the amount of money a worker earns is directly proportional to the number of hours worked.at this rate.thag worker makes $104 in an 8 hour shift.weite a direct variation equation that relates the earnings (e) of the worker to the number of hours (n) worked. use the correct lowercase variables given ,and use no spaces

Kenyan = k

$3.50 per pound

Sri Lankan = s

$5.60 per pound

6lbs of blend

$28.35

s+k = 6

3.50k + 5.60s = 28.35

where:

k = lbs of kenyan

s = lbs of Sri Lankan

Solve the system

s+k = 6

3.50k + 5.60s = 28.35

solve the first equation for s:

s = 6-k

Replace in the second equation:

3.50k + 5.60 (6-k) = 28.35

3.50k + 5.60(6)+ 5.60(-k) = 28.35

3.50k + 33.6 - 5.60k = 28.35

3.50k - 5.60k = 28.35-33.6

-2.1k= -5.25

k= -5.25/-2.1

k= 2.5 lbs

Replace k on any equation and solve for s

s+k= 6

s+ 2.5 = 6

s= 6-2.5

s= 3.5 lbs

We are given coordinates of four points and we are asked to find the best selection of the shape.

In order to know what shape this is, we simply graph all the points and see what shape we get.

Using a graphing calculator, the points make up the following shape:

Now that we have the shape, we know that it can either be a Rectangle or a Square.

If the shape is a rectangle, the lengths x and y are not equal. If the shape is a square, lengths x and y are equal.

In order to find x and y, we use the distance formula given to us as:

Now let us find x and y.

x:

The points that make up the length x are:

(4, 0), and (4, -4)

Therefore, length x can be gotten as:

Now we find y.

y:

The points that make up the length y are:

(4, 0) and (8, 0)

Therefore, length y can be gotten as:

Answer:

Isosceles triangle

Explanation:

An isosceles triangle is one in which two side lengths are congruent while the third is not.

Looking at the triangle given we see that the two side lengths WY and WX are the same; therefore, the triangle is isosceles.

The slope is given by:

In thie case we have:

therefore the slope between this points is 1/5.

So,

Given a quadratic equation of the form:

There's some important facts we could use to determine which options are not correct.

First fact: the y - intercept of the graph is the number c. So, if our graph intercepts at y=1, that means that c=1.

For that reason, option A is not correct, because c=1.

Second fact: the sign of the number "a", will determine the concavity of the graph. This is, in other words:

That means that if "a" is positive, the graph will has the form of the left, and if "a" is negative, it will take the form of the right side.

Based in this, we can see that our graph has the form of the left side, so "a" has to be positive.

For that reason, options A and C are incorrect.

Now we should pick between B or D.

The third fact, is that, when the sign of "b" is negative, our graph seems to be moved to the right.

When the sign of b is positive, the graph seems to be moved to the left.

As you can see, our graph seems to be moved to the right, so the sign of b should be negative.

For these reasons, the appropiate answer is D.

Both numerator and denominator have 5 significant figures, then the quotient will have 5 significant figures too.

We have 4 x's and 2 "units" in the left side. We know that this is equal or equivalent to one X and 8 units, pictured in the right side.

So we can write the left side as: 4x+2

And the rigth side as: x+8

As both sides are equal, we can write:

The answer is Option D: 4x+2=x+8

Given:

The quotient of -4 and the sum of a and b.

Required:

To translate to an algebraic expression.

Explanation:

The sum of a and b is

The quotient of -4 and the sum of a and b is

Final Answer:

Answer:

C.

Explanation:

The number of minutes played by Carter is given below:

Hence, C is the correct option

We would like to find the equation of the line that passes through the point (1.2) and is perpendicular to the line y=-1/5 x +2, and write in slope intercept form. To do this first we have to remeber that the equation of a line is given by

and that to find it we need a point and the slope. In this case we have the point but we don't know the slope yet. To find the slope we notice that the line has to be perpendicular to the line y=-1/5 x +2. We need to remember that two lines are perpendicular if and only if

where m1 and m2 are the slopes of the lines.

The line y=-1/5 x +2 is wirtten in the slope-intercept form:

from this we notice that its slope is -1/5, then using the relation for perpendicular lines we have that

Solving for m we have that

So, our line passes through the point (1,2) and has an slope equal to 5. Plugging this values on the equation for a line we have

so the equation of the line we were looking for is y=5x-3. (Notice that it is already written in the adequate form).

We shall begin by plotting the graph of the equations given which are;

The black line shows the graph of y = [1/3]x + 6

The red line shows the graph of y = [-2/3]x + 3

The solution to these system of equations is at the point (-3, 5)

1)  3.2a , a  and 1 , 4 1/3 , 7 are the like terms in the expression.

2) 2.2a + 1.66 is the simplified linear expression

The greatest power of a variable in a linear equation is always equal to 1. A one-degree equation is another name for it. A linear equation with one variable is typically expressed as Ax + B = 0. Here, the variables x and A and B are constants and coefficients, respectively.

1 )  Merger of similar items 3.2a , a

and 1 , 4 1/3 , 7

2 ) 3.2 a -1 - 4 1/3 + 7 -a

= 3.2a - a - 1 - 4 1/3 + 7

= 2.2a + 6 - 13/3

= 2.2a + 6 - 4.34

= 2.2a + 1.66

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We have the following:

we have that the radius is half the diameter, therefore

replacing:

The surface area is 50*pi yd^2 or approximately 157 yd^2

Answer: 08

Step-by-step explanation:

If we raise a number to a power of 2, we can represent the result graphically as shown below (where n is the number to be raised to a power of 2)

This is a square of side equal to n.

Therefore, the answer is option C, squared.

Answer:

D

Step-by-step explanation:

We should use ratio.

AB is 5

DE is 10

AB/DE = 1/2

BC is 12 and EF is 24

BC/EF=1/2

AC is 13 and DF is 26

AC/DF= 1/2

So we can write the equation like D choice.

The total number of green fish are in the aquarium is 18.

T = Total fishes in aquarium.

G = Green fishes

Y = Yellow fishes

Thus, the linear equation for all fishes are-

T = G + Y   ...eq 1

The aquarium has 6 fewer yellow fish than green fish.

G = Y+6   Put in eq 1

T = (Y+6) + Y  

T = 2Y+6

40% of the fish are yellow = 0.4.

Y = 0.4×T  

T = 2×(0.4×T) + 6  

Solve for total fishes

T = 0.8T + 6

0.2T = 6

T = 30

Solve for Green fishes.

G = 0.6×T   (given)

G = 18

Thus, the number of green fish are in the aquarium is 18.

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With the first term being 28 and the difference being 2, this geometric progression is finite because 28 is divided by 14 and then that number is divided by 2 and so on.

What is geometric progression?

A mathematical sequence known as a geometric progression (GP) is one in which each succeeding term is generated by multiplying each preceding term by a fixed number, or "common ratio." This progression is also referred to as a pattern-following geometric sequence of numbers. A geometric progression is a series in which each term can be obtained by multiplying or dividing the term before it by a predetermined amount. Infinite GP sum refers to the total number of terms in an infinite GP. S_ = a/(1 - r), where an is the first term and r is the common ratio, is the formula for calculating the sum of an infinite geometric progression.

Here,

This is geometric progression with first term 28 and difference 2 and this is finite GP as 28 is divided by 14 then 14 is divided by 2 so on as the definition of GP says, "a series of numbers with a fixed ratio between each and the previous one (e.g., each subsequent number is increased by a factor of 3 in the progression 1, 3, 9, 27, 81 )".

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Answer

Answer = 1000

Explanation

A power of 10 would be a number that can result from multiplying 10 by itself a number of times.

And from the options, we can see that only

1000 = 10 × 10 × 10

Hope this Helps!!!

ANSWER :

The values of x are -8 and 8

EXPLANATION :

From the problem, we have the equation :

Add 47 to both sides :

Take the square root of both sides :

Note that in the picture we are asked about the angles QRW and RWQ. This two angles are part of the the same triangle. So we can ignore the rest of the image and focus only on the triangle that contains both. We have the following

Using this information, we can see that the measure of the three sides of the triangle are different. This means that the triangle is a scalene triangle. This type of triangles have the property that the measure of each angle is different from the other. So, we know that the measure of angles QRW and RWQ are different.

To dig deeper in the problem, we will use the sines law for triangle, which states the following. If we have a triangle of the form

Then, we have the following

In this case, we have c=45 and a=47, so we have

where A is the angle RWQ and C is the angle QRW, if we multiply both sides by 45, we get

In this case, we have that 45/47 < 1. Since angles A and C are less than 180° degrees, the sine of this angles is a positive number, so we have that

Note also that angles A and C should have a measure less than 90°. Over this interval, the sine function is an increasing function, which means that if sin(C)So we have that the measure of angle QRW is less than the measure of angle RWQ.

Supplementary angles are angles that add up to 180 degrees.

To find the supplementary angle to ∠EOD, we find the angle with ∠EOD that makes up a straight line.

Looking at the figure, EC is a straight line and both ∠EOD and ∠DOC fall on this line. These two angles make up 180 degrees.

Thus,

The one supplementary angle to ∠EOD is ∠DOC.

Answer:

Explanation:

The equation o

Two events are independent when one of the events happen and the result does not affect on the result for the second event.

In this case if we have multiple-choice answers on the test the probability of having the correct answer for both of them is the same, however if we get the first one correct it does not mean that we will have the second answer correct.

For this reason the events are independent.

Explanation:

Given the universal set, U and subsets A and B as follows:

• U={a,b,c,d,e,f,g}

• A={b,d,f,g}

• B={b}

Answer:

The Venn diagram representing the sets is given below:

Note:

• The ,letter b is common to both A and B,, so we put it in the intersection of both sets.

• The ,letters a, c, and e do not belong to either A or B,, so we place it outside of the two sets.

The function is:

This means that the output of the function is equal to the input. So when the inputs are 1,7,-3 and -5. The outputs will also be 1, 7, -3 and -5.

You know that "P" represents her total pay (in dollars) and "N" represents the number of copies of English is Fun Jane sales.

According to the information given in the exercise, Jane makes $110 for every copy of English is Fun, then you can set up the following expression for this:

Knowing that her base salary is $1500, you can conclude that her total pay "P" will be the sum of her base salary and the amount of money she makes for every copy she sells. Based on this, you can write the following equation relateion "P" to "N":

If Jane sales 29 copies of English is Fun, then:

Substituting this value into the equation and evaluating, you get:

The answers

- Equation:

- Solution:

Her total pay if she sells 29 copies of English is Fun, is $4690

The equation for the cost y birr in terms of the distance X driven is y = 20 + 2x.

When the car is leased for 5 days, the cost is 100 + 2x.

From the information, the car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km.

The equation for the distance x will be:

= 20 + (2 × x)

= 20 + 2x.

When the car is leased for 5 days, this will be:

= 5(20) + 2x.

= 100 + 2x

= 100 + 2x

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The area of a circle is given by:

Since it is a quarter of the circle, the area is: