a sector of a circle has a central angle measure of 60°, and an area of 14 sq inches, what is the area of the entire circle​

The expression f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3 is a polynomial function

The factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

The expression is given as:

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

Express as difference of two squares

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

Expand

f(x) = (x - 2)(x + 2)(x ^ 2 + x + 3x + 3)

Factorize the expression

f(x) = (x - 2)(x + 2)(x(x + 1) + 3(x + 1))

Factor out x + 1

f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

Hence, the factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

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Answer: 28

Step-by-step explanation: 80 x 0.35 = 28

when we multilpy we get 80×0.35 = 28

Answer:

Step-by-step explanation:

I am not sure but according to my calculation answer of no.1 may be 67. And I am in 8 grade so I couldn't solve others. So sorry !!

The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction)

3/12=0.25

Answer:

The type of function is cexponential and Alinear

The combination shows that the number of ways to select 4 out of the 50 minions will be 230300.

From the information given, it can be noted that this involves a combination rather than permutation.

In this case, the number of ways to select 4 out of the 50 minions will be:

= 50! / (50-4)!4!

= 230300

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Answer:

7

Step-by-step explanation:

As you can see, each time (let's say n) increases by 1, it divides by 1/2. So from a1 to a2, you get 28/2 or 14, then from a2 to a3, 14/2 or 7.

7 being your answer.

Answer:

Step-by-step explanation:

Given the recursive formula.

Use it to determine the value of te third term.

well, he has "x", which oddly enough is 100%, and we also know that 42 is 35% of that, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 42& 35 \end{array} \implies \cfrac{x}{42}=\cfrac{100}{35}\implies \cfrac{x}{42}=\cfrac{20}{7} \\\\\\ 7x=840\implies x=\cfrac{840}{7}\implies x=120[/tex]

The bond's time to maturity for the Ford bond based on the present date and the maturity date is 77 years 6 months.

The time to maturity for a bond is the length of time that a bondholder would receive interest payments on the bonds held. It is the difference between the present date and the matuity date of the bond.

Time to maturity = May 15 2097 - November 16, 2020 = 77 years 6 months

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Answer:

Slope Intercept Form: y=3x-10

Step-by-step explanation:

First, we need to solve the slope.

The formula: y2-y1/x2-x1 = m

Coordinate Points:

(2, -4) ; (4,2)

Do 2 - (-4) for the y's and 4-2 for the x's

Formula: 2-(-4)/4-2

2 - (-4) is a positive answer since the negatives cancel to a positive.

That shall be 6.

4-2 = 2

Now we have 6/2 which means 6 divided by 2 which is 3.

Our slope is 3.

Slope-Intercept Formula: y=mx+b

Our "m" is 3

y = 3x + b

Our b which is the y-intercept is undefined.

We need to plug one of the coordinates into the formula to find it.

Plug (2,-4) into the formula.

-4 = 3(2) +b

Do 3 x 2 first

-4 = 6 + b

Now subtract 6 on both sides

-6-4 = b

Our y-intercept is -10 because negative subtracted by negatives is an addition number followed by the greater number's sign.

Formula: y=3x-10

Answer:

y = 3x - 10

Step-by-step explanation:

To determine the line that passes through the points (2, -4) and (4, 2), we need to determine the slope of the line. Then, using the slope of the line and any point, we can determine the equation of the line using point slope form.

How to determine the slope of the line?

The slope of the line can be determined by using the formula (y₂ - y₁)/(x₂ - x₁), where x₂ and y₂ are the coordinates of the second point; x₁ and y₁ are the coordinates of the first point.

[tex]\implies\large\text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

In this case, our first point and second point are (2, -4) and (4, 2) repectively as stated in the question. Therefore,

When we substitute the following into the formula, we obtain;

[tex]\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 }[/tex]

When we perform subtraction, we obtain;

[tex]\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 } = \dfrac{2 + 4}{2 } = \dfrac{6}{2}[/tex]

Which when simplified, we get;

[tex]\implies\large\text{Slope} = \dfrac{6}{2} = 3[/tex]

As said above, to determine the equation of the line with the slope and a point given, we can use point slope form. The chosen point must be on the line. The question states that "the line that passes through the points (2,-4) and (4, 2)". Therefore, we can tell that (2,-4) and (4, 2) are points that are on the line. Let's choose (4, 2) as our chosen point.

Now, let's substitute the slope of the line and the coordinates of the chosen point in the point slope form equation.

Finally, let's simplify the point slope equation and convert it into slope intercept form (as stated in question).

The slope intercept form states that;

We can see that the "y" variable is isolated on one side of the equation [y = (m)x + (b), Slope intercept form equation]. Thus, we need to isolate the y-variable in y - 2 = 3x - 12 to obtain our equation in slope intercept form. This can be done by adding 2 to both sides of the equation.

Therefore, the equation in slope intercept form is y = 3x - 10.

Answer:

D

Step-by-step explanation:

Answer:

4000

Step-by-step explanation:

V=4/3(3)(10)^3

V= 4/3 (3)(1000)

V=4/3 (3000)

V=4000

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

The parametric equation for the horizontal movement is x = 43.84t

Since

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft

The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t

The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t

So,  y - 50 = 48.84t

y - 50 = 43.84 × 1.37

y - 50 = 60.0608

y - 50 ≅ 60.1 ft

So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

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Answer:

See below ↓↓↓↓

Step-by-step explanation:

4.

5.

6.

7.

Answer:

sqrt(2593)

Step-by-step explanation:

17^2+48^2 = 2593^2

Answer:

A = 390

Step-by-step explanation:

l=14

w= 3

h= 9

A= 2 (wl+hl+hw) = 2 (3.14+9.14+9.3) = 390

Answer: 390in^2

Step-by-step explanation:

2(14 x 3) + 2(9 x 3) + 2(14 x 9)

84 + 54 + 252 = 390 in^2

Answer:

[tex]\fbox{height \: of \: prism = 19 \: mm}[/tex]

Step-by-step explanation:

Given:

Shape of object is pentagonal prism

Side of pentagon= 12mm

Apothem of pentagon= 5 mm

Volume of pentagonal prism= 2,850 cubic mm.

To find:

Hieght of pentagon prism= ?

Solution:

To find height of prism it's necessary to calculate the surface area of base,

[tex]Area \: of \: regular\: pentagon = \frac{5}{2} \times side \: of \: pentagon \: \times apothem \\ Area \: of \: regular\: pentagon = \frac{5}{2} \times 12 \times 5 \\ Area \: of \: regular\: pentagon= \frac{5}{ \not2} \times \not12^{6} \times 5 \\ Area \: of \: regular\: pentagon= 5 \times 6 \times 5 \\ Area \: of \: regular\: pentagon= 150 \: {mm}^{2} [/tex]

[tex]Volume \: of \: prism = surface \: area \: of \: base \: \times height (h) \\ 2850 = 150 \times h \\ h = \frac{2850}{150} \cdot \frac{ {mm}^{3} }{ {mm}^{2} } \\ h = \frac{\not{ {2850}^{19} }} {\not150} \cdot \frac{ {mm}^{\not {3}^{1} } }{ {mm}^{\not2} } \\ \fbox{h = 19 \: mm}[/tex]

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The required height of the pentagonal prism is 19 cm                              

Given that,
A figure of a pentagon prism is shown with
The volume of the prism = 2850 cubic cm
Side of pentagon base = 12 mm.
And the perpendicular distance from the center to the side = 5 mm.

Volume is defined as the ratio of the mass of an object to its density.
Or in mathematics volume can be calculated as the area of the base multiplied by the height.

In order to get the height of the prism first, we have to calculate the area of the base and then divide the volume by its base area to get its height.

The base area = 5/2 * side * perpendicular height to side from center.
                         = 5 / 2 * 12 * 5
                         = 150
The volume of the prism = base area * height
                              2850 = 150 * height
                             height = 2850/15
                                         =  19 cm

Thus, the required height of the pentagonal prism is 19 cm                              

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The total liabilities is $180,338

The total assets is  $1,233,000

The net worth is $1,052,662

Net worth is total assets less liabilities. Assets is the sum of liquid assets and non liquid assets. Liabilities is the sum of car loan and mortgage loan.

Assets = 178,000 + 1,055,000 = $1,233,000

Liabilities = 145,908 + 34,430 = $180,338

Net worth =  $1,233,000 - $180,338 = $1,052,662

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Answer:

360°

Step-by-step explanation:

the sum of the exterior angles of any polygon = 360°

Answer:

x > -10

Step-by-step explanation:

5 - 3x > 35

-5           -5

-3x > 30

[tex]\frac{-3x > 30}{-3}[/tex]= x > -10

Answer:

225

135

450

270

6750

all the answers

Answer:

the total amount owed for the car is $7500

Step-by-step explanation:

5% of $6000 is ($6000×5)÷100= $300

so $300×5= $1500

now the 5 yrs interest auditioned to the $6000 loan equals $7500.

($300×5)+$6000= $7500

I hope this helps, you can ask any questions for clarification

To write something in slope-intercept form

   ⇒ need to know what slope-intercept looks like: [tex]y = mx +b[/tex]

Let us first find the slope:

     Formula of slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

    Slope = [tex]\frac{4-6}{8-5} =-\frac{2}{3}[/tex]

Lets now write in point-slope form:

     ⇒ [tex](y-y0)=m(x-x0)[/tex]

   [tex]y - 6 = -\frac{2}{3} (x-5)[/tex]

To write it into slope-intercept form, we must solve for y

   [tex]y = -\frac{2}{3}(x-5)+6 =-\frac{2}{3}x+\frac{10}{3} +6\\y = -\frac{2}{3} x+\frac{10}{3}+\frac{18}{3} \\y = -\frac{2}{3}x+\frac{28}{3}[/tex]<-- slope-intercept form

Hope that helps!

Answer:

x=34

Step-by-step explanation:

This is a 180-degree angle. This means, that when added, both sides must equal 180.

180-151=29

Since there is a "-5" on the side of x, we must add five to find x.

29+5=34

x=34

Answer:

-9<2

-1>-3

3>-7

-8<-4

Explanation:

< = less than

> = more than

Answer:

2 -1 3 -4 and its always positive if you do the negitives it would be the lowst

Answer:

[B] 1/25

Step-by-step explanation:

From the given:

There are letter tiles in a bag. Four A’s, five B’s, six C’s and five D’s. You select one tile, replace it, and then draw another.

To Find:

P( A and A)=______

Solution:

Since it given that:

Four A’s, five B’s, six C’s and five D’s.

Thus we have:

A,A,A,A,B,B,B,B,B,C,C,C,C,C,C,D,D,D,D,D

Total number of letters tiles = 20

Probability of selecting A = 4/20  = 1/5

Probability of selecting A  = 4/20 = 1/5

P( A and A)= 1/5 × 1/5 = 1/25

Thus, the answer is [B] 1/25

Kavinsky

Answer:

Answer for 1

B and D

Answer for 2

is D 54,811 x 2/4

Step-by-step explanation: