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3 years ago

Please help! If the two triangles are similar, which equation represents the value of side x?

Mathematics

1 answer:

madam [21]3 years ago

5 0

$x=\frac{p q}{m}$ equation represents the value of side x.

Solution:

The two triangles are similar.

<em>If two triangles are similar, then the corresponding sides are in proportional.</em>

$$\Rightarrow \frac{m}{p} =\frac{q}{x}$

Do cross multiplication.

$$\Rightarrow mx=pq$

Divide by m on both sides.

$$\Rightarrow \frac{mx}{m} =\frac{pq}{m}$

$$\Rightarrow x =\frac{pq}{m}$

Therefore, $x=\frac{p q}{m}$ equation represents the value of side x.

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Which of the following statements regarding the expansion of (x + y)^n are correct?

kompoz [17]

Answer:

A, B and D are true statements.

Step-by-step explanation:

We are given a binomial expansion

$(x+y)^n=^nC_0x^ny^0+^nC_1x^{n-1}y^1+^nC_2x^{n-2}y^2+...........+^nC_nx^0y^n$

$(x+y)^n=x^n+nx^{n-1}y+^nC_2x^{n-2}y^2+...........nxy^{n-1}+y^n$

Now we will check each option

Option A: The coefficients of $x^n$ and $y^n$ both equal 1.

If we see first and last term of the expansion, This statement is true.

Option B: For any term $x^ay^b$ in the expansion, a + b = n.

Let we take 3rd term of expansion $^nC_2x^{n-2}y^2$

Here, a=n-2 and b=2

If we do a+b = n-2+2=n

a+b=n is true statement.

Option C: For any term x^ay^b in the expansion, a - b = n.

Let we take 3rd term of expansion $^nC_2x^{n-2}y^2$

Here, a=n-2 and b=2

If we do a-b = n-2-2=n-4≠n

a-b=n is false statement.

Option D: The coefficients of x^ay^b and x^by^a are equal.

If we take second term from beginning and last of the expansion.

$\text{Coefficient From beginning } nx^{n-1}y=n$

$\text{From last } nxy^{n-1}=n$

This statement true.

8 0

3 years ago

The slope of the line shown in the graph is ? and the y intercept of the line is ?

ohaa [14]

Pick 2 points on ur line and use the slope formula : (y2 - y1) / (x2 - x1)

(y2 - y1) / (x2 - x1)
(-9,0)....x1 = -9 and y1 = 0
(0,6).... x2 = 0 and y2 = 6
now sub
slope = (6 - 0) / (0 - (-9) = 6/(0 + 9) = 6 / 9 = 2/3 <==

ur y intercept is where ur line crosses the y axis...and that would be (0,6)....or just 6 <==

5 0

3 years ago

6x + 2 = 26 what is the answer

GrogVix [38]

Answer: x=4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the value of this expression when c=-4 and d = 10?<br> 1/4(c3+d2)

Mumz [18]

What is the value of this expression when c = -4 and d = 10 ? $\frac{1}{4}$ (c³ + d²)

<h3>Given:-</h3>

$\frac{1}{4}$ (c³ + d²) where c = -4 and d = 10

The value of the expression $\frac{1}{4}$ (c³ + d²)

<h2>Solution:-</h2>

$\frac{1}{4}$ (c³ + d²) [Given expression]

Now, putting the value of c = -4 and d = 10 , we get,

$\frac{1}{4}$ { (-4)³ + (10)² }

$\frac{1}{4}$ ( -64 + 100 )

$\frac{1}{4}$ ( 36 )

$\frac{1}{4}$ × 36

$\bf = \: 9 \: ( Answer )$

3 0

3 years ago

14=6n+6-2n solve for n

Anika [276]

Answer:

n=2

Step-by-step explanation:

14=6n+6-2n

Combine like terms

14 = 4n+6

Subtract 6 from each side

14 -6 = 4n+6-6

8 = 4n

Divide by 4

8/4 = 4n/4

2 =n

8 0

3 years ago

Read 2 more answers