Find the perimeter of the triangle whose vertices are (2,−2)
, (−2,0)
, and (−1,−7)
. Write the exact answer. Do not round.

Answer:

Step-by-step explanation:

Let's start by figuring out how many deposits Jennie will make over the 6 month period. Since she receives two deposits per month, she will receive a total of 2 x 6 = 12 deposits.

Next, let's calculate how much money she will receive from these deposits. Each deposit is for $500, so over 12 deposits she will receive a total of 12 x $500 = $6000.

Now we need to figure out how much money Jennie will spend on living expenses over the 6 month period. She spends $450 every month, so over 6 months she will spend 6 x $450 = $2700.

To find the balance of Jennie's bank account after 6 months, we can use the following equation:

Balance after 6 months = starting balance + total deposits - total living expenses

Plugging in the values we calculated earlier, we get:

Balance after 6 months = $110 + $6000 - $2700

Balance after 6 months = $4400

Therefore, Jennie will have a balance of $4400 in her bank account after 6 months.

Answer:

a. The fare for a 9-mile journey =  £ 10.6

Step-by-step explanation:

Fare = £2.50 + £0.90 x miles

Fare(9) = £2.50 + £0.90 x ( 9 miles) = £2.50 +  £ 8.1 =  £ 10.6

a. The fare for a 9-mile journey =  £ 10.6

The loan that will have a lower balance is;

Option B: The PLUS Loan will have a lower balance by $70.47 at the time of repayment.

To determine which loan will have a lower balance at the time of repayment, we need to calculate the total amount of interest that will be accrued on each loan.

1) For the unsubsidized Stafford loan:

The loan amount is $3,725.

The annual interest rate is 4.65%, compounded monthly. This means the monthly interest rate is 4.65%/12 = 0.3875%.

The loan will be repaid in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 x (1 + 0.003875)^6

balance = $3,901.95

So the balance of the unsubsidized Stafford loan at the time of repayment will be $3,901.95.

2) For the PLUS loan:

The loan amount is $3,725.

The annual interest rate is 5.65%, compounded monthly. This means the monthly interest rate is 5.65%/12 = 0.4708%.

The loan will be deferred until graduation, which is in 6 months, so there will be 6 monthly compounding periods.

Using the formula for compound interest, the balance of the loan at the time of repayment will be:

balance = principal x (1 + monthly interest rate)^number of compounding periods

balance = $3,725 * (1 + 0.004708)^6

balance = $3831.47

So the balance of the PLUS loan at the time of repayment will be $3831.47

Difference in balance = $3,901.95 - $3831.47

= $70.47

Therefore, the PLUS loan will have a lower balance at the time of repayment, by an amount of $70.47

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Hence, the graph of g is upward than the graph of f.

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

The functions are

f(x) = 2^x

g(x) = f(x) + 6

so, g(x) = 2^x + 6

Draw the graphs of both the equation

The graph of the g is differ from f because in the graph of g it is upward than the graph of f .

Hence, the graph of g is upward than the graph of .

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The dependent clause in the sentence is: "when I no longer have to turn on the furnace every day."

The sentence has two parts: the first part is an independent clause, which can stand alone as a complete sentence:

"I will put away my winter clothes and store the blankets in the upstairs closet."

The second part is a dependent clause, which cannot stand alone as a complete sentence, and it starts with the subordinating conjunction "when."

The dependent clause provides additional information on when the action of putting away winter clothes and storing blankets will happen, and it depends on the independent clause to make sense.

Hence, "when I no longer have to turn on the furnace every day" is the dependent clause.

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The table that is used to graph g(x) is given by table 3 and 4.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation.

Given that, the function is:

f(x) = 1/3(6x) = 2x

f(x) = 2x

g(x) is the reflection of f(x) across the x-axis.

According to the rule of reflection, the reflection on x-axis is given as:

(x, y) → (x, -y)

Here, the y coordinated of the graph of g(x) has the same value but the opposite sign.

This is satisfied by the table 3 and 4.

Hence, the table that is used to graph g(x) is given by table 3 and 4.

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Answer: When y=1, x=[tex]\frac{1}{2}[/tex]

It will be a point with the coordinates ([tex]\frac{1}{2}[/tex], 1)

Step-by-step explanation:

- Start plotting points from the y-intercept, in this case, -1.

- Since the function is written in the form y=mx+b, where the slope is b which is in this case 4. Meaning to say that from the y-intercept -1 you have to go 4 units up and 1 unit right.

- Continue plotting 2 or 3 points, then connect them with a straight line.

- For the value of x when y=1, we can substitute y with 1 and solve the equation for x.

1=4x-1  (Add 1 to both sides)

2=4x  (Divide by 4)

[tex]\frac{1}{2}[/tex]=x Write the solution.

Answer:

Step-by-step explanation:

3f(x) stretches the graph of the function by a factor of 3 since it is being multiplied to f(x) and 3 is greater than one.

f(x+3) shifts the graph of the function 3 units to the left since 3 equals h in the equation: f(x-h), so you switch the sign and it becomes negative thus moving left.

f(3x) compresses the graph by a factor of 1/3 since it is inside the parenthesis.

f(x) + 3 shifts the graph of the function up by 3 units since it is being added to f(x).

Answer: 62,000

         2,000+4,000+8,000+16,000+32,000

Answer:

y = (-1/5)x + b

Step-by-step explanation:

The given line is y = 5x. To find a line perpendicular to it, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given line y = 5x is 5, so the slope of the line perpendicular to it is -1/5.

Let (x1, y1) be any point on the line L. Then the point-slope form of the equation of L is:

y - y1 = m(x - x1)

where m is the slope of the line, which in this case is -1/5.

So the equation of line L in point-slope form is:

y - y1 = (-1/5)(x - x1)

To find the equation of line L in slope-intercept form, we need to solve the point-slope equation for y. First, we can simplify the equation to:

y = (-1/5)x + (1/5)x1 + y1

This equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case:

m = -1/5

b = (1/5)x1 + y1

Therefore, the equation of line L in slope-intercept form is:

y = (-1/5)x + b, where b = (1/5)x1 + y1.

Answer:

Step-by-step explanation:

Sure, I can provide a step-by-step solution to find the probability of observing 10 tornadoes in Ohio in a given year using the Poisson distribution.

Given information:

Mean number of tornado events in Ohio = 19 per year.

Number of tornadoes follows a Poisson distribution.

To find:

Probability of observing 10 tornadoes in Ohio in a given year.

Solution:

We can use the Poisson probability formula, which is given as:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of tornadoes in a year, λ is the mean number of tornadoes in a year, k is the number of tornadoes we want to find the probability for, and k! is the factorial of k.

Substituting the given values, we get:

P(X = 10) = (e^(-19) * 19^10) / 10!

Now, we can simplify this expression by calculating the values of e^(-19) and 10!.

e^(-19) ≈ 0.0000000000000000008352702118 (using a calculator)

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800

Substituting these values, we get:

P(X = 10) = (0.0000000000000000008352702118 * 19^10) / 3,628,800

Now, we can simplify this expression by multiplying 0.0000000000000000008352702118 and 19^10 and then dividing by 3,628,800.

Multiplying 0.0000000000000000008352702118 and 19^10, we get:

0.0000000176218972

Dividing this by 3,628,800, we get:

P(X = 10) ≈ 0.009

Rounding this to 3 decimal places, we get:

P(X = 10) = 0.009

Therefore, the probability of observing 10 tornadoes in Ohio in a given year is approximately 0.009.

Answer:

Step-by-step explanation:

Let's start by finding the total number of women in the company. We know that 40% of the employees are women, so if we let x be the total number of employees, we can write:

Number of women = 40% of x = 0.4x

Let's then use the given ratio to determine the number of single women in the company. If the ratio of single women to married women is 2:5, we can write:

Number of single women = (2/7) * Number of women = (2/7) * 0.4x = 0.114x

We are also given that there are 30 married women. Since the total number of women is 0.4x, we can write:

Number of married women = 30

0.6x = 30

x = 50

Therefore, there are a total of 50 employees in this company.

Answer:

Step-by-step explanation:

D, 57,500

Answer:

[tex]\frac{26}{3}[/tex]

Step-by-step explanation:

Decimal form would be 8.6

Chelsea has $13,385 in her savings account after 7 years.

A savings account is an effective way to store your money in a secure location where it can earn interest.

After 5 years, the amount in Chelsea's savings account will be:

a = 1000(1.03)^5 = 1000(1.159274) = 1159.27

Let's say that Chelsea sells her car for x dollars. She adds that to her savings account, so the new amount in her account is:

1159.27 + x

After two more years (i.e., 7 years after initially starting the savings account), the amount in her savings account will be:

a = (1159.27 + x)(1.03)^2 = (1159.27 + x)(1.0609) = 1232.56 + 1.0609x

To find the value of x, we need to know the current value of the car. Once we have that, we can substitute it into the equation above to find the final amount in Chelsea's savings account.

For example, let's say that Chelsea sold her car for $5000. Then, the final amount in her savings account would be:

a = 1232.56 + 1.0609(5000) = 13384.91

Therefore, to the nearest dollar, Chelsea has $13,385 in her savings account after 7 years.

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Tippah Antiques uses the periodic inventory system to account for its inventory transactions. The net sales = $714740

Inventory that is updated on a regular basis is known as periodic inventory. Contrasted with perpetual inventory systems, which are updated as necessary, this system does not. While using a periodic inventory system, neither inventory nor cost of goods sold records are attempted to be kept up to date.

Businesses that only sell a few products during a given accounting period frequently employ the periodic inventory method. Due to its simplicity of use and low cost of ownership due to the lack of expensive software requirements, these businesses frequently find it advantageous to employ this system.

Given that,

TIPPAH ANTIQUES:

For the year ended December 31, Year 2: (Schedule of Cost of Goods sold)

Beginning balance of inventory:                         $24500

Add: Purchases:                                                   $306,400

Less: Purchase returns allowances:                $12,600

Add: Freight in:                                                      $1,810

Cost of goods available for sale:

(24500+306400-12600+1810)                          $320,110

Less: Ending inventory on hand:                          $24,400

Cost of goods sold:

(320110 - 24400)                                                  $295,710

Next,

For the year ended December 31, Year 2: (Income statement)

Net sales                                                            $714,740

Less: Cost of goods sold                                    $295,710

Gross Profit:

(714740 - 295710)                                                     $419,030

Operating expenses:                                             $51,100

Income from Operations:

(419030 - 51100)                                                     $367,930

Thus,

Computation of Net sales

Sales                                                                         $721000

Less: Sales returns and allowances:                          $6260

Net Sales (721000 - 6260):                                        $714740

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Let's call the smaller number "x". Since the larger number exceeds the smaller number by 1, we can call the larger number "x + 1".

The problem tells us that the sum of the numbers is 25, so we can set up an equation:

x + (x + 1) = 25

Simplifying and solving for x:

2x + 1 = 25

2x = 24

x = 12

So the smaller number is 12. To find the larger number, we can use x + 1:

x + 1 = 12 + 1 = 13

So the larger number is 13.

Therefore, the two numbers are 12 and 13.

The requried volume of the pedestal is 135 cubic inches.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of a triangular prism is given by the formula V =base x h, where the base is the area of the base and h is the height of the prism.

In this case, the area of the base is given as 9 in², and the height of the prism is given as 15 inches.

Therefore, the volume of the pedestal is:

V = base x h

V = 9 in² x 15 inches

V = 135 cubic inches

So the volume of the pedestal is 135 cubic inches.

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The inverse demand function of the given demand function is p = 50 - q/2.

A graph that depicts the relationship between a product's price and demand is called a demand curve. On a demand graph, the horizontal axis represents the amount desired, while the vertical axis represents the product's price.

The price is a function of the quantity required when there is an inverse demand curve. The inverse of a demand curve indicates that variations in the amount required cause changes in price levels. The formula for calculating the demand curve for a product yields the graph of an inverse demand curve.

Given demand function: q = 100 - 2p.

To find the inverse demand function, we find the inverse of the equation, by isolating p, to get:

q = 100 - 2p,

or, 2p = 100 - q,

or, p = 100/2 - q/2,

or, p = 50 - q/2.

Thus, the inverse demand function of the given demand function is p = 50 - q/2.

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The value of the expression P-q will be 16. The correct option is C.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To find the value of p - q, we need to eliminate r from the two equations given to us.

We can do this by solving for r in one of the equations and then substituting that expression into the other equation.

Let's solve for r in the equation p - r = 11:

r = p - 11

Now we can substitute this expression for r into the equation q - r = -5:

q - (p - 11) = -5

Simplifying this equation by distributing the negative sign, we get:

q - p + 11 = -5

Subtracting 11 from both sides, we get:

q - p = -16

Therefore, p - q = -(q - p) = -(-16) = 16.

So the answer is 16.

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The value of x is 11. 18

The value of y is 8. 67

Using the Pythagorean theorem, we have that;

x² = y² + z²

Substitute the values, we get;

x² = 10² + 5²

find the squares

x² = 100 + 125

Add the values

x² = 125

Find the square root

x = 11. 18

Using the Pythagorean theorem, we have;

y² = 9² - (√6)²

Find the squares

y² = 81 - 6

substract the values

y² = 75

Make 'y' the subject

y = 8. 67

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Therefore , the solution of the given problem of function comes out to be the number of tractors that  should be produced to incur minimum cost is 500.

The study of numbers and their variables, as well as our surrounds, structures, and both real and imagined locations, are all included in the mathematics curriculum. A function is a visual representation of the relationship between the quantities of inputs and the corresponding outputs for each. Simply described, a function is a collection of inputs that, when integrated, produce unique outputs for each input. Each role is given a country, city, or scope (also known as a realm).

Here,

The total cost function is:

C(x) = 23000 - 20x + 0.02x²

To find the minimum cost, we need to find the value of x that minimizes the total cost.

One way to do this is to find the vertex of the parabola that represents the total cost function.

The vertex of the parabola y = ax² + bx + c has an x-coordinate of -b/2a and a y-coordinate of c - b²/4a.

In this case, a = 0.02, b = -20, and c = 23000.

So, the x-coordinate of the vertex is:

x = -b/2a = -(-20)/(2 × 0.02) = 500

The minimum cost occurs at this x-value, so the number of tractors that should be produced to incur minimum cost is 500.

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The percentage of the normal oxygen level after 4 weeks is 52.2%

At week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

The percentage of the normal oxygen level after 5 weeks is 41.9%

At week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 60% per week.

What is the increasing rate of a function?

The increasing rate of a function is the rate at which the function is increasing at a specific point in its domain. It tells us how fast the function is increasing, or how quickly its output values are getting larger, at that particular point.

The increasing rate can be determined using the derivative of the function. Specifically, if the derivative of a function is positive at a certain point, then the function is increasing at that point, and the magnitude of the derivative gives us the rate of increase. If the derivative is negative at a point, then the function is decreasing at that point, and the magnitude of the derivative gives us the rate of decrease.

In general, the sign of the derivative indicates the direction of change of the function, while the magnitude of the derivative indicates the rate of change. So, when we take the derivative of a function, we can use it to analyse how the function is changing and how quickly it is changing at each point in its domain.

The given model is:

o(t) = [0.6t² - t + 2] / [t² + 2]

(a) To find the percentage of the normal oxygen level after 4 weeks, we need to evaluate o(4) and multiply it by 100:

o(4) = [0.6(4²) - 4 + 2] / [4² + 2] = 9.4 / 18 = 0.522

So the percentage of the normal oxygen level after 4 weeks is:

0.522 * 100% = 52.2%

(b) To find how quickly the percentage of the normal oxygen level is changing after 4 weeks, we need to find the derivative of o(t) with respect to t and evaluate it at t = 4:

o'(t) = [1.2t(t²+ 2) - (2t)(0.6t² - t + 2)] / (t² + 2)²

o'(4) = [1.2(4)(4² + 2) - (2)(4)(0.6(4²) - 4 + 2)] / (4² + 2)² = 0.96

So the rate of change of the percentage of the normal oxygen level after 4 weeks is:

0.96 * 100% per week = 96% per week

This means that at week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

(c) To find the percentage of the normal oxygen level after 5 weeks, we need to evaluate o(5) and multiply it by 100:

o(5) = [0.6(5²) - 5 + 2] / [5² + 2] = 11.3 / 27 = 0.419

So the percentage of the normal oxygen level after 5 weeks is:

0.419 * 100% = 41.9%

(d) To find o'(5), we can use the same formula for the derivative of o(t) that we found in part (b), but evaluate it at t = 5:

o'(5) = [1.2(5)(5² + 2) - (2)(5)(0.6(5²) - 5 + 2)] / (5² + 2)² = 0.60

So at week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 0.60 * 100% per week, which is approximately 60% per week.

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In the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.

Angles that add up to 180 degrees are referred to as supplementary angles.

For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°.

Two angles are complementary if their sum equals 90 degrees, and supplementary if their sum equals 180 degrees.

Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary.

We say two angles "Complement" one other when their sums equal 90 degrees.

So, we already are aware of that:

∠A and ∠C are supplementary

∠A is 74°

Then, ∠C would be:

∠A + ∠C = 180

74 + ∠C = 180

∠C = 180 - 74

∠C = 106

Therefore, in the given situation where ∠A and ∠C are supplementary, the angle ∠C is 106°.

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Correct question:

Angles A and C are supplementary. Find the measure of angle C.

(Refer to the image below)

The slope of the line tangent to the quadratic equation f(x) = x² + x + 8 is approximately equal to 27.996.

In this case we need to estimate the slope of a line tangent to a quadratic equation based on behavior exhibited by a set of secant lines. A secant line is a line that passes through only two points of the curve and a tangent line is a line that passes through only one point of the curve. The slope of the secant line can be determined by the following expression:

m = Δf(x) / Δx

Now we proceed to determine the slopes associated with each secant line:

x = 4

f(4) = 4² + 4 + 8

f(4) = 28

x = 4.1

f(4.1) = 4.1² + 4.1 + 8

f(4.1) = 28.91

x = 4.01

f(4.01) = 4.01² + 4.01 + 8

f(4.01) = 28.091

x = 3.9

f(3.9) = 3.9² + 3.9 + 8

f(3.9) = 27.110

x = 3.99

f(3.99) = 3.99² + 3.99 + 8

f(3.99) = 27.910

And the slope of the tangent line can be estimated by average:

m = 0.5 · [f(3.99) + f(4.01)]

m = 0.5 · (27.910 + 28.091)

m = 27.996

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Answer:

Δ JKE

Step-by-step explanation:

the figure is a triangle and is named using its vertices.

the vertices are J, K, E

to name the triangle start with any vertex , then in clockwise/ anticlockwise order the other 2 vertices. in this case starting with J , then clockwise for K and E.

in this case then the figure is Δ JKE

Answer:

Step-by-step explanation:

You want the values of g(1) and f(g(1)), given that f(x) = x² +x -6 and g(x) = 7x +3.

To find the value of a function for a particular argument (value of x), put that value where x is and do the arithmetic.

  g(1) = 7·1 +3 = 7 +3 . . . . . use 1 in place of x in 7x+3

  g(1) = 10

For f(g(1)), we first need to find g(1). We already did that, above.

  f(g(1)) = f(10) = 10² +10 -6 - 100 +10 -6 = 110 -6

  f(g(1)) = 104

Answer:

1,800 grams

Step-by-step explanation:

Answer:

180,000

Step-by-step explanation:

if you add 80+40+60=180kg

180kg is equal to 180,000g

sorry if it is wrong.

The cosine equation of the function is y = 5cos (x + π/4) + (4).

What is the cosine function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

y = A cos (Bx - C) + D

A (amplitude) = max - D

B = Period/2π  --->   Period is the distance from max to next max

C = B · Phase Shift  ---> Phase shift is the distance from the y-axis to the max

D (vertical shift) = (max + min)/2

Maximum = 9, minimum = -1

A = (maximum-minimum)/2 = (9 - -1)/2 = 10/2 = 5

Vertical shift = maximum - A = 9 - 5 = 4

The maximum occurs at x = -π/4, and

for the original function (without shift), the maximum occurs at x = 0

So, the horizontal shift = 0 - (-π/4) = π/4

Hence, the cosine equation of the function is y = 5cos (x + π/4) + (4).

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Answer:

Step-by-step explanation:

2517.02