help.
The points A’ (2, -2), B’(5, -5) and C’(-1, -5) are vertices on a coordinate plane. This triangle can be obtained by applying a translation to a reference triangle with the
vertices points A (0, 1), B(3, 4) and C(-3, 4). Determine the general translation pattern that took place and explain the effect it had on the y-coordinates. You may use the graph provided to assist you.

Answer:

Perpendicular = Y = 34.64 ft (Approx)

Base = X = 20 ft

Step-by-step explanation:

Given:

θ = 60°

Hypotenuse = 40 ft

Perpendicular = Y

Base = X

Find:

X and Y

Computation:

Sinθ = Perpendicular / Hypotenuse

Sin 60 = Y / 40

Perpendicular = Y = 34.64 ft (Approx)

Cosθ = base / Hypotenuse

cos 60 = X / 40

Base = X = 20 ft

Answer:

6666

Step-by-step explanation:

the sales of portable MP3 players in 2008 will be approximately $3.50 billion. To predict the sales of MP3 players in 2008, we need to first understand the exponential growth pattern of sales from 2001 to 2005.

We are given that sales grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. This means that the sales data can be modeled by an exponential function of the form:

\(S(t) = a * b^t\)

where S(t) is the sales at year t, a is the initial sales value (in 2001), and b is the growth factor per year. We can find the values of a and b by using the given sales data.

When t = 0 (in 2001), S(t) = $0.07 billion. So, we have:

\(0.07 = a * b^0\\a = 0.07\)

When t = 4 (in 2005), S(t) = $0.91 billion. So, we have:

\(0.91 = 0.07 * b^4b = (0.91/0.07)^(1/4) = 1.770\)

Therefore, the exponential function that models the sales data is:

\(S(t) = 0.07 * (1.770)^t\)

To predict the sales of MP3 players in 2008, we need to find the value of S(7) (since 2008 is 7 years after 2001). We have:

\(S(7) = 0.07 * (1.770)^7= $3.50 billion\)

Therefore, we can predict that the sales of portable MP3 players in 2008 will be approximately $3.50 billion.

It is important to note that this is a prediction based on the data we have and the model we have used. The actual sales value in 2008 could be different due to various factors such as market changes, competition, and technological advancements.

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Step-by-step explanation:

f(x)=4x-2

g(x)=-2x+1

f(-3)/g(-5)={4×(-3)-2}/{(-2)×(-5)+1}

=-14/-9

=14/9

Answer:

2w-12

Step-by-step explanation:

Jose = 2x(Maria's weight) -12

j = 2w -12

Answer:

21.3:1

Step-by-step explanation:

So we have to find the unit rate, and we do that by getting that 6 down to a 1, and we do that by dividing 6 by 6 and then we gotta do that on the other side too:

6 ÷ 6 = 1

128 ÷ 6 = 21.3 (simplified)

So 128 to 6 days in simplest terms is 21.3 hours to 1 day

hope this helps:)

Answer:

T=35X6.50

Step-by-step explanation:

The slope of the parallel lines AD and BC is 3.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tan.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).

Slope of line AD = y2 - y1 / x2 - x1

points of line AD are -

(1,0) and (2,3)

so the slope of AD becomes = 3 - 0 / 2 - 1

slope = 3

Slope of BC equals y2 - y1 / x2 - x1

points of line BC are -

(9,1) and (10,4)

so the slope of BC becomes = 4 - 1 / 10 - 9

slope = 3

As AD and BC are parallel lines, so their slopes are same.

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The amount in year 6 is $1282.5.

What is simple interest?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Given,

rate of interest = 7%

time = 1 year

Amount on first year = $950

First we will calculate simple interest for 5 years, because amount is available for 1 year.

SI =PRT

SI = 950(7/100)1

SI = $332.5

Therefore, the amount after 6 years = 950+332.5

=$1282.5

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Answer:

\(x=\frac{23}{6}\) or \(4.6\)

Step-by-step explanation:

\(3x + 2x + 7 = 10x - 16\)

\(5x+7=10x-16\)

Subtract 7 from both sides:

\(5x+7-7=10x-16-7\\5x=10x-23\)

Subtract 10x from both sides:

\(5x-10x=10x-23-10x\\-5x=-23\)

Divide both sides by -5:

\(\frac{-5x}{-5}=\frac{-23}{-5}\\x=\frac{23}{5}\) or \(4.6\)

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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p = 18.5

Step-by-step explanation:

a. to find perimeter you have to add all the sides together

So if one side is p, and the other side is 3p+2, just add them together like this

p + 3p + 2, then combine the ps so the expression is

4p + 2

b. now you find out the perimeter is 76

So put the original expression of your perimeter and 76 together like this

4p + 2 = 76

c. So now solve the equation

4p + 2 = 76

subtract 2 from both sides to get the ps alone

4p = 74

now divide by 4 to get the p by itself

74 ÷ 4 is 18.5, or 18 1/2

So p = 18.5 or 18 1/2

Answer:

120⁰

Step-by-step explanation:

the top number shows the degrees

Answer:120 degrees (that's the answer

Step-by-step explanation:

Answer:

A) - Quartic polynomial

- has four roots

- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) - Cubic polynomial

- has 3 roots

- roots are; f(x) = (x - 5)²(x + 5)

Step-by-step explanation:

A) f(x) = x⁴ + 21x² − 100

The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.

Factorizing this polynomial gives;

f(x) = (x² + 25)(x² - 4)

Equating to zero, we can find the roots. Thus, the roots are;

x = 5i

x = -5i

x = 2

x = -2

Thus, the completely factorized polynomial is;

f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)

B) f(x) = x³ − 5x² − 25x + 125

The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.

Factorizing this polynomial gives;

f(x) = (x² - 25)(x - 5)

Equating to zero and Factorizing gives;

x = 5

x = -5

x = 5

Thus, completely factorized with the roots is;

f(x) = (x - 5)²(x + 5)

Answer:

140

Step-by-step explanation:

So all you have to do is multiply 5 * 4 * 7 to find out how many outfits you can make.

140

Answer:

12 x 22 = 264 so that would be 264 - 246 = 18

The answer is 18 square feet.

Step-by-step explanation:

You'll need to simplify 18/264, then divide that number into 18/264 such as 18/264 divided by 2/2 or 3/3.

I hope I helped! ^-^

The value of b is 11.

From the question, we have

ax² + bx + c

using (0, 9)

substituting the value  we get

9 = a(0)² + b(0) + c

c = 9

Therefore,

-1 = a(-1)² + b(-1) + c

-1  = a - b + 9

-1 - 9 = a - b

a - b = - 10

using (-2, -9)

-9 = a(-2)² + b(-2) + 9

-9 - 9 = 4a - 2b

-18 = 4a - 2b

2a - b = -9

combine the equation

a - b = - 10

2a - b = -9

solving the equations we get

a = 1

Then,

1 - b = -10

b = 1 + 10

b = 11

Hence, the value of b is 11.

Subtraction:

The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.

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Answer:

42 ounces

Step-by-step explanation:

5 pounds is equal to 80 ounces

2 pounds is equal to 32 ounces

32+6=38 ounces gone

80-38=42

42 ounces is the total amount of candy left

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The discriminant is:

\(D=4^2-4(1)(2)=8\)

So \(D>0\) which means there are two distinct real solutions.

Hope this helps.

Answer:

2 real solutions

Step-by-step explanation:

x^2 +4x+2 =0

This is in the form ax^2 + bx +c

The discriminant is

b^2 -4ac

4^2 - 4*1*2

16 - 8

8

Since this is greater than 0, we have 2 real solutions

Answer:

Y(0,13)

X(13,0)

Answer:

A. y- 3 = -12(x - 5)

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Subtract 492 from 1500 to get how many toys he needs, you get 1008.  Now divide it by 18, you get 56.  

Answer:

56 days

Step-by-step explanation:

Total cars Johnson wants to make = 1500

Cars he has already made = 492

Cars left to make = 1500 - 492 = 1008

Give he can make 18 cars per day,

number of days = cars left to make ÷ 18 = 1008 ÷ 18 = 56

So it will take him 56 days to get to 1500 cars

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

Answer: 108 pancakes

Step-by-step explanation:

if you make 20 pancakes with  1 and 2/3 of flour,

with 9 cups you will make

(20*9)/ 1 &2/3

1  2/3= 5/3 we enter the whole in the fraction

(180)/(5/3)= 180*3/5=108 pancakes

Answer:

I think you put that } by accident so if its 4+2y=6

your answer is y=1

[] The equation on the left, 292 \(\frac{1}{2}\)  = 18 * 6 \(\frac{1}{2}\)  * h

-> Volume is length times width times height. When we plug in all the values we have to solve for h (height) we get this equation.

[] The height is 2.5 inches

-> We will solve the equation above.

-> Multiply 18 by 6 and a half = 117

-> Divide 292 and a half by 117 = 2.5

-> The height is 2.5 inches or 2 \(\frac{1}{2}\)inches

292 \(\frac{1}{2}\) = 18 * 6 \(\frac{1}{2}\)  * h

292 \(\frac{1}{2}\) = 117h

\(\frac{292 \frac{1}{2} }{117}\)= \(\frac{117h}{117}\)

2.5 = 1h

h = 2.5 inches

Based on the total earnings using the salary bases, Sidumo will earn the most income from Company B.

The total earnings from each company is computed using the following mathematical expressions.

Total sales for the month = R75,000.00

                                Company A           Company B

Sales commission    R3,750                 R7,500

Fixed salary              R3,000                      R0

Total earnings          R6,750                R7,500

Let the total sales in Company A = x

Let the total sales in Company B = x

Total earnings from Company A: 3,000 + 0.05x

Total earnings from Company B: 0.1x

However,, for the earnings from the two companies to be the same, the sales must be equal as follows:

3,000 + 0.05x = 0.1x

3,000 = 0.05x

x = R60,000

Thus, we can conclude that his most income will come from Company B.

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Sidumo's income from the two companies are as follows:

                                Company A           Company B

Sales commission    5% on all sales        10% on all sales

Fixed salary              R3,000                      R0