HARNESS SKILL Direction: Complete the proof by writing the reason for each statement. Choose your answer inside the box. Write your answer on the space provided.

GIVEN: △LMN with exterior angle ∠LNP
PROVE: m∠LNP>m∠MLN

Proof:
Let us prove that m∠LNP>m∠MLN by constructing the following:
1. midpoint Q on LN such that LQ ≅ NQ
2. MR through Q such that MQ ≅ QR

Vertical Angles are congruent
SAS Triangle Congruence Postulate
Substitution Property of Equality
Property of Inequality
By Construction
Angle Addition Postulate
Segment Addition Postulate Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Transitive Property of Equality

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Answer:

101°

Step-by-step explanation:

Answer:

Alice: 82, 84, 86

Pat: 103, 105, 107

Step-by-step explanation:

Alice:

x + (x+2) + (x+4) = 252

3x + 6 = 252

3x = 246

x = 82 so Alice's last term is 82+4 = 86

Pat:

y + (y+2) + (y+4) = Pat's Total

Pat's last term is (y+4) so

Alice's last term + 25 = Pat's last trem

86 + 25 = 111 = y+4

y = 107

Answer:

D

Step-by-step explanation:

you will be multiplying Matrix C with Matrix D so, after using the rule for multiplication of matrices

[ 5x2 +9x4 + 7x1 5x(-4) + 9x0 + 7x7]

[ 10 + 36 + 7 -20 + 0 + 49 ]

[ 53 29]

hope this helps.

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The product of matrices C and D is [53 29]. Therefore, option D is the correct answer.

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.

Given that, C=[5 9 7] and D= [tex]\left[\begin{array}{ccc}2&-4\\4&0\\1&7\end{array}\right][/tex]

Here, CD = [5×2+9×4+7×1 5×(-4)+9×0+7×7]

= [10+36+7 -20+49]

= [53 29]

Therefore, option D is the correct answer.

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Answer:

The length of the missing side is 18yd

Step-by-step explanation:

Sq30 - Sq 24 = Sq (x)

Using translation concepts, it is found that the domain of g(x) = f(x) - 12 is the same domain of f(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x) - 12, that is, g(x) is a shift down of 12 units of f(x).

The domain of a function is the set that contains all possible input values for the function. A shift down does not add any restriction to the function, hence the domain of f(x) and g(x) are the same.

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Answer:

5940 rupees

Step-by-step explanation:

99 multiplied by 29×5 is 5940

Answer:

[tex]\text{(b) }[/tex] ₹[tex]5,940[/tex]

Step-by-step explanation:

Each pair of scissors on the chart represents 5 haircuts, as indicated by the key. There are 2 scissors on Saturday and 10 scissors on Sunday, hence a total of 12 scissors over the weekend. Therefore, there were [tex]12\cdot 5=60[/tex] haircuts over the weekend.

Since the salon charges 99 rupees per cut, they made a total of [tex]99\cdot 60=\boxed{5,940}[/tex] rupees over the weekend.

Answer:

A

Step-by-step explanation:

Linear are the one with straight line

Answer: A limit on how much an ARM's interest rate can change over the

life of a mortgage

Step-by-step explanation: took the quiz.

Answer:82

Step-by-step explanation:

Answer:

∠ 7 = 82°

Step-by-step explanation:

∠ 2 and ∠ 7 are Alternate exterior angles and are congruent, then

∠ 7 = ∠ 2 = 82°

Answer:

Both sports = 15

Step-by-step explanation:

Remark

What an interesting question. At first I didn't think it was possible. Then I saw the word only. That made all the difference in the world.

Givens

Football only = 35

Volleyball only = 15

Ratio = 5/3

Equation

Let the number of students who play both = x

Volleyball / Football = (x + 15) /(x + 35) = 3/5

Solution

(x + 15) / (x + 35) = 3/5                  Cross multiply

5*(x + 15) = 3(x + 35)                     Remove the brackets

5x + 75 = 3x + 105                        Subtract 3x from both sides

3x            3x

2x + 75 = 105                               Subtract 75 from both sides

      - 75   -75  

2x = 30                                        Divide by 2  

2x/2 = 30/2

x = 15

15 people play both sports.

Answer:

b = 8 in

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here A = 12 and h = 3 , then

[tex]\frac{1}{2}[/tex] b × 3 = 12 , that is

1.5b = 12 ( divide both sides by 1.5 )

b = 8

Answer:

Step-by-step explanation:

I think its A

Answer:

20 girls

Step-by-step explanation:

boys : girls  : total

3           5        3+5 = 8

There are 32 students

32/8 = 4

Multiply each term by 4

boys : girls  : total

3*4       5*4     8*4

12        20         32

There are 20 girls

Answer: 20 girls

Step-by-step explanation:

So boys to girls is 3 to 5

It asks for girls in class

Suppose there were 8 people in class, 5/8 of the people would be girls

It states that 32 people are in the class, so do 32 x 5/8 to get 20 girls

Answer:

f(x)=5.05 sin((pi/12)x) + 5.15

Step-by-step explanation:

Answer : B

Step-by-step explanation:

Ape

The statement which is true is  KM = 2 .JM, the correct option is C.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

AJKL is an equilateral triangle

Now,

Using these properties, we can eliminate some of the options.

Option A is false because JK and KM are not equal. JK is half of JL, which is one side of the equilateral triangle AJKL, while KM is a perpendicular bisector of JL.

Option B is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 90 degrees.

Option D is false because AJKM is not a right triangle. The angle JAK is 60 degrees, not 45 degrees.

Option C must be true because KM bisects JL into two equal parts JM and ML. Since JL is one side of the equilateral triangle AJKL, we have JL = AK = AL. Therefore, JM = ML = JL/2 = AK/2 = AL/2. By Pythagoras’ theorem, we have:

KM^2 = AK^2 - AM^2

KM^2 = (AK/2)^2 - (AL/4)^2

KM^2 = (AK/4)^2 + (AL/4)^2

KM^2 = ((AK + AL)/4)^2

Since AK + AL = 2 * JL,

KM^2 = (JL/4)^2 * 4

KM^2 = (JL/4)^2 * 4

KM = JL/4 * 2

KM = JL/2

Therefore, the answer of the triangle will be KM = 2 * JM.

Learn more about a right triangle;

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Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the triangles CAP and HIT are not given. The general explanation to solve sides of similar triangles is as follows;

[tex]\triangle CAP \sim \triangle HIT[/tex] implies that the following sides are similar:

[tex]CA \to HI[/tex]

[tex]AP \to IT[/tex]

[tex]PC \to TH[/tex]

Take for instance:

[tex]CA = y[/tex]     [tex]HI = b[/tex]

[tex]AP = 20[/tex]    [tex]IT = 38[/tex]

Then the solution is:

[tex]CA : HI = AP : IT[/tex]

Substitute values for CA, HI, AP and IT

[tex]y : b= 20 : 38[/tex]

Express as fraction

[tex]\frac{y }{ b}= \frac{20 }{ 38}[/tex]

Multiply both sides by b

[tex]y= \frac{20 }{ 38}*b[/tex]

Substitute 19 for b

[tex]y= \frac{20 }{ 38}*19[/tex]

[tex]y= \frac{20 }{ 2}[/tex]

[tex]y=10[/tex]

Answer:

B: All four triangles are congruent.

C: All four triangles are right-angled.

E; Area of rhombus = 4 times the area of one triangle.

Step-by-step explanation:

A rhombus is a quadrilateral with equal length of sides. It stands on one of its edges, and a simple example is the shape of a diamond. It has two diagonals which bisect the angles of the rhombus.

When a rhombus is cut along its diagonals, the following properties of the shape formed can be observed:

B: All four triangles are congruent.

C: All four triangles are right-angled.

E; Area of rhombus = 4 times the area of one triangle.

Answer:

c < 56

Step-by-step explanation:

Maya buys candy that costs $8 per pound. She will buy less than 7 pounds of candy. What are the possible amounts she will spend on candy? Use c for the amount (in dollars) Maya will spend on candy. Write your answer as an inequality solved for c.

c < 7 × $8

c < $56

Answer: 11

Step-by-step explanation:

g(x)=(2x+1)

g(x)=5

g(5)=2(5)+1

     =10+1

g(5)     =11

Answer:

Angle EBF is the alternate interior angle of BEA.

Step-by-step explanation:

We are taking AE parallel to BF and EB as the transversal.

Hope it helps you.^_^

Answer:

49

Step-by-step explanation:

Answer:

x = 308 feet

Step-by-step explanation:

tan = opp/adj

tan72 = x/100

multiply both sides by 100

100 * tan72 = x

Use calculator

x = 307.76835371752534

Rounded

x = 308 feet