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blsea [12.9K]
3 years ago
13

Complete the proofs using the most appropriate method. may require CPCTC.

Mathematics
1 answer:
n200080 [17]3 years ago
3 0

For the first one, you did good. I will just suggest a couple things.

Statement              Reason

JK ≅ LM                   Given

<JKM ≅ < LMK        Given  (You did both of these steps so well done.)

MK ≅ MK              Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)

ΔJMK ≅ ΔLKM        SAS

Problem 2: (You also have a lot of great stuff here.)

Statement          Reason

DE ║ FG              Given

DE ≅ FG              Given

<DEF≅<FGH       Given

<EDF≅<GFH       Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)

ΔEDF≅ΔGFH        ASA

<DFE≅<FHG       CPCTC  

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Can someone simplify pls
algol [13]

we are given to simplify

\\ \ (x^6y^5)(5xy^2)(-6x^4)\\ \\

Open the bracket and write the like terms together

\\ \ =x^6y^5*5xy^2*(-6)x^4\\ \\ \ =-30x^6*x*x^4*y^5*y^2\\ \\

when the bases are same then the exponents gets added

\\ \ =-30x^{6+1+4}y^{2+5}\\ \\ \ =-30x^{11}y^7

8 0
2 years ago
Read 2 more answers
The cost for x number of gallons of heating oil can be represented by the function f(x)=4x+6 in the context of the problem expla
deff fn [24]

Answer:

This means that the cost of 2 heating oil gallons is 14.

Step-by-step explanation:

f(x) = 4x + 6 , where x is the number of heating oil gallons.

And f(x) = 4x + 6 is the equation for the cost of x gallons.

When the number of gallons are 2 then the cost is;

f(2) = 4(2) + 6 = 8 + 6 = 14

This means that the cost of 2 heating oil gallons is 14.

7 0
3 years ago
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the gi
scoundrel [369]

The given equation is y + 2 = 4(x - 1)

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Step-by-step explanation:

Parallel lines have

  • Same slopes
  • Different y-intercepts

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y + 2 = 4(x - 1)

- Change its form to slope-intercept form to find its slope

∵ y + 2 = 4(x) - 4(1)

∴ y + 2 = 4x - 4

- Subtract 2 from both sides

∴ y = 4x - 6

- Compare it with the slope-intercept form to find m

∵ the slope-intercept form is y = mx + b

∴ m = 4

∵ The parallel lines have same slopes

∴ The slope of the parallel line is 4

- Substitute it in the form of the equation

∴ The equation of the parallel line is y = 4x + b

- To find b substitute x and y in the equation by the

   coordinates of a point on the line

∵ The parallel line passes through point (1 , -3)

∴ x = 1 and y = -3

∵ -3 = 4(1) + b

∴ -3 = 4 + b

- Subtract 4 from both sides

∴ -7 = b

∴ The equation of the parallel line is y = 4x + (-7)

∴ The equation of the parallel line is y = 4x - 7

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Learn more:

You can learn more about the linear equations in brainly.com/question/4152194

#LearnwithBrainly

4 0
3 years ago
Don't get it at all I am have lots of trouble
maks197457 [2]
47. B 9
48, D 81
49. A  5
50 C 45
5 0
2 years ago
Without multiplying all the terms, verify these equalities. a) 10!= 6!7! b) 10!=7!5!3! c) 16!= 14!5!2! d) 9!=7!3!3!2!
Romashka-Z-Leto [24]

Answer:

a)10! = 6×5×4×3×2 ×7!

10! = 6! 7! (Verified)

b)10! = 3! × 5! × 7! = 7!5!3! (Verified)

c)16! = 2! × 5! × 14!

16! = 14!5!2! (Verified)

d)9! = 3! × 3! ×2! × 7!

9! = 7!3!3!2! (Verified)

Step-by-step explanation:

a) 10!= 6!7!

10! = 10×9×8×7!

Reducing to their lowest factors

10! = (2×5)×(3×3)×(2×2×2) × 7!

Rearranging the factors, we have;

10! = (2×3)×(5)×(2×2)×(3)×2 × 7!

10! = 6×5×4×3×2 ×7!

10! = 6! 7! (Verified)

b) 10!=7!5!3!

10! = 10×9×8×7!

10! = (2×5)×(3×3)×(2×2×2) × 7!

Rearranging the factors, we have;

10! = (2×3)×(5)×(2×2)×(3)×2× 7!

10! = (3×2×1) × (5×4×3×2×1) × 7!

10! = 3! × 5! × 7! = 7!5!3! (Verified)

c) 16!= 14!5!2!

16! = 16×15×14!

16! = (2×2×2×2) × (5×3) × 14!

Rearranging the factors.

16! = (2) × (5) × (2×2) × (3) × (2) ×14!

16! = (2!) ×(5×4×3×2) × 14!

16! = 2! × 5! × 14!

16! = 14!5!2! (Verified)

d) 9!=7!3!3!2

9! = 9×8×7!

9! = (3×3) × (2×2×2) × 7!

Rearranging the factors

9! = (3×2) ×(3×2) ×(2) × 7!

9! = 3! × 3! ×2! × 7!

9! = 7!3!3!2! (Verified)

3 0
3 years ago
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