This table shows direct variation. Find k.

Answer:

The positive value of [tex]k[/tex] will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let [tex]h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80[/tex], roots are those values of [tex]t[/tex] so that [tex]h(t) = 0[/tex]. That is:

[tex]19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0[/tex] (1)

Roots are determined analytically by the Quadratic Formula:

[tex]t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}[/tex]

[tex]t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }[/tex]

The smaller root is [tex]t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }[/tex], and the larger root is [tex]t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }[/tex].

[tex]h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80[/tex] has one real root when [tex]\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0[/tex]. Then, we solve the discriminant for [tex]k[/tex]:

[tex]\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}[/tex]

[tex]k \approx \pm 0.028[/tex]

The positive value of [tex]k[/tex] will result in exactly one real root is approximately 0.028.

Answer:

B

Step-by-step explanation:

This is due to the fact that the first equation is saying it is equal to y so you replace the y variable with the equation

Answer:

since y=2x+4 just substitute y with 2x+4

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

so the answer is B

Answer:

270 degrees.

Step-by-step explanation:

A full rotation is equal to 360 degrees. 3/4 * 360 = 270.

Answer:

I think she works 10 hours and 30 minutes

Answer:

8

Step-by-step explanation:

Answer:

52 girls and 39 boys (multiply each by 13)

Step-by-step explanation:

4 x 13 = 52

3 x 13 = 39

         = 91

Answer:

D) I hope this helps you out :)

Answer:

The area is 15 feet

Step-by-step explanation:

So you are going to need two different equations-

l = w(3)

2l + 2w = 40

Insert the first equation into the second-

2(3w) + 2w = 40

Simplify this equation-

6w + 2w = 40

8w = 40

Divide both sides by 5

w = 5

Solve first equation

l = 5(3)

l = 15

Then find the area-

5 x 15 = 75

Answer:

how is that college math

Step-by-step explanation:

Answer:

[tex]1) \frac{37.5}{100} [/tex]

[tex]2) \frac{9}{40} \times 100 = 22.5 \% [/tex]

[tex]3) \frac{7}{10} \times 100 = 70\%[/tex]

[tex]4) \frac{7}{8} \times 100 = 87.5\%[/tex]

[tex]5) \frac{12}{25} \times 100 = 48\%[/tex]

Answer:

C=550 pounds

Step-by-step explanation:

Given the formula: C=p(t+30)

and with p=2 and t=245 known.

We can plug our values of p and t into our formula. Once we do this, the only unsolved variable will be C.

C=2(245+30)

Add 245+30 first because they are in parentheses and we must abide by the order of operations.

C=2(275)

Now we just multiply 2(275) because this is all that's left in the formula.

C= 2*275 = 550

We now know that C=550 when p=2 and t=245, but we need to apply units to finalize the answer. We are told that C represents the total cost in "POUNDS", so pounds is our units for variable C.

Our final answer is...

C=550 pounds

Answer:

I'm pretty sure the answer is 250,000 dollars.

Step-by-step explanation:

I' sorry if it isn't right I tried my best.

Answer:

A 4040 bag sample 25.0425.0 grams. A level of significance of 0.020.02

the decision rule. Assume the standard deviation is known to be 11.011.0.

Step-by-step explanation:

Answer:

im sure its D.)

Step-by-step explanation:

Answer:

divide 88 by the number of x

88/8= 11

X = 11

Answer:

x=11

Step-by-step explanation:

8x=88

You use inverse operation which means you would divide 8 on both sides to isolate x on one side resulting in x=11

Answer:

it would be 5

Step-by-step explanation:

I don't have an explanation I just know it is 5

Answer:

x = 6.1

Step-by-step explanation:

Reference angle = 29°

Hypotenuse = 7

Adjacent side = x

Applying trigonometric ration, we would have:

Cos 29 = x/7

Multiply both sides by 7

7*cos 29 = x

6.12233795 = x

x = 6.1 (nearest tenth)

Answer:

Step-by-step explanation:

A= (7,-9)

B= ( 6,-12)

Answer:

A.) 65x + 35X + 50 = 250

65x = cost of concrete per cubic yard, x is yd³

35X = cost of pouring/finishing concrete per cubic yard, X is yd³

50 = delivery cost

250 = the money you have

B.) 400 + 15n = 505

15n = amount of money you deposite per week, n is # of week

400 = some money in account after n week passed

505 = initial money in bank

C.) 1.1X - 10 = 55

55 = total cost of clothes

1.1X = tax rate where X is the undiscounted clothe cost

10 = discount

Answer:

1

Step-by-step explanation:

Answer:

EF = 7

Step-by-step explanation:

the two triangles shown are congruent triangles

we know this because they share the line FD

and DE and DG are both 5

so the length two sides are definitely congruent, this means that the third side will also be congruent

the third side would be FG and EF

FG is 7 so then EF is 7

Answer:

EF is 7                

Step-by-step explanation:

Key skills needed: Triangle Congruence

1) We need to find out The length of EF

2) To find this, let's use Congruence of Two Triangles

The triangles that we can prove congruent are Δ DFG and Δ DFE

3) Both share the side DF, so we have one side

Both have a right angle, < FDG is a right angle, and < FDE would also be right angle (you can prove this as ---> < FDE is supplementary to a right angle, and therefore it would also be a right angle)

Both share a congruent set of sides (GD and DE both are 5)

4) With the 3 things above we can say -->  Δ DFG ≅ Δ DFE with SAS (side-angle-side)

5) This means that corresponding parts would be congruent.

FG ≅ EF. This means EF would be the same length as FG. Since FG is 7, then EF would be 7.

Hope you understood and have a nice day!! :D

Answer:

Step-by-step explanation:

I'm not sure about number 3, but I have the answer for number. The answer is 1:32.

3: 69

3/69

Then we reduce the fraction to the lowest term

3/69 = 1/32

1:32

Just divide 96/3 and you can see that one bus can hold 32 students

Answer:

7

Step-by-step explanation:

Answer:

the answer is d i took the quiz

Step-by-step explanation:

Answer:

1 lb=2 batches     3/4 lb=1 1/2 batches     1/4 lb= 1/2 a batche

Step-by-step explanation:

1x2=2   b

3/4x2=1   1/2   b

1/4x2=1/2   b

b=batches

Answer:

16/20

Step-by-step explanation:

16/20 = (4*4)/(4*5) = 4/4*4/5 = 4/5