Simplify the expression:

3(2 + 2t) =

Answer:

[tex]x^{2} +9x+8[/tex]

Step-by-step explanation:

Multiply using the terms using the FOIL (first, inside, outside, last) method.

x (x) = [tex]x^{2}[/tex]

1 (x) = 1x

8 (x) = 8x

1 (8) = 8

After combining like terms (1x + 8x) you are left with a polynomial expression in standard form.

First, complete the square in the equation for the second circle to determine its center and radius:

x ² - 10x + y ² = 0

x ² - 10x + 25 + y ² = 25

(x - 5)² + y ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

x = r cos(θ)

y = r sin(θ)

Then

x ² + y ² = 100   →   r ² = 100   →   r = 10

x ² - 10x + y ² = 0   →   r ² - 10 r cos(θ) = 0   →   r = 10 cos(θ)

y = 5   →   r sin(θ) = 5   →   r = 5 csc(θ)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to y = 5 at the point (0, 5).

Split up the region at 3 angles θ₁, θ₂, and θ₃, which denote the angles θ at which the curves intersect. They are

θ₁ = 0 … … … by solving 10 = 10 cos(θ)

θ₂ = π/6 … … by solving 10 = 5 csc(θ)

θ₃ = 5π/6  … the second solution to 10 = 5 csc(θ)

Then the area of the region is given by a sum of integrals:

[tex]\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)[/tex]

[tex]=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta[/tex]

To compute the integrals, use the following identities:

sin²(θ) = (1 - cos(2θ)) / 2

cos²(θ) = (1 + cos(2θ)) / 2

and recall that

d(cot(θ))/dθ = -csc²(θ)

You should end up with an area of

[tex]=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta[/tex]

[tex]=\boxed{25\sqrt3+\dfrac{125\pi}3}[/tex]

We can verify this geometrically:

• the area of the larger circle is 100π

• the area of the smaller circle is 25π

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line y = 5, has area 100π/3 - 25√3

Hence the area of the region of interest is

100π - 25π - (100π/3 - 25√3) = 125π/3 + 25√3

as expected.

Answer:

A.(-1,-1)

E.(4,64)

Step-by-step explanation:

We are given that

Function

[tex]y=x^3[/tex]

We have to find all possible input-output pairs for the function.

Substitute x=-1

[tex]y=(-1)^3=-1[/tex]

Then, the pair is (-1,-1)

Now, substitute x=-2

[tex]y=(-2)^3=-8[/tex]

Then, pair is (-2,-8)

Now, substitute x=3

[tex]y=3^3=27[/tex]

Now, substitute x=4

[tex]y=4^3=64[/tex]

Now, substitute x=1

Then, y=1

Hence, Option A and E are true.

A.(-1,-1)

E.(4,64)

The possible input-output pairs for the function are [tex](-1,-1)[/tex] and [tex](4,64)[/tex]

The given function is,

                     [tex]y=x^{3}[/tex]

When x = -1 then [tex]y=(-1)^{3} =-1[/tex]

When x = 4 then [tex]y=4^{3}=64[/tex]

When x = -2 then  [tex]y=(-2)^{3}=-8[/tex]

Hence,   the possible input-output pairs for the function are [tex](-1,-1)[/tex] and [tex](4,64)[/tex]

Learn more about the input and output relation of function here:

https://brainly.com/question/25983065

Answer:

[tex]x = \frac{5}{3}[/tex]

Step-by-step explanation:

Parallelogram

It's a quadrilateral formed by two pairs of parallel sides. The opposite sides have equal lengths.

We are given a parallelogram with opposite sides of 3x+1 and 6x-4. They must be equal, thus:

6x - 4 = 3x + 1

Subtracting 3x:

3x - 4 = 1

Adding 4:

3x = 5

Dividing by 3:

[tex]\mathbf{x = \frac{5}{3}}[/tex]

Answer:

7 chocolate bars will cost $35

Step-by-step explanation:

if 3 cost $15 then 1 bar would cost 5 dollars and 5x7=35

here is a ratio:

3 = 7

15 = 35

Answer:

2.1/////_____\\\\\\

Step-by-step explanation:

hope this helps

Answer:

3x-5=25

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

The equation is:

y = 0*x + 5

y = 5

Note that this is a horizontal line ()slope of 0) and that y=5 for every value of x.

Answer:The percent decrease was 15%

Step-by-step explanation:

In order to find this, use the percent change equation.  

(New - Old)/(Old) * 100 = % Change

Now input 149.42 for the New price and 175.80 for the Old price.  

(149.42 - 175.80)/(175.80) * 100 = % Change

-26.38/175.80 * 100 = % Change

-.15 * 100 = % Change

-15 = % Change

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope = 0

y-y1=m(x-x1)

y-3=0

y = 3

Answer:

The first one is X=5.

The second one is X=8

Hope this helps!

Given:

In triangle ABC,  a = 6, c = 4, and B = 75°.

To find:

The measure of b.

Solution:

According to the Law of Cosine:

[tex]b^2=a^2+c^2-2ac\cos B[/tex]

Substituting the given values in the above formula, we get

[tex]b^2=(6)^2+(4)^2-2(6)(4)\cos (75^\circ)[/tex]

[tex]b^2=36+16-48(0.2588)[/tex]

[tex]b^2=52-12.4224[/tex]

[tex]b^2=39.5776[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{39.5776}[/tex]

[tex]b=6.291073[/tex]

[tex]b\approx 6.29[/tex]

The measure of side b is 6.29 units.

Therefore, the correct option is B.

Answer:

.45

Step-by-step explanation:

52+31=83

83-12=71

71+23=94

94=49=45

Answer:

2.5

Step-by-step explanation:

1+2+3+4 = 10

10 divided by 4 is 2.5

Answer:

Total volume = 355 cm³

Step-by-step explanation:

Volume of the irregular prism = volume of part A + volume of part B

Volume of part A which is also a rectangular prism = Length × width × height

= (11 - 5) × 5 × 6

= 6 × 5 × 6

= 180 cm³

Volume of rectangular prism B = 5 × 5 × (6 + 5)

                                                   = 5 × 5 × 11

                                                   = 275 cm³

Total volume = 180 + 175

                      = 355 cm³

Answer:

35

Step-by-step explanation:

14 + 9 + 12= 35

Answer:

Step-by-step explanation:

if anna is x years old and her sister is 5 five years older the eqasion would be x=5-5x but there is no further information for the answer. You need to know how old anna is to answer the question. Did you write it correctly

Answer:

It's X

Step-by-step explanation:

Because We know that Anna is X, and we also know that she is 5 years younger we know that her sister's age must be x, as it is asking for her age 5 years ago.

Answer:

4-10x

Step-by-step explanation:

Hey there!

7 - 5x - (3 + 5x)

= 7 - 5x - 1(3 + 5x)

= 7 - 5x -1(3) - 1(5x)

= 7 - 5x - 3 - 5x

COMBINE the LIKE TERMS

= (-5x - 5x) + (7 - 3)

= -10x + 4

Therefore, your answer should be: -10x + 4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

c

Step-by-step explanation:

b + 12 < 3 ( subtract 12 from both sides )

b < - 9 ← Lola's solution

- 3b > 27

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

b < - 9 ← Jasmine's solution

Answer:

X+8y=3, 2x-4y=-14

Step-by-step explanation:

Since we do not know the values of x or y we have to leave them the way they are because you can't combine x and y

Answer:

120

Step-by-step explanation:

120 =1233

100= mk109

Answer:

45

Step-by-step explanation:

because the mass

Answer:

$86.03

Step-by-step explanation:

30% off = 70% of total price. Add .06 to 1 for 6% sales tax.

($115.95*(.70))*1.06

= $86.03

Answer:

you are multiplying baceicly

Step-by-step explanation:

3×2=6

Answer:

10/12

Step-by-step explanation:

3/12 + 7/12 = 10/12

Answer:

1.4

Step-by-step explanation:

$_$

Answer:

I think its -4

Step-by-step explanation: