expand the function f(x)=(x+5)^3

The angle relationship and their reasons are:

The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:

∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are  equal based on the vertical angles theorem.

∠KFE and ∠FEJ are alternate interior angles, therefore, they are  equal based on the alternate interior angles theorem.

∠LFG and ∠FEJ are alternate exterior angles, therefore, they are  equal based on the alternate exterior angles theorem.

∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.

∠DEJ and ∠EFL are corresponding angles, therefore, they are  equal based on the corresponding angles theorem.

∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.

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Answer:

138 slices

Step-by-step explanation:

506 / 22 = 23 slices per loaf

23 x 6 = 138 slices

Answer:

Thomas will need 24 cups of lemon juice.

Step-by-step explanation:

There are 4 quarts in every gallon.

12 x 4 = 48

2 cups of lemon juice for every 2 quarts of water.

48 / 2 = 24

Hope This Helps!

Answer: its A

Step-by-step explanation:

i know this is it

Answer:

-5, -2, 3, 4

They are in the correct order already :)

Step-by-step explanation:

They greater a negative number is the less it becomes and positive numbers are always greater than negative ones.

Good luck :)

Answer: The simplified ratio is 4:3

Step-by-step explanation:

To find the ratio of the number of girls to the number of boys, we can divide the number of girls (28) by the number of boys (21) to get:

28 ÷ 21 = [tex]\frac{28}{21}[/tex]

Next, we can simplify the fraction further to get [tex]\frac{4}{3}[/tex], which equals 4:3.

Applying the triangle sum theorem, m∠N = 41°

Triangle sum theorem states that the sum of the three interior angles of any triangle equals 180°.

Given the following interior angles of ΔMNO:

m∠M = (6x+1)°

m∠N = (3x-10)°

m∠O = (x+19)°

Find the value of x:

m∠M + m∠N + m∠O = 180°

6x+1 + 3x-10 + x+19 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17

m∠N = (3x-10)°

m∠N = 3(17) - 10

m∠N = 41°

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Answer:

  $900

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  I = PRT

  I = ($4500)(0.05)(4) = $900

The total interest was $900.

[tex]\large\tt\green{Answer}[/tex]

[tex]\large\tt\green{Step-by-step \: explanation}[/tex]

Step 1:

Put the numbers in the formula and do the arithmetic.

Step 2:

Rename 5% into decimal

Step 3:

Solve the problem with the full solution.

Therefore, the total interest was $900

Answer:

28x^2+16x-12

Step-by-step explanation:

(4x+4)(7x-3)

28x^2+28x-12x-12

28x^2+16x-12

Answer:

Step-by-step explanation:

First 1 ÷ 5 ×16

= 3.2

Then 3.2 × 1 ÷ 3

= 1.06

Answer:

y=88

Step-by-step explanation:

Answer:

7.5lbs

Step-by-step explanation:

82/11 = 7.45454545lbs

Rounded to 7.4lbs

Hope that helps

Answer:

7 5/11

Step-by-step explanation:

you divide 82 and 11 and you get 7.45454545

Answer:

4

Step-by-step explanation:

I think its 4 because the max DVD's he could have bought if shipping was free was 7 but since shipping is not free,he has to equal the amount so 12.99+9.99= 22.98 and the maximum multiplication by 22.98 with the maximum number as 100 would be 91.92, thats my answer

Answer:

31.25

Step-by-step explanation:

Divide 250 by 8=31.25

Answer: least

Step-by-step explanation: because 0.23 is closer to 1

Least

If you removed the last term from 0.136, it would become 0.13

Compared to 0.25, it is lower.

-92

Step-by-step explanation:

If a quadratic equation has the following form:

[tex]ax^2 + bx + c =0, \;\;\;a \neq 0[/tex]

then its discriminant D is defined as

[tex]D = b^2 - 4ac[/tex]

In our given quadratic equation, a = 4, b = -2 and c = 6, so its discriminant is

[tex]D = (-2)^2 - 4(4)(6) = -92[/tex]

Note: The value of the discriminant D will determine the characteristics of the roots of the quadratic equation according to the following rules:

[tex]D > 0,\;\;[/tex] there will be 2 real roots

[tex]D = 0,\;\;[/tex] there will be 1 real root

[tex]D < 0,\;\;[/tex] there will be 2 imaginary roots

Hence our given quadratic equation will not have any real roots but only imaginary ones.

Answer:

-36/5

- . 2/5-=+2/5

-36/5+2/5

34/5 or 6 4/5

Step-by-step explanation:

remark : it is very unusual for a map to mix two measurement norms. they are normally either fully in the American or fully in the metric system.

but let's do the exercise.

the scale says 1/2 in = 10 km

but our measurement on the map brought us quarter inches.

so,

1/2 in = 2/4 in = 10 km

therefore

1/4 in = 10/2 = 5 km

now,

2 1/4 = 9/4 in

this is 9 times 1/4.

therefore, the distance between the 2 cities is

9 × 5 = 45 km.

Answer:

read step-by-step explanation

Step-by-step explanation:

it's a trick question u can't u can get close doing (7+7)×(7+1)-7=105 but it's not 100

This is the same as typing in 0.5x^7

Other equivalent forms are (1/2)x^7 or (x^7)/2

=====================================================

Work Shown:

[tex]\frac{d}{dx}\left[f(x^2)\right] = x^8\\\\f'(x^2)*\frac{d}{dx}(x^2) = x^8\\\\f'(x^2)*2x = x^8\\\\f'(x^2) = \frac{x^8}{2x}\\\\f'(x^2) = \frac{x^7}{2}\\\\f'(x^2) = \frac{1}{2}x^7\\\\f'(x^2) = \boldsymbol{0.5x^7}\\\\[/tex]

I used the chain rule on the second step. The chain rule will apply the derivative to the outer function f(x^2). Then we also apply the derivative to the inner function x^2 to get 2x, which is multiplied with f ' (x^2). From that point, we isolate f ' (x^2).

Side note: When applying the first derivative, it might help to think of f(x^2) as simply f(x) on a temporary basis.

Answer:

33y

Step-by-step explanation:

since the equation of perimeter for a rectangle is lengthX2 + widthX2

and the width is given to be 5 1/2y is it? If it is so then the length will be 11y since 2X5 1/2y is 11y

and the perimeter will then be calculated as so;

11yX2 + 5 1/2yX2

so it will be 22y+11y which will give you 33y

Answer:

it would be the last one

Step-by-step explanation:

lmk if you want an explanation

Answer: 1200

Step-by-step explanation:

12*100 = 1200

Add the two 0’s in 100 to the end of 12 and get 1200

Answer:

Unit Price for Brand A: $0.31 per Pencil.

Unit Price for Brand B: $0.35 per Pencil.

Brand A is the better buy.

Step-by-step explanation:

Divide 7.49 by 24 to get 0.312 and round down to 0.31.

Divide 9.97 by 28 to get 0.356 and round down to 0.35 (0.36 is too much making the price $10.08)

Compare 0.31 and 0.35. (0.31 < 0.35)

The third ordered pair that satisfies the equation of the circle is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]

The radius of the circle is calculated as;

[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

[tex]b < r\\\\b < 388.96[/tex]

[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]

Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).

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Answer:

800 shrimp

Step-by-step explanation:

100 plates of shrimp

8 shrimp on each plate

100 × 8 = 800

= 800 shrimp were prepared by the chef

Hope this helps.