In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x?

Using a trigonometric realtion, we can see that x = 23.18cm

Here we have a right triangle, we can see that y = 6cm, and the angle theta is 15°.

Notice that y is the opposite cathetus to the known angle, and we want to find the value of x, which is the hypotenuse.

Then we can use the trigonometric relation:

sin(a) = (opposite cathetus)/hypotenuse.

Reaplacing what we know, we will get:

sin(15°) = 6cm/x

Solving that for x:

x = 6cm/sin(15°9

x = 23.18cm

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The answer for the given equation in decimal is -2.357.

An equation is a mathematical expression in terms of one or more unknown variable.

Given the equation : 2 +2/3x =3/7

Simplify by Cross multiplication, we get

6 +2x = 9/7

Simplifying further and solving for x

2x = 9/7 -6

2x = -4.714

x = -2.357

Hence, the equation is solved and the value of x is  -2.357.

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Answer:

A = 16803.2 in^2

Step-by-step explanation:

The area of a regular polygon is [tex]A=\frac{1}{2}(a)\cdot{P}[/tex], where a is apothem and P is the perimeter.

Given side length s = 59 in, and the knowledge that this is an octagon (8 sides): P = 8s.

Now substitute all known values into the area formula: [tex]A=\frac{1}{2}(71.2)\cdot{472}[/tex]

Add the two trips together for total Km’s:

4500 + 11700 = 16,200 km.

divide total km by speed:

16,200 / 1,100 = 14.727272 hours

0.727272 x 60 minutes per hour = 43.636363 minutes, round up to 44 minutes

total time: 14 hours and 44 minutes

Answer:

sin(4)

Step-by-step explanation:

sin(-184) is the equivalent to sin(4) (degree), positive and acute angle.

The mode of a given data set is the number that is repeated most often in a given data set. The mode of the given stem-and-leaf plot is 70.

The mode of a given data set is the number that is repeated most often in a given data set. It can also be described as the number that has the highest frequency of repetition.

As per the given Stem and leaf plot, the number of people who attended the carnival on different days is 54 60 70 70 75 78 79 81 86, since the mode is the number that is repeated very frequently, therefore, the mode of the given data is 70.

Hence, the mode of the given stem-and-leaf plot is 70.

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Answer:

see the attachment photo!

Using proportions, it is found that 804.54 pounds of vegetables will be transported to the market in August.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the weight increases by 15% every month, the August amount will be the July's amount multiplied by 1.15, hence:

A = 1.15 x 699.60 pounds = 804.54 pounds.

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The best definition of the phrase "like terms" is as follows: terms that have identical variable parts.

Like terms is used to describe terms that contain the same variable which is raised to the same power.

Algebra is an aspect of mathematics that involves the system of computation using letters or other symbols to represent numbers.

For example; in the algebraic expression: x² + 3 - 2x², x² and 2x² are like terms because they are terms that have identical variable parts.

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Answer:

An angle whose measure is equal to 90° is called a right angle.

An angle whose measure is more than 0° but less than 90° is called an acute angle. Angles having magnitudes 30°, 40°, 60° are all acute angles.

An angle more than 90 degrees and less than 180 degrees, is called an obtuse angle.

Based on the above, it can be inferred that the best option to produce the 15,000 units is the factory with the lowest cost per unit.

Unit cost is a term to refer to the value per unit of a product that a factory charges to produce it.

In this case, the best alternative to produce 15,000 products is the factory with the lowest cost per unit, since this will reduce the cost of the order.

To find the cost per unit we divide the total cost of the order by the number of units. For example:

To know which one is more convenient, I must divide the total value by the number of units

According to the above, the second option would be the cheaper.

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Answer:

.53 facory B

Step-by-step explanation:

10000/15000 =.66

8000

The object reaches the lowest height at 5 seconds

The function is given as:

f(t) = -2t² +22t + 6

Differentiate the function

f'(t) = -4t +22

Set to 0

-4t +22 = 0

Subtract 22 from both sides

-4t = -22

Divide both sides by -4

t = 5.5

Remove decimal points

t = 5

Hence, the object reaches the lowest height at 5 seconds

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Answer:

13.4meters

Step-by-step explanation:

13.4×3×1.5 = 60.3

vol = L X W X H

60.3 = 3 X 1.5 X H

60.3 / 3 / 1.5 = H

This is how the linear function looks.

Answer:

6000.

Step-by-step explanation:

Hundreds digit is 6 so we round up the thousand digit (5) to get 6000.

Answer:

5:9

Step-by-step explanation:

the circumference is d*pi

so you must find the diameter of both circles

31/pi = 9.86760647

which is about 10

57/pi = 18.1436635

which is about 18

10:18 is your ratio

but you can simplify this down to

5:9

Answer:

The shape of the data in the histogram is Symmetrical.

Step-by-step explanation:

This is because the distribution, or data set is the same to the left and right of the center point.

Using it's concept, it is found that the probability of an odd number other than seven being generated is of 40.0%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these number of outcomes are taken from previous trials.

In this problem, 200 numbers have been generated, and 80 are odd numbers that are not seven, hence the probability is given by:

p = 80/200 = 0.4 = 40%.

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Answer:

40

Step-by-step explanation:

Answer:

20 x 9 = $180 just multiply hours worked times rate per hour

The probability that the next elk that will be caught will be unmarked is 5400/ 5625, 0.96 and 96%

The probability that the next wolf that will be caught will be unmarked is 696 / 928,  0.75 and 75%.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the next elk that will be caught will be unmarked = number of unmarked elks / total number of elks

number of unmarked elks  = 5625 - 225 = 5400

5400/ 5625 = 0.96 = 96%

The probability that the next wolf that will be caught will be unmarked = number of unmarked wolfs / total number of wolfs

number of unmarked wolfs  = 928 - 232 = 696

696 / 928 =  0.75 =  75%.

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Answer:

280 drinks

Step-by-step explanation:

Answer:

280 drinks. We need to divide 1 2/5 by 1/200 in order to get this answer.

Answer:

11 points

Step-by-step explanation:

Claire had 11 points  because 18-7=11

C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

Two or more expressions with an Equal sign is called as Equation.

Given that Ava scored 18 points in a basketball game.

Let Ave score be represented as A.

Ave scored seven points more than Claire.

Let C be the Claire score.

A=7+C

As given Ava scored 18 points in a basketball

so the value of A is 18

18=7+C

Now let us find the value of C

Subtract 7 from both sides

18-7 =C

11=C

Hence, C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

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Answer:

27

Step-by-step explanation:

30% of 90 is 27

30/100 = ?/90

by cross multiplying, we can see that 30 times 90 is equal to 2700.

2700/100 = 27

? = 27

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Hope this helps :)

For the cosecant we will get:

   [tex]csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}[/tex]

So the correct option is the third one.

First, we can write:

[tex]csc(x) = \frac{1}{sin(x)}[/tex]

Now, remember that:

[tex]cos(x) = \frac{\sqrt{2} }{2} \\\\for\ x = \pm \frac{pi}{4}[/tex]

And for the sine we have:

[tex]sin(pi/4) = \frac{\sqrt{2} }{2} \\\\sin(-pi/4) = -\frac{\sqrt{2} }{2} \\[/tex]

Then the cosecant for these possible values of x gives:

[tex]csc(\pm \frac{pi}{4}) = \frac{1}{sin(\pm \frac{pi}{4})} = \pm \frac{2}{\sqrt{2} } = \pm \sqrt{2}[/tex]

So the correct option is the third one.

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Answer:

Model the expression as 3 groups of x+2.

There are 3 x-tiles.

There are 6 +1 tiles.

The equivalent expression is 3x+6

Step-by-step explanation:

see image. This program is trying to help you learn algebra (here it looks like distributive property) by using a physical model. The bars are x's and the +1's are numbers. The little squares are 1 each (positive or negative, but you only need the positives for this question)

see image.

The lesson is:

3(x+2) = 3x + 6

[tex]\left(- \dfrac 38 \right) \div \left(-\dfrac 13 \right)\\\\\\=-\dfrac 38 \times (-3)\\\\\\=\dfrac 98[/tex]

Answer:

The intersection is at (1,3) and the answer is in the graph. (see image below)

Step-by-step explanation:

Answer:

2(7x-4) = 7x(2)-4(2) = 14x-8

but

(7x-4)^2 = (7x-4) (7x-4)