Denise subtracted -9
8 and came up with an answer of -17 feet. Is
Denise correct? Why or why not?

Answer:

314

Step-by-step explanation:

1. Divide 63 by pi (equals 20)

2. Divide 20 by 2 which equals 10.

3. Multiply 10 by itself to get the square. which would be 100

4. Multiply 100 by pi

3. Finally A=314

Answer:

41-29=12
756+223=979
821-690=131
eleventh, fifteenth, nineteenth

4
2

The expression which represents the area of the triangle : [tex]2x^{2}-16x+24[/tex].

Length of base = B = 2x - 12

Height = H = Length of base + 8

                  = 2x - 12 + 8

                  = 2x - 4

Area = [tex]\frac{1}{2}(B)(H)[/tex]

        = [tex]\frac{1}{2}(2x-12)(2x-4)[/tex]

        = [tex]\frac{4}{2}(x-6)(x-2)[/tex]

        = [tex]2(x^{2} -8x+12)[/tex]

       = [tex]2x^{2}-16x+24[/tex]

Hence, the expression is [tex]2x^{2}-16x+24[/tex].

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The volume of a drill bit with a radius of 3 centimeters is of:

16.32 cm³.

To obtain the numeric value of a function or of an expression, each instance of the input variable of the function has to be replaced by the value at which we want to find the numeric value.

The volume of a drill bit with a radius of r centimeters is given by the equation presented as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi r^3[/tex]

Hence, for a radius of 3 centimeters, as is the case in this problem, the lone instance of r is replaced by 3, and the volume is obtained as follows:

[tex]V = \frac{\sqrt{3}}{9}\pi (3)^3 = 16.32[/tex]

The unit of the volume is in cubic centimeters, as the radius is measures in centimeters and then it is cubed.

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1)

angle 1 is 41

angle 2 is also 41

2)

angle 1 is 124

angle 2 is also 124

Answer:

3/2

Step-by-step explanation:

1/2 ÷2/3

1/2x3/2

1x3=3

1x2=2

=3/2

Mrs. Hoeting have approximately 4 times of serving.

Given,

The quantity of snozzberry Mrs. Hoeting purchased = 1 7/8 cups = 15/8 cups

The quantity of snozzberry she eats per serving = 1/2 cups

We have to find the number of servings does Mrs. Hoeting have;

Number of servings = Quantity of snozzberry purchased / Quantity of snozzberry eats per serving

Number of servings  = 15/8 ÷ 1/2

Number of servings = 15/8 × 2

Number of servings = 15/4

Number of servings = 3.75 ≈ 4

That is,

Mrs. Hoeting have approximately 4 times of serving.

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A company's profit is determined by its revenue less its cost of operations.Subtract costs from revenue to get the profit function.

Let P(x) stand for the profit, R(x) for the revenue, and C(x) for the expense.Profit thus equals P(x) = R(x) -C. (x).The revenue and expense can be modeled as fixed values or as functions,

Profit = Revenue - Cost

We need to find an equation for the revenue R(x).

R(x) = number of units * unit price = x * p(x) = x(72-x) = 72x - x2

Therefore: Profit P(x) = 72x - x2 - (20 + 52x) =  - x2 + 20x -20

To find max profit, run the 1st derivative test, so set P'(x) = 0 and solve for x:

P'(x) = -2x + 20

set P'(x) = 0 ----> -2x+20 = 0 ----> -2x = -20 -----> x = 10

The number of units, x, that produces the maximum profit is 10.

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Answer:

the answer is 99 because the difference between the numbers is 11 and if you do 9 ×11 you get 99

Answer: The nth term of this sequence is a n= 11n-2

Step-by-step explanation:

Sequence : 9, 20, 31, 42

Difference : +11, +11, +11

The formula for nth term of an arithmetic progression is a n= d.n+a1-d

The formula for nth term of an arithmetic progression is d= 11 and a1=9

so.

a n=d.n+a 1-d

a n=11.n+9-11

a n=11n-2

Hope it helps :)

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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Answer:

7/5

Step-by-step explanation:

12x - 15 = 6 - 3x

15x = 21

x = 7/5

Denise got $30 for her birthday, spending $6 on lunch, and having $24 left.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the money that Denise get for her birthday.

Denise split her birthday money with her two sisters. the spent 6$ on lunch, so he has $24 left. Hence:

Amount gotten for birthday = $6 + $24

y = $6 + $24 = $30

Denise had $30

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Answer:

10%

Step-by-step explanation:

A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and  A score that is the same as the mean is 0.

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

Given that, a normal distribution of BMCC MAT51 scores has a standard deviation of 1.5.

At above 1.5

Z = (μ + 1.5 - μ)/2 = 1

At below 1.5

Z = (μ -1.5 - μ)/2 =-1

At above 1.36

Z = (μ + 1.36 - μ)/2 = 0.90

At same as the mean

Z = (μ - μ)/2 = 0

Hence, A score that is 1.5 points above the mean is 1, A score that is 1.5 points below the mean is -1, A score that is 1.36 points above the mean is 0.90 and  A score that is the same as the mean is 0.

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Answer:

$418.00

Step-by-step explanation:

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2-(3\sqrt{5})^2}=a\implies \sqrt{81-3^2(5)}=a \\\\\\ \sqrt{81-9(5)}=a\implies \sqrt{81-45}=a\implies \sqrt{36}=a\implies \boxed{6=a}[/tex]

Answer:

180 / (13 + 2) =12 bands of 15 students each.

Since 2 from each band are sidelined, then:

12 x 2 = 24 - number of students on the sidelines, so that:

13 x 12 + 24 =180 - total number of students.

The solution set of 'b' for the given compound inequality is

-2 < b < 4.

Given, a compound inequality 6b < 24 and 4b + 12 > 4.

Now, solving the first inequality,

6b < 24

On dividing both the sides by 6, we get

6b/6 < 24/6

b < 4.

Now, solving the second inequality,

4b + 12 > 4

On subtracting 12 from both the sides, we get

4b + 12 - 12 > 4 - 12

4b > -8

On dividing both the sides by 4, we get

4b/4 > -8/4

b > -2.

So, the solution set of b to satisfy the compound inequality be,

greater than -2 and less than 4 i.e.

-2 < b < 4.

Hence, the solution set of 'b' is -2 < b < 4.

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Answer:

Step-by-step explanation:

y=-x-7........(1)

5y+3x=-13..........(2)

(2) - 3x(1)=>

5y+3x= -13

3y + 3x = - 21

(-)    (-)      (+)

-----------------------

2y+0=8

=>y=4

  (1)=>

  y= -x-7

=>x= -y-7

=>x= -4-7

=>x= -11 .

Answer:

x=-11 & y= 4

Step-by-step explanation:

y=-x-7

5y+3x=-13

y+x=-7—eqn i

5y+3x=-13—eqn ii

multiply eqn i by 5

5y+5x=-35

multiply eqn Ii by 1

5y+3x=-13

put eqn I and Ii together

5y+5x=-35

5y+3x=-13

subtract

2x=-35--13

2x=-35+13

2x=-22

divide both sides by 2

2x/2 = -22/2

x=-11

put x=-11 into eqn i

y+x=-7

y-11=-7

y=-7+11

y=4

Answer:

Problem: 0.5(5-7x)=8-(4x+6)

Answer: x= -1

The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive exponents is (7)²⁰  .

In the question ,

it is given that ,

the expression is 7⁻⁴/(7⁻⁴)⁶ .

we need to find the simplified value of the expression .

So ,

= 7⁻⁴/(7⁻⁴)⁶

we know that (xᵃ)ᵇ = (x)ᵃˣᵇ

By using the above property , we get

= 7⁻⁴/(7)⁻⁴ˣ⁶

= 7⁻⁴/(7)⁻²⁴

we know that xᵃ/xᵇ = xᵃ⁻ᵇ

By using the above property , we get

= (7)⁻⁴×(7)²⁴

= (7)²⁴⁻⁴    ... by using the property xᵃ.xᵇ = xᵃ⁺ᵇ

= (7)²⁰

Therefore , The expression 7⁻⁴/(7⁻⁴)⁶ in simplified form using positive

exponents is (7)²⁰  .

The given question is incomplete , the complete question is

Simplify the following expression. Write your answer using positive exponents.

7⁻⁴/(7⁻⁴)⁶

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Answer:

The total amount of college students enrolled part-time that year would be approximately 2 million.

Step-by-step explanation:

In order to find out the amount of college students enrolled part-time that year, we need to convert the 23% into 0.23, and then use a calculator, with this equation:

0.23 x 6,600,000 = 1,518,000

Now, it says to "round your answer to the nearest million."

1.518 million is closer to 2 million than 1 million, so our answer would be 2 million.

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The expression using distributive property becomes 7n - 35

The distributive property is also known as the distributive law of multiplication over addition and subtraction.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.

Using this distributive law, A × (B + C) = AB + AC. to re-write the expression -7(5 - n), A = -7, B = 5 and C = -n

we have -7(5 - n) = (-7 x 5) + (-7 x -n)

which is further simplified as (-35) + (7n) = 7n - 35

In conclusion, the re-written form of -7(5 - n) in distributive form is 7n - 35

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Reflection is along line x = 1, using plotting of points.

What do you mean by reflection , rotation and translation?

An object can be reversed across a line through reflection without changing its size or shape.

Rotation is the movement of an item around a fixed point while maintaining its original size and shape.

A figure can be translated if it is moved in any direction without altering its size, form, or orientation.

An object is always translated, but it is never turned, flipped, or shrunk.

It is given that Jayden is drawing the top view of a square sandbox on a coordinate plane with vertices at D(1, 1), E(1, 6), F(6, 6) , and G(6, 1) .

On plotting these points on graph paper we get below graph, (1)

Now , to move the sandbox so that it is in the shade, he reflects it and the new  vertices of the image are at D′(1, 1), E′(1, 6), F′(−4, 6) , and G′(−4, 1)

On plotting these new coordinates we get below graph (2)  

Square box in the second graph shifted to left side of x = 1.

Therefore, reflection is along line x = 1.

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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Using the distance, 5/4 far distance that they ride in all.

In the given question,

Carlos and his mom went out on a bike ride.

They rode 5/8 of a mile to the park and then rode 5/8 of a mile back home.

We have to check how far did they ride in all.

We have to find the total distance that he ride to park and from the park.

We can find the total distance by adding the whole distance that he ride.

Total distance = Distance to the park + Distance back home

Total distance = 5/8+5/8

Since the denominator is same. So

Total distance = (5+5)/8

Total distance = 10/8

Now simplifying.

Total distance = 5/4

Hence, 5/4 far distance that they ride in all.

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The equations that is true for the values x = -2 and x = 2 is x² – 4 = 0  and 4x² = 16.

Equations:

Equation is an an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

For example, 3x² − 2x + 9 is an algebraic expression.

Given,

Here we have the following equations

x² – 4 = 0

x² = –4

3x² + 12 = 0

4x² = 16

2(x – 2)² = 0

Now, we need to find which of these equations are tur for the values x = -2 and x = 2.

In order to find the true equation, we have to apply the given values on each of these to find which one is correct,

When x = 2 then,

(2)² – 4 = 0 => 4 - 4 = 0 (True)

(2)² = –4 => 4 ≠ -4 (Not true)

3(2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(2– 2)² = 0 => 2(0) = 0 = 0 = 0 (True)

Similarly, when we apply the value of x = -1, then we get,

(-2)² – 4 = 0 => 4 - 4 = 0 (True)

(-2)² = –4 => 4 ≠ -4 (Not true)

3(-2)² + 12 = 0 => (3x4) + 12 = 0 => 12 + 12 = 0 => 24 ≠ 0 (Not true)

4(-2)² = 16 => (4 x 4) = 16 => 0 = 0 (True)

2(-2– 2)² = 0 => 2(-4)² = 0 => 32 ≠ 0 = 0 (Not true)

Therefore, the resulting equations are x² – 4 = 0  and 4x² = 16.

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