Find a formula for the quadratic
function whose graph has its vertex
at (−1, 2) and its y-intercept at
y = 3.

Answer:

leg lengths are 5 units and 3 units.

Step-by-step explanation:

ヾ(•ω•`)o

For given transformation of ΔABC to ΔA'B'C' the line of reflection is x = y

Triangle A'B'C' is the image of ΔABC under a reflection.

Given A(-2, 5), B(0, 9), C(3, 7),

A'(5,-2), B'(9, 0), and C'(7,3)

We need to find the line of reflection.

We can observe that the coordinates (x, y) of preimage are transformed to (y, x) in image.

This means, the line of reflection is x = y

Therefore, for given transformation of  ΔABC to ΔA'B'C' the line of reflection is x = y

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Assume that Chris is not a housekeeper for anyone else. Assume that Angel paid $2,250 in wages for the fourth quarter of 2021. The social security tax is $1,116, Medicare tax is $261 and FUTA tax is $42.

Social security  =12.4%

Medicare = 2.9%

FUTA = 0.6%

a. Social security tax

Yearly salary = $750 × 12 months

Yearly salary  = $9,000

Social security tax  = $9,000 ×12.4%

Social security tax = $1,116

b.  Medicare tax

Yearly salary =$750 × 12 months

Yearly salary = $9,000.00

Medicare tax = $9,000×2.9%

Medicare tax = $261

c. FUTA tax

Yearly salary = $750 × 12 months

Yearly salary = $9,000

The first $7,000 will be  subject to FUTA tax.

FUTA tax = $7,000 ×0.6%

FUTA tax = $42

Therefore the social security tax is $1,116.

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The graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

In this question, we have been given  Holly is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly

needs to bring at most 10 drinks but doesn't want to spend more than $50.

Let x be the number of soda cans and y be the number of soda cans(or bottles)

Holly needs to bring at most 10 drinks

So, we get an inequality,

x + y ≤ 10

She doesn't want to spend more than $50.

So, we get an inequality,

2x + 5y ≤ 50

In following graph, an inequality x + y ≤ 10 is represented by blue shaded region and the inequality 2x + 5y ≤ 50 is represented by red shaded region.

The solution set for the given inequalities is represented by a purple region (common region for both the inequalities)

Therefore, the graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

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The domain of the given graph is x≤ 2, option A is correct.

A relation is a function if it has only One y-value for each x-value.

We have to find the domain of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

As we observe the graph the value of x are less than 2

Hence, the domain of the given graph is x≤ 2

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a) The break-even quantity (in units) is 59 units.

b) If the company is selling no more than 34 units, A. The product should not be produced because it will lead to a loss of $625.

The break-even point is the production and sales point at which the total costs equal the total revenue.

At the break-even point, there is no profit or loss.

Total units produced = x

Let the cost of production = C

Let the revenue = R

C = 84x+1,475

R = 109x

At the break-even point, 109x = 84x + 1,475

109x - 84x = 1,475

25x = 1,475

x = 59 units

If x = 34 units:

Total cost = 84x+1,475

= 84(34) + 1,475

= 2,856 + 1,475

= $4,331

Total revenue = 109x

= 109(34)

= $3,706

Loss = $625 ($3,706 - $4,331)

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(a) Find the break-even quantity units (Simplify your answer.)

(b) Decide whether the product should be produced on the basis of whether it will earn a profit. (Profit = Revenue - Cost.)

Choose the correct answer below and, if necessary, in the answer box to complete your choice.

A. The product should not be produced because it will lead to a loss of  B. The product should be produced because it will lead to a profit of

The base of a cylinder is circular and it's area is given as B= πr^2

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

The base of a cylinder is circular . If the base area is B, then the area of the base is πr^2.

where r is the radius of the circle and π is 22/7

The volume of a cylinder is V = B × h

where B is the base area and h is the height or length of the cylinder.

Therefore the volume of a cylinder is V= πr^2h

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The unit rate of discovery of the new species of marine animals are; 2000 per year.

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

We have been given about 4000 new species of marine animals were discovered in the last 2 years.

We need to find the unit rate of discovery.

Total = 4000 new species

Time = 2 year.

Unit rate = new species of marine animals/ time period

Unit rate = 4000/ 2

Unit rate = 2000/1

Therefore, the unit rate of discovery of the new species of marine animals are; 2000 per year.

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The depth of the bottom of the hole after the second day is 425 feet using addition operation.

What is addition?

In math, addition is the process of adding two or more integers together. The terms addends and sum describe the input and output of the addition operation, respectively.

Given the depth on the first day is 232 feet.

Depth on the second day = 193 feet more than on the first day i.e. 193 feet + depth on the first day

This implies, depth on the second day = 193+232

=  425 feet

The hole's bottom will therefore be 425 feet deep after the second day.

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The volume of the cube with the given side length is 1/125b⁹

From the question, we are to determine the volume of the given cube.

The volume of a cube is given by

V = s³

Where V is the volume of the cube

and s is the side length of a side of the cube

From the given information,

s = 1/5b³

Thus,

The volume of the cube will be

V = 1/5b³ × 1/5b³ × 1/5b³

V = 1/5 × 1/5 × 1/5 × b³ × b³ × b³

V = 1/125 × b⁹

V = 1/125b⁹

Hence,

The volume is 1/125b⁹

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Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

Answer: 493/16

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 493 and 16 is 1

Divide both the numerator and denominator by the GCD

493 ÷ 1

16 ÷ 1

Reduced fraction:

493

16

Therefore, 493/16 simplified to lowest terms is 493/16. or 30.8125

The values of a = 6.3 and b = -5

Presenting extremely big or extremely small numbers in a simpler format is done through the use of scientific notation. The full numbers can, as we all know, go on forever, but we are unable to write such enormous quantities on paper. In addition, there was a need for a simpler way to express numbers that appear in the million's place.    

Here we have

(a × 10ᵇ) x (3.1 × 10⁹) = 1.953 x 10⁵

=> [tex](a\times 10^{b} ) = \frac{1.953 \times10^{5} }{ (3.1\times 10^{9} )}[/tex]  

=> (a × 10ᵇ) = 0.63 × 10⁵ × 10⁻⁹  

=> (a × 10ᵇ) = 0.63 × 10⁻⁴      

=> 6.3 × 10⁻⁵    

Here 6.3 × 10⁻⁵  is in the form of a × 10ᵇ

=> a = 6.3 and b = -5

Therefore,

The values of a = 6.3 and b = -5  

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Answer:

option A - 2

Step-by-step explanation:

event A { 2 4 6 8 10 12 }

event B { 3 6 9 12 }

The set AnB means A intercept B, which simply means all the elements that are common in event A and event B

So we just have to look at all the elements in A and B, we can see that the common elements are 6 and 12 so therefore:

set AnB = { 6 12 }

and the number of elements in set AnB is 2

It is worthwhile to enter the race if it costs $1000.

Total cost is an economic measure that includes not only the initial cash outlay but also the opportunity cost of their choices when producing a product, purchasing an investment, or acquiring a piece of equipment. TVC + TFC = TC

The sum of fixed and variable costs is the total cost. For example, if a company has a fixed cost of $30 per unit and a variable cost of $5 per unit as output increases, the total cost is $35.

In this case, first place pays $4800 to the winner, second place $3300 and third place $1300. It is therefore worthwhile since the amounts are more than $1000.

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The value of the 10th term for the sequence 11,12,13,14 is 20.

It's important to note that this is an arithmetic sequence. The formula for an arithmetic sequence is:

= a + (n - 1)d

where a = first term = 11

d = common difference = 1

n = number of terms = 10

The 10th term will be:

= a + (n - 1)d

= 11 + (10 - 1)1

= 11 + (9 × 1)

= 11 + 9

= 20

The value is 20.

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Complete question

The first four terms of an arithmetic sequence are 11,12,13,14. Find the 10th term.

Answer: 46 ft

Step-by-step explanation:

You didn't specify what those numbers mean, so I'm going to assume they're the length of the sides of the shape.

The perimeter equals the sum of all sides' lengths of the shape.

So, it equals 8 + 8 + 15 + 15 = 46 ft

Answer:

[tex]5\frac{1}{3} or \frac{16}{3}[/tex]

Step-by-step explanation:

endless 3’s are always 1/3

So now we just add 5 in front of it

5 1/3

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[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

5.333333

= [tex]\frac{16}{3}[/tex]

We see that,

3 ) 16 ( 5.333333

    15

      10

       9

        10

         9

           1

and so on...

Thus,

[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

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Answer:

Step-by-step explanation:

We know that corresponding parts of congruent figures are congruent.

It means:

Answer:

The slope is -1.

Step-by-step explanation:

When given two points, the formula for slope is [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

4 - 7 / -2 - (-5) = -3 / 3

-3 / 3 = -1, so the slope is -1.

The first number is 8  and the second number is 20

let the first number =  X

the second number = 4 + 2X

sum = 28

X + (4 + 2X) = 28

3X + 4 = 28

3X = 24  

X = 8                                                                  

The first number is 8

and the second number is 4 + 2X = 4 + 2(8) = 20

Addition:

When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.

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The Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ

The derivative of a function is a function that indicates how quickly another function is changing. Differentiation is a term used to describe the process of finding a derivative. In an equation, it is shown as the dependent variable with respect to the independent variable. A value's derivative is a change in value relative to its input. The symbol for a derivative is f'(x).

Here we have

d²y/dx²-3(dy/dx) - 4y = 0

As we know (d/dx) = D

=> D²-3D - 4 = 0

=> D²- 4D + D - 4 = 0

=> D(D - 4) + (D - 4) = 0

=> (D - 4) (D + 1) = 0

=> (D - 4) = 0 and (D + 1) = 0  

=>  D = 4 and  D = -1  

Here, roots are real and distinct

Therefore,

Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ

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Answer:

10%

Step-by-step explanation:

3/30

1/10

10/100

10%

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|-2.65| can be found between numbers 2.6 and 2.7

Absolute value means to remove any negative sign in front of a number and to think of the number as positive.  This is what the vertical lines |  | surrounding -2.65 means.

Thus,   |-2.65| = 2.65

If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7

Therefore,  |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer

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According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given,

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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Area of rectangle is 86 square inches.

What is area of triangle?

What is area of rectangle ?

Area of triangle = 1/2 * b* h

43 = 1/2 *b * h

86 = b * h

Area of rectangle = Length * Breadth

We know that base of triangle = Breadth of the rectangle and

Height of triangle = length of triangle

So, Area of rectangle is 86 square inches.

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You can ask where you don't understand.

Liu will earn $472 on an investment of $1298.

Given, Liu earned $316 on an investment of $869.

We have to find how much he would earned if he invest $1298 in the same investment.

Now, $869 investment = $316 earned

$1 investment = 316/869 earned

$1298 investment = 316/869 × 1298 earned

$1298 investment = $472 earned

Hence, Liu will earn $472 on an investment of $1298.

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The formula that can be used to estimate the population of California in 2020 is P = Poe^rt.

Population growth has to do with how the number of people in a place is increasing in a given time. We know that the population growth is a positive exponential function.

Initial population (Po) = 37 million

Population growth rate (r) = 1.0%

Time interval (t) = 10 years

Now using the formula;

P = Poe^rt

P = 37 * 10^6 e^0.01 * 10

P = 41 million

There would be about 41 million people within the next ten years.

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