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Determine the solution to the system of equations below. Explain your reasoning.

Answer:

D) (x + 9)(x-9)

Step-by-step explanation:

[tex]x^2-81[/tex]

Let's Rewrite 81 as → 9^2

[tex]x^2-9^2[/tex]

Now, apply difference two squares formula

[tex]\left(x+9\right)\left(x-9\right)[/tex]

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Answer:

B  (x - 6)² + (y + 4)² = 16

Step-by-step explanation:

From inspection of the graph:

General equation of a circle:  (x - a)² + (y - b)² = r²

(where (a, b) is the center and r is the radius)

Therefore, substituting the given values into the equation:

equation of the circle:  (x - 6)² + (y + 4)² = 16

Answer:

Answer B

Step-by-step explanation:

Centre of Circle (6,-4)

Radius = 4

Substitute in the Equation attached

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

[tex](x-6)^{2} +(y-(-4))^{2} =4^{2}[/tex]

[tex](x-6)^{2} +(y+4)^{2} =16[/tex]

The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².

Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.

Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:

A = median length × height

Given the following:

Area of trapezium = 25 × 8 = 200 cm².

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Answer:

The reflection of a horizontal line has the same result as a rotation of 90 degrees clockwise.

Answer: Choice B

270 degree rotation clockwise

=======================================================

Explanation:

Notice that 270+90 = 360

Going 90 degrees in one direction is the same as going 270 degrees in the other direction because the two combine to a full 360 degree rotation.

Check out the image below for an example. In the example, the point P starts at (0,5). Doing either rotation mentioned will get us to (-5,0).

Answer:

5x-4y+5=0.

Step-by-step explanation:

1) if the point A(-5;-5) and B(3;5), the formula is:

[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A}[/tex]

2) according to the formula above:
[tex]\frac{x+5}{3+5} =\frac{y+5}{5+5}; \ = > \ \frac{x+5}{4}=\frac{y+5}{5};[/tex]

or 5x-4y+5=0.

Answer:

y+3=-(x+5)5

y+3=-5x-25

y+3+5x+25=0

y+5x+28=0

Answer:

238.76

Step-by-step explanation:

I believe

Answer:

C≈527.79in

Solution

C=2πr=2·π·84≈527.78757in
                                                                                                                                                                                                                               

Answer:

[tex]2 \times 3.14 \times 6 = 37.68[/tex]

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Answer:

y=−2/5x+2

Step-by-step explanation:

^

The number of batches she can make is = 5 batches

The amount of dough used to make each batch = 12oz

The total amount of dough she has= 60oz

Therefore, the number of batches she can make from the total dough available = b

Using the equation:

(dough for one batch) × (number of batches) = (total amount of dough)

which is = 12× b = 60

b= 60/12

b= 5 batches

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Answer:

3 weeks

Step-by-step explanation:

Set the equations. Let "amount of weeks" be signified by the variable, x.

First, note that Haley starts with $155, and saves $10 each week:

10x + 155

Next, note that her brother has $230 saved and spends $15 each week:

230 - 15x.

Set the two equations equal to each other:

10x + 155 = 230 - 15x

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

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First, subtract 155 and add 15x to both sides of the equation:

10x (+15x) + 155 (-155) = 230 (-155) - 15x (+15x)

10x + 15x = 230 - 155

25x = 75

Next, divide 25 from both sides of the equation:

(25x)/25 = (75)/25

x = 75/25 = 3

3 weeks is your answer.

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Answer: Evie will be 6 years old in one year.

2 years ago, Evie was 3 years old. Now, she is 5. 4 years after 5 would make her 9. 3*3=9

If  In four years time Evie will be three times older than she was two years ago, then in one year's time Evie will be 6

Two or more expressions with an Equal sign is called as Equation.

Given,

In four years time Evie will be three times older than she was two years ago,

Let the age of Evie be x in one year.

By the given information we formulate a equation.

In four years time means we have to add 4 to the present age, x+4.

three times older than she was two years ago can be written as 3(x-2)

Now,

In four years time Evie will be three times older than she was two years ago

x + 4 = 3(x − 2)

Apply distributive property on RHS side

x+4=3x-6

x-3x=-6-4

-2x=-10

x=5

Therefore in one year's time Evie will be x+1 =6, 6 years old.

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Answer:

18. The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. The statement is:  p------->q [If you ran 1 mile, then you ran 5280 feet]

Decide whether statement is true: So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

Step-by-step explanation:

18. The product of two negative even integers.

Let the integers be -2m and -2n, m and n are positive integers

Product in (-2m) × (-2n) = 4mn = 2(2mn)

= 2p, p = 2mn

The conjecture is: The product of two negative even integers is an even integer.

Testing: Let integers be -4 and -6. [Two negative even integers]

Then (-4) × (-6) = 24 [Even integer]

19. The sum of two negative odd integers.

Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers

Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1

= -2m - 2n - 2

= -2(+m + 2 + 1)

= -2p, p = m + n + 1

The conjecture is: Sum of two negative odd integers is a negative even integer.

Testing: Let the two negative odd integers be -3 and -7.

Then -3 + (-7) = -10 is a negative even integer

20. The sum of two even integers and two odd integers.

Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)

Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)

= 2r, r = m + n + p + q + 1

The conjecture is: Sum of two even integers and two odd integers is an even integer.

Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)

Then 4 + 12 + 13 + 17 = 46 (Even integer)

21. Let p: You ran 1 mile

Let q: You 5280 feet

The statement is:  p------->q [If you ran 1 mile, then you ran 5280 feet]

Since 1 mile = 5280 feet

So if p is True then q is also True.

Hence p------->q is True. So the given statement is True.

Answer: X=1 Y=-5

Step-by-step explanation:

−9x+2y+−2y=−19+−2y(Add -2y to both sides)

−9x=−2y−19 (Divide by 9 on both sides)

x= 2/9y+19/9 now Substitute 5(2/9y+19/9)+4y=-15=

46/9+95/9=-15 (simplify both sides)

46/9+95/9+-95/9=-15+-95/9 (Add (-95)/9 to both sides) =

46/9y=-230/9 (now divide both sides by 46/9) than equals

y=-5

for X we plug in -5 like this: X=2/9(-5)+19/9 now just evaluate than simplify both sides which equals: 1

The profit function of the business is the difference between the revenue and the cost functions

For the revenue function, we have the following points

(x,y) = (0,0) and (6,8.0)

Since the line passes through the origin, the equation of the line would be:

[tex]y = \frac{y_1}{x_1} * x[/tex]

So, we have:

[tex]y = \frac{8.0}{6} * x[/tex]

[tex]y = \frac 43x[/tex]  

For the cost function, we have the following points

(x,y) = (0,3.5) and (9,36) for x > 5

The equation of the line would be:

[tex]y = \frac{y_1-y_2}{x_1-x_2} * (x - x_1) + y_1[/tex]

So, we have:

[tex]y = \frac{6.5-3.5}{6-0} * (x - 0) + 3.5[/tex]

[tex]y = 0.5x + 3.5[/tex]

Hence, the equations of the cost and the revenue functions are: [tex]y = 0.5x + 3.5[/tex] and [tex]y = \frac 43x[/tex]

This is calculated as:

Profit = Revenue - Cost

So, we have:

[tex]y = \frac 43x - 0.5x - 3.5[/tex]

Evaluate the difference

[tex]y = \frac 56x - 3.5[/tex]

Substitute 10 for x in [tex]y = \frac 56x - 3.5[/tex]

[tex]y = \frac 56 * 10 - 3.5[/tex]

[tex]y = \frac {50}6 - 3.5[/tex]

Evaluate the difference

[tex]y = \frac {50-21}6[/tex]

[tex]y = \frac {29}6[/tex]

Hence, the profit after 10 months of operation is 29/6

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Answer:

40°

Step-by-step explanation:

As we have,

[tex]\rm\hookrightarrow[/tex]The Sum of all sides of a triangle is 180°

Now,

[tex]\rm\hookrightarrow 79+x+52+x+73=180\\\\\rm\hookrightarrow x=180-79-52-73\\\\\rm\hookrightarrow x=-12[/tex]

Again, finding the measure of ∡A by putting the value of x.

[tex]\rm\hookrightarrow x+52\\\\\rm\hookrightarrow -12+52\\\\\rm\hookrightarrow 40[/tex]

The sales growth of the business of owner of a bike shop is $25000 and this business is growing.

Sales growth is the amount of by which a business is growing. Sales growth is the difference of sales revenue of current year and the sales revenue of last year.

The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data:

Sales Revenue Last Year =$125,000

Sales Revenue Current Year = $150, 000

As, the sales growth is the difference of sales revenue of current year and the sales revenue of last year. Thus, the sales growth of the business is,

[tex]\rm SG=150000-125000\\SG=25000[/tex]

Hence, the sales growth of the business of owner of a bike shop is $25000 and this business is growing.

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Answer:

then the height would be 2 because 3*2=6

Step-by-step explanation:

Answer:

4 cm

Step-by-step explanation:

area of triangle is: area = (base*height)/2.

since the area is 6 m^2, and base is 3 cm,

6 m^2  = (3 m*height)/2

12m^2 = 3 m*height

height = 4 m

Answer:

C

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the 2 lines.

the lines here are parallel and never intersect. Thus there is no solution

Answer:

1525.6

Step-by-step explanation:

Answer:

zb = 46°

Step-by-step explanation:

za + zb = 90

44° + zb = 90°

90° - 44° = zb

zb = 46°

Step-by-step explanation:

DB/EC = AD/BE

5/EC = 4/12

5 = 4/12 EC

5×12/4 = EC

15 = EC

EC = 15

Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.

APR on a credit card is the way of saying that the interest you are charged over a year is equal to roughly of your balance.

Julius currently pays the minimum monthly payment of $34.15 on his credit card, which has a balance of $1,289.

His credit card has an APR of 20%.

If Julius wants to pay off the balance in 12 months, determine the monthly payments he needs to make.

Choose the following modification with the least cuts to his current expenses that will allow Julius to pay off his credit card balance in 12 months.

Income wages $2,456.00

Expenses rent $900.00

Utilities $186.35

Food/clothes $298.00

Entertainment $330.00

Car $385.00

Credit card $34.15

Cell phone $89.49

net income $233.01

The net amount will be over 12 months is 1432.92.

Monthly payback will be

[tex]\rm Monthly\ pay = \dfrac{1432.92}{12}\\\\Monthly\ pay = 119.41[/tex]

She was paying 105.68 dollars per month. Then the amount will be

Amount = 119.41 – 34.15 = 85.26

Julius can eliminate $31 from entertainment and $55 from food/clothes. Then the correct option is A.

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Answer:

a

Step-by-step explanation:

Steps provided below .

Answer:

Properties of a rectangle:

Given:

See attached for image if the rectangle

Answer:

based on the equation he would make $2.5 in the first month but realistically he would earn around $30 in the first month

Step-by-step explanation:

2000+2000(.015)(1/12)=2002.5

2002.5-2000=2.5

The account balance will take time for the account to grow to $5,000 in 2 years and 4 months.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Miguel deposits $2000 into a bank account that earns simple interest. He writes the equation A(t) = 2000(1.07)t to represent the value of the account after t years.

The account is to grow to $5,000. Then the time will be

5000 = 2000(1.07)t

On simplifying, we have

t = 2.33

It will take for the account to grow to $5,000 in 2 years and 4 months.

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Using proportions, it is found that the best estimate for the squirrel population is of 8000.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 43 squirrels out of 430 had tags. Considering that in the entire population, 800 are tagged, and we want to find the total population, the rule of three is given by:

43 tagged - 430 squirrels

800 tagged - x squirrels

Applying cross multiplication:

[tex]43x = 430 \times 800[/tex]

[tex]x = \frac{430 \times 800}{43}[/tex]

[tex]x = 8000[/tex]

The best estimate for the squirrel population is of 8000.

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Answer:

7

Step-by-step explanation:

4y²-106=90

4y²=90+106

4y²=196

4y²/4=196/4

y²=49

y=√49

y=7

Answer:

4x-3y=-6

Step-by-step explanation: