a. What is KL? __. b. What is the coordinate of the midpoint of KL? __?c. Point C lies between points K and L. The distance between points K and C is __ of KL. What is the coordinate of point C? __.

Given that the triangles are corresponding triangles, then ∠B ≅ ∠E, therefore:

m∠B = m∠E

Replacing with data:

3v + 4 = 8v - 6

3v is adding on the left, then it will subtract on the right

6 is subtracting on the right, then it will add on the left

4 + 6 = 8v - 3v

10 = 5v

5 is multiplying on the right, then it will divide on the left

10/5 = v

2 = v

Then, the measure of B is:

m∠B = 3v + 4 = 3(2) + 4 = 10°

The measure of angle B is 10°

Note that the graph shows us that the minimum and maximum value of the ages are 40 and 75, respectively.

We can count the number of bars on the histogram. We see that the are 7 bars in total.

Each bar consider the same age span, so that means that each bar represent an age span of the same amount of years.

To calculate this range, we first find the difference between the maximum and the minimum, that is

Now, we divide this number by the total number of bars. That is

So, each bar represents a range of 5 years .

Since the minimu is 40, this means that the first bar should represent ages from 40-44. Note that despite the difference between 44 and 40 is only 4, since we are including age 40 in the first bar, we have numbers 40,41,42,43,44 (5 numbers ) associated to the first bar.

This means that for the next one, which is the range T we are looking for, the correspondent age range should be 45-49

Width = 4x + 7

The perimeter of the rectangle shown = 16x + 6

The width of the rectangle = 4x - 4

Perimeter of a rectangle = 2(Length + Width )

16x + 6 = 2[ (4x - 4) x Width]

(16x + 6)/2 = (4x - 4) x width

8x + 3 = (4x - 4) x width

Width = 8x + 3 - (4x - 4)

Width = 8x - 4x + 3 + 4

Width = 4x + 7

An arithmetic sequence has the form:

where d is the common difference.

For this sequence the common difference is 3 and the first term is:

Plugging this values in the general expression we have:

Therefore the sequence is:

Now, from this expression we can determine the value of the zeroth term:

Hence the zeroth term is:

Let p be: John goes to the beach

Let q be: He will go surfing.

Then in symbolic form, the argument becomes:

p ⇒ q

p

---------------------

∴ q

An argument is valid if the conjuction of the premises implies the conclusion.

p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q

---------------------------------------------------------------------\

F | F | T | F | T

F | T | T | F | T

T | F | F | F | T

T | T | T | T | T

The table above shows that the argument is a tautology.

Hence, the argument is valid

Answer:

79.10900 kilometers

Step-by-step explanation:

Answer:

79 kilometers 109 meters

Given the quadratic equation:

To find the solutions for the given equation you have to apply the quadratic formula:

Where

a is the coefficient of the quadratic term

b is the coefficient of the x-term

c is the constant of the equation

For this equation, a= 16, b= -24, and c= -27, replace the values into the formula:

Solve the addition and subtraction separately to determine both possible values of x:

-Addition:

-Subtraction

The solutions of the quadratic equation are x=9/4 and x=-3/4

Ok, the number of different permutations are:

8!/3! (Considering the three O's)

To find the missing angle we use that the sum of the inner angles of a triangle must add up 180º:

We know W and V, so we clear X:

To order the sides, you don't need the size of them. Let's take a look at the angles:

So, since the angle with vertex on W is the widest, the opposite side to it (the segment XV) will be the longest. Then, the second angle is the one in X, so the second largest side will be it's opposite side (segment WV).

And finally but not last, the shortest side will be the oposite one to the narrowest angle, the one in V.

In summary, the sides ordered from shortest to longest are: c-a-b

the interval notation is [-7,8] but i have no idea what roster notation is

Since the segment MN is the diameter of the circle, the arc MACN has an angle with a measure of 180°, Then by adding the measures of the angles of the arcs MA, AC and CN we should get 180°, like this:

mMA + mAC + mCN = 180

By replacing 55° for mMA and 65° for mCN, we can solve for mAC to get:

55 + mAC + 65 = 180

120 + mAC = 180

120 - 120 + mAC = 180 - 120

mAC = 60

The measure of the arc ACN is calculated by adding the measures of the angles AC and CN, then we get:

mACN = mAC + mCN

mAC = 60 + 65

mAC = 125

Then, the angle of ACN has a measure of 125°

The capacity of the mug is 7/6 cups.

Given,

A mug is 3/7 full.

The mug contains 1/2 of a cup of water.

Solution:

Let x be the water.

Water the mug has = 3/7 of x

= 3/7x

Since the water in the mug is 1/2 cup,

3/7x = 1/2

x = 1/2 ÷ 3/7

= 1/2 × 7/3

= 7/6

Therefore,

The capacity of the mug is 7/6 cups.

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We will solve the following:

***Explanation***

We will have that in order to expand a polynomial of the form:

We will proceed by using the following rule:

In our case the solution for the given polynomial is [Step by step]:

The formula for calculating the percent change over time is:

In this case, we have:

The value of the house when purchased is 250,000.

I'm not sure the right equation that we need to used for this problem.

The solution is, :

8x  = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

David buys milk and lemons at the store.

. He pays a total of $40.01.

• He pays $2.89 for the milk.

• He buys 8 bags of lemons that each cost the same amount.

Cost of 1 bag of lemons = $ x

Cost of 8 bags of lemons = 8 *x = 8x

Cost of 8 bags of lemons = Total cost - cost of the eggs

                             8x           = $40.01 - $2.89

so, 8x  = 40.01 -2.89, is the equation.

Hence, The solution is, :

8x  = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.

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The equation that represents the total distance the bird travels would be; d =  1/3.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Given that bird flies downward 2 feet per second for 6 seconds. Therefore, the bird flies up 7 feet.

Since, a bird flies 2 feet = 1 second

Thus, for 6 seconds = 6 x 2 = 12 feet.

for 6 seconds  = 12 feet.

Similarly, the bird flies up 7 feet = 6/12 x 7

= 42/12 = 3.5

Hence, the equation that represents the total distance the bird travels would be; d = 2/6 = 1/3.

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To graph the system

y ≤ 2x + 1

y < -x - 1

first, you have to graph the lines

y = 2x + 1

y = -x - 1

From the y-intercept and the slope, we know that the first line passes through the points:

(0, 1)

(0+1, 1+2) = (1, 3)

From the y-intercept and the slope, we know that the second line passes through the points:

(0, -1)

(0+1, -1-1) = (1, -2)

Next, we have to find if a point satisfies each equation or not, in order to know which region we have to shade. Taking for example the point (0, 0) and replacing it into the first inequality,

0 ≤ 2(0) + 1

0 ≤ 1

which is true, then we have to shade the region below the line y = 2x + 1

Replacing (0, 0) into the second inequality,

0 < -0 - 1

0 < -1

which is false, then we have to shade the region below the dotted line y = -x - 1

The final result is shown in the next picture.

This corresponds to graph X

Systems of Equations

Given the system:

It's required to graph and find the solutions of the system.

Solving the first equation for y:

We can see both equations are exactly the same, so there is only one equation and one line.

Let's give x some values and graph the line.

x = 0:

x = 2

With the points (0, 2) and (2, 1) we graph the line as follows.

Since the number of equations is greater than the number of unknowns, the system has infinitely many solutions. For example, (0, 2) and (2, 1) are solutions for the system.

Let the formula be for time in seconds

Thus, we have:

T_a would be the freezer temperature, 4

T_0 would be the initial temp, which is 73

t is the time [9 minutes afterwards, t = 9]

k is 0.05

Substituting, we get:

To nearest degree Fahrenheight, T = 48 degrees F

Answer: 47 degrees celcius

Step-by-step explanation:

Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.

What is an equation graph?

Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.

example y = 1-1/3x,

x = -3,0,3,6

solution:

given x = -3,0,3,6 to above equation of a graph to get the points

         y = 2,0,0,-1

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The value of X is ([tex](A-CB)^{-1}[/tex] CD.

Given,

AX[tex](D+BX)^{-1}[/tex] = C

Multiply both sides on the right by (D+BX):

AX[tex](D+BX)^{-1}[/tex] × (D+BX) = C × (D+BX)

AX ([tex](D+BX)^{-1}[/tex] (D+BX)) = C(D+BX)

AX × I = CD + CBX

AX = CD + CBX

Subtract CBX on both sides and factor:

AX – CBX = (CD + CBX) – CBX

AX – CBX = CD + (CBX – CBX)

AX – CBX = CD + 0

(A – CB)X = CD.

Multiply both sides on the left by [tex](A-CB)^{-1}[/tex] :

([tex](A-CB)^{-1}[/tex] × (A – CB)X = ([tex](A-CB)^{-1}[/tex]  × CD

([tex](A-CB)^{-1}[/tex] × (A – CB)) X = ([tex](A-CB)^{-1}[/tex]  CD

IX = ([tex](A-CB)^{-1}[/tex] CD

X = ([tex](A-CB)^{-1}[/tex] CD.

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Using a system of equations, it is found that:

1.

2. Tables are good for summarized data, that is, containing a few pairs of input - outputs solutions.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

In the context of this problem, the variables are given as follows:

Considering that they want to raise $100, and the prices of $4 for each chocolate chip and of $2 for each brownie, the equation is:

4x + 2y = 100.

In intercept form, the equation is given by:

2y = 100 - 4x

y = -2x + 50.

When x = 10, the solution of the system for y is given as follows:

y = -2(10) + 50 = -20 + 50 = 30.

Hence one possible solution is (x,y) = (10,30), meaning that she can sell 10 chocolate chips and 30 brownies.

In this question, we are given pairs of input-output that satisfy the given condition, hence tables are more appropriate than graphs.

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Answer:

1. 100=4x+2y and y = -2x+50

X=19, and Y=12

2. Graphs are better for showing trends. tables are better for showing precise data.

Step-by-step explanation:

Luna makes $4 per cookie, so her equation for her income is 4x. Miles makes $2 per cookie, so his equation is 2y. Since they want to make $100, that means that 100 = 4x+2y. Then put this in y-inercept form. Or, y=-2x+50

So now I need to find a solution for y = -2x+50, or 100=4x+2y. One way to do this is through substitution. We can use 12 as the y input.

​

This would mean that miles sold 12 brownies.  Then,  ---> = 19.

​

Therefore, a solution is x=19 and y=12. Meaning Luna sold 19 cookies and Miles sold 12 cookies. (19,12)

We have the following data set

17482

14987

13521

14550

18570

14981

there are 6 values, so we can find the mean by adding them all and dividing by 6

Then, the mean is $15,681.83

SOLUTION

We want to find the unit rate for number of cookies per dollar. This can be done using the diagram below

So the unit rate is calculated thus

Hence the answer is 2

Answer:

Step-by-step explanation:

The least common multiple of the denominators 5 and 7 is 35. Make the denominators of the fractions as 35 using multiplication. Compare the numerators. So, 3 : 5 is greater than 4 : 7.

Hope this helps!

The area of the figure = Area of the Triangle + Area of the semi-circle

Area of the Triangle = 1/2 x b x h

Base = 6 feet

Height = 8 feet

Area of the Triangle = 1/2 x 6 x 8 = 48/2 = 24 feet^2

Area of the circle = pi x r ^2 radius = 8/2 = 4 ft

= 3.14 x 4 x 4

= 50.24 feet^2

Total area = 24 + 50.24 = 74. 24 feet ^2

EXPLANATION:

We are given the unit cost to produce x number of airplanes as follows;

However, to minimize the unit cost, we need to first take the derivative of the cost function and then find its value at zero.

Thuis is shown below;

Note that for a derivative, the constant term is always equal to zero. We can now simplify what we have above;

We now set this equal to zero and simplify;

Add 150 to both sides;

ANSWER:

Therefore, to minimize the unit cost, 150 engines must be made.

The marks on the test tube where the liquid will be after the sixth drop is added is d. 4/5 and 5/5, between 0.8 and 1 ml.

From the information, the scientist adds drops of liquid to a test tube. The test tube has marks every 1/5 ml while each drop contains 0.14 mL.

In this case, it was stated that each drop is about 0.14mL. Therefore, it's important to note that the value of the 6th drop will be:

= Number of drops × Amount on each drop

= 6 × 0.14

= 0.84

In this case, 0.84 is between 0.8 and 1ml.

Therefore, the correct option is D.

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Given

Round to the nearest tenth, this is:

Answer: 1.5

The given experiment is a die that is tossed three times.

X is the sum of the three numbers obtained.

You need to determine if the random X variable has a binomial distribution.

First, we need to understand what makes a random variable has a binomial distribution. There are 4 conditions to be met:

1. There are a fixed number of trials N

2. Each trial has only two possible outcomes: success or failure

3. The probability of success is equal in each trial

4. The trials are independent.

In this case, condition 1 is met, but condition 2 is not met, since in each trial we can obtain 6 different numbers, then there are not only two possible outcomes, but 6, then the sum of the three numbers has more than two possible outcomes. So, the random X variable doesn't have a binomial distribution.