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3 years ago

In ΔNLM, if m∠M=(4x-4)°, m∠L=(3x+12)°, and m∠N=(6x+3)°, what is x?

Mathematics

1 answer:

GarryVolchara [31]3 years ago

5 0

Answer:

x = 13

Step-by-step explanation:

The sum of angle measures in a triangle is 180°.

m∠M + m∠L + m∠N = 180°

(4x-4)° + (3x+12)° + (6x+3)° = 180°

13x +11 = 180 . . . . . . collect terms, divide by °

13x = 169 . . . . . . . . . subtract 11

x = 13 . . . . . . . . . . . . . divide by 13

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Factorise 9w² - 100

ohaa [14]

Answer:

$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$ .

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$ .

In other words, $(a^{2} - b^{2})$ , the difference of two squares in the form $a^{2}$ and $b^{2}$ , could be factorized into $(a - b)\, (a + b)$ .

In this question, the expression $(9\, w^{2} - 100)$ is the difference between two terms: $9\, w^{2}$ and $100$ .

$9\, w^{2}$ is the square of $3\, w$ . That is: $(3\, w)^{2} = 9\, w^{2}$ .
On the other hand, $10^{2} = 100$ .

Hence:

$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$ .

Apply the fact that $a^{2} - b^{2} = (a - b) \, (a + b)$ to factorize this expression. (In this case, $a = 3\, w$ whereas $b = 10$ .)

$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$ .

8 0

3 years ago

Find the value of x in the following diagram, 3x + 10 Here, B and D are points of tangency.

SVEN [57.7K]

Given:

The given circle with center at C. The lines AB and AD are tangents to the circle C.

The length of AB is (3x + 10)

The length of AD is (7x - 6)

We need to determine the value of x.

Value of x:

Since, we know the property of tangent that, "if two tangents from the same exterior point are tangent to a circle, then they are congruent".

We shall determine the value of x using the above property.

Thus, we have;

AB = AD

Substituting the values, we get;

$3x+10=7x-6$

Subtracting both sides of the equation by 7x, we get;

$-4x+10=-6$

Subtracting both sides of the equation by 10, we get;

$-4x=-16$

Dividing both sides of the equation by -4, we get;

$x=4$

Thus, the value of x is 4.

5 0

3 years ago

Find the lengths of sides e, f, & g

valentinak56 [21]

Answer:

e 7 f 5 g is the square root of 74 I don't have a calculator on me sry

8 0

3 years ago

The length of a rectangular floor is 2 feet more than the width. The area of the floor is 168 square feet. Kim wants to use a ru

defon

The area of the rectangular is expressed in the formula A = l*w where l is the length and w is the width. from the first satement, l = 2 + w; then A = (2+w)*w = 2w + w^2. If A is equal to 168, then w should be equal to 12 feet and l is equal to 14 feet. Hence the width due to the border limits is 12- 2*2 equal to 8 feet

4 0

3 years ago

10 time as much as25

Paha777 [63]

Answer:

250

Step-by-step explanation:

10 times as much as 25 equals:

10 * 25 = ?

10 * 25 = 250

You just have to look for keywords and turn it into a [math] problem.

I hope this helps!

<h2>PLEASE MARK BRAINLIEST!</h2>

6 0

3 years ago