Select ALL TRUE statements about Linear Functions:
Group of answer choices

The degree of the function is one.

The y values change by a common difference.

The graph is a straight line.

Vertex form is used for graphing.

Answer:

The possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Step-by-step explanation:

From statement we know that [tex]AB = 2\cdot BC[/tex]. By Analytical Geometry, we use the equation of a line segment, which is an application of the Pythagorean Theorem:

[tex]AB = 2\cdot BC[/tex]

[tex]\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}} = 2\cdot \sqrt{(x_{C}-x_{B})^{2}+(y_{C}-y_{B})^{2}}[/tex] (1)

Where:

[tex]x_{A}[/tex], [tex]x_{B}[/tex], [tex]x_{C}[/tex] - x-Coordinates of points A, B and C.

[tex]y_{A}, y_{B}, y_{C}[/tex] - y-Coordinates of points A, B and C.

[tex](x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2} = 4\cdot (x_{C}-x_{B})^{2}+4\cdot (y_{C}-y_{B})^{2}[/tex]

Then, we expand and simplify the expression above:

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} +x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot (x_{C}^{2}-2\cdot x_{C}\cdot x_{B}+x_{B}^{2})+4\cdot (y_{C}^{2}-2\cdot y_{C}\cdot y_{B}+y_{B}^{2})[/tex]

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} + x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot x_{A}^{2}-8\cdot x_{C}\cdot x_{B}+4\cdot x_{B}^{2}+4\cdot y_{C}^{2}-8\cdot y_{C}\cdot y_{B}+4\cdot y_{B}^{2}[/tex]

If we know that [tex]x_{A} = 5[/tex], [tex]y_{A} = 6[/tex], [tex]x_{B} = 1[/tex], [tex]y_{B} = b[/tex], [tex]x_{C} = 1[/tex] and [tex]y_{C} = -3[/tex], then we have the following expression:

[tex]1 -10 +25 +b^{2} -12\cdot b+36 = 100 -8 +4 +36+24\cdot b +4\cdot b^{2}[/tex]

[tex]b^{2}-12\cdot b +52 = 4\cdot b^{2}+24\cdot b +132[/tex]

[tex]3\cdot b^{2}+36\cdot b +80 = 0[/tex]

This is a second order polynomial, which means the existence of two possible real solutions. By Quadratic Formula, we have the following y-coordinates for point B:

[tex]b_{1} \approx -2.944[/tex], [tex]b_{2} \approx -9.055[/tex]

In consequence, the possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Answer:

x=4

Step-by-step explanation:

1. Rearrange terms

[tex]2(-3x+3)=-18[/tex]

2. Distribute

[tex]-6x+6=-18[/tex]

3. Subtract 6 from both sides of the equation

[tex]-6x+6-6=-18-6[/tex]

4. Simplify by subtracting the numbers

[tex]-6x + 6-6=-18-6[/tex]

[tex]-6x=-18-6[/tex]

[tex]-6x=-24[/tex]

5. Divide both sides of the equation by the same factor

[tex]\frac{-6x}{-6} = \frac{-24}{-6}[/tex]

6. Simplify

a) Simplify the fraction

[tex]\frac{-6x}{-6} = \frac{-24}{-6}[/tex]

[tex]x = \frac{-24}{-6}[/tex]

b) Divide the numbers

[tex]x=+4[/tex]

7. Remove the postive sign.

[tex]x=4[/tex]

Answer:

136 ft²

Step-by-step explanation:

floor = 7 x 6 = 42 ft²

sides = 2 x 7 x 5 = 70 ft²

ends = 1/2 x 6 x 4 x 2 = 24 ft²

42 + 70 + 24 = 136 ft²

Answer:

g=1

Step-by-step explanation:

6g+3g=-3g+9+3g, add 3g to both sides and you get closer to the answer

Answer:

g=1

Step-by-step explanation:

solved and got the same answer

Answer:-1

Step-by-step explanation:f(x)=3-x2

This is also...

f(x)=3+[(-1)(x2)]

We will execute the exponential. Then, we will multiply the result by the coefficient of -1.

f(-2)=3-(-2)2

f(-2)=3-(+4)

f(-2)=3-4

f(-2)=-1

Answer:

60 minutes

Step-by-step explanation:

She painted 2/5 of the wall.

She still needs to paint 3/5 of the wall.

3 is 50% more than 2, so 3/5 is 1.5 times 2/5, so it will take her 1.5 times the time it took so far.

1.5 * 40 minutes = 60 minutes.

Answer: 60 minutes

Answer: The First Cylinder has more volume

Step-by-step explanation:

1. V = 471.24

2. V = 282.74

Answer:

Distributive property says that:

(A + B)*C = A*C + B*C

Now let's try to use it in our expression:

3 + 5*c*(2 + 6*c)

Here we can take the two terms inside the parentheses as A and B, and the term that multiplies them as C, then distributing we get:

3 + (5*c)*2 + (5*c)*(6*c)

Now remember that the multiplications are associative and commutative, then we can write this as:

3 + (2*5)*c + (5*6)*(c*c)

3 + 10*c + 30*c^2

And we can't simplify it anymore.

Answer:

i dunno if this will help any but i think 1/4 and 25% is the same since 100/4=25

Step-by-step explanation:

if it doesn't i'm sorry for waisting ur time-

Answer:16 is the answer of your question

hope it is helpful to you

9514 1404 393

Answer:

  D

Step-by-step explanation:

Choices A and D agree in all but one term: row 2 column 3 is (-2)(3) = -6. The term with the correct sign is only found in choice D.

Answer:

(Length x Width x Height)

6x18x12=

I hope this helped! ♡+*

Answer:

i think B

Step-by-step explanation:

Answer:

$800 is the original price

Step-by-step explanation:

15% discount

if 85% = $680

100% =?

100/85 * $680

=$800

Answer:

800

Step-by-step explanation:

Step-by-step explanation:

Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points.

Step-by-step explanation:

- 35/10(2-15n/10) 145n/10 - 7 - 6n

-70/10 +35*15n/100.145n/10 -7-6n

-7 + 525n/100.145n/10 -7- 6n

-14 +5.25n .14.5n -6n

-14 +76.125n^2 -6n is final answer

Answer:

53

Step-by-step explanation:

106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.

Answer:

64 inches

Step-by-step explanation:

There are 12 inches in a foot

12 x 5 is 60

64 is greater then 60

Answer: 40%

Step-by-step explanation:

HOPE THIS HELPS ^^

Answer:

5x+11

Step-by-step explanation:

Hope this helped!!!

Answer:

2x+14

Step-by-step explanation:

hope this helps!

have a great day!!

Divide Total time into two Time Periods. A regular Demand and a High Demand Time Period. Since 75% of the 1,200 calls occur between 9:30 am and 3:30 pm. We multiply .75 x 1,200 to get 900. We get an average of 900 calls every day between the hours of 9:30 am and 3:30 pm – Our net time for this time period is 6 hours.

Therefore, 6 Hours/900 becomes our quotient

Again, since the denominator is larger we invert it to 900 calls/6 Hours

To get a demand of 150 calls per hour.

We need to be able to handle 150 calls per hour.

So how Many Call Representatives are needed?

Again, our historical data tells us that each person can handle 10 calls an hour.

Therefore 150 calls per hour /10 Minutes = 15 Customer Service Representatives are needed during Peak Time!

Now, Subtract the Peak Hours from the 21 Hours Net Time Per day, gives us 15 Non-Peak hours we have to staff.

Answer:

C- The size of the initial water sample, in gallons.

Step-by-step explanation:

Answer:

[tex](a)\ g(x) = \frac{2}{3}(x+1)[/tex]

[tex](b)\ h(y) = \frac{1}{3}[1 + 4y][/tex]

[tex](c)[/tex] [tex]P(x>0.5) =\frac{5}{12}[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.[/tex]

Solving (a): The marginal density of X

This is calculated as:

[tex]g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy[/tex]

[tex]g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy[/tex]

[tex]g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy[/tex]

Integrate

[tex]g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for y

[tex]g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}[/tex]

[tex]g(x) = \frac{2}{3}[(x+1)}[/tex]

Solving (b): The marginal density of Y

This is calculated as:

[tex]h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx[/tex]

[tex]h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx[/tex]

[tex]h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx[/tex]

Integrate

[tex]h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for x

[tex]h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ][/tex]

[tex]h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)][/tex]

[tex]h(y) = \frac{1}{3}[1 + 4y][/tex]

Solving (c): The probability that the drive-through facility is busy less than one-half of the time.

This is represented as:

[tex]P(x>0.5)[/tex]

The solution is as follows:

[tex]P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)[/tex]

Represent as an integral

[tex]P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy[/tex]

Integrate w.r.t. x

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}[/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + 0.5][/tex]

[tex]P(x>0.5) =\frac{2}{3} * 0.625[/tex]

[tex]P(x>0.5) =\frac{2 * 0.625}{3}[/tex]

[tex]P(x>0.5) =\frac{1.25}{3}[/tex]

Express as a fraction, properly

[tex]P(x>0.5) =\frac{1.25*4}{3*4}[/tex]

[tex]P(x>0.5) =\frac{5}{12}[/tex]

Answer:

t = 0.86 or t = 1.45

Step-by-step explanation:

Answer: 166 2/3m

Step-by-step explanation:

Area of a rectangle = length times width

Length: 16 2/3

To find the width, multiply it by 3/5.

w = 16 2/3 ·  3/5

w = 10

Then, multiply the length by the width.

a = l · w

a = 16 2/3 · 10

a = 166 2/3m

Answer:

it will look the same, just shifted.

Step-by-step explanation:

The parabola will be the same shape, size, etc., it will simply be in a different location. Instead of the bottom of the parabola being at (0,0), it will be at (3, -8). translated right 3, down 8.

Answer:

6 gallons = 3.785 liters

Answer:

1.5850323141      

Step-by-step explanation: