Apply It 1LFAC is a straight angle and/BAD is a right angle. Find m/FAE Show your work. A B E D (2x + 10) 3x C​

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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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: 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.

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:

230

Step-by-step explanation:

trying to find (in this case, 46.0), P is the percentage (20%), and B is the whole amount we're looking for. We can write this equation as:

46.0 = 0.20B

To solve for B, we can divide both sides by 0.20:

B = 46.0 / 0.20

B = 230

Therefore, 20% of 230 is 46.0.

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:

The polynomial in factored form is:

P(x) = (x-10)(x+1)(x+1)

or, we can write it in expanded form as:

P(x) = x^3 - 8x^2 - 11x + 40.

Step-by-step explanation:

If the x-intercepts are at (10,0) and (-1,0), then the polynomial must have factors of (x-10) and (x+1). If the y-intercept is at (0,-40), then the constant term must be -40.

To satisfy the given requirements, we can write the polynomial as:

P(x) = (x-10)(x+1)(x-a)

where a is a constant that we need to determine. To find a, we can use the fact that the leading coefficient is 1.

Expanding the expression above, we get:

P(x) = (x^2 - 9x - 10)(x-a)

= x^3 - ax^2 - 9x^2 + 9ax - 10x + 10a

= x^3 - (a+9)x^2 + (9a-10)x + 10a

Since the leading coefficient is 1, we know that the coefficient of x^3 is 1. Therefore, we must have:

1 = 1*(-a-9)*(9a-10)

Simplifying and solving for a, we get:

a = -1

Therefore, the polynomial in factored form is:

P(x) = (x-10)(x+1)(x+1)

or, we can write it in expanded form as:

P(x) = x^3 - 8x^2 - 11x + 40.

Answer:

The speed is: 186000 Miles/Sec

Step-by-step explanation:

The explanation is given in the picture.

Thank you!

The answer is A. x y 2 4 3 6 4 9 for the given values.

What is proportional relationship ?

A proportional relationship is a type of relationship between two quantities, where the ratio of one quantity to the other remains constant. In other words, as one quantity increases or decreases, the other quantity changes in a way that maintains the same ratio between them.

For example, if we have a proportional relationship between

The table that shows a proportional relationship between x and y is A.

In a proportional relationship, the ratio of y to x remains constant. We can check this ratio for each table:

A. For x=2, y=4, so y/x=2. For x=3, y=6, so y/x=2. For x=4, y=9, so y/x=2. The ratio of y to x remains constant at 2.

B. For x=3, y=4, so y/x=4/3. For x=9, y=16, so y/x=16/9. For x=15, y=20, so y/x=4/3. The ratio of y to x is not constant.

C. For x=4, y=12, so y/x=3. For x=5, y=15, so y/x=3. For x=6, y=18, so y/x=3. The ratio of y to x remains constant at 3.

D. For x=1, y=4, so y/x=4. For x=2, y=8, so y/x=4. For x=3, y=15, so y/x=5. The ratio of y to x is not constant.

Therefore, the answer is A. x y 2 4 3 6 4 9 for the given values.

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The correct statement regarding the sign of the function is given as follows:

A. The function is negative when x < 0.

We have to look at the graph of the function relative to the x-axis, as follows:

Hence the sign of the function for this problem is given as follows:

Meaning that option A is the correct option.

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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:

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:

I assume around 700 people vist the zoo

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:

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:

200

Step-by-step explanation:

300=150%

300/3=100

150/3=50

100x2=200

50x2=100

100%=200

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.

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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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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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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Answer:

Step-by-step explanation:

I got you

So,

The perimeter of a square is the sum of the lengths of all its sides, and since a square has all sides equal, we can find the length of one side by dividing the perimeter by 4:

32 cm ÷ 4 = 8 cm

Therefore, each side of the square measures 8 centimeters. To find the area of the square, we can use the formula:

Area = side length x side length

So, the area of the square is:

Area = 8 cm x 8 cm = 64 square centimeters

Therefore, the area of the square with a perimeter of 32 centimeters is 64 square centimeters.

Answer:33 1/3

Step-by-step explanation:

Answer: 33.35

Step-by-step explanation:

6 2/3 is 6.67 in decimal form. 6.67 x 5 = 33.35

So, the answer is 33.35

I hope this helps!

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:

Step-by-step explanation:

caca

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.

Answer:

(w^4 - 81)(y^4)

Step-by-step explanation:

The following conclusions can be made regarding the given graph -

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is the graph of a straight line as shown in the image.

Only one single graph of a straight line is given. We cannot compare it, so we will analyze its meaning itself.

        {m} = (0 - 2.4)/(0.8 - 0)

        {m} = -2.4/0.8

        {m} = - 3

Therefore, the following conclusions can be made regarding the given graph -

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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

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