For the following right triangle find the side length X. Round your answer to the nearest hundredth.

The values of x and y using angle relationships are as follows:

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

Therefore, the angle relationship can be used to find the value of x and y in the diagram.

In the diagram, l and m are parallel lines and are cut by a transversal line.

Therefore,

10.

10x - 17 = 8x + 1(alternate exterior angles are congruent)

10x - 8x = 1 + 17

2x = 18

x = 18 / 2

x = 9

8x + 1 + 6y + 29  = 180(sum of angles on a straight line is 180 degrees)

72 + 1 + 29 + 6y = 180

102 + 6y = 180

6y = 180 - 102

6y = 78

y = 78 / 6

y  = 13

11.

7x - 30 = 5x + 14(Corresponding angles)

Corresponding angles are congruent.

7x - 5x = 14 + 30

2x = 44

x = 44 / 2

x = 22

3y + 11 + 7x - 30 =  180(sum of angles on a straight line)

3y + 11 + 7(22) - 30 =  180

3y + 11 + 154 - 30 = 180

3y = 180 - 11 - 154 + 30

3y = 45

y = 45 / 3

y = 15

12.

7y - 23 = 23x - 16 (vertically opposite angles)

7y - 23x = 7

8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)

31x  - 37 = 180

31x = 180 + 37

31x = 217

x = 217 / 31

x = 7

7y - 23(7) = 7

7y = 7 + 161

7y = 168

y = 168 / 7

y = 24

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The measurement of angles ∠1 is 126° and ∠2 is 154°.

According to the question,

We have the following information:

We have a figure of two triangles and some of the measurements of the angles are given.

We know that the sum of three angles of a triangle is 180°.

So, for the larger triangle, we have the following expression:

96+30+third angle = 180

Third angle = 180-126

Third angle = 54°

We know that sum of angles on a straight line is 180°.

So, we have:

∠1+54 = 180

∠1 = 180-54

∠1 = 126°

Now, finding the sum of angles in smaller triangle:

126+28+third angle = 180

Third angle = 180-154

Third angle = 26°

Now, angle 2 and this angle will make a straight line.

∠2+26 = 180

∠2 = 180-26

∠2 = 154°

Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.

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The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.

An elevation simply means the height above sea level.

In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:

= 12.2 × 4

= 48.8 feet

He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:

= 3.6 × 10

= 36 feet.

Therefore, the change in elevation will be:

= Elevation up - Elevation down

= 36 - 48.8

= 12.8 feet.

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Answer: I think you would earn $8.35 per hour

Step-by-step explanation:

Answer: $880

Step-by-step explanation:

As I understand you are working 20 hours a day for 4 days.

[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880

Answer:

C. Trust me on this one, it is an easy one.

The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d)  .

In the question ,

four set of sides is given ,

we need to find the set of side that forms a right triangle ,

we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .

Option(a)

the sides are 4 , 8 , 11.

4 + 8 = 11

16 + 64 = 121

80 = 121

we know that 80 121 ,

So , the sides do not form a right triangle

Option(b)

the sides are 6 , 8 , 13

6 + 8 = 13

36 + 64 = 169

100  169

we know that 100 169 ,

So , the sides do not form a right triangle .

Option(c)

the sides are √3, √5 , 8

√3 + √5 = 8

3 + 5 = 64

8 = 64

we know that 8  64 ,

So , the sides do not form a right triangle .

Option(d)

the sides are √3, √13 , 4

√3 + √13 = 4

3 + 13 = 16

16 = 16

Yes , the sides form a right triangle .

Therefore , The sides {√3 , √13 , 4} forms a right triangle  .

The given question is incomplete , the complete question is

Determine which set of side measurements could be used to form a right triangle ?

(a) 4, 8, 11

(b) 6, 8, 13

(c)√3, √5,8

(d)√3, √13, 4

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Answer:

Exact Form: 16/3

Decimal Form: 5.3

Mixed Number Form: 5 1/3

Step-by-step explanation:

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .

Answer:

27/8 or 3.375 or 3 3/8

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

15%*40=46

Answer:

15%

Step-by-step explanation:

[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]

The boy was 40 inches tall so that means 40 inches is the old value

The boy is currently 46 inches tall now, so 46 is the new value

Plug these values into the equation:

[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]

Simplify:

[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]

[tex]Percent of change =\frac{600}{ 40} \\[/tex]

[tex]Percent of change =15[/tex]

I hope this answers your question :)

The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of hours be given as h.

Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:

c = 3 + (5 × h)

c = 3 + 5h

where c = total cost

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The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

In the question ,

it is given that ,

the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,

In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .

In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .

that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

let us find the roots of the function ,

f(x) [tex]=[/tex] 0

x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0

taking x³ common ,

x³(x² - 8x [tex]+[/tex] 16) = 0

x³(x² - 4x - 4x + 16) = 0    .... by using splitting the middle term method

x³(x(x - 4) - 4(x - 4)) = 0

x³(x - 4)(x - 4) = 0

which means x³ [tex]=[/tex] 0   and x-4 = 0  

that is x=0    and x = 4 .

So , the roots of the function f(x) are x=0 and x=4 .

This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.

Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

The given question is incomplete , the complete question is

What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?

(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞

(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞

(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞

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The true equations are :

2 + 7 = 9

8 × 5 = 4 0

6 ÷ 3 = 2

2 - 1 = 1

We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.

The first true equation is 2 + 7 = 9.

The second true equation is 8 × 5 = 4 0.

The third true equation is 6 ÷ 3 = 2.

The fourth true equation is 2 - 1 = 1.

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Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

What is Geometric Series?

The total of a geometric sequence's finite or infinite terms is known as a geometric series. The analogous geometric series is a + ar + ar2 +..., arn-1 + for the geometric sequence a, ar, ar2,..., arn-1,... The word "series" is known to mean "sum." The geometric series specifically refers to the total of phrases with a common ratio between every pair of neighboring terms. Geometric series can be of two different types: finite and infinite.

In the given question, we have:

The series: 3 + 12 + 48 +

So, here the first term (a) = 3;

The second term = +12;

and, we know that the common ratio in the geometric series is the ratio of the second term and the first term.

So,

Common ratio, r = [tex]\frac{12}{3}[/tex]

r = 4;

so, The common ratio will be the same everywhere. So, It will be 4 in all the cases.

And, The first term, a is 3;

Hence,

Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

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Answer:

t - 10 = 61

Step-by-step explanation:

We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61

so t = 71.

Answer:

[tex]y=-43x-173[/tex]

Step-by-step explanation:

[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]

The solution to the equation given as (x - 7)² = 36 are x = 1 and x = 13

From the question, the equation is given as

(x - 7)² = 36

To start with, we take the square roots of both sides

This gives

x - 7 = ±6

Add 7 to both sides of the equation

So, we have

x = 7 ± 6

Evaluate the like terms

x = 1 and x = 13

Hence, the values of x are x = 1 and x = 13

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Answer:

4(13)

Step-by-step explanation:

[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]

The measure of the exterior angle to triangle X is D. 97.55°.

It is important to note that the sum of the angles in a triangle is 180°.

In this case, triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6.

The exterior angle to X will be:

= Total angle - (43.85 + 38.6)

= 180 - 82.45

= 97.55°

In conclusion, the correct option is D.

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Answer:

I got the answer d when I took the test

Step-by-step explanation:

I hope this helps...

The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.

It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:

= 16 + 15 + 16 + 8 + 17

= 72 feet

The area will be:

= Area of triangle + Area of rectangle

= (1/2 × base × height) + (length × width)

= (1/2 × 8 × 17) + (15 × 16)

= 68 + 240

= 308ft²

Therefore, the correct option is B.

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Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.

When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.

Hope this helps.

Step-by-step explanation:

Answer:  

48

Step-by-step explanation:

The measure of angles are

The sum of angles around a point is equal to 360 degrees

The consider the angle a

The equation will be

∠a + 312 = 360 degrees

∠a = 360 - 312

∠a = 48  degree

The angle a is less than 90 degrees then it is an acute angles

Consider the angle b

∠b + 220 = 360

∠b = 360 -220

∠b = 140 degrees

Angle b is greater than 90 degrees and less than 180 degrees then it is an obtuse angle

Consider the angle c

∠c + 36 = 360

∠c = 360 - 36

∠c = 324 degrees

Angle c is grater than 180 degrees and less than 360 degrees then it  is a reflex angle

Hence, the measure of angles are

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Answer:

40% decrease

Step-by-step explanation:

[tex]\frac{1090-654}{1090}[/tex] = .4  x 100 to make a percent equals 40%

Answer:There is no decrease from 2,820 kilograms to 2,820 kilograms.

The percent of decrease in the size of the sugar order is 0%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7*5

Answer:

he got 8 apples left and made a profit of 16

Step-by-step explanation:

The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer: 0.051, 0.134, 0.2, 0.46

Step-by-step explanation:

The intervals for the concavity of the odd function are given as follows:

The definition of even and odd functions depends on the relation between f(x) and f(-x), as explained as follows:

In this problem, we have that the function is odd, hence the following statement is true:

f(-x) = -f(x) for all values of x.

This means that the concavity intervals are exchanged, hence:

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By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).

A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In order to plot the system of equations on a graph, we would simplify the second equation as follows:

4u = 2v - 12

Dividing both sides of the equation by 4, we have the following:

4u/4 = 2v/4 - 12/4

u = v/2 - 3

Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.

By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).

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Answer:-48

Step-by-step explanation:

a + 85 = 48

first we need to find what a

86-48=a

a=38

now we calculate

a-86?

38 - 86 = -48

Answer:

a - 86 = -124

Step-by-step explanation:

a + 86 = 48

a = 48 - 86

a = -38

Then:

a - 86 = -38 - 86

= -124