I
If f(x) = 2x² - x -9 , find:
a. f(-2)
b. f(x-2)
c. r?

Given:

Height of cylinder = 6 inches

Volume of cylinder = 60π in³

To find:

The area of the cross section.

Solution:

Volume of cylinder:

[tex]V=\pi r^2h[/tex]

[tex]\pi r^2h=60\pi[/tex]

Cancel the common factor π on both sides.

[tex]r^2h=60[/tex]

Substitute h = 6.

[tex]r^2\times 6=60[/tex]

Divide by 6 on both sides, we get

[tex]r^2=10[/tex]

Taking square root on both sides.

[tex]r=\sqrt{10}[/tex] inch

Area of cross section = [tex]\pi r^2[/tex]

                                   [tex]=\pi (\sqrt{10} )^2[/tex]    

                                   [tex]=10 \pi[/tex] in²

The area of the cross section is 10π in².

Answer:

y=(x+6)

2

−6

Step-by-step explanation:

Answer:

They both contain circles or its either they both are nets.

Step-by-step explanation:

Answer:

Time taken to reach maximum height=4.69 seconds

Maximum Height=371.56feet

Step-by-step explanation:

Given the height function of the pumpkin:

[Tex]h = -16t^2 + 150t + 20[/tex]

The pumpkin reaches it's maximum height at its axis of symmetry.

Therefore, we determine its equation of symmetry.

The equation of symmetry:

[Tex]t=-\frac{b}{2a}[/tex]

a=-16, b=150.

Therefore:

[Tex]t=-\frac{150}{2*-16}=4.6875[/tex]

The pumpkin reaches maximum height after 4.6875 seconds.

At t=4.6875

[Tex]h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet[/tex]

The pumpkin's maximum height is 371.56 feet.

Answer:

see below

Step-by-step explanation:

m/n = 1/7

Using cross products

7m = n

This is a direct proportion

Step-by-step explanation:

[tex] \because \: {a}^{m} . {a}^{n} = {a}^{m + n} \\ \therefore \: {4}^{8} . {4}^{2} = {4}^{8 + 2} = {4}^{10} \\ \\ \because \: ({a}^{m})^{n} = {a}^{m \times n} \\ \therefore \:({2}^{4})^{5} = {2}^{4 \times 5} = {2}^{20} \\ \\ {5}^{6} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15625[/tex]

The solution are:

To solve for each variable using the properties of exponents, we can use the following steps:

Identify the base and exponent in each expression.

Use the properties of exponents to simplify the expressions.

Solve for the variable.

4^8 •4² = 4^a

Identify the base and exponent in each expression:

Base: 4

Exponent: 8 in the first expression, 2 in the second expression, and a in the third expression

Use the properties of exponents to simplify the expressions:

4^8 •4² = 4^(8+2) = 4^10

Solve for the variable:

4^a = 4^10

a = 10

(2^4)^5 = 2^b

Identify the base and exponent in each expression:

Base: 2

Exponent: 4 in the first expression, 5 in the second expression, and b in the third expression

Use the properties of exponents to simplify the expressions:

(2^4)^5 = 2^(4*5) = 2^20

Solve for the variable:

2^b = 2^20

b = 20

5^6

Identify the base and exponent:

Base: 5

Exponent: 6

Simplify the expression:

5^6 = 5*5*5*5*5*5 = 15625

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The area in square millimeters of the triangle outlined on the origami figure is 441 square millimeters.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

Conversion:

7 cm to mm = 7 × 10

7 cm to mm = 70 mm.

1.26 cm to mm = 1.26 × 10

1.26 cm to mm = 12.6

By substituting the given side lengths into the formula for the area of a triangle, we have the following;

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 70 × 12.6

Area of triangle = 35 × 12.6

Area of triangle = 441 square millimeters.

Answer:

5/12

Step-by-step explanation:

Let the unknown number of sugar requires by 1/2 recipe be x

1 recipe requires 5/6 cup of sugar

1/2 recipe requires x cup of sugar

Cross multiply

x=1/2×5/6

x=5/12

So the amount of sugar requires to make 1/2 recipe is 5/12

Answer:

It would open upward.

Step-by-step explanation:

If you see on the equation, there is a positive (+) sign on the [tex]3x^2[/tex].  If you see the positive sign on anything that is squared, and it is asking for a quadratic function, then it will always open upward.  If you see a negative sign on anything that is squared, and is asking for a quadratic function, then it will open downward.

Answer:

Upwards

Step-by-step explanation:

The reason is this quadratic function has a positive coefficient which is 3. The reason 3 is the coefficient is that 3 is the one with the X with a square in it. if 3 would have been negative, well the answer would be the opposite.

Hope That Helped

Answer: (1) The least number of meals is 26 (2) She loses 150 if she caters no meal in one week. (3) Her profit would be 2,650 if she caters for 50 meals in one week

Step-by-step explanation: The weekly profit is given as a quadratic equation which is;

P = 2x² -44x - 150

We begin by solving for the value of x.

When 2x² -44x - 150 = 0

Divide all through by 2

x² - 22x - 150 = 0

By factorization,

(x - 25) (x + 3) = 0

(x -25) = 0 OR (x + 3) = 0

When x - 25 = 0

x = 25

When x + 3 = 0

x = -3

What this implies is that when Amelia caters for 25 meals in a week, her profit is calculated as follows

P = 2x² - 44x -150

P = 2(25)² - 44(25) - 150

P = 2(625) - 1100 - 150

P = 1250 - 1100 - 150

P = 0

(1) Therefore she must cater for at least 26 meals before she can begin to make any profit.

(2) She loses 150 if she caters no meal in one week.

This can be calculated as follows;

When x = 0,

P = 2x² - 44x - 150

P = 2(0)² - 44(0) - 150

P = 0 - 0 -150

P = -150

(3) When she caters 50 meals her profit becomes 2,650

P = 2x² - 44x - 150

P = 2(50)² - 44(50) - 150

P = 2(2500) - 2200 - 150

P = 5000 - 2200 - 150

P = 2650

1) The least number of meals Amelia needs to cater in order to begin making a profit is 25.

2) Amelia loses $150 if she caters no meals in a week.

3) For catering 50 meals, Amelia's profit is $2650.

1) To find the least number of meals Amelia needs to cater in order to begin making a profit, we need to determine when her profit, P, becomes positive. In other words, we need to solve the quadratic equation 2x^2 - 44x - 150 = 0 for x. This equation can be factored as (2x + 6)(x - 25) = 0. Therefore, x = -3 or x = 25. Since the number of meals cannot be negative, the least number of meals Amelia needs to cater in order to begin making a profit is 25.

2) If Amelia caters no meals one week, the profit, P, is given by P = 2(0)^2 - 44(0) - 150. Simplifying this equation, we get P = -150. Therefore, Amelia loses $150 if she caters no meals in a week.

3) To find Amelia's profit for catering 50 meals, we substitute x = 50 into the profit equation P = 2x^2 - 44x - 150. Plugging in x = 50, we get P = 2(50)^2 - 44(50) - 150 = 5000 - 2200 - 150 = $2650.

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Answer:

58 should be the answer

Step-by-step explanation:

<CBD is 90 and <BDC is 32 as well since its the same as angle <BDA and 180 in every triangle so 180-90-32=58.

Answer:

22

Step-by-step explanation:

If x=2 and y=4

7•4 - 3•2

28-6

So the answer is 22

Each bottle of shampoo contains 10.5 ounces. The formula for the total volume of shampoo (y) in terms of the number of bottles (x) is y = 10.5x.

Let's denote the amount of shampoo in each bottle as b (in ounces). Since there are 12 bottles of shampoo, the total volume of shampoo in ounces (y) is given by the product of the number of bottles (x) and the amount in each bottle (b). So, the equation is:

y = x * b

The problem states that the case of 12 bottles holds a total of 126 ounces. This can be expressed as:

126 = 12 * b

Now, we can solve for b by dividing both sides of the equation by 12:

b = 126 / 12

Simplifying:

b = 10.5

So, each bottle of shampoo contains 10.5 ounces.

Therefore, the formula for the total volume of shampoo (y) in terms of the number of bottles (x) is:

y = 10.5x

Answer:

Step-by-step explanation:

it is A

Answer:

The diagonal length of the square equals:

diagonal ^ 2 = 7^2 + 7^2

diagonal ^ 2 = 49 + 49

diagonal ^ 2 = 98

diagonal = 9.899 cm

The diagonal is smaller than the circle's diameter and so it will ft inside the circle.

Step-by-step explanation:

Answer:

We need to find the area of the semicircles + the area of the square.

The area of a square is equal to the square of the lenght of one side.

As = L^2 = 58m^2 = 3,364 m^2

Now, each of the semicircles has a diameter of 58m, and we have that the area of a circle is equal to:

Ac = pi*(d/2)^2 = 3.14*(58m/2)^2 = 3.14(27m)^2 = 2,289.06m^2

And the area of a semicircle is half of that, so the area of each semicircle is:

a =  (2,289.06m^2)/2 = 1,144.53m^2

And we have 4 of those, so the total area of the semicircles is:

4*a = 4* 1,144.53m^2 = 4578.12m^2

Now, we need to add the area of the square 3,364 m^2 + 4578.12m^2 = 7942.12m^2

This is nothing like the provided anwer of Val, so the numbers of val may be wrong.

Answer:

The answer is 4,112.00 m

Step-by-step explanation:

Val subtracted the​ square's area from area of the semicircles when it should be added to it.

I think I would be 30% maybe... I could be wrong

Answer:

27%

Step-by-step explanation:

First get the decrease

Decrease = $23500 - $17155

= $6345

Percentage decrease = decrease/initial price x 100%

That’s

$6345/$23500 x 100%

0.27 x 100%

27%

The percentage decrease in the price of the car is 27%

Answer:

5n

Step-by-step explanation:

The result of n x 5 is equal to 5 times the value of n.

The equation 'n x 5' represents the product of a number n and 5. The result can be positive or negative based on the value and sign of n. Also, parenthesis placement in expressions greatly affects the outcome due to the order of operations.

Understanding the Multiplication of Numbers and Order of Operations

The equation n x 5 indicates that a number n is being multiplied by 5. The results of this product will depend on the value of n and whether n is positive, negative, or zero. For example, if n is positive, like 2, then the product is also positive: 2 x 5 = 10. If n is negative, like -3, the result is negative: (-3) x 5 = -15. It's important to remember that when two positive numbers multiply, the answer has a positive sign, and when two negative numbers multiply, the result is also positive. However, if the two numbers have opposite signs, the answer will have a negative sign.

Furthermore, the placement of parentheses can affect the result of mathematical expressions. For instance, 2 + (3 x 5) is not the same as (2 + 3) x 5 due to the order of operations. In the first expression, multiplication is performed first, resulting in 17, whereas the second expression results in 25.

Understanding the rules of multiplication, including the signs of the numbers involved and the order of operations, is essential for solving equations and expressions correctly.

Answer:

In (3x)^2, you are squaring both the 3 and the x:

9x^2

in 3x^2, you are squaring just the x:

3x^2

Answer:

(3x)^2=9x^2

(3x^2)=3x^2

Step-by-step explanation:

The difference between the two is that

(3x)^2 means the square applied to both the 3 and the x to give 9x^2

But on the other side

(3x^2) means that the square only applies to x without involving 3 which gives 3x^2

So there is difference between them

Answer:

- The scale factor is one-half

- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle

-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure

Step-by-step explanation:

The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.

The perimeter of a rectangle is: [tex]P=2l+2w[/tex], where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.

Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.

The area of a rectangle is: [tex]A=lw[/tex], where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.

Notice that 12 * (1/4) = 3, which means that E is correct, but D is wrong.

Hope this helps!

Answer:

Statement 2: The scale factor is One-half

Statement 3: The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle.

Statement 5: The area of the reduced figure is (One-half) squared, one-fourth times the area of the original figure.

Step-by-step explanation:

A smaller rectangle has a length of 3 and width of 1

Perimeter: 2(3+1) = 8

Area: 3×1 = 3

A larger rectangle has a length of 6 and width of 2

Perimeter = 2(6+2) = 16

Area = 6×2 = 12

Comparing areas:

Smaller : larger

3 : 12

1 : 4

Comparing perimeters:

Smaller : larger

8 : 16

1 : 2

Answer:

The answer is 56 cm2

Step-by-step explanation:

You have to multiply the height times the base then divide that answer by two.

8x14= 112

112/2= 56

Answer:

Step-by-step explanation: Area = 1/2 b.h

= 1/2 8cm.14cm

= 1/2 112 Square cm

= 112/2

= 56 Square cm.

Answer:

A=6

Total base area is 12

A=96

Total surface area is 108

Answer:

Step-by-step explanation:

A=6

There are two bases, so total base area is 12

A= 96

The total surface area is 108

Answer:

C sqrt (4) or 2

Step-by-step explanation:

(x + 4)^2 + (y − 3)^2 = 4

We know that the equation for a circle can be written in the form

(x -h)^2 + (y − k)^2 = r^2  where (h,k) is the center and r is the radius

Rewriting the above equation

(x - -4)^2 + (y − 3)^2 = 2^2

The center is (-4,3) and the radius is 2

Answer:

p=2

Step-by-step explanation:

9(p - 4) = -18

Divide each side by 9

9/9(p - 4) = -18/9

p-4 = -2

Add 4 to each side

p-4+4 = -2+4

p = 2

Answer:

13

Step-by-step explanation:

If they are equal to each other, than angle DF is the same as angle AC, and angle AC is 13, so DF must be 13

Answer:

Hence the length of line segment BA as 98 units

Step-by-step explanation:

Given:

BA as tangent to circle ,DB as secant which intersect at point C at circle

Length BC= 55 and CD=120

To Find:

Length of line segment AB.

Solution:

This follows the relationship between tangent and secant  in circle terms as:

Consider as figure such that ,

AB as tangent , DB as secant C be point at circle

So secant total distance = DB=BC+CD =55+120=175

Using formula as ,

[tex]AB^2=BC(BC+CD)[/tex]

We have to find AB

Here BC=55 and CD=120

[tex]AB^2=55(120+55)[/tex]

[tex]AB^2=55(175)[/tex]

[tex]AB^2=9625[/tex]

[tex]AB=98.10[/tex]

So nearest unit for length will be 98

Hence the length of line segment BA as 98 units

Answer:

98 units

Step-by-step explanation:

edge

Answer:

i think disagree ._.

Answer:

[tex]\sqrt{38}[/tex]

Step-by-step explanation:

Given that:

The 3 demensions of the right rectangular prism measures 5 centimeters by 3 centimeters by  2 centimeters.

Because we do not know which one is the height, the length and the width of the box, so we assume them (it does not affect the length of the interior

diagonal )

To find the length of the interior  diagonal of the prism, we use the following formula:

d = [tex]\sqrt{l^{2} +w^{2} +h^{2} }[/tex] = [tex]\sqrt{5^{2} +3^{2} + 2^{2} } = \sqrt{38}[/tex]  

Hope it will find you well.

Answer

38 or about 6.16

Answer:

659.4 cm^2

Step-by-step explanation:

The area of the curved surface of the cone = πrL

=  π*7*16

= 3.14 * 112

= 351.68 cm^2,

Surface area of the hemisphere = 2 π r^2

= 2*3.14*7^2

= 307.72 cm^2.

Total area = 351.68 + 307.72

= 659.4 cm^2.