Find the perimeter of the triangle whose vertices are (−2,−2)
, (4,−2)
, and (4,6)
. Write the exact answer. Do not round.

Option D:

32 ÷ (–16) is equivalent to –18 ÷ (9).

Given expression:

–18 ÷ (9)

Let us first solve this expression.

                = -2  (negative by positive is negative)

To find which expression has the same value for the given expression:

Option A: –18 ÷ 2

            = –9 (negative by positive is negative)

This is not equivalent expression.

Option B: –12 ÷ (–3)

                = 4  (negative by negative is positive)

This is not equivalent expression.

Option C: –10 ÷ 5

            = –2 (negative by positive is negative)

This is not equivalent expression.

Option D: 32 ÷ (–16)

                = -2  (positive by negative is negative)

This is the equivalent expression to the given expression.

Hence ,32 ÷ (–16) is equivalent to –18 ÷ (9).

Option D is the correct answer.

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Loren could receive a monthly payout of approximately $4,646.81 from the annuity to last for 30 years at a 10% annual interest rate.

What is annuity?

A contract between you and an insurance company known as an annuity entails you making a lump sum payment or a series of payments in exchange for regular payments starting either right away or in the future.

To calculate the monthly payout that Loren can receive from an annuity for 30 years, use the formula for the present value of an annuity -

PV = PMT x [(1 - (1 + r)^(-n)) / r]

Where PV is the present value of the annuity (the amount of money Loren has at retirement), PMT is the monthly payout, r is the monthly interest rate (10%/12 = 0.00833), and n is the number of monthly payments (30 years x 12 months/year = 360 months).

Substituting the given values into the formula -

$500,000 = PMT x [(1 - (1 + 0.00833)^(-360)) / 0.00833]

Solving for PMT -

PMT = $500,000 / [(1 - (1 + 0.00833)^(-360)) / 0.00833]

PMT = $4,646.81

Therefore, The value is obtained as $4,646.81.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{100}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{100}-\stackrel{y1}{70}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 30 }{ 2 } \implies 15[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{ 15}(x-\stackrel{x_1}{2}) \\\\\\ y-70=15x-30\implies {\Large \begin{array}{llll} y=15x+40 \end{array}}[/tex]

Answer:

15.81 units

Step-by-step explanation:

Let the hypotenuse of the triangle be x.

Let us use the Pythagorean theorem to find x.

x² = 9² + 13²

x² = 81 + 169

x² = 250

x = √250

x = 15.81 units

Answer:

Step-by-step explanation:

Since the probability of rain on any given day is 0.5, and the weather on each day is independent of the others, we can calculate the probability of it raining all three days by multiplying the probabilities of rain on each individual day:

P(rain on day 1) x P(rain on day 2) x P(rain on day 3) = 0.5 x 0.5 x 0.5 = 0.125

Therefore, the probability of it raining all three days of your trip to Seattle in October is 0.125, or 12.5%.

The graph of the piecewise function is attached at the end.

A piecewise function is a function that is defined on a sequence of intervals. For example -

[tex]$|x| =\left \{ {{-x\;\;\;\;x < 0} \atop {x\;\;\;\;x > 0}} \right.[/tex]

Given is the piecewise function as -

[tex]$f(x) =\left \{ {{-x-1\;\;\;\;x < 3} \atop {-x+1\;\;\;\;x \geq 3}} \right.[/tex]

Refer to the graph of the piecewise function. The graph of the function is attached. The line one does not include the point {x = 3}. The second line includes the point {x = 3}

Therefore, the graph of the piecewise function is attached at the end.

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The pitch of the roof with one foot horizontal run and 4 inches elevation is 4 in per foot

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

The roof pitch (steepness) is given as a ratio of inch rise per horizontal foot, It is given by:

Pitch = rise / run

For every 1-foot horizontal run, the roof was elevated by 4 inches, hence:

Pitch = rise / run = 4 in / 1 ft = 4 in per foot

The pitch is 4 in per foot

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The solution of the system of equations is

A system of equations are a pair of equations.

Given the system of equations

4/x - 2/y = 12 (1) and

5/x + 1/y = 8 (2)

We proceed to solve as follows.

Since we have

4/x - 2/y = 12 (1) and

5/x + 1/y = 8 (2)

Multiplying equation (1) by 1 and equation (2) by 2, we have that

4/x - 2/y = 12 (1) × 1 and

5/x + 1/y = 8 (2) × 2

4/x - 2/y = 12 (4)  and

10/x + 2/y = 16 (5)

Now, adding equations (4) and (5), we have that

4/x - 2/y = 12 (4)  

+

10/x + 2/y = 16 (5)

14/x = 28

14 = 28x

x = 14/28

x = 1/2

Substituting x = 1/2 into equation (1), we have that

4/x - 2/y = 12 (1)

4/(1/2) - 2/y = 12 (1)

4 × 2 - 2y = 12

8 - 2y = 12

-2y = 12 - 8

-2y = 4

y = 4/-2

y = -2

So,

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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:

integers . whole number and nutural number

The number of hamburgers sold in the winter is 57 million.

What is percentage ?

Percentage is a way of expressing a fraction or ratio as a portion of 100. It is denoted by the symbol "%".

For example, if there are 10 green balls in a bag of 20 balls, we can say that the percentage of green balls is:

(10/20) x 100% = 50%

This means that 50% of the balls in the bag are green.

Percentages are often used to represent proportions or amounts in many contexts, such as finance, statistics, and everyday life. They can be used to express changes, comparisons, and relationships between different quantities.

In addition, percentages are commonly used in calculations involving tax, interest rates, discounts, and other types of financial transactions. It is important to have a good understanding of percentages in order to manage personal finances, make informed business decisions, and interpret data accurately.

Let's suppose that the total number of hamburgers sold by the fast food chain in a year is represented by the height of the bars in the bar graph. We know that 25% of the hamburgers are sold in the fall, which means that the bar representing the fall sales must be 25% of the total height of the bars.

Since there are four seasons in a year, each season must represent 25% / 4 = 6.25% of the total height of the bars. Therefore, the height of each bar is 6.25% of the total number of hamburgers sold.

Let's denote the number of hamburgers sold in the winter by x. Then, the height of the winter bar is also x/100 of the total height of the bars.

We know that the winter bar is covered by a smudge, but we can still use the information we have to set up an equation. Since the heights of the bars must add up to the total height, we can write:

25% + 6.25% + 6.25% + 6.25% + x/100 = 100%

Simplifying the left-hand side, we get:

43% + x/100 = 100%

Subtracting 43% from both sides, we get:

x/100 = 57%

Multiplying both sides by 100, we get:

x = 57 million hamburgers.

Therefore, the number of hamburgers sold in the winter is 57 million.

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Answer:

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

Step-by-step explanation:

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

 = 10 * 0.0676 * 0.4052

 = 0.211

The solution is, 0.211 is the probability assignments for the x distribution.

Here, we have,

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

now, we have,

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

= 10 * 0.0676 * 0.4052

= 0.211

So, 0.211 is the probability assignments for the x distribution.

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It can't because 15 + 8=23 and the sum of the first 2 sides have to be greater than the third side
So the answer is 18

Answer:

C

Step-by-step explanation:

x + y + 10 = 0 ( subtract x + 10 from both sides )

y = - x - 10 → (1)

x² + y - 2 = 0 → (2)

substitute y = - x - 10 into (2)

x² - x - 10 - 2 = 0

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 4 = 0 ⇒ x = 4

Answer:

while True:

   user_input = input("Please enter a sequence of comma-separated numbers: ")

   if user_input.replace(",", "").isdigit():

       break

   print("Invalid input! Please try again.")

num_list = user_input.split(",")

num_list = [int(num) for num in num_list]

total_sum = sum(num_list)

print("The sum of the numbers is:", total_sum)

Step-by-step explanation:

This program uses a while loop to repeatedly ask the user for input until they provide a valid sequence of comma-separated numbers (all-digit input). The .isdigit() function is used to check if the input is all-digit. If the input is valid, the program splits the input string at each ',' using the .split() function, converts each item in the resulting list into an integer using list comprehension, then adds all numbers together using the sum() function. Finally, the program outputs the total sum.

Answer:

x=5

Step-by-step explanation:

26=4x+6
20=4x

x=5

Answer:

x = 2

Step-by-step explanation:

1) Based on the given conditions, formulate: 4 × x = 8

2) Divide both sides of the equation by the coefficient of variable: x = 8 ÷ 4

3) Calculate the product or quotient: x = 2

4) You then get the result x = 2

The product of 4 and a number w is 8.

[tex]4\times w=8[/tex]

This can also be written as:

[tex]4w=8[/tex]

Divide both sides by 4:

[tex]\dfrac{4w}{4}=\dfrac{8}{4}[/tex]

[tex]\boxed{w=2}[/tex]

Answer:

To simplify the expression −8(1+x)+7x, we can use the distributive property of multiplication over addition, which states that a(b+c) = ab + ac. Applying this property, we get:

−8(1+x) + 7x = −81 − 8x + 7x (distributing the -8)

= -8x - 8 + 7x (simplifying the multiplication)

= -x - 8 (combining like terms)

Therefore, the simplified form of the expression −8(1+x)+7x is −x − 8.

The answer comes to $43,592.00. 28 can be wiped from the account after 20 years, leaving nothing behind.

Think about taking out a $1,000 loan with a seven-year, 10% interest rate. The first year's interest would cost you $100. You would pay $1,100 in interest the next year, which is the sum of the initial amount plus interest. Because of this, your salary for the upcoming year will be $110 (1,100 times 0.10).

Calculate the Yearly Amount (A) given the Prepaid Value (P), at interest rate I over n periods using the equation (A/P, I n).

The equation is:

[tex]A=P \frac{i(1+i)^n}{(1+i)^n-1}[/tex]

Where:

P is the Present value = $500,000

A is the monthly Amount

i is the interest rate = 0.06

20 years are the number of periods (n).

Substituting values:

[tex]A=\$ 500,000 \frac{0.06(1.06)^{20}}{(1.06)^{20}-1}=\$ 43,592.28[/tex]

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The tables that show a valid probability density function, are tables 1 to 3

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

Table of values

For a table to show a valid probability density function, the following must be true

Sum of P(X = x) = 1

Using the above as a guide, we have the following:

Table 1: Sum = 0.37  + 0.06 + 0.01 + 0.56 = 1

Table 2: Sum = 3/8 + 3/8 + 1/4 = 1

Table 3: Sum = 1/8 + 1/8 + 1/8 + 3/8 + 1/4 = 1

Table 4: Sum = 0.03 + 0.01 + 0.61 + 0.31 + 0.21 = 1.17

Table 5: Sum = 1/10 + 3/10 + 4/5 + 1/5 = 1.4

Hence, the tables are tables 1 to 3

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The evaluation of equations by resolving into quadratic equations and factoring are presented as follows;

A quadratic equation is an equation which can be expressed as; f(x) = a·x² + b·x + c, where a, b, and c are real numbers and a ≠ 0.

1. √(30 - x) = x

x = √(30 - x)

x² = 30 - x

x² + x - 30 = 0

Factoring the above quadratic equation, we get;

(x + 6)·(x - 5) = 0

2. x = √(42 - x)

x² = 42 - x

x² + x - 42 = 0

(x + 7)·(x - 6) = 0

3. √(12 - r) = r

Squaring both sides of the equation, we get;

(12 - r) = r²

r² = 12 - r

r² + r - 12 = 0

(r + 4)·(r - 3) = 0

4. m = √(56 - m)

m² = 56 - m

m² + m - 56 = 0

(m + 8)·(m - 7) = 0

5. r = √(-1 - 2·r)

r² = -1 - 2·r

r² + 2·r + 1 = 0

(r + 1)² = 0

6. √(4·n + 8) = n + 3

4·n + 8 = (n + 3)² = n² + 6·n + 9

4·n + 8 = n² + 6·n + 9

n² + 6·n + 9 - (4·n + 8) = 0

n² + 6·n + 9 - 4·n - 8 = 0

n² + 2·n + 1 = 0

(n + 1)² = 0

7. -n + √(6·n + 19) = 2

-n + √(6·n + 19) = 2

√(6·n + 19) = n + 2

(6·n + 19) = (n + 2)² = n² + 4·n + 4

6·n + 19 = n² + 4·n + 4

n² + 4·n + 4 = 6·n + 19

n² + 4·n + 4 - (6·n + 19) = 0

n² - 2·n - 15 = 0

(x - 5)·(x + 3) = 0

8. 4 + √(-3·m + 10) = m

√(-3·m + 10) = m - 4

-3·m + 10 = (m - 4)² = m² - 8·m + 16

-3·m + 10 = m² - 8·m + 16

m² - 8·m + 16 = -3·m + 10

m² - 8·m + 16 + 3·m - 10 = 0

m² - 5·m + 6 = 0

(m - 3)·(m - 2) = 0

9. x - 5 = √(x + 1)

Squaring both sides, we get;

(x - 5)² = (√(x + 1))²

(x - 5)² = x + 1

x² - 10·x + 25 = x + 1

x² - 10·x + 25 - (x + 1) = 0

x² - 10·x + 25 - x - 1 = 0

x² - 11·x + 24 = 0

(x - 8)·(x - 3) = 0

10. n - 7 = √(3·n - 21)

(n -7)² = (3·n - 21)

n² - 14·n + 49 = 3·n - 21

n² - 14·n + 49 - (3·n - 21) = 0

n² - 14·n + 49 - 3·n + 21 = 0

n² - 17·n + 70 = 0

(n - 10)·(n - 7) = 0

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The true statements about the populations of the town based on the linear equations in the table are;

A linear equation is an equation of the form; y = m·x + c, where the slope of the graph of the equation is m and the y-intercept of the graph is c.

The analysis of the equations in the table are as follows;

Equation for Pinehill is; P = 800 - 20t

The slope of the above equation is; -20 and the y-intercept is 800. The negative sign for the slope indicates that the population is decreasing;

Therefore, the initial population of 800 in Pinehill is decreasing at a rate of 20 per unit time, t

Population for Rye; P = 500 + 15t

The population of Rye is increasing at a rate of 15 per unit time

Population for Smithfield; P = 10t + 950

The population of Smithfield is increasing at a rate of 10 per unit time

Population for Troy; P = -50·t + 600

The -50 indicates that population is decreasing at a rate of 50 per unit time

The true statements are therefore;

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The answer is 4 times the cube of the first number minus the sum of the second number and two times the third number. That is the result of the calculation is -6.

To calculate this, first, we multiply the first number by itself twice to get the cube of the first number. Then, we subtract the sum of the second and third numbers multiplied by two from the cube of the first number. This result is our answer.

For example, let's say we have the numbers 2, 3, and 4. We first calculate the cube of 2, which is 8. Then, we subtract the sum of 3 and 4 multiplied by two, which is 14. So, the final answer is 8 - 14 = -6.

We can also show the stepwise calculation as follows:

= 2³ - (3 + 2 × 4)

= 8 - 14

= -6

Therefore, the result of the calculation is -6.

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If two parallel lines are crossed by a transversal, the value of x is option (b) x = 70 degrees

When two parallel lines are intersected by a transversal, eight angles are formed. Two of these angles are vertical angles, which are opposite angles that share the same vertex and are formed by the intersection of two lines.

Vertical angles are always congruent, meaning they have the same measure. This is a geometric property that is true regardless of the angle's degree measurement.

In this problem, one of the vertical angles is given to be 70 degrees. Therefore, the other vertical angle must also have a measure of 70 degrees. This means that the value of x, which is the measure of one of the vertical angles, is also 70 degrees.

So, correct option is (b) x = 70 degrees.

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The given question is incomplete, the complete question is:

Two parallel lines are crossed by a transversal. What is the value of x? a) x = 40 b) x = 70 c) x = 110 d) x = 130.

The values of h is v3 in span fv1; v2g and h is fv1; v2; v3g is 4.

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

We are given that;

v1 and v2 are not scalar multiples to each other

So, they are not linearly dependent

Now,

1(10h -42) -3(-14 +3h) +2 (18-20) =0

10h -9h-4 =0

h = 4

Therefore, by vectors the answer will be 4 so that the vector v3 is in {v1,v2}.

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Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by.

here, we have,

In this problem, considering a standard deviation of 40, we have that:

440 - 2 x 40 = 360.

440 + 2 x 30 = 520.

Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.

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Joanna can assemble her bracelet in 30 ways.

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

here, we have,

to find the number of ways in which the bracelet can be assembled:

It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.

The rest 4 are of different colors.

Six beads can be arranged in a circle in 6!/6 ways.

This means that the six beads can be arranged in 5! ways.

Since this is a bracelet, it can be flipped around.

Therefore, it can be arranged in 5!/2 ways.

5!/2

= 5*4*3*2*1/2

= 60

Now, we know that two beads are of the same color. Therefore, we must divide this by two again.

Therefore, we get:

60/2 = 30

The six beads can be arranged in 30 ways to make the bracelet.

Therefore, we have found that Joanna can assemble her bracelet in 30 ways.

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Answer:

See below

Step-by-step explanation:

It's basically the perimeter of a circle, or it's total distance around it.

Answer:

              The x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore, the x-intercept of Line A is less than the x-intercept of Line B.

Step-by-step explanation:

              The x-intercept of a graph or function is where the line hits the x-axis on a coordinate plane. In other words, the y-value of the x-intercept is 0. Since we are looking for the x-intercept of Line A, we can use the given equation to solve for it by inserting the value y = 0 (as mentioned above, the x-intercept of a function will have the y-value as 0). By solving the equation, you'll get that [tex]-2=\frac{1}{3} (x-3)[/tex] ⇒ [tex]-6=x-3[/tex] ⇒ [tex]x = -3[/tex]. Therefore, the x-intercept of Line A is (-3, 0).

              The x-intercept on a graph is easier to find, as it is where the line touches the x-axis. So the x-intercept of Line B would be (-1, 0). Now that we have both x-intercepts, we can compare them and come up with the final answer that is required. As -3 is less than -1, we can conclude that the x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore the x-intercept of Line A is less than the x-intercept of Line B.

Have a great day! Feel free to let me know if you have any more questions :)

The original number that satisfies the condition the square of a non-zero number is equal to 68% of the original number is 1.68.

Variables and constants are used to create algebraic expressions using a variety of techniques.

It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions.

An algebraic expression (or variable expression) is the name given to a grouping of terms that have undergone operations including addition, subtraction, multiplication, and division.

Let us suppose a non zero number = x.

Given that, the square of a non-zero number is equal to 68% of the original number.

This can be represented algebraically as follows:

x² = x(1 + 68/100)

x² = x(1 + 0.68)

x² = x(1.68)

x = 1.68

Hence, the original number that satisfies the condition the square of a non-zero number is equal to 68% of the original number is 1.68.

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