Solve each system of the equation by elimination. y=-4x+14y=10x-28

Answer:

∠VYZ = 65

∠VXY = 75

∠WZY = 50

∠XWZ = 80

∠WXY = 150

Explanation:

The angle ∠VYZ and the angle ∠VZY are complementary , meaning they add up to 90 degrees. Since ∠VZY = 25 we have

The idea of being representative of the population is actually reflecting the characteristics (features) we want to study of the whole population.

In this case, the samples that better represent the whole population are B and D. Why? Because they give us the possibility of taking a student of every grade. The other options, excluding the "bus option" and the first option, fail doing that. Finally, these options (bus option and lunch option) are related to the council president.

Answer:

90 degrees

Explanation:

Please note that whenever a triangle is inscribed in a circle and one side of the triangle is a diameter of the circle as in the given figure, then the angle that is opposite the diameter of the circle is a right angle;

In the table says that every letter that weighs less that 1 oz. have a price of 42, in the graphic we represented that in this part:

Following the data in the table as above we got the final graphic.

And for the question:

If you have a letter that weighs 1.7 oz. it will be more than 1 oz. but less than 2 oz. so you will pay 66, as we can see in the following graphic:

(a)

The class width of the histogram is given by the range of each bar in the histogram, that is, the upper limit minus the lower limit of a bar (plus 1, since we need to include the boundary values of the range).

Looking at the first bar, the upper limit is 19 and the lower limit is 11, therefore the class width is 9 (because there are 9 elements between 11 and 19, so we need to add 1 to the subtraction of 19 and 11)

(b)

The most frequent class is the third one (third vertical bar).

The frequency of this bar (that is, the value in the y-axis) is equal to 8.

Therefore 8 women are in this class.

(c)

The number of women with 28 or fewer blouses is given by the frequency of the first two bars.

Adding the frequency of the first bar (1) and the frequency of the second bar (5), we have that 6 women have 28 or fewer blouses.

The percent mark up on the cost is 30.26%.

JCPenney sells jeans for $49.50 that cost $38.00.

The percent mark up can be calculated as follows:

Mark up percentage is calculated by dividing the gross profit of a unit by the cost of that unit.

In other words, Mark-up percentage is the difference between a product's selling price and cost as a percentage of the cost.

Hence,

selling price = $49.50

cost price = $38.00

mark up = 49.50 - 38 = 11.5

Therefore,

percent mark up = 11.5 / 38 × 100

percent mark up = 1150 / 38

percent mark up = 30.2631578947

Therefore,

percent mark up = 30.26%

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we know that

The unit rate is equal to

1.2 oz per mile

so

To obtain the number of ounces

multiply the unit rate by the number of miles driven

1.2*(15)=18 oz

step 2

Convert ounces to cups

Remember that

1 oz=0.125 cups

so

18 oz=18*0.125=2.25 cups

therefo

We need find the tax on the first 7500

7500 * 10%

7500 * .10 = 750

Now we find the tax on what is over 7500

20000 -7500 =12500

The tax rate for this amount is 16%

12500 * 16%

12500 * .16

2000

Add the tax for both amounts together

750 + 2000

2750

The total tax paid is 2750

The solution is x = 2, y = -2 and z =0

The system of equations is given as

x – y - 3z = 4

2x + 3y – 3z = -2

x + 3y – 2z = -4

Start by eliminating y

To do that, we subtract (2) from (3)

x + 3y – 2z = -4 - (2x + 3y – 3z = -2)

This gives

-x + z = -2

Make x the subject in the above equation

x = z + 2

Substitute x = z + 2 in (1) and (2)

z + 2 – y - 3z = 4

z + 2 + 3y – 2z = -4

Solve the equations

-2z - y = 2

-z + 3y = -6

Multiply -z + 3y = -6 by 2

-2z + 6y = -12

Start by eliminating z

Subtract -2z + 6y = -12 from -2z - y = 2

7y = -14

Evaluate

y = -2

Substitute y = -2 in -z + 3y = -6

-z + 3(-2) = -6

Evaluate

-z - 6 = -6

Evaluate

z = 0

Recall that x – y - 3z = 4

So, we have

x + 2 - 3(0) = 4

Evaluate

x = 2

Hence, the values of the variables are x = 2, y = -2 and z =0

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The equation is modelled by the function,

c(x) = 2.1x^2 - 12.7x + 167.4

The general form of a quadratic equation is expressed as

ax^2 + bx + c

The given function is quadratic and the graph would be a parabola which opens upwards because the value of a is positive

Since x represents the speed, the speed at which the he

We are presented with a group of graphs in which the x-axis represents time and the y-axis represents speed.

We are told that Joy started by accelerating when she took off, which means the graph should start with a line with positive slope.

She then maintained her speed, which means the slope of the line is 0, orin other words, the line is parallel to the time axis.

Finally, we are told that she saw a sign saying the speed limit had been increased, so she probably accelerated again, meaning the line should have a positive slope again.

Thus, the graph representing the situation is the third option.

Answer:

W = A/L

Step-by-step explanation:

We are given the following formula:

A = LW

We want to solve for the width W. So

LW = A

L multiplies W, so it can go to the other side of the equality dividing. Then:

W = A/L

The three statements that are true include:

Amy's age is a factor of the age of her grandmother.

The age of Amy's grandmother is a composite number.

The number 6 is a factor if the age of Amy's grandmother.

A factor simply means a number that can be multiplied by another number to get the original number.

Let's say Amy is 10 years. The grandmother will be 69 years. In this case, 10 is a factor of 60. Therefore, Amy's age is a factor of the age of her grandmother.

The complete options are given below.

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Which three statements below must be true?

1.The age of Amy’s grandmother is a prime number.

2.Amy’s age is a factor of the age of her grandmother.

3.The age of Amy’s grandmother has exactly two factors.

4.The age of Amy’s grandmother is a composite number.

5.The number 6 is a factor of the age of Amy’s grandmother.

6.The age of Amy’s grandmother has exactly four factors.

Calculate:

The fractional exponent can be written as:

The square root of 81 is 9, thus:

All answers are kind of similar and none of these options are perfect.

We are going to chose the opcion b, the advantage is that the daily high temperature at cities give us a statistical sample about how latitude impact the temperature and how is the clime in those days.

Disadvantages is that we dont know the lower temperature and how the latitude impact in this case.

Let's begin by listing out the information given to us:

Line m is perpendicular to line P

Line P: (x, y) = (-4, -1), (1, 1)

We will proceed to calculate for the slope of the line P (as shown below):

Slope (m) = Δy/Δx

Slope (m) = (1 - - 1)/(1 - - 4) = 2/5

Slope (m) = 2/5

The slope of a parallel line is the negative reciprocal of the slope of the line.

Line m: slope (m) = -1/(2/5) = -5/2

Line m: slope (m) = -5/2

We calculate for the equation of the line using the point-slope equation. We have

y - y1 = m(x - x1) ⇒

(x1, y1) = (1, 1)

y - 1 = 2/5 (x - 1) ⇒ y - 1 = 2/5x - 2/5

y = 2/5x - 2/5 + 1

y = 2/5x + 3/5

We will proceed to put the value of the new slope into the equation. We have:

y = -5/2x + b ; (x, y) = (1, 1) ⇒ 1 = -5/2(1) + b

⇒ b = 5/2

Substitute the value of b into the point-slope equation, and we obtain the equation of line m. We have:

y = -5/2x + 5/2

By evaluating the equation in x = 2040, we can estimate the price to be $1507.7.

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Given that,

We know that the equation:

y = 1.83*x - 2225.5

Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.

We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.

if we use x = 2040

we will get

y = 1.83*2040 - 2225.5 = 1507.7

Hence, The price will be 1507.7, in dollars, of a game in the year 2040.

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We have the following:

We know that 100% is the value of the purchase of $ 75, therefore, if we add 5%, it would be 105%, that is equal to 1.05, so we multiply the value of 75 by 1.05, and we are left with the following

Total value is $78.75 and taxes are 3.75

Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.

Given,

The total number of students in a group = 23

Cost of ticket for member of planetarium's frequent visitor program = $11

Cost of ticket for the student who is not a member = $13

The total cost of the students ticket = $261

Lets take,

The number of students with membership = x

The number of students without membership = y

Total number of students, x + y = 23 -----------(1)

Now,

Total cost for the tickets, 11x + 13y = 261

Now, Multiply 13 with (1)

We get,

13x + 13y = 299

Solve for x

13x + 13y = 299 -

11x + 13y = 261

2x + 0 = 38

2x = 38

x = 38/2

x = 19

Now, put x in (1)

19 + y = 23

y = 23 - 19

y = 4

That is,

The number of students with membership is 19 and the number of students without membership is 4.

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Recall that the constant of variation of a straight line is the slope of the line.

To compute the slope we will use the following formula for the slope of a line:

Now, notice that points (-1,3) and (1,-3) are on the line, then substituting these points in the above formula we get:

Answer: -3.

ANSWER

Function f(t) represents a growth by 4%

EXPLANATION

If the function represents a decay it is written as:

and if it represents a growth it's:

We can see if it's a growth or decay by looking at the number we have between parenthesis: if it's greater than 1, then it's a growth and if it's less than 1 then it's a decay.

For function f(t) we have

Therefore, r = 0.04 which, expressed as a percent is 4%

Create a quadratic function in one of the forms and show how to convert it to the other two forms.

Step-by-step explanation:

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

The vertex of the parabola is written as (h, k) where b is the x - coordinate and c - is the y - coordinate

Work Shown:

P = 580

r = 0.135

t = 18 months = 18/12 = 1.5 years

A = P*(1+r*t)

A = 580*(1+0.135*1.5)

A = 697.45

SOLUTION:

Case: Outliers in a data set

Given: A set of numbers:

117, 211, 186, 176, 372, 7, 51, 229, 222, 83, 129, 142, 197, 102.

Required:

A) Identify the outliers

B) Mean with outliers

C) Median with outliers

D) Mode with outliers

E) Mean without outliers

F) Median without outliers

G) Mode without outliers

Final Answers

A) The outliers

First we arrange the data:

7, 51, 83, 102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372

Now we select the outliers

Because of the space in the data, the suspected outliers are:

7

because it is far from the central values

B)

The mean with outliers

C)

Median with outlier

Median = (142+176)/2

Median= 159

D) Mode with outlier

This data has no mode

E) Mean without outlier

51, 83,102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372

F) Median without outlier

Median = 176

G) Mode without outlier

The data has no mode

Answer

11) a > 3

12) b > (2/3)

Explanation

11) a - 15 > -4 (-6 + 3a)

a - 15 > 24 - 12a

a + 12a > 24 + 15

13a > 39

Divide both sides by 13

(13a/13) > (39/13)

a > 3

In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.

But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.

Then, the direction of the graph depends on the direction of the inequality sign, for example, the answer here says a is greater than 3. So, the graph will start with an unshaded circle and cover the numbers greater than 3.

12) 3 (6b - 2) > (8 - 3b)

18b - 6 > 8 - 3b

18b + 3b > 8 + 6

21b > 14

Divide both sides by 21

(21b/21) > (14/21)

b > (2/3)

This answer is similar to that of number 11. For the graph, it will start with an unshaded circle and move towards the numbers greater than (2/3)

Hope this Helps!!!

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A(2, 3), B(8, 7), C(6 1)

Step 02:

Line AB

Slope formula

m = (y2 - y1) / (x2 - x1)

A (2 , 3) x1 = 2 y1 = 3

B (8 , 7) x2 = 8 y2 = 7

Step 03:

Slope of the perpendicular line, m’

m' = -1 / m

Step 04:

Line CD

m' = (y2 - y1) / (x2 - x1)

C (6 , 1) x1 = 6 y1 = 1

D ( x2, y2) x2 = x2 y2 = y2

We must test the numerical values to verify equality,

x2 = 9

y2 = 3

x2 = 4

y2 = 4

1.19)

In general, the area of a rectangle is given by the formula

In our case,

The area of figure A is 16 square units, the area of B is 12 square units and the area of shape C is 12 square units.

As for the area of a rectangle, in general,

Then, in the case of each rectangle,

11.10)

Therefore, figures A and C have the same perimeter, whereas rectangles B and C have the same area.

Answer:

I may be wrong but I think it's D.

Step-by-step explanation:

I made an educated guess.

The amount compounded is given by the formula ;

Here, P = $3500, r = 1.75%, n = 52 , t = 18 years.

Therefore, the interest the account will earn is 4795.65-3500 = $1295.65, Option A