the pentagons ABCDE and JKLMN are similar find the length x of JK

Problem 1 (on the left)

[tex]10^2+12^2 = \boldsymbol{244}\\\\14^2 = \boldsymbol{196}\\\\\text{What kind of triangle?} \textbf{ Acute}[/tex]

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Explanation:

The converse of the pythagorean theorem can be used to determine what kind of triangle we're dealing with.

Here are 3 important rules to have in your notes:

[tex]\cdot \text{If } a^2+b^2 > c^2 \text{ then the triangle is } \underline{\text{acute}}\\\\\ \cdot \text{If } a^2+b^2 < c^2 \text{ then the triangle is } \underline{\text{obtuse}}\\\\\cdot \text{If } a^2+b^2 = c^2 \text{ then the triangle is a } \underline{\text{right}} \text{ triangle}\\\\[/tex]

The third rule is probably the most familiar as it's the pythagorean theorem itself.

In this case, we have [tex]a^2+b^2 = 10^2+12^2 = 244[/tex] larger than [tex]c^2 = 14^2 = 196[/tex], which fits the first rule mentioned.

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Problem 2 (on the right)

[tex]8^2+15^2 = \boldsymbol{289}\\\\17^2 = \boldsymbol{289}\\\\\text{What kind of triangle?} \textbf{ Right}[/tex]

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Explanation:

We follow the same idea as problem 1. This time, both [tex]a^2+b^2[/tex] and [tex]c^2[/tex] result in the same value (289). Therefore, [tex]a^2+b^2 = c^2[/tex] is a true equation, and we go for the third rule mentioned earlier. An 8-15-17 right triangle is one of the infinitely many pythagorean triples.

Answer: 11.9

Step-by-step explanation:

The opposite is across from the 35 degree angle and the ajacent is the side valued at 17.

Answer:

A. 11.9

Step-by-step explanation:

35° = opposite/adjacent

tan(35°) = x/17

tan(35) x 17 = 11.90352814

x = 11.90352814

x = 11.9

Answer:

90

Step-by-step explanation:

q

It will take 21.53 hours for 8 workers and 5 bandits to lay 1400 bricks.

Given that one worker can lay 10 bricks every hour, and one bandit steals 3 bricks every hour, to determine how long it would take 8 workers and 5 bandits to lay 1400 bricks, the following calculation must be performed:

Therefore, it will take 21.53 hours for 8 workers and 5 bandits to lay 1400 bricks.

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Answer:

Add  7 to both sides of the equation [it would look like: 4b - 7 +7 = 13+7]

Step-by-step explanation:

The multiplication property of equality states that if [tex]x=y[/tex] is true, then [tex]xz=yz[/tex] must also be true.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the: Multiplication Property of Equality.

The properties of equality describe the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the Multiplication Property of Equality.

This property states that if you multiply both sides of an equation by the same nonzero number, the equality still holds true.

In this question, both sides of the equation are multiplied by -2, maintaining the equality between the expressions.

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Answer:

more than 23.3 $

Step-by-step explanation:

if we say she will work minimum 4 hours in day that mean it will be 28 hours

so she left 7 hours behind

and she make 3.33$ per hour (70/21=3.33) so (7 * 3.33 = 23.3) she need more than 23.3$

The value of x and y are 5/6 and 8/5 respectively

Given the systems of equations

Solving the equations using the elimination method

12x + 15y = 34

-18x + 15y = 9

Subtract both expressions:

12x-(18x) = 34 - 9

12x+18x = 25

30x = 25

x = 5/6

Substitute x = 5/6 into equation 1 to have:

12x + 15y = 34

12(5/6) + 15y = 34

10 + 15y = 34

15y = 24

y = 8/5

Hence the value of x and y are 5/6 and 8/5 respectively

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Answer:

Step-by-step explanation:

Using DMAS, let's solve.

Conclusion:

Therefore, the answer is:

Hoped this helped.

[tex]GeniusUser[/tex]

Answer:

Step-by-step explanation:

Let the number of dimes be x and quarters be y.

We have equations:

Multiply the first equation by 10 and subtract from the second one:

Find the value of x:

If you filled out the chart fully:

a = 4

b = 7

c = 6

d = 9

e = 17

Based on the chart, their 7 girls and 10 boys. In this case, it is a better chance of selecting a boy which ratio is:

7:10

There is a greater chance of picking a boy than a girl where there is three more boys than girls.

Answer:

the baseball traveled 66 feet per second if that helps

Step-by-step explanation:

Answer:

5n-2

Step-by-step explanation:

collect like terms

-> (7n-2n)+(-3+1)

simplify

=> 5n-2

Answer:

6,12,18,24,36,42,48,5,60,66,72,78,84,90,96

Step-by-step explanation:

got a friend help

Answer:

1/3 of the day

Step-by-step explanation:

8/24 simplifies to 1/3

Answer:

15yx^2-34y-16

Step-by-step explanation:

Answer:

.......!!!!

I think so this is the. answer.....!!!

Answer:Nooo please don’t put B. It’s A,C, and D

Step-by-step explanation:

Answer:

Step-by-step explanation:

14%  increase

if their corresponding angles are congruent and the corresponding sides are in proportion ...so it will be similar triangle

Answer:

x ≈ 7.1

Step-by-step explanation:

Using the cosine ratio in the right triangle.

cos27° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{KL}{KM}[/tex] = [tex]\frac{6.3}{X}[/tex] ( multiply both sides by x )

x × cos27° = 6.3 ( divide both sides by cos27° )

x = [tex]\frac{6.3}{cos27}[/tex] ≈ 7.1 ( to the nearest tenth )

The zeros of

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

are

x=0,x=-2,x=-5x=0,x=−2,x=−5

EXPLANATION

The given function is

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

To find the zeros of the above function, we just have to equate the function to zero and solve for x.

x(x + 2)(x + 5) = 0x(x+2)(x+5)=0

This implies that,

x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0

x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5

To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,

x < - 5x<−5

When

x = - 10x=−10

y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0

The graph is below the x-axis.

- 5 \: < \: x \: < \: - 2−5<x<−2

When

x = - 3x=−3

y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0

The graph is above the x-axis.

- 2 \: < \: x < \: 0−2<x<0

when

x = - 1x=−1

y = -1(1)(4) \: < \: 0y=−1(1)(4)<0

The graph is below the x-axis.

Finally the interval,

x \: > \: 0x>0

when

x = 1x=1

y = 1(3)(6) \: > \: 0y=1(3)(6)>0

The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above

Answer:

sin ( 180* + x ) = - x

Step-by-step explanation:

This is the correct answer

The value of x in the expression is 18(24/30).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8(3/5) = (3/4)x - 5(1/2)

43/5 = 3x/4 - 11/2

43/5  + 11/2 = 3x/4

(86 + 55)/10 = 3x/4

141/10 = 3x/4

3x = 141 x 4 / 10

x = 564/30

x = 18(24/30)

Thus,

The value of x is 18(24/30).

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Answer:

Triangles QST and RST are similar.  Therefore, the following is true:

q       s

--- = ----   This results in 10q=rs.

r      10

Also, since RST is a right triangle, 4^2 + s^2 = q^2.

Since QST is also a right triangle, s^2 + 10^2 = r^2.  

           4      s

Also:  ---- = -----    which leads to s^2 = 40

           s      10

Because of this, 4^2 + s^2 = q^2 becomes 16 + 40 = 56 = q^2

Then q = sqrt(56) = sqrt(4)*sqrt(14) = 2*sqrt(14) (answer)

Answer:

2

Step-by-step explanation:

slope formula : [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where the x and y values are derived from known points

We are given the points (3,1)and (4,3)

Given these points we can define our variables

(x1,y1) = (3,1) so x1 = 3 and y1 = 1

(x2,y2) = (4,3) so x2 = 4 and y2 = 3

Now that we have defined our variable, we plug them into the formula

Recall formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

x1 = 3 , y1 = 1 , x2 = 4 , y2 = 3

* plug in values *

[tex]\frac{3-1}{4-3}[/tex]

subtract 3 and 1 , and 4 and 3

[tex]\frac{3-1=2}{4-3=1} =\frac{2}{1} =2[/tex]

the slope is 2

Answer:

y = -2x + 5

Step-by-step explanation:

Slope = -2

m = slope

y-intercept = 5

b = 5

y = mx + b

y = -2x + 5