2. What is the solution for the system of equations?
16x - 32y = 27
8x - 16 = 16y
a) Use the linear combination (elimination) method to solve the system of equations.
b) What does the solution tell you about the two lines of the system?

Simplifying the equations will give 3x -1 = 4x, 3x + 18 = 4x + 7 and 7x = 1

Lets simplify each of the equations in order to match with the  equivalent equation from the second set

3x+6=4x+7

Collecting like terms

3x +6 - 7 = 4x

3x -1 = 4x

The second equation

3(x+6)=4x+7

expanding the bracket

3x + 18 = 4x + 7

The third equation

4x+3x=7-6

simplifying the equation

7x = 1

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The expression which has the same value as the given expression; 4² - 6 × 2 among the answer choices is; Choice C; 10 - 3 x 2 + 4¹.

According to the task content; the given expression whose equivalent is to be determined is;

Given;

4² -6 ×2.

It follows from PEMDAS that the exponent should be evaluated and then the multiplication.

Hence, the value of the expression is; 16 - 8

= 8.

For answer choice C, which is correct, the evaluation is as follows;

10 - 3 × 2 + 4¹

= 10 -6 + 4

= 8.

Ultimately, choice C has the same value as the given expression.

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Comparing both data sets, we have: "Parker's team has a median of 75 points per player, with an IQR of 54 points. The opposing team has a median of points 74 points per player, with an IQR of 3 points.

Given that the data set for Parker's Basketball team is: 35, 32, 60, 80, 36, 90, 45, 76, 96, 92, 100, 120, 60, 38, 75, find the IQR and the median of the team:

The First Quartile is the middle of the first part of the data which is: 38

The middle of the data is the Median which is: 75

Third Quartile is: 92

IQR = third quartile - first quartile = 92 - 38 = 54.

Using the box plot given for the opposing team:

Median = 74

IQR = 76 - 73 = 3

Therefore, we can conclude that: "Parker's team has a median of 75 points per player, with an IQR of 54 points. The opposing team has a median of points 74 points per player, with an IQR of 3 points.

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Answer:

Last option.

Step-by-step explanation:

Corresponding sides are in proportion.

JM is x², then 6² = 36

LM is x², then 8² = 64

1/3

The notation P(x) is used to describe the probability of event x occurring.

Divisors

Before we can do the probability question, we need to find the divisors of 6. Divisors are numbers that can evenly divide another number. The factors and divisors of a number are the same. So, 6 has 4 divisors:

All of these values are on a 6-sided dice. So, in this probability question, there are 4 unsuccessful outcomes.

Probability

The probability of a simple event is the number of successful outcomes divided by the number of possible outcomes. In this situation, there are 6 possible outcomes, each side of the dice. Four of these outcomes do not satisfy the given condition (not a divisor of 6). Thus, there are 2 successful outcomes.

The probability of rolling a number that is not a divisor of 6 is 1/3.

Answer:

f(n) = 0.2n + 4.8

4.8

Step-by-step explanation:

Given the explicit formula :

an = 5 +0.2(n - 1)

Expressing an in function form f(n):

f(n) = 5 + 0.2(n - 1)

f(n) = 5 + 0.2n - 0.2

f(n) = 5 - 0.2 + 0.2n

f(n) = 0.2n + 4.8

The y - intercept :

Set n = 0

f(n) = 0.2n + 4.8

f(0) = 0.2(0) + 4.8

= 0 + 4.8

= 4.8

y intercept = 4.8

Answer:

The equation is likely (x2 -2x -3)/(x+2) and to simplify you can do polynomial synthetic division or long division. Using long division because it works in all cases:

       ________

x+2√x2 -2x -3             how many times does x go into x2  , x times

       x - 4 ______

x+2√x2  - 2x -3            multiply x by x + 2 and create the next row

     -(x2 )

          -4x - 3             bring down the -3 and repeat first step. how many times does x go into -4x, -4 times

        -(-4x - 8)            multiply x + 2 by -4

                   5             (this is the remainder but it must be in the form 5/(x+2)

so the answer is x - 4 + 5/(x + 2). Hopefully, this is what your teacher considers "simplified".

Step-by-step explanation:

Copied this from wyzant.com.  

Answer:

B and B

Step-by-step explanation:

Answer:

the correct answer is A

and A

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

Answer:

It is marked down by 26 percent.

Step-by-step explanation:

Hope this helps and have a great day!!!

Answer:

It would be marked down by 26%.

Answer:

CIRCLE

Explanation

A cylinder is made of a circular base as shown;

From the diagram shown, you can see that the base is a circle, hence the possible cross-sections of a right cylinder is a CIRCLE

The survey would also ask the respondent to provide an estimate of their total credit card spending in the past 12 months.

The survey would ask questions about the respondent's credit card usage, such as how often they use credit cards, what types of purchases they make with credit cards, how much they spend on average each month, and any other related questions.

The survey would also ask the respondent to provide an estimate of their total credit card spending in the past 12 months. The survey should also include a margin of error of +/- $3500 to ensure the accuracy of the results.

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Answer:

The square root of 3 is 9

Answer: $3703.70

Step-by-step explanation:

200x.054=$3703.70

The cost of producing 250 candidate posters is K400, and that 660 potential posters can be provided for K2500. This means that K400 + (x - 250) * K5 + K50 = K2500, and that K400 + (x - 250) * K5 + K50 = K2500. Finally, K400 + (x - 250) * K5 + K50 = K2500, and that K400 = 250.

The unitary method is a mathematical approach used to handle proportional and rate issues. We obtain the value of one unit of a quantity and then use it to get the value of any other quantity that is proportional to it using this procedure.

This generally recognized ease, preexisting variables, and any significant elements from the initial Diocesan customizable query may all be used to complete the task. If so, your may have another chance to interact alongside the item. Otherwise, all important influences on how algorithmic proof acts will be eliminated.  

Here,

(a)

=>  C(x) = K400 for 0  x  250.

=>  C(x) = K400 + (x - 250) * K5 + K50 for x > 250

(b)

(i)

=> C(1250) = K400 + (1250 - 250) * K5 + K50

=> K400 + 1000*K5 + K50

=>  K5400

In light of this, the cost to produce 1250 candidate posters is K5400.

We use the first portion of the charging function since 250  250 to determine the cost for printing 250 candidate posters. So:

=> C(250) = K400

Therefore, K400 is required to produce 250 candidate posters.

(ii)

=> K400 + (x - 250) * K5 + K50 = K2500

=>  (x - 250) * K5 = K2050

=>  x - 250 = 410

Therefore, 660 potential posters can be provided for K2500.

=>  C(x) = K400

=>  x = 250

250 applicant posters can be provided for K400 as a result.

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For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = (Rx/Ry)

Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.

I have every vector in 2D that has both vertical and horizontal components.

There are vectors say:  A = xi + yj

                              and, B =zi + wj

For example, adding two vectors gives the result

R = (x +z)i + (y + w) j.

The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B

The direction of the angle is found as

tan∅ = Rx/Ry

     ∅ = (Rx/Ry)

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If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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The expected value is a weighted average generalization. The company must choose to mine on site A.

The expected value is a weighted average generalization. Informally, the expected value is the arithmetic mean of a large number of independently chosen random variable outcomes.

To know on which site the company should mine, we need to calculate the expected profit that the company will get from each site. Therefore, the expected profit from each site will be,

Site A:

Expected profit = (0.2)($70 million) + (0.8)(-$15 million) = $2 million

Site B:

Expected profit = (0.1)($140 million) + (0.9)(-$21 million) = -$4.9 million

Since the value from Site B is negative, therefore, the company must choose to mine on site A.

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Answer:

36.36

Step-by-step explanation:

18.79 + 2.11 - 1.92 + 17.38

20.90 - 1.92 + 17.38

18.98 + 17.38

36.36

My first answer I didn't notice there was a subtraction sign.

Answer:

Step-by-step explanation:

imagine you chop off a right triangle from the left side

now you have a rectangle and a right triangle

the rectangle

height 5

width 12

5 x 12 = 60

triangle

height 5

width 3

3 x 5 = 15

15 / 2 = 7.5

60 + 7.5 = 67.5 m^2

Answer: 67.5 m^2

Step-by-step explanation:

To find out the area of the yard, we split the shape up into a triangle and rectangle. The area of the triangle is,

A = 1 × b × h/2 = 1 × 3 × 5/2 = 7.5 m^2.

And the area of the rectangle is,

A = 12 × 5 = 60 m^2.

We then add the area of the triangle and the area of the rectangle.

A = 7.5 + 60 =67.5 m^2

Rounded to one decimal place, the area of the yard is 67.5 square meters.

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

a.

Vladivostok is three hours ahead of Bangkok.

Step-by-step explanation:

Time the train left Bangkok is 1:50am

It traveled for 16 hours 40 minutes.

If the train was to be in Bangkok.

The Time Will be 1+16 hours then 50+40 minutes

Which is 17 hours + 1 hour 30 minutes

Which is 18 hours and 30 minutes

And 18 hours = 6:00 pm

So if it was in Bangkok the time with be 6:30 pm

But in Vladivostok, it was 9:30 pm

It's clear that Vladivostok time is faster by 3 hours

The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

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Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses