Look at the long division problem shown on the right. Complete the division to determine what the remainder will be.

What is the remainder?

–10

–7

7

10
x + 4 StartLongDivisionSymbol 4 x Superscript 4 Baseline + 18 x cubed + 3 x squared minus 18 x + 15 EndLongDivisionSymbol. minus 4 x Superscript 4 Baseline + 16 x cubed to get a remainder of 0 x Superscript 4 Baseline + 2 x cubed + 3 x squared. minus 0 x Superscript 4 Baseline + 2 x cubed + 8 x squared to get a remainder of 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 18 x. minus 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 20 x to get a remainder of blank and a quotient of 4 x cubed + 2 x squared minus 5 x + c.

\(\displaystyle\\Answer:\ y=\frac{8}{3}x-5\)

Step-by-step explanation:

(0,-5)      (3,3)

Equation of a straight line:

\(\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=3\ \ \ \ y_1=-5\ \ \ \ y_2=3\\\\Hence,\\\\\frac{x-0}{3-0} =\frac{y-(-5)}{3-(-5)}\\\\\frac{x}{3} =\frac{y+5}{3+5} \\\\\frac{x}{3} =\frac{y+5}{8} \\\)

Multiply both parts of the equation by 24:

\((8)(x)=(3)(y+5)\\8x=(3)(y)+(3)(5)\\8x=3y+15\\8x-15=3y+15-15\\8x-15=3y\)

Divide both parts of the equation by 3:

\(\displaystyle\\\frac{8}{3}x-5=y\)

Answer:

Evaluate each expression:

Answer:

5 = 10

6 = 13

7 = 5

8 = 17

Step-by-step explanation:

5.

1: simplify

\(\sqrt{8^2+6^2}\)

2: take both to power

\(\sqrt{64+36}\)

3: sqrt

\(\sqrt{100} = 10\)

6.

1: simplify

\(\sqrt{5^2+12^2}\)

2: take both to power

\(\sqrt{25+144}\)

3: sqrt

\(\sqrt{169} = 13\)

7.

1: simplify

\(\sqrt{4^2+3^2}\)

2: take both to power

\(\sqrt{16+9}\)

3: sqrt

\(\sqrt{25} = 5\)

8.

1: simplify

\(\sqrt{15^2+8^2}\)

2: take both to power

\(\sqrt{225+64}\)

3: sqrt

\(\sqrt{289} = 17\)

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ1

Answer:

the two words that means addition are

plus, sum and calculation..............

Answer:

The diagonal length is 7.42 inches.

Explanation:

The disk with its diagonal is:

Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:

use me as a like button for this question lol

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

solve : 2(5x + 3) = 25

▶️2(5x + 3) = 25

▶️ 2 × 8x = 25

▶️ 16x = 25

▶️ x = 25/16

▶️ x = 1.5625

1.5625

Step-by-step explanation:

Step 1:

2(5x+3)=25

(2)(5x) + (2)(3)=25 (distribute)

10x+6=25

Step 2:

10x+6 - 6 = 25 - 6

10x =19

Answer :

X=19 of 10

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

-5 1/3 - 3 1/3

Step-by-step explanation

both expressions equal -8 2/3

Answer:

-125

Step-by-step explanation:

Answer:

The answer you're looking for is B. 27.55 m

Answer:

36

Step-by-step explanation:

Angles in a triangle sum to 180 degrees.

The angle in the bottom left will equal 180 - (3x + 6) as angles along a staight line also sum to 180 degrees.

180 - ( 3x + 6)

180 - 3x - 6   [expand bracket]

174 - 3x

Now we can add up all the angles and equate them to 180 to solve for x.

24 + 2x + 18 + 174 - 3x = 180

216 - x = 180

216 = 180 + x

x = 36

Answer:

Zach has 14 apples left.

Step-by-step explanation:

This equation is 12 - 4 + 18 - 6 + 14 - 20.

8 + 12 + 14 - 20

20 + 14 - 20

14

Answer:

5x+27 > -24

Don't forget the greater than or equal to sign, I just don't know how to type it. If you're not sure, it's the symbol I have typed above with a line underneath.

Hope this helps :)

Answer:

Option D) 5

Step-by-step explanation:

In the given graph of a parabola, and the equation in vertex form, y = (x - k )²: The variable k represents the x-coordinate of the vertex, and the point where the axis of symmetry lies on the graph.  In the given graph, the vertex is the minimum point, occurring at point (5, 0). The x-coordinate of the vertex is also the value of k = 5.

Therefore, the correct answer is Option D) k = 5.

Answer:

I am so confused I don't know how to answer this.

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

Read more on reflection here: brainly.com/question/27912791

#SPJ1

Answer:

x-intercept: (3,0)

y-intercept: (0,-4)

Step-by-step explanation:

To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).

Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.

x-intercept

4x-3y=12            [plug in y=0]

4x-3(0)=12          [multiply]

4x-0=12              [add both sides by 0]

4x=12                 [divide both sides by 4]

x=3

---------------------------------------------------------------------------------------------------------

y-intercept

4x-3y=12            [plug in x=0]

4(0)-3y=12         [multiply]

0-3y=12             [subtract both sides by 0]

-3y=12               [divide both sides by -3]

y=-4

Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).

Answer:

21.9

Step-by-step explanation:

assuming you are asking about how much miles per gallon you got 21.9 would be the answer you just simply divide 527 by 24

Answer:

21.96 miles per gallon

Step-by-step explanation:

Equation that represents the relationship is y = 4x if A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolized by the proportional symbol, ∝.

Given,

A straight line's general equation is -

[y] = [m]x + [c]

where -

The slope of the line, [m], indicates the unit rate at which [y] changes in relation to [x].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

Another symbol for direct proportionality is y = mx. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.

The proportional relationship can be expressed as follows:

y = kx

Using the information provided, we can now write:

Use 0.5 gallons of water for 2 scoops.

Need 1.5 gallons of water for 6 scoops.

k = 2/0.5

k = 4

The relationship's equations can be expressed as -

y = 4x + c

2 scoops now require 0.5 gallons of water.

2 = 1/2 × 4 +c

c = 0

So, y = 4x will be the equation.

To learn more about direct proportionality, visit:

https://brainly.com/question/29434431

#SPJ1

Angles 1 = 2 = 3 = 98° and 4 = 82° are measured.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The image serves as a right angle indicator. The angle formed when two chords cross paths inside of a circle is equal to half the sum of the chords' intercepted arcs. Hence, m1 = 50° and m2 = 130°.

The other angle measurements can be calculated using the diagram as follows:

∠1: ∠1 is a vertical angle to ∠2, so it is also 98°.

∠3: ∠3 is a corresponding angle to ∠2, so it is also 98°.

∠4: ∠4 and ∠2 form a straight angle, which means they add up to 180°. Therefore, ∠4 = 180° - ∠2 = 180° - 98° = 82°.

So, the angle measures are:

∠1 = ∠2 = ∠3 = 98°

∠4 = 82°

To know more about Angles visit:-

https://brainly.com/question/28451077

#SPJ1

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

Learn more on length : https://brainly.com/question/23008020

#SPJ1

Daniela's graph of the function describing Monday's storm depicted the storm's temporal evolution, showcasing the changing intensity of rainfall, intermittent spikes, shifting wind direction, and overall duration. Analyzing the graph allowed Daniela to gain insights into the storm's behavior and better understand its impact on the area.

Daniela graphed the function describing Monday's storm and observed several key features. The graph displayed a rapid increase in precipitation during the early morning hours, with rain intensifying steadily until reaching its peak around midday. Afterward, the precipitation gradually subsided, leading to a decline in rainfall amounts throughout the afternoon and evening.

The graph exhibited a distinct pattern of fluctuation, reflecting the storm's dynamic nature. Intermittent spikes in rainfall were visible, indicating periodic bursts of heavy precipitation throughout the day. These spikes were followed by brief periods of relative calm, during which the rainfall decreased temporarily before resuming its intensity.

Furthermore, Daniela noticed a gradual shift in wind direction as the storm progressed. Initially, the wind blew from the east, but it gradually veered towards the south as the storm system moved across the region. The change in wind direction was evident on the graph, showing a gradual rotation of the wind vector over time.

The graph also revealed the storm's duration, spanning from the early morning hours until late evening. The rainfall accumulation steadily increased during the storm's initial phase and reached a maximum before gradually tapering off towards the end of the day.

for more questions on Daniela's graph

https://brainly.com/question/28699268

#SPJ8

Answer:66.5 degrees

Step-by-step explanation:

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

for more questions on down payment

https://brainly.com/question/1698287

#SPJ8

Farhana's cycling speed was 120 m/min.

time = distance/speed

We know that Janet's speed is 150 m/min and the distance to the swimming pool is 3000 m (since 1 km = 1000 m, then 3 km = 3000 m).

Therefore, the time it took for Janet to reach the swimming pool is:

time = 3000 m / 150 m/min = 20 minutes

At the moment when Janet reached the swimming pool, Farhana was 600 m behind her.

Since both of them were cycling for the same amount of time, this means that Farhana covered a distance of 3000 m - 600 m = 2400 m in 20 minutes.

Now we can find Farhana's cycling speed using the formula:

speed = distance / time

speed = 2400 m / 20 min = 120 m/min

So, Farhana's cycling speed was 120 m/min.

Read more about speed here:

https://brainly.com/question/13943409
#SPJ1