 First we have to find slope (m) of line.

                       [tex]m=\frac{0-(-5)}{1-0} =5[/tex]

So, equation of line becomes,

                           [tex]y=5x+c[/tex]

Since, line passing through (1, 0). Therefore, substituting point (1, 0) in above equation of line.

We get,     c = - 5

Thus, equation of line is,  [tex]y=5x-5[/tex]

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Answer:

P(white region) = 0.75 or 75%

Step-by-step explanation:

Find the area of the shaded region:

A = πr²

A = π(2)²

A = 12.56

Find the area of the entire dartboard:

A = πr²

A = π(4)²

A = 50.24

Find the probability that the dart hits the blue region:

P(blue region) = Area of blue region/ Total Area

P(blue region) = 12.56 / 50.24

P(blue region) = 0.25

As total probability is equal to 1, find the probability of throwing a dart that hits the white part of the board by substracting 0.25 from 1

P(white region) = 1 - P(blue region)

P(white region) = 1 - 0.25

P(white region) = 0.75

your work for the first one is perfect!!

the second one gives you the side lengths of x+2 and x-5. the formula for the area of a rectangle is l×w so you have to multiply (x+2)(x-5) and im sure you can figure that out but the answer to that is x^2-3x-10

you set up number 3 right, you just need to continue with the distribute property which would give you 4x^2-20x+25

number 4 is the same as the other ones and the answer is 36x^2-1

number 5 is just distributing the -z^3 into everything in the parenthesis giving you -5z^3-z^4+4z^5

I cant see all your work for number 6, but I can see that your term for c is 5, when it is actually -5. it looks like you didnt subtract it to make the quadratic equal to zero and to do that you would have to subtract 5.

tbh I cant read number 7

hope that helped :)

Answer:

∠B = 63°, ∠F = 59°

Step-by-step explanation:

Given that  angle D measures 31° and angle A measures 27°.

From the diagram attached, ∠ E = 90°, ∠G = 90°.

Also ∠C + ∠G = 180° (sum of angles on a straight line)

∠C + 90 = 180

∠C = 180 - 90 = 90°

To find the measure of ∠B and ∠F, we use the triangles ABC and DEF, remember that the sum of all interior angles of a triangle is 180°. In triangle ABC:

∠A + ∠B + ∠C = 180° (angles in a triangle).

27 + ∠B + 90 = 180

∠B + 117 = 180

∠B = 180 - 117

∠B = 63°

Also in triangle DEF:

∠D + ∠E + ∠F = 180° (angles in a triangle).

31 + 90 + ∠F = 180

∠F + 121 = 180

∠F = 180 - 121

∠F = 59°

Answer:

The slope is 1

Step-by-step explanation:

there's actually a trick you can do to find the slope. if you go from where the y-intercept is and go over to the x- intercept it will give you the slope hope this helps you

Answer:

x = 29

Step-by-step explanation:

If the lines are parallel

< CBA = < DAB due to the fact that they are alternate interior angles

42 = DAB

We also know that

DAB + BAC + CAE = 180 since they form a straight line

Substituting the given values

42+ 109 + x = 180

Combine like terms

151 + x = 180

151+x-151 = 180-151

x = 29

Answer:

Hey there!

4 1/5 · 7 2/3= 32 1/5

Hope this helps :)

Answer:

32 1/5

Step-by-step explanation:

4 1/5 * 7 2/3

Change to improper fractions

( 5*4+1)/5 * ( 3*7+2)/3

21/5 * 23/3

Rewriting

21/3 * 23/5

7 * 23/5

161/5

Change back to a mixed number

5 goes into 161  32 times  with 1 left over

32 1/5

Answer:

$6250

Step-by-step explanation:

6250x.075x8=3750

6250+3750=10,000

Answer:

Hey there!

We have the absolute value of x is greater than two.

Thus, to solve absolute value inequalities, we want to break the inequality down.

We break this down to

x>2

x<-2

Thus, we don't need to simplify this any further, and have our answer.

Hope this helps :)

Answer:

x >= 2 or x <= -2

Step-by-step explanation:

|x|>= 2

Means the absolute value of x is greater than or equal to two.

When we deal with absolute value, we can equivalently break into two cases

+x >= 2    => x >= 2

-x >= 2    =>  x <= -2

On the number line it looks like what is shown in the attached figure.    

Answer:

a(n) = 1(2.5)^(n - 1)

Step-by-step explanation:

The geometric sequence is 1, 2.5, 6.25, 15.625, and so on; the first term is 1.  The common ratio is 2.5; each new term is 2.5 times the previous term.

The explicit formula desired is thus a(n) = 1(2.5)^(n - 1)

Answer:

ITS CCCCCCC (2.5)

Answer:

441 rectangles

Step-by-step explanation:

Formula for the number of rectangles in a chessboard=

n²(n + 1)²/ 4

We are told in the question that is a 6×6 chessboard

Hence, n = 6

= 6²(6 + 1) ²/ 4

= 6²× 7²/4

= 36 × 49/4

= 1761/4

= 441 rectangles

Therefore, the number of rectangles in 6×6 chessboard is 441 rectangles.

Answer:

C. outlier = 138

mean with outlier = 27.1

median with outlier = 11

mean without outlier = 8.7

median without outlier = 8

Step-by-step explanation:

Hey there!

Well if the outlier is 138 then we can cross out choices A and B.

So let's find the mean with and without the outlier.

With - 27.1

Without - 8.7

Median)

With - 11

Without - 8

By using this information we can conclude that the answer is C.

Hope this helps :)

Answer:

Won't they be on the same place, so 360° i think

Answer:

10 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

If there are illustrations to given problems, please share those illustrations.  Thank you.  

The only value of x for which  [x-5]=1 is true is 6:   [6-5]=1

Steps to solve:

x - 5 = 1

~Add 5 to both sides

x - 5 + 5 = 1 + 5

~Simplify

x = 6

Best of Luck!

Answer:

a constant multiplied by y can affect the linear, because it determines a dependent variables.

Step-by-step explanation:

a linear relationship is a statistical term used to described a straight line relationship between two variables.

Answer:

[tex]PQ = x + 13[/tex]

The dimension of the garden is 52.5ft by 43.5ft

Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

[tex]W = x[/tex]

[tex]L = x + 9[/tex]

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

[tex]PQ = L + 4[/tex]

Substitute [tex]x + 9[/tex] for [tex]L[/tex]

[tex]PQ = x + 9 + 4[/tex]

[tex]PQ = x + 13[/tex]

Also;

[tex]QR = W + 4[/tex]

Substitute [tex]x[/tex] for [tex]W[/tex]

[tex]QR = x + 4[/tex]

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

[tex]Area_1 = L * W[/tex]

Recall that  [tex]W = x[/tex] and [tex]L = x + 9[/tex]

So;

[tex]Area_1 = x * (x + 9)[/tex]

For the bigger rectangle

[tex]Area_2 = PQ * QR[/tex]

Recall that  [tex]PQ = x + 13[/tex] and [tex]QR = x + 4[/tex]

So;

[tex]Area_2 = (x + 13)(x + 4)[/tex]

Given that the Area of the walkway is [tex]400ft^2[/tex]

This implies that

[tex]Area_2 = Area_1 + 400[/tex]

Substitute [tex]Area_1 = x * (x + 9)[/tex] and [tex]Area_2 = (x + 13)(x + 4)[/tex]

[tex](x + 13)(x + 4) = x * (x + 9) + 400[/tex]

Open All Brackets

[tex]x^2 + 13x + 4x + 52 = x^2 + 9x + 400[/tex]

[tex]x^2 + 17x + 52 = x^2 + 9x + 400[/tex]

Collect Like Terms

[tex]x^2 - x^2 + 17x - 9x = 400- 52[/tex]

[tex]8x = 348[/tex]

Divide both sides by 8

[tex]\frac{8x}{8} = \frac{348}{8}[/tex]

[tex]x = \frac{348}{8}[/tex]

[tex]x =43.5[/tex]

Since the dimensions of the garden is [tex]W = x[/tex] and [tex]L = x + 9[/tex]

Substitute 43.5 for x in both cases

[tex]L = 43.5 + 9 = 52.5[/tex]

[tex]W = 43.5[/tex]

Hence, the dimension of the garden is 52.5ft by 43.5ft

Answer:

$11095.45

Step-by-step explanation:

This is a problem in continuous compounding, for which the formula is

P = Ae^rt, r being the annual interest rate as a decimal fraction and t being the time in years.  Here we have:  

P = $9900e^(0.019)(6) = $11095.45

Answer:

11095

Step-by-step explanation:

Rounding to the nearest dollar

-(1/-11)(77+1100)=107

Answer:

107

Step-by-step explanation:

-(1/-11)(77+1100)

1/11(1177)

=107

HL = hypotenuse leg

We see that WX = PM are the congruent legs (they are the same length due to the similar single tickmark). Also, XY = ME is the congruent pair of hypotenuses. The HL rule only works for right triangles, as the term "hypotenuse" would not apply for a non-right triangle.

The theorem used is HL.

A theorem is a statement which has been proved true by a special kind of logical argument called a rigorous proof.

Given:

In both triangles

XW = MP  (given)

XY = ME (given)

As, hypotenuse of both triangle is equal and leg of one right triangle are congruent to the hypotenuse.

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Answer:

$2216.72

Step-by-step explanation:

Simply plug in your known variables into the formula:

a = 1000

r = 0.04 (4%)

n = 4

t = 20

A = 1000(1 + 0.04/4)⁴⁽²⁰⁾

A = 1000(1 + 0.01)⁸⁰

A = 1000(1.01)⁸⁰

A = 1000(2.21672)

A = 2216.72

Answer:

[tex]P(At\ least\ 1) = 0.985[/tex]

Step-by-step explanation:

Given

Proportion = 55%

Required

Probability that at least one out of 7 selected finds a job

Let the proportion of students that finds job be represented with p

[tex]p = 55\%[/tex]

Convert to decimal

[tex]p = 0.55[/tex]

Let the proportion of students that do not find job be represented with q

Such that;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

[tex]q = 1 - 0.55[/tex]

[tex]q = 0.45[/tex]

In probability; opposite probabilities add up to 1;

In this case;

Probability of none getting a job + Probability of at least 1 getting a job = 1

Represent Probability of none getting a job with P(none)

Represent Probability of at least 1 getting a job with P(At least 1)

So;

[tex]P(none) + P(At\ least\ 1) = 1[/tex]

Solving for the probability of none getting a job using binomial expansion

[tex](p + q)^n = ^nC_0p^nq^0 + ^nC_1p^{n-1}q^1 +.....+^nC_np^0q^n[/tex]

Where [tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex] and n = 7; i.e. total number of graduates

For none to get a job, means 0 graduate got a job;

So, we set r to 0 (r = 0)

The probability becomes

[tex]P(none) = ^nC_0p^nq^0[/tex]

Substitute 7 for n

[tex]P(none) = \frac{7!}{(7-0)!0!} * p^7 * q^0[/tex]

[tex]P(none) = \frac{7!}{7!0!} * p^7 * q^0[/tex]

[tex]P(none) = \frac{7!}{7! * 1} * p^7 * q^0[/tex]

[tex]P(none) = 1 * p^7 * q^0[/tex]

Substitute [tex]p = 0.55[/tex] and [tex]q = 0.45[/tex]

[tex]P(none) = 1 * 0.55^7 * 0,45^0[/tex]

[tex]P(none) = 0.01522435234[/tex]

Recall that

[tex]P(none) + P(At\ least\ 1) = 1[/tex]

Substitute [tex]P(none) = 0.01522435234[/tex]

[tex]0.01522435234+ P(At\ least\ 1) = 1[/tex]

Make P(At least 1) the subject of formula

[tex]P(At\ least\ 1) = 1 - 0.01522435234[/tex]

[tex]P(At\ least\ 1) = 0.98477564766[/tex]

[tex]P(At\ least\ 1) = 0.985[/tex] (Approximated)