choose 2 parabolas from the equation, one opening up and one opening down. Then Find the equation of one of your chosen parabolas in vertex form and then in standard form. Then Find the equation of your second parabola in factored form and then in standard form. Then Find the domain and range of both parabolas, then Find the y-intercept for both parabolas and lastly For one of your chosen parabolas, describe the transformations compared toy = x^2.

Answer:

Hence the possible values of m are m > 14

So, the dairy farm produced greater than 14 kg of cheese

Step-by-step explanation:

We have m = kg of cheese,

let y = yogurt

and i = ice cream,

The dairy farm also produced 28 kg more yoghurt than cheese

y = m + 28

3 times as much ice cream as cheese

i = 3m

The dairy farm produced more kilograms of ice cream than yoghurt last week

i > y

so we have,

y = m + 28  (i)

i = 3m  (ii)

i > y  (iii)

Now, using (i) and (ii) in (iii),

i > y

3m > m + 28     (i = 3m, y = m + 28)

subtracting m from both sides,

3m - m > m - m + 28

2m > 28

dividing by 2 on both sides,

m > 28/2

m > 14

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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The length of the real life plane is 8000 centimetres.

The scale model as a ratio is  1:2000.

A model of a plane has a length of  4 cm. The real life plane has a model of 80 m.

The length of the real life plane in centimetres is as follows:

1 metre = 100 centimetres

80 metres = ?

cross multiply

length of the real life plane in cm = 80 × 100

length of the real life plane in cm = 8000 centimetres

The scale model can be calculated as follows;

scale model = 4 / 8000

scale model = 1 / 2000 = 1:2000

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Option B.

2, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis

Given the function f(x) = 2(x - 2)(x - 6)^3

We need to get the zeros of the polynomial, its multiplicity and determine whether the graph crosses pr touches the x-axis

Get the zeros of the polynomial

Equating the function to zero will give;

2(x - 2)(x - 6)^3 = 0

This can be splitted as shown:

2(x - 2) = 0

x - 2 = 0

x = 2

Similarly,

(x - 6)^3 = 0

x - 6 = 0

x = 6

This shows that the zeros of the polynomial are 2 and 6

Get the multiplicity and determine whether the graph crosses or touches the x-axis at each x-intercept

First, you must note that zeroes with odd multiplicity cross through the x-axis, while zeroes with even multiplicity just touch the x-axis

For the factor (x-2), since the power of the linear factor is 1, hence its multiplicity is 1 showing that the graph crosses the x-axis at this point.

Similarly, for the other factor (x-6)^3, the multiplicity is 3 (Odd) showing that the graph crosses the x-axis at this point.

Based on the explanation above, the correct option will be Option B.

2, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis

Answer:

d 13

Step-by-step explanation:

Answer: x = -1

Step-by-step explanation:

Step 1: Distribute. 6 + 3x - 2x = 11 + 4 + 10x

Step 2: Subtract like-terms. x + 6 = 10x + 15

Step 3: Leave x by itself. x + (6-6) = 10x + (15-6)

Step 4: Subtract 10x to x, and simplify. (x - 10x) = (10x - 10x) + 9

Step 5: Divide. -9x/9 = 9/9

The answer is x = -1. Hope this helps

when we evaluate the given expression:

5*(x^2 - y)/z

in x = -3, y = 7 and z = 10 the value of the expression is 1.

Here we start with the expression:

5*(x^2 - y)/z

Where x, y, and z are called variables, meaning that can take any number we want.

And we want to evaluate this, given the values:

x = -3

y = 7

z = 10

Evaluating just means that we need to change the correspondent variables by the given numbers, if we do that in the given expression we will get:

5*( (-3)^2 - 7)/10

5*( 9 - 7)/10 = 5*(2)/10 = 10/10 = 1

So, we can see that when we evaluate the given expression in x = -3, y = 7 and z = 10 the value of the expression is 1.

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Answer:

No. It is EF and GH

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The answer will be EF and GH, both are 7 units long.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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The easiest way to calculate square root is from a calculator. That's what i typically do.

So, lets solve this.

\(\sqrt{927369} =963\)

Hope this helps!

Answer:

Step-by-step explanation:

15% of 20 is 3

Answer:

The question is not complete

Answer:

iTS UPside dOWn

But you were supposed to multiply so your answer is 476

aka the last one

HOPE THIS HELPS!

Answer: With 7 gallons of gas, the car can travel 147 miles.

The proportion is:

N*(63 miles/3) = total distance the car can travel with N gallons of gas.

Step-by-step explanation:

We know that with 3 gallons of gas, the car can travel 63 miles.

Then for N gallons of gas, we first need to count the number of times that 3 is in N.

This is equal to the quotient between N and 3:

N/3

This is the number of times that we have 3 gallons of gas, in a total of N gallons of gas.

And for each one of these, the car can travel 63 miles.

Then the total distance that the car can travel with N gallons of gas is:

(N/3)*63 miles. = N*(63 miles/3) = total distance the car can travel.

In this case, we want to know how many miles the car can travel with 7 gallons of gas, then if we use that equation we get:

(7/3)*63 miles = 147 miles.

Answer:

C. 18.33%

Step-by-step explanation:

300 x .1833 = 354.99

Rounded up, it equals $355

18.33 % is the per cent increase in waiter tips from Friday to Saturday. Therefore, option C is the correct answer.

Given that, a waiter earned $300 in tips during his shift on Friday. On Saturday, he earned $355 in tips.

Subtract the original value from the new value, then divide the result by the original value. Multiply the result by 100. That is, % increase = Increase ÷ Original Number × 100.

Now, increase=355-300=55

% increase =55/300 × 100

=18.33 %

18.33 % is the per cent increase in waiter tips from Friday to Saturday. Therefore, option C is the correct answer.

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Answer:

Exact Form:

x = 0, 1/4

Decimal Form:

x = 0, 0.25

Step-by-step explanation:

Step 1: Factor 3x^2 out of 12x^3 - 3x^2

Factor 3x^2 out of 12x^3:

3x^2 (4x) - 3x^2 = 0

Factor 3x^2 out of -3x^2:

3x^2 (4x) + 3x^2 (-1)  = 0

Factor 3x^2 out of -3x^2 (4x) + 3x^2 (-1) :

3x^2 (4x-1) = 0

Step 2: Divide each term by 3 and simpify

divide each term in 3x^2 (4x-1) = 0 by 3.

3x^2 (4x-1) / 3 = 0 / 3

simplify 3x^2 (4x-1) / 3.

Cancel the common factors.

3 x^2 (4x -1) / 3 = 0 / 3

divide x^2 (4x-1) by 1.

x^2 (4x-1) / 3 = 0 / 3

Apply the Distributive Property

Reorder.

Rewrite using the commutative property of multiplication.

4x^2 x + x^2 · -1 = 0 / 3

Move -1  to the left of  x^2

4x^2 x -1 · x^2  = 0 / 3

Simplify each term

multiply x^2 by x^2 by adding the exponents.

Move x

4 (x · x^2) -1 · x^2= 0 / 3

Multiply x by x^2

Rase x to the power of 1.

4 (x^1 · x^2) -1 · x^2= 0 / 3

Use the power rule a^m a^n = a^m+n to combine exponents

4x^1+2 -1 · x^2= 0 / 3

Add 1 and 2.

4x^3 -1 · x^2= 0 / 3

Rewrite -1x^2  as -x^2.

4x^3 -x^2= 0 / 3

Divide 0 by 3

4x^3 -x^2= 0

Step 3: Factor x^2 out of 4x^3 -x^2.

Factor x^2 out of 4x^3

x^2 (4x) -x^2 = 0

Factor x^2 out of -x^2

x^2 (4x) x^2 · -1 = 0

Factor x^2 out of x^2 (4x) x^2 · -1

x^2 (4x -1) = 0

If any individual factor on the left side of the equation is equal to 0,  the entire expression will be equal to  0

x^2 = 0

4x -1 = 0

Set x^2 equal to 0 and solve for x

x = 0

Set 4x -1 equal to 0 and solve for x

x = 1/4

The final solution is all the values that make x^2 (4x-1) = 0 true

x= (0, 1/4)

Answer:

7 and 5

Step-by-step explanation:

The present age of Khalil is 7 years and the present age of Angela is 2 years.

Given that, in five years, Angela will be the age that Khalil is now. In three years, Khalil will be twice as old as Angela.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the present age of Khalil be x-5.

In five years:

Khalil's age = x-5+5=x

Angela's age = Khalil's present age

Angela's age = x-5

So, present angle of Angela's age = x-5-5=x-10

In three years:

Khalil's age = x-5+3=x-2

Angela's age =x-10+3=x-7

So, x-2=2(x-7)

⇒ x-2 = 2x-14

⇒ x=12

Khalil's present age = x-5=7 years and Angela's present age = x-10=2 years.

Therefore, the present age of Khalil is 7 years and the present age of Angela is 2 years.

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Answer:

The correct option is A. Parallel line.

Answer:

x=0

Step-by-step explanation:

Answer:

B. 8

Function's:

Given following:

To solve for f(g(-2)), substitute x = -2 in function g(x)

⇒ f(g(-2))

⇒ f((-2)² + 1)

⇒ f(5)

Now, substitute x = 5 in function f(x)

⇒ 2(5) - 2

⇒ 8

Answer: 38.5

Step-by-step explanation:

calculator

Answer:

about 21 students

Step-by-step explanation:

total students: 150 students enrolled

recognize all letters: 6/7 of the students

To find 1/7 of the students: divided the 150 by 7

150/7 = 21.4285           this is for 1/7th of students

since 1/7th of the students need to learn the alphabet (7/7 - 1/7 = 6/7)

OR

150/7 = 21.4285           this is for 1/7th of students

150/7 x 6 = 128.57        this is for 6/7th of students

150 - 128.57 = 21.4285

a. Playing Surface: Rectangular region

b. Corner of Serving Box: Vertex

c. Baseline: Line segment

d. Net: Plane

e. Intersection of Baseline and Side Line: Vertex

Since it covers the entire area where the game is played, the playing surface of the tennis court lacks a precise geometric description. It might be called a rectangle area.

The serving box's corner can be thought of as a vertex, which is the intersection of two line segments or rays.

A one-dimensional geometric object, the baseline is a segment of a straight line.

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a rectangle

Quadrliaterals which have 4 right angles are squares and rectangles.

The 4 sides of the a square are equal. Hence, it cannot be a square.

Properties of a rectangle:

- It has 4 right angles

- the opposite sides are parallel

- the opposite sides are congruent

- diagonals are congruent

The quadrilateral which fits the desciption in the question is a rectangle.

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The mean is approximately 9, the median is 9, the mode is 8, and the range is 7.

To find the mean, we add up all the numbers in the data set and divide by the total number of numbers:

Mean = (7 + 6 + 8 + 12 + 9 + 13 + 8) / 7 = 63 / 7 ≈ 9

So the mean is approximately 9.

To find the median, we need to arrange the numbers in order from smallest to largest:

6, 7, 8, 8, 9, 12, 13

Since there are an odd number of values in the data set, the median is the middle value, which is 9.

To find the mode, we need to look for the value that occurs most frequently in the data set. In this case, 8 occurs twice, which is more than any other value, so the mode is 8.

To find the range, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value = 13 - 6 = 7

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Answer:

the answer is 9

Step-by-step explanation:

if you divide it together you will get 9

1. They keywords are polynomial, factors, and zeroes.

2. This question is related to the unit/topic of polynomial functions in Algebra.

3. To solve this question, put the polynomial in factored form, let each factor equal to zero, and solve for the variable.

4. 0, 3, 2/3, -7. Option  B

For the polynomial that has factors x, (x-3), (3x-2), and (x+7), we will start by removing their brackets and equaling them to Zero (0)

x = 0,

x - 3 = 0

3x - 2 = 0

x + 7 = 0

We can now solve for the variable x

x = 0,

x - 3 = 0 => x = 3,

3x - 2 = 0 => x = 2/3,

x + 7 = 0 => x = -7.

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