Find the surface area of the prism a.120cm. B180cm. C34cm. D 333cm

The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.

To find the sum of two expressions, we simply add their like terms.

The given expressions are x+9 and 7x²-2x+1.

The first expression has two terms - x and 9.

The second expression has three terms - 7x², -2x, and 1.

We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.

First, we can simplify the second expression by combining the like terms -2x and 1.

7x² - 2x + 1 = 7x² - (2x - 1)

Now, we can add the like terms from both expressions.

(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9

= 7x² - x + 10

Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.

(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1

= 7x² - x + 10

In either case, the final answer is 7x² - x + 10.

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The scale factor will be one-third which is 1/3. Then the correct option is A.

Given that:

Dimension of a small triangle, 6, 8, and 10

Dimension of a giant triangle, 18, 24, and 30

Dilation is the process of increasing the size of an item without affecting its form. The object's size can be raised or lowered depending on the scale factor. There is no effect of dilation on the angle.

The scale factor is calculated as,

SF = 6 / 18

SF = 1 / 3

The scale factor will be one-third which is 1/3. Then the correct option is A.

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Answer:

1/3

Step-by-step explanation:

I took the test!

Answer:

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Step-by-step explanation:

Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.

The surface area of the box (excluding the top) is given by:

2(x^2) + 4(x^2) = 6(x^2)

The surface area of the metal top is:

x^2

The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:

6(x^2) + x^2 = 7(x^2)

The cost of the wood for the box is:

5 cents per square inch * 6(x^2) = 30x^2 cents

The cost of the metal for the top is:

12 cents per square inch * x^2 = 12x^2 cents

The total cost of the box is:

30x^2 + 12x^2 = 42x^2 cents

We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:

42x^2 = 3000

Solving for x, we get:

x^2 = 71.429

x ≈ 8.445

Therefore, the maximum volume of the box is:

V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Answer:

The greatest area enclosed by the fence will be a square. If the farmer has 60 metres of perimeter fencing, he can use 15 meters of fencing for each side of the square. This would give him an area of 15² = 225 m². Since he can keep one chicken for every square meter, he can keep 225 chickens. Therefore, the farmer should arrange his fence in the shape of a square to get the greatest area.

Answer: 4

Step-by-step explanation: because he needs to divided by 2

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

62 degrees

Step-by-step explanation:

Hope this helps! If it’s wrong I’m really sorry. I used the formula θ = s/r then converted it from radians to degrees.
Pls give brainliest!

Answer:

The answer is C

Step-by-step explanation:

The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.

Answer:  B, C, D

Step-by-step explanation:

Looking at the parabola, this is a width vs area graph.

A)    Incorrect.  the greatest possible area is not 10.  Area goes higher

B) True.  The highest possible area, highest point for area is 100

C) True.  The area is 0 when width is 0

D)True.  The area is also 0 when the width is 20

The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1

From the question, we have the following parameters that can be used in our computation:

The exponential expressions a to f

The general rule is that

a^b = a * a * a..... in b places

Using the above as a guide, we have the following:

a. 7⁴ = 7 * 7 * 7 * 7 = 2401

b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000

c. 5¹ = 5

d. 0⁴ = 0 * 0 * 0 * 0

e. –6² = -6 * -6 = 36

f. –3⁰ =  1

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The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))

A sinusoidal function is a periodic function that is based on either the sine or the cosine function.

The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D

The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4

The vertical shift, D = (4 + (-4))/2 = 0

The period, P = 2·π/B

A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval

P = 10 = 2·π/B

Therefore; B = π/5

When x = -8, y = 0, therefore;

0 = 4·sin((π/5)·((-8) - C)) + 0

4·sin((π/5)·((-8) - C)) = 0

sin((π/5)·((-8) - C)) = 0

(π/5)·((-8) - C) = 0

((-8) - C)  = 0

C = -8

When x = 2, y = 0, therefore;

0 = 4·sin((π/5)·(2 - C)) + 0

4·sin((π/5)·(2 - C)) = 0

sin((π/5)·(2 - C)) = 0

(π/5)·(2 - C) = 0

(2 - C)  = 0

C = 2

Similarly; When x = -3, y = 0, therefore; C = -3

y = 4·sin((π/5)·(x + 3))

The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left

The sinusoidal function, where π ≈ 3.1416 is therefore;

y ≈ 4·sin((0.628)·(x + 3))

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a) The velocity function is v(t) = -3 cos(t) - 1.

b) The object's displacement is 3sin(3) - K - 3.

c) The total distance traveled by the object from time 0 to time 3 is 3sin(3) + 3 meters.

a) To find the equation for the velocity of the object, we need to integrate the function for acceleration with respect to time. The velocity function v(t) is the antiderivative of a(t). Since a(t) = 3 sin(t), the antiderivative of a(t) is v(t) = -3 cos(t) + C, where C is the constant of integration.

We can find C using the initial velocity given. Since v(0) = -2m/s, we substitute t=0 and v(0) = -2m/s into the velocity function to get:

v(0) = -3 cos(0) + C = -2

Solving for C, we get C = -1. Now we can write the velocity function as:

v(t) = -3 cos(t) - 1

b) To find the displacement of the object from time 0 to time 3, we need to integrate the velocity function with respect to time over the interval [0,3]. The displacement function s(t) is the antiderivative of v(t):

s(t) = ∫v(t) dt = ∫(-3cos(t) - 1) dt = 3sin(t) - t - K

where K is the constant of integration. Since we want to find the displacement from time 0 to time 3, we evaluate s(3) - s(0):

s(3) - s(0) = (3sin(3) - 3) - (0 - K) = 3sin(3) - K - 3

c) To find the total distance traveled by the object from time 0 to time 3, we need to calculate the area under the absolute value of the velocity curve over the interval [0,3]. Since the velocity is negative for some time intervals, we take the absolute value of the velocity function:

|v(t)| = |-3cos(t) - 1| = 3cos(t) + 1

We can integrate this function from 0 to 3 to get the total distance traveled:

∫|v(t)| dt = ∫(3cos(t) + 1) dt = 3sin(t) + t + C

Evaluating this at t=3 and t=0, we get:

∫|v(t)| dt = (3sin(3) + 3) - (0 + 0) = 3sin(3) + 3

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The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,

a + b = < 3, -5 >

The graph of the vector sum is given below.

The addition of vectors suggests the addition of the corresponding components of the involving vectors.

Given the vectors are:

a = < 4, - 3 >

b = < - 1, - 2 >

So doing vector addition we get,

a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>

Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.

Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,

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Answer: Look at the image below

Step-by-step explanation: I took the test.

Step 1: Select Vector

Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)

Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)

Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)

Your answer should now look like mine, now go get that A.

Answer:

B. y=5

Step-by-step explanation:

3y-4<11

3y-4+4<11+4

3y<15

3y/3<15/3

y<5

Answer: Given b=2√14 and c=9,

a = 5

Step-by-step explanation:

The annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).

The annual insurance premium can be calculated using the following formula:

Annual premium = (Amount of insurance coverage / $100) x Rate per $100 of insurance

The amount of insurance coverage is 80% of the replacement value of the home, which is $250,000, so it is:

Amount of insurance coverage = 0.8 x $250,000 = $200,000

The rate per $100 of insurance depends on the fire protection class of the home. According to industry standards, fire protection class 5 has a rate of $0.308 per $100 of insurance.

Therefore, the rate per $1 of insurance is:

Rate per $1 of insurance = $0.308 / 100 = $0.00308

The rate per $100 of insurance is:

Rate per $100 of insurance = $0.00308 x 100 = $0.308

Using the formula above, we can calculate the annual insurance premium:

Annual premium = ($200,000 / $100) x $0.308 = $616

Therefore, the annual insurance premium for John Noel and his wife is $616, which corresponds to option (b).

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The ratio that could also be included in this table is (c) 18 : 30

From the question, we have the following parameters that can be used in our computation:

Games won   Games played

6                    10

24                  40

36                60

42                70

From the above, we have the ratio of the number of games won to the number of games played to be

Ratio = 6 : 10

Simplify

Ratio = 3 : 5

From the options, we have

(c) 18 : 30

Simplify

Ratio = 3 : 5

Hence, the ratio that could also be included in this table is (c) 18 : 30

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Answer:

Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.

Answer:

When n is greater than 1/2 or always true

n > 1/2

Step-by-step explanation:

Rewrite.

0+0+6(n−1)=2(n+1)

Simplify by adding zeros.

6(n−1)=2(n+1)

Apply the distributive property.

6n+6⋅−1=2(n+1)

Multiply 6 by −1.6n−6=2(n+1)

Simplify 2(n+1).

6n−6=2n+2

Move all terms containing n to the left side of the equation.

4n−6=2

Move all terms not containing n to the right side of the equation.

4n=8

Divide each term in 4n=8 by 4 and simplify.

n=2

Answer:

[tex]y - 4 = - 3(x - 2)[/tex]

The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.

The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)

The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.

Let say Initial quantity demanded is:

x = -0.7(6) + 10

x = 5.8

Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:

= -0.7(6.01) + 10

= 5.793

The % change in quantity demanded will be:

= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%

= [(5.793 - 5.8) / 5.8] x 100%

= -0.12%

As price has changed from 6 to 6.01, we can calculate the percentage change as follows:

% change in price = [(new price - initial price) / initial price] x 100%

= [(6.01 - 6) / 6] x 100%

= 0.17%

Elasticity of demand = (% change in quantity demanded) / (% change in price)

= (-0.12% / 0.17%)

= -0.71

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Answer:

figure A = square ( All sides are equal)

figure B = Rectangle (Two sides are equal)

Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)

Answer:

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The expression is:

1234 - 4566 / 45.44 + 67 * 755.34

First, we need to perform the division operation since it comes before addition and multiplication.

4566 / 45.44 = 100.50

Now, we can substitute that into the expression:

1234 - 100.50 + 67 * 755.34

Next, we need to perform the multiplication operation:

67 * 755.34 = 50,548.78

Now, we can substitute that into the expression:

1234 - 100.50 + 50,548.78

Next, we can perform the addition and subtraction operations:

1234 + 50,448.28 = 51,682.28

Therefore, the result of the expression is 51,682.28.

The quadratic equation representing the new patio area after adding a decorative tile of width x all the way around is: 0 = 4x^2 + 44x - 60

Options A and E are correct.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

Since the area of the new patio is given as 180 square feet, we can create a quadratic equation to represent the new patio area:

Area = length × width

180 = (12 + 2x) × (10 + 2x)

After we expand, the answer is given as 0 = 4x^2 + 44x - 60

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Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,

8x-10 =6x

8x-6x = 10

2x =10

x= 5.

Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.

Answer: -161

Step-by-step explanation: you solve by plugging 9 in for x so you get f(9) = -2(9)^2 +9-8 you solve using PEMDAS and you get -161

The volume of the pyramid is 936 mi³

A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The volume of a pyramid is expressed as;

V = 1/3bh

where b is the base area and h is the height of the pyramid.

Area of the hexagon = 1/2 × p × a

perimeter = 6 × 6 = 36 mi

area = 1/2 × p × a

= 1/2 × 36 × 5.2

= 187.2/2

= 93.6 mi²

Volume = 93.6 × 10

= 936 mi³

therefore the volume of the pyramid is 936 mi³

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Answer:

1. 30; 2. 6.25.

Step-by-step explanation:

1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;

2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.

The area of a sector is 8.75 [tex]m^{2}[/tex].

A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

where r is the radius, and θ is the central angle.

Given a circle whose area is 45 sq. m.; then;

area of a circle = π[tex]r^{2}[/tex]

45 = π[tex]r^{2}[/tex]

r = [tex]\sqrt{\frac{45}{\pi } }[/tex]

Then,

area of a sector = (θ/ 360)π[tex]r^{2}[/tex]

                  = ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]

                  = [tex]\frac{7}{36}[/tex]*π*45/π

                  = [tex]\frac{7}{36}[/tex]*45

                  = 8.75 sq. m.

The area of the sector is 8.75 [tex]m^{2}[/tex].

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Answer:

19π/6 radians and 31π/6 radians

Step-by-step explanation:

To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:

The angle of point B = angle of point A + 7π/6 radians

= 0 radians + 7π/6 radians

= 7π/6 radians

Angle of point B in degrees = (7π/6) * (180/π) degrees

= 210 degrees

To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:

angle of rotation 1 = angle of point B + 2π radians

= 7π/6 radians + 2π radians

= 19π/6 radians

angle of rotation 1 in degrees = (19π/6) * (180/π) degrees

= 285 degrees

angle of rotation 2 = angle of point B + 4π radians

= 7π/6 radians + 4π radians

= 31π/6 radians

angle of rotation 2 in degrees = (31π/6) * (180/π) degrees

= 465 degrees

So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.

Note:

To convert the angles from radians to degrees, we can use the conversion factor:

1 radian = 180/π degrees