Divide, using the polynomial long division algorithm. Fill in your work below

Answer:

6m²-m²+5m-1

Step-by-step explanation:

Polynomial 1 = m³ + 3m² - 18m

Polynomial 2 = 23m - 4m²

Polynomial 3 = 5m³ - 1

(m³+3m²-18m)+(23m-4m²)+(5m³-1)

When adding polynomials, you'll add like terms.

(m³+5m³)+(3m²-4m²)+(-18m+23m)+(-1)

(6m³)+(-m²)+(5m)+(-1)

6m³-m²+5m-1

The distance to run to minimize the time needed to reach the island is

3.4 miles

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let x = distance to run.

Remaining distance to the point that is closest to the island = (4 - x) miles.

The distance d to the point x from the island is

using the Pythagorean theorem:

d² = 1² +(4 - x)²

d² = 1 + 16 -8x + x²

d² = 17 - 8x + x²

d = √(x² - 8x + 17)

Total travel time.

= Times running + Time swimming.

Speed = Distance / Time

Time = Distance/Speed

Total time:

T = x/6 + d/3

T = x/6 +√(x² - 8x + 17)/3

Minimized time is when T' is zero.

T' = 0

1/6 + 1/3 x 1/{2(√(x² - 8x + 17)} x (2x - 8) = 0

1/6 + (2x - 8)/6√(x² - 8x + 17) = 0

Multiply 6 on both sides.

1 + (2x - 8)/√(x² - 8x + 17) = 0

√(x² - 8x + 17) + 2x - 8 = 0

√(x² - 8x + 17) = 8 - 2x

Square both sides.

(x² - 8x + 17) = (-(2x - 8))²

(x² - 8x + 17) = (2x - 8)²

x² - 8x + 17 = 4x² - 32x + 64

4x² - x² - 32x + 8x + 64 - 17 = 0

3x² - 24x + 47 = 0

Finding the roots of the quadratic equation.

We get,

x = 3.4 and 4.6

Thus,

The distance to run to minimize the time needed to reach the island is

3.4 miles

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

Answer:

B = 0

Step-by-step explanation:

If you have y = 2x + b and are trying to get to y = 2x

Then just remove the B itself meaning it's value would be 0 so it is as if that variable was never in the actual equation.

Basing ourselves off of the formula "y = mx + b"

B = 0 would mean that the y-intercept of the line is 0

Answer:

0

Step-by-step explanation:

if y=2x and y=2x+b is the same then b must be 0.

Answer:

9

Step-by-step explanation:

In order to solve this problem, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense

Answer:

simple random sample

Step-by-step explanation:

I hope that's it

Yooooo what up how u doin ?

[tex]21.2x + c = 5.3(4x - 2.6)[/tex]

[tex]21.2x + c = 21.2 x - 13.78[/tex]

Subtract both sides 21.2x

[tex]21.2x - 21.2x + c = 21.2x - 21.2x - 13.78 \\ [/tex]

[tex]c = - 13.78[/tex]

There u go.... Don't have a good day , Have a great day ❤

Answer:

Step-by-step explanation:

Side-Angle-Side postulate (SAS)

There are ΔAED and ΔCFD triangles that are congruent due to the SAS congruence postulate.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given question,

D is the midpoint of AC, ED = FD, and angle EDA = angle FDC

In ΔAED and ΔCFD,

Side DE = Side DF

m∠EDA  = m∠FDC

Side AE= Side FC

According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Thus, both triangles are congruent.

Hence, there are ΔAED and ΔCFD triangles that are congruent due to the SAS congruence postulate.

Learn more about congruent triangles here:

brainly.com/question/4364353

#SPJ2

The total amount that Fred keeps (and does not put in his savings account) is $20

Total earnings of Fred = $45

Amount spent on music = $5

Amount remaining after spending on music = $40

Fred puts half of what's left in a savings account.

Total amount put in the savings account = 40/2

Total amount put in the savings account = $20

The total amount that Fred keeps (and does not put in his savings account) is $20

Learn more here: https://brainly.com/question/25698362

Answer:pretty sure the -4 would be on the right of the seven. And to the left of -1.

Step-by-step explanation:

Answer:

c. the relationship is proportional because the graph passes through the origin

Answer: 27.6/2.3 = 12 bags of trail mix

Step-by-step explanation: Hope this helps :)

Answer:

a. 1/13

b. 0.077

c. 7.7

Step-by-step explanation:

a. there are 4 of the 6 in a deck of cards so the probability of taking this cards from the deck of 52 cards is 4/52. Given you 1/13.

Answer:

C) 1

Step-by-step explanation:

Its the closest to 1.04

Answer:

$20.40

Step-by-step explanation:

20% off means that the new price of the skirt will be 80% of the original price:

$30(100%  – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100%  – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

Answer:

y = -1/5x - 1

Step-by-step explanation:

Perpendicular lines slopes are negative reciprocals of each other.

Write the given equation in the slope-intercept form: y = mx + b

5x - y = 3

-y = -5x + 3

y = 5x - 3       multiply by -1

The slope of the given line is 5 ( the coefficient of the x-term).

The slope of the new equation will -1/5 (this is the negative reciprocal of 5).

Next find "b"  using y = mx + b, the new slope -1/5 and the point (0, -1)

y = mx + b

-1 = -1/5(0) + b

-1 = 0 + b

-1 = b  

Now write the equation y = -1/5x - 1

Answer:

17L

Step-by-step explanation:

Volume of cone = 1/3(Volume of cylinder )

= 1/3 * 51L

= 17L

Answer:

B

Step-by-step explanation:

Step 1: Divide both sides by 4.

4x/4 = 32/4

4x/4 leaves you with x by itself, and 32/4 is 8. So x = 8

Answer:

450

Step-by-step explanation:

Step-by-step explanation:

if 1425 then the answer is 100

if it's 62.25 then 77 percent

Answer:

The correct option is;

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).

Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give

Step-by-step explanation:

We have that for reflection across the x-axis, (x, y) → (x, -y)

For reflection across the y-axis, (x, y) → (-x, y)

Therefore, given that the pre-image before the reflection across the y-axis is (x, -y), we have;

For reflection across the y-axis, (x, -y) → (-x, -y)

For reflection across the line, y = x, gives (x, y) → (y, x) which is not the same as (-x, -y)

9514 1404 393

Answer:

  x-axis

Step-by-step explanation:

The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that. In a graph of distance versus time, for example, the independent variable is likely to be time, and the horizontal axis is likely to be named something that suggests that--"t," for example, or perhaps "days".

It is fairly conventional to use "x" to name a general independent variable. The corresponding dependent variable in a two-variable relation is conventionally called "y". The horizontal axis in x-y graphs is usually labeled "x" and is called the "x-axis."

This convention is sufficiently well-used that we often call the horizontal number line of the graph the "x-axis" even if it is labeled something else.

Answer:

c)the line should be solid

As per <= sign the line should be solid

Next

Let's isolate x and y

[tex]\\ \sf\longmapsto y\leqslant 12x+4[/tex]

[tex]\\ \sf\longmapsto 12x-y\geqslant 4[/tex]

[tex]\\ \sf\longmapsto 0-0\geqslant 4[/tex]

Shading should go below the line towards origin

Answer:

1 2/3

Step-by-step explanation:

You divide -3 2/3x to -2 1/5 and you will get 1 2/3

Answer:

308 miles

Step-by-step explanation:

speed * time = distance

56 * 5.5 = 308

308 miles

Answer:

C 9

D 12

Step-by-step explanation:

9 is a corresponding angle to 5 and 12 is an opposite angle to 9

Also by convention, grid lines are at right angles to each other so 5, 6, 7, 8, 9, 10, 11, and 12 are all equal at x = 90°

Answer:

i just stole your points thank you

Step-by-step explanation:

5 – 6w – 5 – 95 + 2w = –48w – 70

-6w + 2w + 48w = -70 -5 + 5 +95

44w = 25

w=25/44

Answer: 3/8

Step-by-step explanation: We don't know how many votes are there for the class secretary.

Answer:

[tex] \: [/tex]

1. C = 81 , D = 4

2. E = 625, F = 4

3. G = 10,000 , H = 4

4. J = 0.01 , K = -2

Hope it helps you ™