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2 years ago

1. Find the measurement of angle J. 2. (5x - 13) (3x + 17)

Mathematics

1 answer:

Alex Ar [27]2 years ago

8 0

Answer:

Q1. x= 18, y=59

Q2. m∠J= 56°

Step-by-step explanation:

Q1. (3x +5)°= y° (base ∠s of isos. △)

y= 3x +5 -----(1)

(3x +5)° +y° +(4x -10)°= 180° (∠ sum of △)

3x +5 +y +4x -10= 180

7x +y -5= 180

7x +y= 180 +5

7x +y= 185 -----(2)

Substitute (1) into (2):

7x +3x +5= 185

10x= 185 -5

10x= 180

x= 180 ÷10

x= 18

Substitute x= 18 into (1):

y= 3(18) +5

y= 59

Q2. (5x -13)°= (3x +17)° (base ∠s of isos. △)

5x -13= 3x +17

5x -3x= 17 +13

2x= 30

x= 30 ÷2

x= 15

∠LKJ

= 3(15) +17

= 62°

∠KLJ= 62° (base ∠s of isos. △)

m∠J

= 180° -62° -62° (∠ sum of △JKL)

= 56°

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An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near

tino4ka555 [31]

Answer:

The height of the triangle is 5.2 inches

Step-by-step explanation:

we know that

An <u>equiangular triangle</u> is a triangle where all three interior angles are equal in measure

Remember that an equilateral triangle has three equal sides and three equal interior angles

An equiangular triangle Is the same that an equilateral triangle. The measure of its interior angles is equal to 60 degrees

Let

h ----> the height of triangle

b ---> the length side of the triangle

Applying Pythagoras Theorem

$h^2=b^2-(b/2)^2$

we have

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substitute

$h^2=6^2-(6/2)^2$

$h^2=36-9$

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see the attached figure to better understand the problem

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3 years ago

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mariarad [96]

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3 years ago

Find the product (8/6n-4)(9n^2-4)

Leokris [45]

Answer:

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Step-by-step explanation:

Given expression is:

$(\frac{8}{6n-4})(9n^{2}-4)$

The numerator of the fraction will be multiplied with 9n^2- 4

So, Multiplication will give us:

$=\frac{8(9n^2-4)}{6n-4}$

We can simplify the expression before multiplication.

The numerator will be broken down using the formula:

$a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}$

We can take 2 as common factor from denominator

$=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)$

Hence the product is 4(3n+2) or 12n+8 ..

6 0

2 years ago