If EF = 18, FG = x + 20, and EG = 5x - 14, what is EG?

Answer:

x=5, y=2 | Equations: 4x+y=22 (or see below) and 12x-5y=50

Step-by-step explanation:

Here's my attempt:

First Equation:

Because triangles ΔSTU and ΔXYZ are congruent, then we can say that:
m∠S = m∠X
m∠T = m∠Y
m∠U = m∠Z

We know that m∠X = 130°, and that m∠X = m∠S, so m∠S = 130°

We also know that the sum of angles in a triangle = 180°

We also know the rest of the angles in ΔSTU: 28° and (4x+y)°

So, we can say that ∠S + ∠T + ∠U = 130+28+4x+y = 180 (we can remove the degree sign)

Now, you can either enter this as it is or simplify it: ❗

130+28+4x+y=180

4x+y+158=180

4x+y=22

Second Equation:

We can do the same thing as for the first equation and get the angles of ΔXYZ:

∠X = 130, ∠Y = 8x-6y, ∠Z = 4x+y

Then, add them and set it to 180:

130+8x-6y+4x+y=180

Simplify:

12x-5y+130=180

12x-5y=50

To solve for x and y:

Now, we have to solve the systems.

Let's start with the first one:

4x+y=22

Isolate y:

y=22-4x (Equation 1)

Then, we plug it into the second equation:

12x-5y=50

12x-5(22-4x)=50

12x-110+20x=50

32x=160

x=5

So we got x, but to find y, we need to plug in x into Equation 1 (where we isolated y

y=22-4x

y=22-4(5)

y=22-20

y=2

We have both our x and y values

That was my attempt, hope it helped!

all squares are parallelogram but all parallelogram are not squares

Answer:

−3.5, −0.3, 0.6, 3.3

Step-by-step explanation:

This is because negative numbers are less than positive numbers, and numbers with a smaller absolute value are less than numbers with a larger absolute value. Therefore, the smallest number in the given list is −3.5, followed by −0.3, 0.6, and finally 3.3. When we put the numbers in this order, we get the correct order from least to greatest.

Answer:

c 5

Step-by-step explanation:

2=10

1=5

5+5=10

hope this helps by now

Answer:

Blue: 1/5

Step-by-step explanation:

To find the rate of change you use your slope formula which is y2-y1 over x2-x1.

You'd set your equation and you'd get 4-2 over 20-10. You solve and you get 2/10 and because it isn't one of the answer choices you have to simplify it. To simplify it you find the common number they both share and they both share 2 so you divide both by 2. 2 divided by 2 is 1 and 10 divide by 2 is 5. So then the rate of change or slope is 1/5.

Answer: B

Step-by-step explanation: TRUST

The horizontal component of the force vector is 260 pounds, and the vertical component is 150 pounds. (Option B).

To find the horizontal and vertical components of the force vector, we can use trigonometry. The horizontal component is the force acting in the direction parallel to the ground (x-axis), and the vertical component is the force acting in the direction perpendicular to the ground (y-axis).

Given that the force is 300 pounds and makes a 30° angle with the ground, we can calculate the components as follows:

Horizontal component (F_horizontal) = Force * cos(angle)

Vertical component (F_vertical) = Force * sin(angle)

Inserting in the values:

Horizontal component (F_horizontal) = 300 pounds * cos(30°)

Vertical component (F_vertical) = 300 pounds * sin(30°)

Now, let's calculate:

Horizontal component (F_horizontal) = 300 pounds * 0.866 (rounded to 3 decimal places, cos(30°) ≈ 0.866)

F_horizontal ≈ 259.8 pounds

Vertical component (F_vertical) = 300 pounds * 0.5 (rounded to 3 decimal places, sin(30°) ≈ 0.5)

F_vertical ≈ 150 pounds

Therefore, the required components of the force vector are approximately 260 pounds and 150 pounds.

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Answer:

Step-by-step explanation:

you get a tutor

" BRAINLY TUTOR "

press that link

Answer:

1 Green Sack = 2

1 Red Sack = 2

1 Elf Mask = 8

1 Christmas List = 5

Step-by-step explanation:

g=Green sack

r= Red sack

e = Elf mask

c = Christmas list

Answer:

To have 4 times as many apples as bananas, Amadou could have bought 4 apples for every 1 banana, or 8 apples for every 2 bananas, or 16 apples for every 4 bananas.

4 apples : 1 banana

8 apples : 2 bananas

16 apples : 4 bananas

We can use the fact that the total cost of the apples and bananas was $9 to determine the number of apples and bananas that Amadou bought. Since each apple costs $1, Amadou bought 9 apples if he bought no bananas, or 7 apples if he bought 2 bananas, or 5 apples if he bought 4 bananas.

9 apples : 0 bananas

7 apples : 2 bananas

5 apples : 4 bananas

Therefore, the possible combinations of apples and bananas that Amadou could have bought are 9 apples and 0 bananas, 7 apples and 2 bananas, or 5 apples and 4 bananas.

The midrange for the data items in the given frequency distribution is 30.5.

Generally, To find the midrange for the data items in the given frequency distribution, we need to calculate the midpoint of each score range. The midpoint of a range is calculated by taking the average of the lower and upper bounds of the range.

For the first score range (29-30), the lower bound is 29 and the upper bound is 30, so the midpoint is (29 + 30) / 2 = 29.5.

For the second score range (30-31), the lower bound is 30 and the upper bound is 31, so the midpoint is (30 + 31) / 2 = 30.5.

Therefore, the midrange for the data items in the given frequency distribution is 30.5.

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The probability that a randomly chosen person from the given population makes a purchase is [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] *0.25.

We can calculate the probability in the following way,

Let the total population of visitors visiting to the online shopping site be P.

The estimated odds of visitors making a purchase on the online shopping website are 0.25

P(E)=0.25 and n=P

We know that the probability mass function is also known as p.m.f. of Binomial Distribution with parameters n and P.

P(X=x) = [tex]\left(\begin{array}{ccc}n\\x\end{array}\right){p^x}[/tex]* [tex](1-p)^{(1-x)}[/tex] ; 0 < p < 1 And x=0,1,2,3,...

Probability of one randomly chosen visitor making a purchase= P(x=1)

=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] 0.25^1 * 0.75^0

=[tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex]*0.25

Therefore, the Probability of a random visitor making a purchase depends on the value of the population and is equal to [tex]\left(\begin{array}{ccc}p\\1\end{array}\right)[/tex] * 0.25

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Vertical angles are two angles that are opposite each other and share a common vertex. Adjacent angles are two angles that share a common side and vertex.

To find the measure of an unknown angle using these relationships, you can use the vertical angle theorem which states that if two angles are vertical, then they have equal measure. For example, if angle A and angle B are vertical angles, then angle A = angle B.

Example:

Given: Angle A = 40°

Find the measure of angle B

Solution:

Since angle A and angle B are vertical angles, then angle A = angle B

Therefore, the measure of angle B = 40°

An angle is created when two straight lines or rays intersect at the same point. The point where all points converge is known as an angle's vertex. The Latin word angulus, which meaning "corner," is where the term "angle" comes from.

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Answer:

The end behavior of the function f(x) = 2^-xsin3x is that it approaches 0 as x approaches positive infinity and approaches infinity as x approaches negative infinity.

Step-by-step explanation:

13) y= 3/5 x +2

14) y= x + 2

Answer:

d. 4x − 5y = 27x + 6y = 10

I hope my answer helps you.

Answer: 890 downloads the high-quality version

Step-by-step explanation:

Let x be the number of downloads of the high-quality version

1420-x be the number of downloads of the standard version

So, we have the equation

4.5x + 2.7(1420-x) = 5436

4.5x + 3834 - 2.7x = 5436

1.8x + 3834 = 5436

Subtract 3834 on both sides

1.8x = 1602

x = 890

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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Answer:

x=-4/3

Step-by-step explanation:

For an saving account in a bank, With the given value of the rate 'r' and the compounding period 'n' , The AER on the saving account is given by :

AER = [tex](1+\frac{r}{n})^{n} -1[/tex] .

The interest rate on a savings account or investment product with multiple compounding periods is known as the annual equivalent rate (AER). The next interest payment will be based on the marginally higher account amount, and AER is computed under the presumption that any interest paid is included in the balance of the principle payment.

The main benefit of AER is that it takes compounding effects into account, making it the real rate of interest.

Unfortunately, the AER is typically not mentioned when investors are comparing various investment possibilities. Investors are required to perform the calculations themselves.

n= compounding periods.

r= rate

Annual Equivalent Rate (AER) = [tex](1+\frac{r}{n})^{n} -1[/tex]

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Answer:

153°

Step-by-step explanation:

Angle EHG is a right angle, so it measures 90°.

The measures of angles EHF and FHG add to 90°.

m<EHF + m<FHG = 90°

m<FHG = 27°

m<EHF + 27° = 180°

m<EHF = 153°

What would happen is the result would increase by a factor of 2. The result of dividing the fractions will be 4.

From the question, we are to determine what would happen if we divide by 2/5 instead of 4/5

That is,

We are to carry out the division operation

1 3/5 ÷ 2/5

Evaluating

1 3/5 ÷ 2/5

8/5 ÷ 2/5

8/5 × 5/2

= 8/2

= 4

The answer increased by a factor of 2.

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Therefore, in order for them to enjoy a party, they must be rewarded a minimum of 26 extra times.

The equals sign (=) must appear in an equation. You can think of an equation as having a left and a right side since there will be a mathematical expression on either side of it. Consider an equation to be a set of scales. Although you can use different amounts on either side, for it to be solved, each side must be equally balanced. An unknown will always be present in an algebraic equation. This is symbolized by a symbol, such x, y, or z.

Here,

Given: Given: To reward her students for good behavior, Mrs. Morton fills a marble jar with three marbles.

if there are 24 marbles in the jar. When r denotes the quantity of additional rewards for the class, then the necessary equation is 24 + 3r 100.

If we can figure it out, we'll obtain the minimum number of marbles the jar holds—24.

In order to solve the problem, take 24 away from both sides.

=> 3r ≥100 -24

=> 3r  ≥76

=> r  ≥76/3

=> r ≥ 25.33

=> r≈ 26

Therefore, in order for them to enjoy a party, they must be rewarded a minimum of 26 extra times.

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To calculate the amount of commission that Nancy Bell earned last month, we can use the following formula:

Commission = Sales * Commission Rate

In this case, the sales are $59,400 and the commission rate is 14%, so the commission is:

Commission = $59,400 * 14% = $8,356

To calculate Nancy's gross pay, we can add her salary to her commission:

Gross Pay = Salary + Commission

Gross Pay = $1,710 + $8,356 = $10,066

Therefore, Nancy earned $8,356 in commission and her gross pay was $10,066.

Answer:

804.063 is the answer

Step-by-step explanation:

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Variance is the only meaningful measure of the central location for a categorical variable.

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a group of data is from one another.

Descriptive statistics, statistical inference, hypothesis testing, the goodness of fit, and Monte Carlo sampling are just a few of the concepts that make use of a variance. In the sciences, where statistical data analysis is widespread, a variance is a crucial tool.

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Under the null hypothesis, the expected number of strongly opposed juniors is 50.

The term null hypothesis refers the typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

Here we have given that suppose we wish to test the null hypothesis that there is no association between student year in school and student opinion.

And we need to find under the null hypothesis, what is the expected number of strongly opposed juniors.

Here let us consider there are 100 students.

Then according to the given statement, there is no association between student year in school and student opinion.

Which refers that half of them are supported and half of them are opposed.

Therefore, the expected value is 50.

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for a binomial random variable x, it can only takes on two possible values, 0 or 1 is True

A binomial random variable is a discrete random variable, which means that it can only take on certain values, in this case 0 or 1. This means that the answer to the question is true. A binomial random variable is the sum of two independent Bernoulli random variables, where each Bernoulli random variable has a probability of success equal to the probability of success for the binomial random variable. This means that the binomial random variable is a summation of two Bernoulli random variables, and can only take on values of 0 or 1.

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if the sum of two digits is divided by the sum of the digits, the number is  80.

Generally, Let the two digits of the number be x and y. The number can be written as 10x + y.

We are given that (x+y)/(x+y) = 6, which means that x + y = 6x + 6y.

Subtracting x + y from both sides, we get 5x = 5y. Therefore, x = y.

We are also given that the number is 9 greater than the number formed by reversing the digits, which means that 10x + y = 9 + 10y + x.

Combining like terms, we get 9x = 8y, or x = 8/9y.

Substituting this expression for x into the equation x = y, we get 8/9y = y, which means that y = 0.

Therefore, the number is 10x + y = 10 * (8/9y) + 0 = 80.

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The system of equations that should be used is the second one:

-15 = 5A

10 = -2A + B

Here we have the following equation:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]

If we multiply and divide the first therm in the right side by (5x - 2) we will get:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A*(5x - 2)}{(5x - 2)^2} + \frac{B}{(5x - 2)^2}[/tex]

The numerators must be equal, then we can write:

-15x + 10 = A*(5x - 2) + B

-15x + 10 = A*5x - 2A + B

Then we can write two equations, one that has x as a factor and other that does not, these are:

-15 = 5A

10 = -2A + B

That is the system of equations.

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Answer:

B.

Step-by-step explanation:

took unit test