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MaRussiya [10]
2 years ago
5

Triangles G H L and K H J are connected at point H. Angles Angles L G H and H K J are congruent. Sides G H and H K are congruent

.
Which congruency theorem can be used to prove that △GHL ≅ △KHJ?
SSS
ASA
SAS
AAS
Mathematics
1 answer:
stira [4]2 years ago
3 0

The congruence theorem that can be used is: B. ASA

<h3>What is the ASA Congruence Theorem?</h3>

If we have two triangles that have two pairs of corresponding congruent angles (e.g. ∠LGH ≅ ∠HKJ and ∠LHG ≅ ∠KHJ), and a pair of corresponding congruent sides (e.g. GH ≅ HK), the triangles are said to be congruent triangles by the ASA congruence theorem.

Therefore, triangles GHL and KHL in the image given are congruent triangles by the  ASA congruence theorem.

Learn more about the ASA congruence theorem on:

brainly.com/question/2398724

#SPJ1

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Solve the following system of equations: 2x + 4y − 3z = −7 3x + y + 4z = −12 x + 3y + 4z = 4
lukranit [14]

2x + 4y − 3z = −7 ---> first equation

3x + y + 4z = −12   ---> second equation

x + 3y + 4z = 4   ---> third equation

We try to eliminate z  and make two equations

Multiply first equation by 4 and second equation by 3. then add both equations

8x + 16y -12z = -28

9x + 3y +12z = -36

----------------------------

17x + 19y = -64   ---------------> equation 4

multiply third equation by -1  and add second and third equation

3x + y + 4z = −12  

-x - 3y - 4z = -4    

-------------------------------------

2x -2y = -16        ---------------> equation 5

Multiply equation 4 by 2 and equation by 19

34x + 38y = -128

38x - 38y = -304

------------------------------------

72x  = -432

Divide by 72 on both sides

x = -6

use equation 2x -2y = -16        ---------------> equation 5

2(-6) - 2y = -16

-12 -2y = -16

-2y = -4

So y = 2

Now plug in 2 for y  and -6 for x

Using any one of the three equations

x + 3y + 4z = 4  

-6 + 3(2) +4z = 4

4z = 4 (divide by 4 on both sides)

So z=1

So x= -6, y = 2  and z= 1





4 0
3 years ago
Read 2 more answers
A sample of 38 observations is selected from one population with a population standard deviation of 3.4. The sample mean is 100.
kaheart [24]

Answer:

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

Step-by-step explanation:

We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

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30, it’ll take 30 men to dig 8 hactares in 12 days.
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