Gor trapezoid HJKL, T and S are midpoint of the legs. If HJ = 14 and LK = 42, find TS.

SOLUTION

We want to find the magnitude of the vector (-3, 4)

Magnitude of a vector is given as

Hence the answer is 5 units, the last option

1) Considering that, let's find each term:

2) So the sequence is

As each term, from the 2nd one is 4 units more that's why we can make it using a recursive formula

Beginning inventory = 16,000 Purchase = 115,000 Sales = 140,000 Mark up = 25% on cost Undamanged inventory = 2,000

The value of the inventory lost in fire is 2,000

How do you take inventory loss due to fire into account?

The cost of products available for sale is then subtracted from the cost of goods sold. The quantity will reflect how much inventory the fire has actually destroyed. As an illustration, $275,000 minus $80,000 = $195,000, which represents the amount of inventory destroyed in the fire.

Calculate the quantity of inventory destroyed by deducting the cost of sold goods from the cost of goods that are still in stock. In this scenario, the amount of merchandise lost in the fire was $275,000 less $70,000, or $205,000.

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Explanation

Step 1

Let the vertices

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed)

then, apply the rule to find the new coordinates

I hope this helps you

This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.

To simplify this fraction, we will have to find the common factors of both the numerator and denominator, then divide.

Common factors of 30 and 36 are: 2, 3, and 6

Now both numerator and denominator by the highest common factor which is 6:

After simplifying the fraction, we have:

a. probability of drawing a red ace (first draw)

In a standard deck, there are 52 cards. Out of these 52 cards, two are red aces. Hence, the probability of drawing a red ace is 2/52 or 1/26.

b. probability of drawing a spade (second draw)

On the second draw, 51 cards are left. Assuming that a red ace was taken on the first draw, 13 spades are left on the deck. Hence, the probability of drawing a spade is 13/51.

So, to get the probability of drawing a red ace AND a spade, simply multiply the two probabilities above.

Then, reduce 13/1326 into its simplest form by dividing both numerator and denominator by 13.

Hence, the probability of drawing a red ace AND a spade is 1/102. (Option A)

an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4

What is vertical stretch/vertical compression ?

• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.

• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.

The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.

The function g(x) is defined as |x|.

To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.

g(x) = f(x)/3

f(x) is equal to (|x|)/4.

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Answer: x[tex]\leq[/tex]18

Given:

-36m + 16

To factor out the common factor, let's find the Greatest Common Factor (GCF) of both values.

GCF of -36 and 16 = -4

Factor out -4 out of -36 and 16:

Factor out -4 out of [-4(9m) - 4(-4)] :

ANSWER:

Given:

The given numbers are 5,6,7,8,9.

Required:

Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.

Explanation:

Let n is the total number then the way to write m digits number is given by the formula:

So the way to write 3 digits numbers are:

Final Answer:

Option D is the correct answer.

The line passes through the points given.

Select any two points from the table, (-4,2) and (-3,5).

The slope is given by:

Hence the slope is:

The slope is 3.

Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.

What is Addition?

The sum of all the numbers are called the Addition of numbers.

Given that;

Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.

And, The table shows how much data Gordon uses each week before his next billing cycle as;

WEEK =               1     2    3    4

DATA USAGE = 0.8  1.3  0.9  1.1

Now,

Since, Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.

And, The table shows how much data Gordon uses each week before his next billing cycle.

So, We can add all the given data usage in 1 to 4 week as;

Data usage = 0.8 + 1.3 + 0.9 + 1.1

                  = 4.1 GB

Thus, Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.

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Given data:

Gracie has 5 more than times mary have G=5+a(x).

Nancy has 1 ore than ties mary have N=1+b(x)

Given that G=N

5+ax=1+bx

4=x(b-a)

We will have the following:

[Third option]

Answer:

Over 98 years, London scored 75.14% per season between 254 and 338 points.

Step-by-step explanation:

Given a quadratic equation in standard form

The discriminant D

tells the types of roots the equation has.

In this case, we have

Then, the discriminant of this quadratic equation will be

Finally, the value of discriminat is 49 and as he discriminant is greater than zero then this quadratic equation has 2 different real solutions.

Answer:

The radius = 12 inches.​

Explanation:

Given a sphere with radius, r units:

If the volume of a sphere is 2304π in³, then:

We solve the equation for r:

Next. take cube roots of both sides.

The radius of the sphere is 12 inches.​

The triangle formed is shown in the diagram below

The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as

Tan# = opposite side/adjacent side

opposite side = 150

adjacent side = 40

Tan x = 150/40 = 3.75

x = Tan^-1(3.75)

x = 75.069

To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees

H = height in cm

M = months

The plant is already 44 cm tall

GRowth every month = 1 cm

Equation:

H (m) = 44 + m

The height after m months, will be equal to the initial height (44) plus the number of months.

For 32 months, replace m by 32 and solve:

H (32) = 44+32

H (32) = 76 cm

After 32 months, the plant will be 76 cm tall

Step 1: Write out the equation.

Step 2: Divide both sides of the equation by 5Q, we have

this implies that

We want to find the measure of the angles 1 to 8, given that the diameter is AC and the measure of the Arc BC is 74°.

The angle 5, ∡BOC is central and it is equal to the measure of the arc it intercepts, the arc BC. Thus the angle 5 is 74°.

The angle 4, ∡AOB also is central, and it is equal to the measure of the arc AB. As the line AC is the diameter of the circle O, the arc AC is equal to 180°, and thus, the sum of the angles 4 and 5 will be 180°:

Thus, the angle 4 is 106°.

The angle 6 is an inscribed angle, and thus it is half of the arc it intersects, the arc AB. This means that the angle 6 is 106°/2=54°.

The angle 2 also is an inscribed angle, half of the arc BC, and thus, the angle 2 is 74°/2=37°.

Now, the triangle BOC has the angles 5, 6 and 7, and the sum of those angles is 180°. This means that:

Thus, the angle 7 is 52°.

Following a same argument, we can get the angle 8, as being part of the triangle AOB.

This means that the angle 8 is 37°.

As the line AD is tangent to the circle O, this means that the lines AC and AD are perpendicular, and thus, the angle 1 is 90°.

Lastly, as the angles 1, 2 and 3 are coplanar, their sum is 180°. This is:

Thus, the angle 3 is 53°.

Solution:

Given the inequality:

To solve the inequality,

step 1: Add -3 to both sides of the inequality.

Thus,

Step 2: Apply the absolute rule.

According to the absolute rule:

Thus, from step 1, we have

This implies that

Hence, in interval notation, we have:

Accoring to the given figures, the pentagon is the one without parallel sides.

When Hector opens up the refrigerator he finds the next :

He drinks 2/5 of the milk he found, then he drank:

And he left in the bottle of milk:

And after that Kevin open up the refrigerator and finds the next:

Kevin drinks 1/3 of what is left, then he drinks:

And then he left:

And the milk he left in the bottle is:

Th formula for the area of the triangle is as follows.

where b is the base of the triangle and h is its height.

Substitute the given values into the formula and then simplify.

Therefore, the area of the triangle is 30 square feet, which is option B.

We are asked to find which of the measurements form a right triangle.

A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.

The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:

Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.

We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.

Option A. 7in, 24in, and 25 in.

We define:

And apply the Pythagorean theorem:

And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.

-Solving for c:

Taking the square root of both sides we find c:

Since we get the third measure as the value of c option A is a right triangle.

Option B. 18ft, 23ft, and 29 ft.

we do the same as did with option A. First, define a and b:

Apply the Pythagorean theorem:

And solve for c:

We get 29.2 instead of just 29, thus option B is NOT a right triangle.

Option C. 10in, 24in, and 26 in.

Define a and b:

Apply the Pythagorean theorem:

Solve for c:

We get 26 which is the third measure given, thus, option C is a right triangle.

Option D. 10yd, 15yd, and 20yd.

Define a and b:

Apply the Pythagorean theorem:

We don't get 20yd as the value of c, thus, option D is NOT a right triangle.

Option E. 15mm, 18mm, and 24 mm

Define a and b:

Apply the Pythagorean theorem

We don't get 24 as the value of c, thus, option E is Not a right triangle.

Answer:

Option A and Option C are right triangles.

To solve this problem, first, let's remember the definitions of even and odd functions.

• A function f is ,even, if the graph of f is ,symmetric about the y-axis,.

• A function f is ,odd, if the graph of f is ,symmetric about the origin.

a) To make the function even, we must complete the graph such the graph result is symmetric about the y-axis (the vertical axis). Doing that we get:

b) To make the function odd, we must complete the graph such the graph result is symmetric about the origin (the horizontal axis). Doing that we get: