Consider the figure. If <7 and <11 are supplementary then lines

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠D +  m∠E +  m∠F = 180°

(3x + 27) + (4x + 22) + 68 = 180

7x + 49 + 68 = 180

7x = 63

x = 9

So,  m∠D = (3(9) + 27)° = 54°.

The exterior angle of D = 180- 54 = 126°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".

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Given:

1 yard = 3 feet

1 meter = 100 cm

Nicholas walked 20 yards to get his mail.

Here, we are required to convert 20 yards to meters.

Where,

1 yard = 0.9144 meter

20 yards = x meters

thus, we have:

Therefore, Nicholas walked 18.29 meters to get to his mail.

ANSWER:

18.29 meters

Step-by-step explanation:

Givens.

• The amount borrowed was $100,000.

• The time elapsed is 9 months.

• The annual interest rate of 4%.

The simple interest formula is

Where P = 100,000, R = 0.04, and T = 9/12.

the answer would be 3,000

The relation between the function is X cannot repeat itself.

We have given that,

functions table

We have to determine which relation is a function.

What is the function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

The relation between the function is

X cannot repeat itself

Therefore option C is correct.

Complete question: Determine which of the following relations is a function [see in attachment]

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Given the following function:

notice that the transformation:

can be written like this:

first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.

Correct deduction for social security Medicare and fit at 6.3% = 8,996.967

Correct deduction for Medicare at rate of 1.45% = 2,070.731

Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.

After deductions the total earning = 140,460

The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;

= 6.3/100 × 142,809

= 899696.7/100

= 8,996.967

The correct deduction for Medicare at the rate of 1.45%;

= 1.45/100 × 142,809

= 207,073.05/100

= 2,070.731.

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Answer:

286

Step-by-step explanation:

there are 365 in a year

365-79

286

m(4) = 110° due to the Transitive Property.

The Transitive Property states a that if a = b and b = c, then a = c.

m(3) + m(4) = 180 due to the definition of Supplementary Angles. All supplementary angles add up to 180°.

m(3) = 70° because 180 - 110 = 70.

ANSWER:

B.

STEP-BY-STEP EXPLANATION:

A parent function is the simplest formula in which no transformations have been made. Therefore, the function that would be the parent one of the answer options is:

Given: An equation where

To Determine: the nature of the solution of the equation

Solution

Nature of solution: The example below relates to the nature of solution

Hence, the equation has no solution

To know the length of the railing from point A to point B you can use Pythagoras Theorem.

You draw a right triangle:

You use the given information to know the measure of the legs in the triangle:

You can see that the value of x is the height of 5 steps: 5(7.5 in).

Then:

The B is equal to the lenght of 10 steps: 10(9.5in):

Then:

You have the next triangle:

You use the Pythagoras Theorem to find the h:

We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.

9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.

We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.

We can think of it of a combinatorial problem.

In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.

Repetition is not allowed: a kitten selected can not be selected again.

We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:

The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.

Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).

We can calculate this as:

We can now calculate the probability as the ratio of combinations 1890/5005:

Answer: the probability is 0.378.

In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).

The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.

Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.

Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.

Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.

You follow a similar step for every one of the other coordinates, which are;

Please note that I've just attached the same graph, but this time I've labelled the points one by one.

This should help with reading the coordinates at every point.

The graph that represents the solution to the system of inequalities is given in the attachment below.

To find the correct graph that represents the solution to the system of inequalities, determine which inequality represents each of the line that is plotted on the graph.

The first inequality, y < -3x - 2, has a slope of -3, a y-intercept of -2, and an inequality sign "<" which means the shaded part will be below the a dotted or dashed boundary line.

The second inequality, y ≤ x − 2, has a slope of 1, a y-intercept of -2, and an inequality sign "≤" which means the shaded region is below a solid boundary line.

The graph that represents the above stated features is the graph of the system of inequalities shown below.

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Answer:

f(x) = -∞ as x → ±∞

Explanation:

The given function is

f(x) = -x² - 4

To know the end behavior, let's replace x by a greater number and by a smaller number, so

If x = 100

f(x) = -100² - 4

f(x) = -10000 - 4

f(x) = -10004

If x = -100

f(x) = -(-100)² - 4

f(x) = -10000 - 4

f(x) = -10004

So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is

f(x) = -∞ as x → ±∞

Answer:

Easy;

Substitute m (miles) for 45.

250+6(45)

(6 dollars per mile, times 45 miles, plus the 250 flat rate)

250+270

520

So you would be charged 520 dollars total at the end of the evening.

Hope this helped!

Answer:

520

Step-by-step explanation:

so first you would multiply 6 by 45 which is 270 then add 250 which is 520

hope this helped, have a great day

The angles ∠IDA, ∠YDA, and ∠RDI measures 121°, 59°, and 29.5°.

The angle ∠YDF is equal to 121°. The ∠IDA is vertically opposite angle. So, ∠ADI is equal to the ∠YDF. Hence, ∠IDA = 121°.

The angle ∠YDA and the angle ∠ADI form a linear pair. It means ∠YDA and ∠ADI are complimentary angles.

∠YDA + ∠ADI = 180°

∠YDA + 121° = 180°

∠YDA = 180° - 121°

∠YDA = 59°

The ∠FDI is vertically opposite angle to ∠YDA. So, ∠FDI is equal to the ∠YDA. Hence, ∠FDI = 59°. The ray DR bisects the ∠FDI. So, the angle ∠RDI is half of the angle ∠FDI.

∠RDI = (1/2)∠FDI

∠RDI = (1/2)59

∠RDI = 29.5°

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The expression in the simplest form is -9x/10 + (5).

Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an expression / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.

We can —

For the given equation;

= (-3x/5 - 7) - (-12 + 3x/10)

open the parenthesis;

= -3x/5 - 7 + 12 - 3x/10

Bring the variable part together.

= -3x/5 - 3x/10 - 7 + 12

Add variables and constant separately.

= -9x/10 + 5

Thus, the simplest form of the given expression is found as  -9x/10 + 5.

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Answer:

4x + 3

Step-by-step explanation:

Three more means you're adding three to the number. So, you have + 3 right now. Four times the number of shells Talia collects is 4x with x representing Talia's shells. We don't know how many she has so it's represented by x. Now, put everything we have together. 4x + 3.

Hope this helps! :)

Statement Problem: The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.

Find the length of the third side c.

Solution:

Thus, the perimeter of a triangle with lengths a, b and c is;

Thus, we have;

Thus, the length of the third side is 7inches

The total number of people that drove to the meeting is 240

80% drove to the meeting

Let the total number of people who attended the meeting be x

Using the percentage and whole relationship

Part = percentage x whole

whole = x

part = 240

percentage = 80%

240 = 80/100 * x

240 = 0.8x

Divide both sides by 0.8

240/0.8 = 0.8x/0.8

x = 300

The total number of people that attended the meeting is 300

The equation that represents the total cost is C = $400 + $125p .

The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.

Total cost = fixed cost + total variable cost

Total cost = fixed cost + (variable cost x total output)

C = $400 + ($125 x p)

C = $400 + $125p

Total cost when 0 phones are made =  $400 + $125(0) = $400

Total cost when 1 phone are made =  $400 + $125(1) = $525

Total cost when 2 phones are made =  $400 + $125(2) = $650

Total cost when 3 phones are made =  $400 + $125(3) = $775

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Based on the number of jumping jacks that Robbie can do in 60 seconds, the number of seconds it will take to do 14 jumping jacks is 24 seconds

To find the number of seconds that it takes Robbie to do 14 jumping jacks, find the number of seconds it takes to do a single jumping jack.

The number of seconds to do a single jumping jack is:

= 60 / 35

= 1.71 seconds

If 14 jumping jacks are to be done then the number of seconds would be:

= 1.71 x 14

= 24 seconds

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The equation of the line perpendicular to the given equation is;

Option C is the correct answer

Here, we want to select which of the equations in the option is perpendicular to the given equation

Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1

Before we proceed to compare, we need to write the equation in the general form

The equation of the line written in the general form will be;

where m represents the slope and the term b represents the y-intercept

Now, let us proceed to write the equation in the standard form;

We have this as;

Compared with the general form, we can see that the slope of this line is -2/3

Now let us get the slope of the line that would be perpendicular to it;

Now, the equation perpendicular to what was given will have a slope of 3/2

Fortunately, all the options in the question have been written in the general form

The one with a slope of 3/2 is option C

Answer:

B

Step-by-step :

The quotient is 6.5 so the estimate is closest to 6.

Given the relation:

The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is: