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2 years ago

Solve the system using the elimination method.

Mathematics

1 answer:

spayn [35]2 years ago

6 0

Answer:

(x, y, z) = (-22/13, 29/13, 6/13)

Step-by-step explanation:

Adding the first and second equations, we get ...

(3x +2y -3z) +(7x -2y +5z) = (-2) +(-14)

10x +2z = -16 . . . . collect terms

5x + z = -8 . . . . . . divide by 2 . . . [eq4]

Adding twice the second equation to the third, we get ...

2(7x -2y +5z) +(2x +4y +z) = 2(-14) +(6)

16x +11z = -22 . . . . . . [eq5]

Now, we have two equations with the variable y eliminated. We can subtract [eq5] from 11 times [eq4] to eliminate z:

11(5x +z) -(16x +11z) = 11(-8) -(-22)

39x = -66

x = -66/39 = -22/13

From [eq4], we can find z as ...

z = -8 -5x = -8 -5(-22/13) = 6/13

And from the second equation, we get ...

y = (1/2)(7x +5z +14) = (1/2)(7(-22/13) +5(6/13) +14) = 29/13

The solution is (x, y, z) = (-22/13, 29/13, 6/13).

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If AJKL = ARST, which congruences are true by CPCTC? Check all that apply.

evablogger [386]

Based on the CPCTC theorem, the congruences that are true about the given triangles are:

B. ∠K ≅ ∠S

C. KL ≅ ST

D. JK ≅ RS

<h3>What is the CPCTC Theorem?</h3>

According to the CPCTC theorem states that if two triangles are congruent to each other, then, all their corresponding parts will be congruent to each other.

Given that triangles JKL and RST are congruent to each other, therefore:

∠J ≅ ∠R

∠K ≅ ∠S

∠L ≅ ∠T

JK ≅ RS

KL ≅ ST

JL ≅ RT

Therefore, the congruences that would be true by CPCTC are:

B. ∠K ≅ ∠S

C. KL ≅ ST

D. JK ≅ RS

Learn more about the CPCTC theorem on:

brainly.com/question/14706064

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2 years ago

I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS 3

sveticcg [70]

Answer:

$x=8$

Step-by-step explanation:

The best way to go about this is to use a trig identity. You have the unknown opposite the angle and the hypotenuse, so its best to use the sine identity: $sin(x)=\frac{O}{H}$ , where O is the opposite side, and H is the hypotenuse.

Set up the equation as: $sin(27)=\frac{x}{17}$ , and solve for X.

I got x=7.718, rounded to x=8.

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2 years ago

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egoroff_w [7]

Answer: OPTION A

Step-by-step explanation:

The distance between any number is always positive so we should apply the absolute value.

The distance between numbers=number 1-number2 (or vise versa, and that is why we need absolute value)

In your question, the two numbers are 3/4 and 2. Applying to the expression above, the distance between two numbers should be |3/4-2| or |2-3/4|.

The only option in your case is |3/4-2| and this is it.

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