Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)

Answer:

7 pi cm^2 or  approximately 21.98 cm^2

Step-by-step explanation:

First find the area of the large circle

A = pi r^2

A = pi 3^2

A = 9 pi

Then find the area of the small unshaded circle

A = pi r^2

A = pi (1)^2

A = pi

There are two of these circles

pi+ pi = 2 pi

Subtract the unshaded circles from the large circle

9pi - 2 pi

7 pi

If we approximate pi as 3.14

7(3.14) =21.98 cm^2

Answer:

[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]

Step-by-step explanation:

[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]

[tex](2) \pi (1)^2[/tex]

[tex]2\pi[/tex]

[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\pi (3)^2[/tex]

[tex]9\pi[/tex]

[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]9\pi -2\pi[/tex]

[tex]7\pi[/tex]

Answer:

2

Step-by-step explanation:

The term 3x² has 2 as an exponent, the correct option is C.

Exponents are the base raised by power, it is written in the superscript of a number.

The expression is  3x² +y-5

The term 3x² has 2 as an exponent.

Therefore, the correct option is C.

The missing options are

A.3x2

B. y

A 2

C. -5

D. None of these choices are correct.

To know more about Exponents

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Answer:

x = 58

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

90  = 32+x

Subtract 32 from each side

90-32 = x

58 =x

Answer:

5a³ - 40

Step-by-step:

The algebraic expression is:

5a³ - 40

Answer:

A. 340 grams

Step-by-step explanation:

My brain

Answer:

1256 i think

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Hello!

What we do to one side of the equation we have to do to the other side.

3x - 6 = 18

Add 6 to both sides

3x = 24

Divide both sides by 3

x = 8

The answer is 8

Hope this helps!

Answer:

x=8

Step-by-step explanation:

(3x-6)=18

Add 6 to each side

(3x-6+6)=18+6

3x= 24

Divide by 3

3x/3 = 24/3

x = 8

Answer:

9x³ + 27x²

Step-by-step explanation:

What the question is asking is to multiply f(x) and g(x) together:

Step 1: Write out expression

(fg)(x) = 3x²(3x + 9)

Step 2: Distribute

(fg)(x) = 9x³ + 27x²

Answer:

[tex]\huge\boxed{Option \ 3 : (fg)(x) = 9x^3+27x^2}[/tex]

Step-by-step explanation:

[tex]f(x) = 3x+9\\g(x) = 3x^2[/tex]

Multiplying both

[tex](fg)(x) = (3x+9)(3x^2)\\(fg)(x) = 9x^3+27x^2[/tex]

Answer: [tex]4x^2-21x-2[/tex] .

Step-by-step explanation:

Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].

Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])

[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]

Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .

Answer:

h(-4) = -2

Step-by-step explanation:

h(x)=-2x-10

Let x = -4

h(-4)=-2*-4-10

       =8-10

       = -2

Answer:

[tex]\huge \boxed{{-2}}[/tex]

Step-by-step explanation:

[tex]\sf The \ function \ is \ given:[/tex]

[tex]h(x)=-2x-10[/tex]

[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]

[tex]h(-4)=-2(-4)-10[/tex]

[tex]h(-4)=8-10[/tex]

[tex]h(-4)=-2[/tex]

Answer:

A

Step-by-step explanation:

Answer:

(6, 4 )

Step-by-step explanation:

Given the 2 equations

2x - 10y = - 28 → (1)

- 10x + 10y = - 20 → (2)

Adding (1) and (2) term by term eliminates the term in y, that is

- 8x = - 48 ( divide both sides by - 8 )

x = 6

Substitute x = 6 into either of the 2 equations and evaluate for y

Substituting into (1)

2(6) - 10y = - 28

12 - 10y = - 28 ( subtract 12 from both sides )

- 10y = - 40 ( divide both sides by - 10 )

y = 4

Solution is (6, 4 )

Answer:

$522.49

Step-by-step explanation: 549.99*.05=27.50 (discount)

549.99-27.50=$522.49

Answer:

$522.49

Step-by-step explanation:

First, find the discount amount. You can do this by multiplying the original cost by the discount amount. A little trick for remembering to multiply instead of divide is to think "five percent of the original amount"

5% = 0.05

549.99 ⋅ 0.05 = 27.4995

That means the discount amount is $27.50

Subtract the discount amount from the original price

$549.99 - $27.50 = $522.49

Answer:

19.5 pounds

Step-by-step explanation:

1 foot = 12 inches

3 inches = 3/12 = 0.25 feet

3 feet 3 inches = 3.25 feet

then:

24 pounds is 4 feet

A pounds is 3.25 feet

A = 24*3.25/4

A = 19.5 pounds

Answer:

19.50 pounds

Step-by-step explanation:

1 foot = 12 inches

3 inches = 3/12 = 0.25 feet

3 feet 3 inches = 3.25 feet

then:

24 pounds is 4 feet

A pounds is 3.25 feet

A = 24*3.25/4

A = 19.50 pounds

Answer:

Perimeter= 29.12 unit

Step-by-step explanation:

Perimeter of the triangle is the length of the three sides if the triangle summef up together

Let's calculate the length of each side.

For (-4,-6),(3,3)

Length= √((3+4)²+(3+6)²)

Length= √((7)²+(9)²)

Length= √(49+81)

Length= √130

Length= 11.40

For (-4,-6),(7,2)

Length= √((7+4)²+(2+6)²)

Length= √((11)²+(8)²)

Length= √(121+64)

Length= √185

Length= 13.60

For (3,3),(7,2)

Length=√( (7-3)²+(2-3)²)

Length= √((4)²+(-1)²)

Length= √(16+1)

Length= √17

Length= 4.12

Perimeter= 4.12+13.60+11.40

Perimeter= 29.12 unit

Answer:

Yes , it satisfies the hypothesis and  we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]

Step-by-step explanation:

Given that:

[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]

which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]

Differentiating the function with respect to x is;

f(x) = 8x - 3

Using the Mean value theorem to see if the function satisfies it, we have:

[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]

[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]

since the polynomial function is differentiated in [0,2]

[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]

[tex]8c -3 = \dfrac{10}{2}[/tex]

8c -3  = 5

8c = 5+3

8c = 8

c = 8/8

c = 1

Therefore, we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]

Answer:

Step-by-step explanation:

If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).

Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.

29C3 = 29!/(29-3)!3!

29C3 = 29!/(26!)!3!

29C3 = 29*28*27*26!/26!3*2

29C3 = 29*28*27/6

29C3 = 3,654 different ways.

This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders

Answer: see below

Step-by-step explanation:

The standard form of an exponential equation is: y = a(b)ˣ    where

Growth:

Exponential growth is where the final value (y) is greater than the initial value (a).

An example would be the spreading of a rumor:  

You tell 1 person (a = 1) who then tells 2 people each minute (b = 2).  How many people will they have spread the rumor to after 5 minutes (x = 5)?

y = 1(2)⁵

  = 32

Decay:

Exponential decay is where the final value (y) is less than the initial value (a).

An example would be the decrease of bacteria in a person:

A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2).  How many bacteria will the person have after 2 hours (x = 2)?

[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]

Answer:

Approximately 38.56 kilometers

Step-by-step explanation:

So, from the picture, we want to find x.

To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:

[tex]c^2=a^2+b^2-2ab\cos(C)\\[/tex]

The c in this equation is our x, and the C is the angle we need to find.

From the picture, you can see that angle C is the sum of the red and blue angles.

From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.

From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.

Therefore, angle C is 42+10 which equals 52 degrees. Now we can plug this into our formula:

[tex]x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}[/tex]

Answer:

I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.

Step-by-step explanation:

edmentum answer

Answer:

The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

Yes  the test  suggest that the true average percentage of organic matter in such soil is something other than 3%

Step-by-step explanation:

From the question we are told that

  The  sample mean is  [tex]\= x = 2.482\%[/tex]

  The  standard deviation is [tex]\sigma = 1.614[/tex]

   The  standard error is [tex]SE = 0.295[/tex]

     The  sample size is [tex]n = 30[/tex]

   The  level of significance is  [tex]\alpha = 0.05[/tex]

  The  null hypothesis is [tex]H_o : \mu = 3\%[/tex]

   The  alternative hypothesis is  [tex]H_a : \mu \ne 3\%[/tex]

Now  the degree of freedom is evaluated as

       [tex]df = n - 1[/tex]

       [tex]df = 30 - 1[/tex]

       [tex]df = 29[/tex]

The test statistics is mathematically evaluated as

         [tex]t = \frac{ 2.482 - 3}{ 0.295}[/tex]

         [tex]t = -1.756[/tex]

The p-value is obtained from the the student t -distribution table , the value is  

        [tex]p-value = P( T \le t)= 2 * t_{ t, df } = t_{ -1.756 , 29 } = 2 *0.0448= 0.0896[/tex]

The reason for the 2 in the equation is because the test is a two -tailed test i.e  -1.756 and  1.756

Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis

Hence the test the suggest that the true average percentage of organic matter in such soil is something other than 3%

Answer:

50k

Step-by-step explanation:

Answer & Step-by-step explanation:

The ratio of square feet to gallons of paint:

[tex]1440:6[/tex]

This can also be written as:

[tex]\frac{1440}{6}[/tex]

This fraction can be simplified by dividing the numerator and denominator by 6:

[tex]\frac{1440}{6}=\frac{240}{1}[/tex]

So, the ratio of square feet to gallons of paint is:

1 gallon for every 240 ft².

:Done

The answer would be the first image.

Step-by-step explanation:

From context, it appears that to be circumscribed is to be drawn about; thus the square circumscribed about the circle is the first graph.

Answer:

The first image which is a circle in a square

Answer:

if x = 2

f(x) = -3x^2 + 180x -285

f(x) = -3*2*2 + 180*2 -285

f(x) = -12 + 360 -285

f (x) = 63

Step-by-step explanation:

Answer:

The z-score is [tex]z = 0.6[/tex]

The percentile is  [tex]p(Z < 0.6) = 72.57\%[/tex]

Step-by-step explanation:

From the question we are told that

   The  data value is  0.6 standard deviations above the mean i.e  [tex]x = \mu + 0.6 \sigma[/tex]

Where  [tex]\mu[/tex] is the population mean and [tex]\sigma[/tex] is the standard deviation

Generally the z-score is mathematically represented as

        [tex]z = \frac{x - \mu }{\sigma }[/tex]

=>     [tex]z = \frac{(\mu + 0.6\sigma ) - \mu }{\sigma }[/tex]

=>    [tex]z = 0.6[/tex]

The percentile is obtained from the z-table and the value is

     [tex]p(Z < 0.6) = 0.7257[/tex]

=>   [tex]p(Z < 0.6) = 72.57\%[/tex]

Answer:  5.22 seconds

Step-by-step explanation:

t represents time and y represents the height.

Since we want to know when the ball hits the ground, find t when y = 0

Ball 1 starts at a height of 109 --> h = 109

0 = -16t² + 109

16t² = 109

   [tex]t^2=\dfrac{109}{16}\\[/tex]

   [tex]t=\sqrt{\dfrac{109}{16}}[/tex]

   [tex]t=\dfrac{\sqrt{109}}{2}[/tex]

   t = 5.22

=> H = 109

=> 0 = -16t² + 109

=> 16t² = 109

=> t² = 109/16

=> t = 109/2

=> t = 5.22 sec

Therefore, 5.22 second is the answer.

Answer:

The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Step-by-step explanation:

Given that:

F(x,y) = 8 sin (xy) at (0,9)

The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]

[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]

[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]

[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]

We can conclude that the  maximum rate of change of f at (0, 9) is 72 and the direction of the vector is  [tex]\mathbf{\hat i}[/tex]

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

Slope of the tangent line (m) = (y2-y1) / (x2-x1)

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2

Answer:

[tex]\boxed{x \geq 353}[/tex]

Step-by-step explanation:

Hey there!

Info Given

- Dot is solid

- Line goes to the right

- Dot is at 353

So by using the given info we can conclude that the inequality is,

x ≥ 353

Hope this helps :)

Answer:

Inequality: 100 + 50w ≥ 18000

What to put on graph: w ≥ 358