determine whether each pair of expressions is equivalent 4(x + y) and 4y + 4x

The prove that triangle ABE is congruent to triangle CDE is given below

Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.

First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.

Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.

Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.

Therefore, we have proven that triangle ABE is congruent to triangle CDE.

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Answer:

I would solve for x with the first equation, then use that to solve for y in the second, then check by inputting values.

3x+y=-2

x-y=6

x=6+y

then...

3(6+y)+y=-2

18+3y+y=-2

18+4y=-2

4y=-20

y=-5

So..

3x+-5=-2

3x=3

x=1

3(1) + -5 = -2

Step-by-step explanation:

this might be correct.

Answer:

7b + 29 ≤ -26

Step-by-step explanation:

Given information:

The sum of a number times 7 and 29 is at most -26.

Sum- is referring to Addition ( + )

Times- is referring to Multiplication ( × )

At most - is referring to maximum. The maximum amount that it can get. Which ≤ means less than or equal to which refers to "At Most"

Hence, the inequality is

7b + 29 ≤ -26

RevyBreeze

Let the 7 letters A through G represent the ages of the 7 person family.

7/2 = 3.5 which rounds to 4 represents the slot number of the median, aka the middle-most position. The 4th letter is D. Because the median is 16, we know that D = 16.

We go from this

A,B,C,  D,  E,F,G

to this

A,B,C,  16,  E,F,G

I put a bit of spacing to help show why D is the middle.

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

The modes are 12 and 45, which means those values show up more than once. Let's assume they show up 3 times each.

That tells us A,B, and C are all equal to 12. Furthermore, that assumption indicates E,F,G are all equal to 45.

We go from this

A,B,C,  16,  E,F,G

to this

12,12,12,  16,  45,45,45

But we run into a problem. The range is max-min = 45-12 = 33 and not 35 like we want.

We have no choice but to remove one copy of "12" and remove one copy of "45". We need to remove both because removing only one of those would result in the mode being just one value (rather than two).

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

So we have this now

A,12,12,  16,  45,45,G

where A < 12 and G > 45

range = max - min = G-A = 35

G-A = 35 solves to G = 35+A

We can update the set to

A,12,12,  16,  45,45,35+A

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

Now to figure out what "A" is.

The bit of info we haven't used yet is the mean.

Recall the mean has us add up the numbers and then divide by the number of values.

mean = (sum of the values)/(number of values)

mean = (A+B+C+D+E+F+G)/7

mean = (A+12+12+16+45+45+35+A)/7

mean = (2A+165)/7

Set that equal to the stated mean of 23 so we can solve for "A".

mean = (2A+165)/7

(2A+165)/7 = 23

2A+165 = 7*23

2A+165 = 161

2A = 161-165

2A = -4

A = -4/2

A = -2

That's not good. We should have gotten a positive whole number for "A". Since "A" is negative, it means there is a typo somewhere in the given instructions.

It's impossible to have a family of 7 people where the mean age is 23, the median is 16,  the modes are 12 and 45, and the range is 35. At least one of those starting values needs to change. If for instance the "45"s were changed to "41", then the equation above would solve to A = 2.

I would ask your teacher for clarification.

So the balloon payment six years from now will be approximately $24,612.09.

(P, R, and T) / 100 is the SI unit.

In this case, SI stands for Straightforward Interest. P is the initial investment or loan amount, and R is the interest rate.

To find the amount of the balloon payment six years from now, we can use the formula for the present value of a series of payments:

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

where PV is the present value of the payments, PMT is the monthly payment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years for the loan.

In this case, we have:

PMT = $1,300 (paid for 5 years)

r = 0.05 (5% APR)

n = 12 (monthly compounding)

t = 6 (total loan term, including the first year with no payments)

To calculate the present value of the payments, we first need to find the present value of the $93,500 loan, one year from now, when the payments begin. This is equivalent to finding the future value of the loan now, and then discounting it back one year using the interest rate.

The future value of the loan after one year is:

FV = $93,500 x (1 + r)¹ = $98,175.00

The present value of this future amount, discounted back one year at an interest rate of 5%, is:

PV = $98,175.00 / (1 + r)¹ = $93,500.

So the present value of the loan one year from now, when the payments begin, is approximately $93,500.

Using this present value as the principal amount for the remaining 5 years of payments, we can calculate the balloon payment using the present value formula above:

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

PV = $1,300 x (1 - (1 + 0.05/12)⁻⁶⁰) / (0.05/12)

PV = $68,887.91

Therefore, the balloon payment six years from now will be the remaining principal on the loan after five years of payments, which is:

Balloon payment = $93,500 - $68,887.91 = $24,612.09.

So the balloon payment six years from now will be approximately $24,612.09.

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In response to the supplied query, we may state that Draw a dot to coordinates  indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.

A coordinate system is a technique used in geometry to precisely locate points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional plane is located using a pair of numbers known as coordinates. The x and y coordinates are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.

Plotting the coordinates of the point (4.5, -2.25) requires the following actions:

Create the x- and y-axes.

Identify the intersection of the x and y axes. The coordinates of this place, which is known as the origin (0, 0).

Find the coordinates (4.5, -2.25) on the x- and y-axes.

Move 4.5 units to the right of the origin to find the point on the x-axis.

Go 2.25 units down from the origin to find the point on the y-axis.

Draw a dot to indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.

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Answer:

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively. Substituting the given values, we get:

V = (3/5) x (4/3) x (5/4)

V = (12/60) x (20/60)

V = 240/3600

V = 1/15

Therefore, the volume of the rectangular prism is 1/15 cubic units.

Answer:

1

Step-by-step explanation:

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

The amount that Fatima will pay each month for the student loan of $15,000 for 10 years at 8.25% interest is $183.98.

The monthly payment can be computed using an online finance calculator below.

The monthly payment shows the periodic amount that the borrower repays the financier to settle the student loan, including accumulated interest.

N (# of periods) = 120 months (10 years x 12)

I/Y (Interest per year) = 8.25%

PV (Present Value) = $15,000

FV (Future Value) = $0

Results:

Monthly payment (PMT) = $-183.98

Sum of all periodic payments = $-22,077.47

Total Interest = $7,077.47

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Answer:

Step-by-step explanation:

45

Student 1's answer is the correct answer: (x+2)(x+12).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something. An equation is a mathematical statement wherein two expressions are set equal to each other.

Student 2's answer, 3(x+2)(x+12), is incorrect because they multiplied the factors by 3, which is not necessary and changes the value of the expression.

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Answer: Read One Piece and Check Explanation.

Step-by-step explanation: Yes, Mr Thapelo's claim is valid.

Let's assume that the salary of the messenger is $1,000.

Therefore, the salary of the five additional cleaners should be 10 x $1,000 = $10,000.

Answer:

Step-by-step explanation:

This problem involves a binomial distribution where the probability of success (passing on the first attempt) is 0.65, and the probability of failure (not passing on the first attempt) is 0.35. We want to find the probability that less than 3 out of 5 people pass on their first attempt.

We can use the binomial probability formula to calculate this:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Where X is the number of people who pass on their first attempt.

P(X = 0) = (5 choose 0) * 0.65^0 * 0.35^5 = 0.0024

P(X = 1) = (5 choose 1) * 0.65^1 * 0.35^4 = 0.0289

P(X = 2) = (5 choose 2) * 0.65^2 * 0.35^3 = 0.1323

So,

P(X < 3) = 0.0024 + 0.0289 + 0.1323 = 0.1636

Therefore, the probability that less than 3 out of 5 people pass their driver's tests on the first attempt is approximately 0.164, rounded to three decimal places.

Answer:

d) 360

Step-by-step explanation:

To solve this problem, we can use a Venn diagram. Let R, C, and J represent the sets of students who like rock, country, and jazz, respectively. We can fill in the diagram with the given information:

       J

      / \

     /   \

    /     \

 RC-----C

    \     /

     \   /

      \ /

       R

We know that:

The total number of students surveyed is 500.

9 students like all three types of music, so we can put 9 in the intersection of all three sets (RCJ).

24 like rock and country, so we can put 24 in the intersection of R and C (RC).

29 like rock and jazz, so we can put 29 in the intersection of R and J (RJ).

29 like country and jazz, so we can put 29 in the intersection of C and J (CJ).

We can calculate the number of students who like only one type of music by subtracting the number of students who like two or three types of music from the total number of students surveyed:

Total = R + C + J - RCJ

500 = 204 + 164 + 129 - 9

We can use this equation to solve for R, C, and J:

R = 204 - 24 - 29 - 9 = 142

C = 164 - 24 - 29 - 9 = 102

J = 129 - 29 - 29 - 9 = 62

So there are 142 students who like rock only, 102 students who like country only, and 62 students who like jazz only. Therefore, the total number of students who like exactly one type of music is:

142 + 102 + 62 = 306

Therefore, the answer is (d) 360.

Answer:

The first step is to calculate the daily interest rate. We can do this by dividing the annual percentage rate (APR) by 365 (the number of days in a year):

Daily interest rate = 15% / 365 = 0.00041096

Next, we need to calculate the interest that accrues on the outstanding balance for the first month. Since there are 30 days in a typical month, we can multiply the daily interest rate by the outstanding balance and the number of days in the month:

Interest for first month = 0.00041096 × $400 × 30 = $4.93

This means that the outstanding balance after the first payment will be:

$400 + $4.93 - $75 = $329.93

So the balance after the first payment will be $329.93.

Answer:

The speed is: 186000 Miles/Sec

Step-by-step explanation:

The explanation is given in the picture.

Thank you!

Hi

im pretty sure 88m2 is the answer

here is the workong out

hope it helps

good luck:)

Answer:

112m squared

Step-by-step explanation:

1/2 * b * h is the formula for a triangles so 1/2 * 6 * 8 is 24 * 2 because the other triangle is symmetrical and the formula for a square is b * h so 8 * 8 is 64 and adding 24 + 24 + 64 = 112 m squared

Answer:

I assume around 700 people vist the zoo

A_n = A_n-1 + 2 represents the recursive formula.

A recursive formula is a formula or equation that describes a sequence or function in terms of itself. In other words, the formula for a given term or value depends on the formula for one or more previous terms or values.

For example, the Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

This sequence can be described recursively using the following formula:

F(n) = F(n-1) + F(n-2)

where F(n) is the nth term of the sequence, F(n-1) is the (n-1)th term, and F(n-2) is the (n-2)th term.

Another example of a recursive formula is the factorial function, which is defined for non-negative integers n as:

n! = n * (n-1)!

This formula states that the factorial of n is equal to n multiplied by the factorial of (n-1). This recursive definition can be used to compute the factorial of any non-negative integer.

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Answer:

To set up this problem, you have to begin with Newton's second law, F = ma. There are two forces acting on this mass, gravity and air resistance. The force of gravity is constant and equal to -mg, where g = 9.8 m/s^2 and m is the given mass.

Step-by-step explanation:

Answer:

the velocity of the mass when it hits the ground is approximately 58.4 m/s.

Step-by-step explanation:

We can solve this problem using the equations of motion for a particle under constant acceleration. The acceleration of the particle is the sum of the gravitational acceleration and the air resistance force, which is given by 5v:

a = -g + 5v/m

where g is the acceleration due to gravity (9.8 m/s^2) and m is the mass of the particle (50 kg).

Using the initial conditions, we can find the velocity of the particle as a function of time. At t=0 (when the particle is shot from the cannon), the initial velocity is 10 m/s, and the initial position is 100 m above the ground. Therefore, we have:

v(0) = 10 m/s

y(0) = 100 m

Using the equation of motion for the position of the particle, we have:

y = y(0) + v(0)t + (1/2)at^2

where y is the position of the particle as a function of time t.

Solving for t when the particle hits the ground (y=0), we get:

0 = 100 + 10t + (1/2)(-g+5v/m)t^2

Simplifying, we get a quadratic equation in t:

-gt^2/2 + (5v/m)t + 100 = 0

Solving for t using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac))/2a

where a = -g/2, b = 5v/m, and c = 100. Using the positive solution (since we're interested in the time it takes for the particle to hit the ground), we get:

t = (-5v/m + sqrt((5v/m)^2 + 4g100))/(-g)

Simplifying, we get:

t = (-5v/m + sqrt((5v/m)^2 + 3920))/(-4.9)

Now we can use the equation of motion for the velocity of the particle to find the velocity when it hits the ground:

v = v(0) + at

Substituting the time t we just found and solving for v, we get:

v = 10 + (-g + 5v/m)t

Substituting the value of t we just found and solving for v, we get:

v = 10 + (-g + 5v/m)(-5v/m + sqrt((5v/m)^2 + 3920))/4.9

Simplifying and solving for v, we get:

v ≈ 58.4 m/s

Therefore, the velocity of the mass when it hits the ground is approximately 58.4 m/s.

Answer:

Step-by-step explanation:

We can use the rule of 72 to estimate the time it takes for Arthur's investment to double. The rule of 72 states that the time it takes for an investment to double is approximately 72 divided by the annual rate of return.

To apply this rule, we need to calculate the annual rate of return that Arthur is earning on his investment. We can do this by calculating the percentage increase in his account balance from year to year.

From year 1 to year 2, his account balance increased by (118.81 - 109)/109 = 9.81/109 = 0.09 = 9%.

From year 2 to year 3, his account balance increased by (129.5 - 118.81)/118.81 = 10.69/118.81 = 0.09 = 9%.

So the average annual rate of return over this period is approximately 9%. Using the rule of 72, we can estimate that it will take approximately 72/9 = 8 years for Arthur's investment to double.

Therefore, the closest option among the given responses is option D. It will take about 8.04 years for Arthur's investment to double.

The equation deduced by Malik is the correct equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, the Boy Scout troop raised money in a fundraiser. they donated $400 to the food bank and half of the remaining amount to the animal shelter, they both represented the amount donated for the animal shelter :-

Malik: y = (x-400) / 2

Jacob: y = x/2 - 400

So, if we consider y as the money donated for the animal shelter and x is the total-raised money,

Therefore, according to the question,

$400 donated to food bank, then the left amount = x-400

Half of the money donated to the animal shelter based = (x-400) / 2

Therefore, the equation will be:-

y = (x-400) / 2

Hence, the equation deduced by Malik is the correct equation.

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Answer: The atmospheric pressure decreases with altitude. This is because as we move higher above the earth's surface, there is less air above us and therefore less weight pushing down on us. Therefore, the correct answer is:

C. An altitude of 7 km above sea level

At an altitude of 7 km above sea level, a person would experience the least atmospheric pressure because they would be furthest from the earth's surface and there would be very little air above them. This is why the air pressure in the Earth's upper atmosphere is much lower than at the surface of the Earth.

Step-by-step explanation:

Answer:

The answer is no. It ought to be X-(16*10) given that she has made 10 necklaces out of 16 shells each using 160 total shells. To determine how many shells she still has, you would need to subtract those 160 from the initial number of shells she purchased, which was X.

Answer:

x = 12

Step-by-step explanation:

96 / 24 = 4, 28/ 7 = 4, assuming that it dilated by 4, so use 4 to multiply 25, 4 x 25 = 100 so 6x+28 = 100 then plug it in 6(12) + 28 = 100., 100 = 100

To check use a^2 + b^2 = c^2

28^2 + 96^2 = (6(12)+28)^2

784 + 9216 = (72+28)^2

784 + 9216 = 100^2

784 + 9216 = 10000

10000 = 10000

The length of the side z is equal to 16.94 to the nearest hundredth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠Z as follows:

9/sin32° = 15/sinY

sinY = (15 × sin32)/9 {cross multiplication}

Y = sin⁻¹(0.8832)

Y = 62.0308

m∠Z = 180 - (32° + 62.0308)

m∠Z = 180 - 94.0308

m∠Z = 85.9692

z/sin85.9692 = 9/sin32

z = (9 × sin85.9692)/sin32 {cross multiplication}

z = 16.9357

Therefore, the length of the side z is equal to 16.94 to the nearest hundredth using the sine rule.

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Answer:

4x+14

Step-by-step explanation:

Let x represent the cost of one movie ticket. If we have 4 sisters, we can write the first term as 4x.

Then, because we have the additional $14, we just add 14 to the expression.

Thus the answer is 4x+14

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3. The solutions are (3, 8) and (–1, 0).

4. The solutions are (5, 7) and (-2, 0).

5. Data is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola

7. The graph of y = -x² is a downward-facing parabola

8. The graph of y = 2x² is an upward-facing parabola

9. The graph of y = 3x² - 4 is an upward-facing parabola

What is  solutions to the system?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations.

A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

3. The solutions to the system are (3, 8) and (–1, 0).

To solve the system, we can substitute y = x + 5 from the first equation into the second equation:

x + 5 = x² – x + 2

Rearranging and simplifying, we get:

x² - 2x - 3 = 0

Factoring, we get:

(x - 3)(x + 1) = 0

Therefore, x = 3 or x = -1.

Substituting each value of x into y = x + 5, we get the corresponding y-value:

When x = 3, y = 3 + 5 = 8

When x = -1, y = -1 + 5 = 4

Therefore, the solutions are (3, 8) and (–1, 0).

4. The solutions to the system are (3, 7) and (-4, -2).

To solve the system, we can substitute y = x + 2 from the second equation into the first equation:

x² - 2x - 8 = x + 2

Rearranging and simplifying, we get:

x² - 3x - 10 = 0

Factoring, we get:

(x - 5)(x + 2) = 0

Therefore, x = 5 or x = -2.

Substituting each value of x into y = x + 2, we get the corresponding y-value:

When x = 5, y = 5 + 2 = 7

When x = -2, y = -2 + 2 = 0

Therefore, the solutions are (5, 7) and (-2, 0).

5. The data shown in the graph is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola that opens up and has a y-intercept of (0, 2).

7. The graph of y = -x² is a downward-facing parabola that opens up and passes through the origin (0, 0).

8. The graph of y = 2x² is an upward-facing parabola that opens up and has a y-intercept of (0, 0).

9. The graph of y = 3x² - 4 is an upward-facing parabola that opens up and has a y-intercept of (0, -4).

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The answer is C) 18/48 and 21/56.

Two ratios are proportional if they have the same ratio when simplified to lowest terms.

A) 7/10 and 10/10 cannot be proportional because 7/10 cannot be simplified further, while 10/10 simplifies to 1/1.

B) To simplify the first ratio, we can divide both the numerator and denominator by 4, giving us 5/7. To simplify the second ratio, we can divide both the numerator and denominator by 3, giving us 5/6. Since these simplified ratios are not equal, the two ratios are not proportional.

C) To simplify the first ratio, we can divide both the numerator and denominator by 6, giving us 3/8. To simplify the second ratio, we can divide both the numerator and denominator by 7, giving us 3/8. Since these simplified ratios are equal, the two ratios are proportional.

D) To simplify the first ratio, we can multiply both the numerator and denominator by 2, giving us 6/10, which simplifies to 3/5. The second ratio is already in simplified form. Since these simplified ratios are not equal, the two ratios are not proportional.