Find the distance between the two points
rounding to the nearest tenth (if
necessary).
(3,-4) and (9,-9)

Each of the quadratic function should be factorized as follows;

x² - 6x + 8 ⇒ (x - 4)(x - 2).

x² - 4x - 32 ⇒ (x - 8)(x + 4).

x² + x - 42 ⇒ (x - 6)(x + 7).

In Mathematics, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Next, we would solve each of the quadratic function by using the factorization method as follows;

x² - 6x + 8 = 0

x² - 4x - 2x + 8 = 0

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

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

x² - 4x - 32 = 0

x² - 8x + 4x - 32 = 0

x(x - 8) + 4(x - 8) = 0

(x - 8)(x + 4) = 0

x² + x - 42 = 0

x² - 6x + 7x - 42 = 0

x(x - 6) + 7(x - 6) = 0

(x - 6)(x + 7) = 0

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See below for the description of the enlarged shapes when dilated

From the question, we have the following parameters that can be used in our computation:

Scale factor = 4

This means that if Mai enlarges the triangular sign by a multiple of 4,

Then the corresponding side in the enlarged sign to side EG is 4 times the length of side EG.

i.e Corresponding side = 4 * Original side

If Mai wanted to turn the sign so that side JK was on the bottom,

Then the corresponding side of the original sign would be the side that was previously opposite to JK.

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The required, Rich's monthly mortgage payment will be $1,246.91.

A mortgage payment is the amount of money that a borrower pays to a lender in order to repay a home loan.

Here,
The amount that Rich is financing with the mortgage is the difference between the total cost of the home and the down payment:

Amount financed = $244,800 - 0.15($244,800) = $208,080

To calculate the monthly mortgage payment, we can use the formula for the present value of an annuity,
[tex]PMT = (PV * r) / (1 - (1 + r)^{-n}[/tex]

First, we need to calculate the monthly interest rate. Since the annual interest rate is 5.25%, the monthly interest rate is:

r = 0.0525 / 12 = 0.004375

Next, we need to calculate the total number of payments. Since Rich is taking out a 25-year loan, he will be making 25 x 12 = 300 monthly payments.

Now we can plug these values into the formula and solve for PMT:

PMT = ($208,080 × 0.004375) / (1 - (1 + 0.004375)^(-300))

= $1,246.91

Therefore, Rich's monthly mortgage payment will be $1,246.91.

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The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.

To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:

In this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

where X is the random variable representing the number of seeds that germinate.

Using the binomial distribution formula, we can calculate the probability of each outcome:

P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]

where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].

Plugging in the values, we get:

P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057

P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205

P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324

Therefore,

[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586

So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.

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Answer: The two lines never intersect

Step-by-step explanation:

An algebraic solution for a system of equations means that the graphs of the two equations intersect at some point. If no such point can be found, it means the graphs never intersect.

The monthly revenue of the business grows by 8%, monthly.

The definition of revenue?

The total income a firm receives from the sale of products or services that are connected to its core business operations is referred to as revenue.

                           Since it appears at the top of the income statement, revenue, also known as gross sales, is frequently referred to as the "top line." An organization's whole earnings or profit is known as income, or net income.

An exponential function is represented as

   y = abˣ

From the  table we have the following ordered pair

(x,y) = {(0,72000) (3,90000)}

So, we have

   90000 = 72000 * b³

     Divide both sides by 72000

      b³  = 1.25

Take the cube roots of both sides

   b = ∛1.25

    b = 1.08

Recall that

b = 1 +r

  1 + r = 1.08

  r = 0.08

  r = 8%

Hence, the monthly revenue of the business grows by 8%, monthly.

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If the area of  a rectangle 1/3 square mile and length of the field is 2/5 mile then the width of the field is

What is Area of a Rectangle?

The quantity of unit squares that can fit inside a rectangle called its area. In other terms, the area of a rectangle is the area that it occupys. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes.

Given in the question,

Area of rectangle [tex]= \frac{1}{3} square mile[/tex]

The length of the field [tex]= \frac{2}{5} mile[/tex]

Let breadth be x.

As we know that,

Area of rectangle = [tex]length * breadth[/tex]

Now,

[tex]\frac{1}{3} = \frac{2}{5} *x[/tex]

[tex]x=\frac{1}{3} * \frac{5}{2}[/tex]

[tex]x=\frac{5}{6}[/tex]

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Answer: x = 233

Step-by-step explanation:

get the hypotenuse and solve

Answer:

[tex]104 ft^2[/tex]

Step-by-step explanation:

The answer is [tex]104 ft^2[/tex].

Divide the shape into 3 different rectangles. Now we have 2 rectangles that are 5 by 4.

The last rectangle is 16 by 4. (8-4 =4)

This is because 6+5+5=16.

Then you add up the area to get the whole figure.

The two smaller rectangles are 20 each or 40 altogether and the larger rectangle is 64.

When you add it up you get an area of [tex]104 ft^2[/tex]

The value of 5% of 260 is 13 as it is 5 times of 1% of 260 and the value of 1% of 260 is 2.6.

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

so, according to the question

Let 1% of 2600 = X

1/100 * 260 = X

X = 2.6

5% is 5 times of 1% so we can just multiply the value we got after 1% of 260

i.e., 2.6

so 5% of 260 is 5 * 2.6

            = 13.0

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There are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers. Hence, the accurate answer is option (b) 28.

To determine the number of ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers, we will use the formula for combinations, which is given by -

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items to be selected, and ! denotes the factorial function (the product of all positive integers up to a given number).

Here, we are given n = 8 fish and k = 2 fish.

Thus, the number of ways to select and place 2 fish from 8 fish will be -

8C2 = 8! / (2!(8-2)!) = (8 x 7) / (2 x 1) = 28

Therefore, there are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers.

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The area occupied by the ship is 10 inches².

The area of a parallelogram is -

A{||gm} = base x height

Given is that Ships in a first generation video game were modeled like the one shown in the image.

We can write the area occupied by the ship as -

Area = A{||gm} + A{triangle}

Area = {b x h} + {L x B}

Area = [tex]$(3\frac{2}{5}\times 2)\;+\; (3\frac{2}{5}-1)\times1\frac{1}{3}[/tex]

Area = (17/5 x 2) + (17/5 - 1) x (4/3)

Area = 34/5 + 12/5 x 4/3

Area = 34/5 + 16/5

Area = 50/5

Area = 10 inches²

Therefore, the area occupied by the ship is 10 inches².

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10% of the next 10 people Liz sees would be expected to be wearing sandals.

Liz is recording what kinds of shoes people are wearing at the mall. sandals 2 sneakers 12 high heels 6 Considering this data.

We have to determine how many of the next 10 people Liz sees would you expect to be wearing sandals.

Since 12 out of the 20 people Liz has seen were wearing sneakers, and 6 were wearing high heels, then 2 must have been wearing sandals.

Then, Expect to be wearing sandals = Number of people wearing sandals/Total number of records

Expect to be wearing sandals = 2/20 × 100

Expect to be wearing sandals = 1/10 × 100

Expect to be wearing sandals = 10%,

So 10% of the next 10 people Liz sees would be expected to be wearing sandals.

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The equation of line shown on the coordinate plane is,

⇒ y = - 1/4x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (4, -1).

Now,

Since, The equation of line passes through the points (0, 0) and (4, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 0) / (4 - 0)

m = - 1 / 4

Thus, The equation of line with slope - 1/4 is,

⇒ y - 0 = - 1/4 (x - 0)

⇒ y = - 1/4x

Therefore, The equation of line passes through the points (0, 0) and

(4, -1) will be;

⇒ y = - 1/4x

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If the amount of medication in the body decrease by a factor of 1/3 each hour , then the exponential function is y = 1.8(2/3)ˣ .

Let M = the initial amount of medication administered = 1.8 milliliters , and

Let y = the amount of medication remaining in the patient's body after x hours.

We know that the medication amount will decrease by a factor of 1/3 each hour, which means that after 1 hour, only (1-1/3) = 2/3  of the medication will remain, after 2 hours, only (2/3)² will remain, and so on.

So we can write the equation in exponential form as :

⇒ y = M × (1-1/3)ˣ

⇒ y = M × (2/3)ˣ ;

substituting the initial value as 1.8  ,

we get ;

⇒ y = 1.8 × (2/3)ˣ ;

where x = number of hours that have passed since the medication was administered.

Therefore , the exponential function for the situation is y = 1.8 × (2/3)ˣ  .

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The given question is incomplete , the complete question is

Elizabeth is a nurse, and she just administered 1.8 milliliters of medication to one of her patients. Elizabeth knows that the amount of medication remaining in the patient's body will decrease by a factor of 1/3 each hour .

Write an exponential equation in the form y = a(b)ˣ that can model the amount of medication (y) , remaining in the patient's body after x hours .

The regression analysis provides important insights into the relationship between single-parent households and student math performance.

To begin our analysis, we will run a simple linear regression of math4 on pctsgle. This will help us understand the relationship between the percentage of single-parent households in a school's ZIP code and the math performance of the students in that school.

Mathematically, the simple linear regression model can be written as:

math4 = β₀ + β₁pctsgle + ε

where math4 represents the average math score for a given school, pctsgle represents the percentage of single-parent households in the school's ZIP code, β₀ and β₁ are the intercept and slope coefficients respectively, and ε represents the error term.

After running the regression, we will obtain the following results:

math4 = 63.91 - 0.52pctsgle

Interpreting the results, we can see that for every one percent increase in the percentage of single-parent households in a school's ZIP code, the average math score of the students in that school decreases by 0.52 points.

The effect of single parenthood may seem small based on the slope coefficient of -0.52. However, it is important to note that this is just one variable and there may be other factors that could be contributing to the decrease in math performance.

Therefore, further analysis may be needed to fully understand the impact of single-parent households on student math performance.

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Complete Question:

Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The socioeconomic variables are obtained at the ZIP code level (where ZIP code is assigned to schools based on their mailing addresses).

Run the simple regression of math4 on pctsgle and report the results in the usual format. Interpret the slope coefficient. Does the effect of single parenthood seem large or small?

The probability that they have dinner at the health food restaurant is 0.643.

To calculate the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere, we need to use conditional probability.

Let A be the event that the first one to arrive has dinner at the health-food restaurant, and let B be the event that the first one to arrive waits only 20 minutes before leaving to eat elsewhere.

We want to find P(A|B), the probability that A occurs given that B occurs.

We know that P(A) = 0.3, the probability that the first one to arrive has dinner at the health-food restaurant. We also know that P(B|A) = 0.6, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they have dinner at the health-food restaurant.

To calculate P(B), the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere, we need to use the law of total probability:

P(B) = P(B|A) x P(A) + P(B|A') x P(A')

where A' is the complement of A, i.e., the event that the first one to arrive does not have dinner at the health-food restaurant. We know that P(A') = 1 - P(A) = 1 - 0.3 = 0.7, and we are given that P(B|A') = 0.1, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they do not have dinner at the health-food restaurant.

Therefore, we can calculate P(B) as:

P(B) = P(B|A) x P(A) + P(B|A') x P(A')

= 0.6 x 0.3 + 0.1 x 0.7

= 0.21 + 0.07

= 0.28

Finally, we can calculate P(A|B) using Bayes' theorem:

P(A|B) = P(B|A) x P(A) / P(B)

= 0.6 x 0.3 / 0.28

= 0.643

Therefore, the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere is approximately 0.643 or 64.3%.

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The variables representing the total cost of the items bought are x and y.

Where X is the total cost of the items bought during the first trip and Y is the total cost of the items bought during the second trip.

Items bought on the first trip:

Boards = 15

Boxes of nails = 3

Total cost = x

Items bought on the second trip:

Boards = 9

Boxes of nails = 1

Total cost = y

Let a piece of board = b

Let a box of nails = n

Let the total cost for the first trip = x

Let the total cost for the second trip = y

x = 15b + 3n

y = 9b + n

Answer: 12

Step-by-step explanation:

we divide 156 by 13, however, we can stop as soon as we reach the tenths column as we only care about full glasses.

if done correctly, you get 13

We can describe the output of the graph for:

This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.

From the graph given, we can deduce that the variation at 0-1 curve is small while the variation at 3-4 curve is large which is therefore the reason why slow and rapid output were chosen respectiviely.

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The equation of the line are;

a. y = 5/2x + 2

b. y = -1/5x - 1

c. y = -5/2x - 3

d. y = -x - 7

a.

The line passes through point (-2, -3) and it is perpendicular to y = -2/5x

The equation of the line is y = 5/2x + 2

b.

The line passes through the point (5, -2) and it is perpendicular to y = 5x + 4

The equation of the line is y = -1/5x - 1

c.

The line passes through (-2, 2) and it is perpendicular to y = 2/5x - 4

Th equation of the line is y = -5/2x - 3

d.

The line passes through (-4, -3) and it is perpendicular to y = -x + 2

The equation of line is y = -x - 7

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Answer: X=3  Y=8/5 and Z= 24/5

Step-by-step explanation:

3.9979(depends on what place you need to round to

The equation is V=πr2h. First plug in what you know, 314=π5^2h. 5x5=25 and its multiplied with π. It would look like 314=25πh. Divide the 25π by both sides, leaving your h. Plug it into your calculator.

Check answer:

(I rounded the 4 to the nearest whole number) 4*25*π is approximately 314

Answer:

4 ft

---------------

Volume of cylinder formula:

Given:

Find h:

Answer:

[tex]-1[/tex]

Step-by-step explanation:

[tex](x+y)+(3x-y)=4 \implies 4x=10 \implies x=2.5 \\ \\ 2.5+y=6 \implies y=3.5 \\ \\ \therefore x-y=2.5-3.5=-1[/tex]

The length of AC is √(4x⁴+ 16x³ + 76x² - 16x + 64). In order to find the unit length of AC you have to get more measurement and solve for x in the equation.

We can use the fact that the diagonal of a rectangle is the square root of the sum of the squares of its sides. If the sides of the rectangle are "a" and "b", then the length of the diagonal is given by: √(a² + b²)

Let's call the length of AC "d". Then, from the information given, we have: d = √((2x² + 4x - 6)² + (x² - x + 8)²)

Expanding and simplifying the squares, we get:

d = √(4x⁴ + 16x³ + 12x² + 64x² - 16x + 64)

d = √(4x⁴+ 16x³ + 76x² - 16x + 64)

So, the length of AC is √(4x⁴ + 16x³ + 76x² - 16x + 64).

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Rate of change of Panting A over a year period

Rate of change of Panting B over a year period

Painting B increases more quickly

Rate of change of Panting A over a year period, using the function f(x)=30,000(1.068)^x

at x = 0, f(x) = 30,000

at x = 1, f(x) = 32,040

rate of change = (30 000 - 32 000) / (0 - 1) = -2000 / -1 = 2000

Rate of change of painting B over a year period

= (25 - 27.5) * 1000 / (0 - 1)

= -2.5 * 1000 / -1

= 2500

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Another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

If the relationship between the number of hours worked and total earnings for Reece at Fries n More is given by y = 8.25x, where y is total earnings and x is the number of hours worked, then Reece earns $8.25 per hour worked.

To compare Reece's earnings per hour to another person, we would need to know the hourly wage of the other person. For example, if another person named John earns $9.00 per hour, then John earns more per hour than Reece. Conversely, if another person named Sarah earns $7.50 per hour, then Reece earns more per hour than Sarah.

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