Ask question

Ask question

All categories

Zigmanuir [339]

3 years ago

9

Answers:

1 answer:

ryzh [129]3 years ago

4 0

Answers:

☆☆☆☆☆☆☆☆aTriangle ZYX
bTriangle YZX
cTriangle XZY
dTriangle XYZ

You might be interested in

Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

5 0

3 years ago

Evaluate the expression - |7-9|

timama [110]

Answer: -2

Step-by-step explanation: As our first step, we simplify inside the absolute value. 7 - 9 is -2 so we have -|-2|.

A common mistake at this point in the problem is to change the minus a negative to plus a positive but don't fall into this trap.

We must ignore the negative outside the absolute value until our very last step in this problem.

So we take the absolute value of -2 which is 2 and we have -(2) or -2.

Notice that I used parentheses around the 2 as it comes out of the absolute value.

5 0

4 years ago

Susanne wants to put up a fence around her

Anettt [7]

Answer:

44 feet

Step-by-step explanation:

The garden is square and one side is 11 feet. Therefore the equation is 11 x 4

8 0

3 years ago

Given square WXYZ. If ZY = 20, find WV. Write your response in the form WV=_____.

Citrus2011 [14]

Answer:

14.14

Step-by-step explanation:

Recall :

The sides of a square are always equal ;

Since all sides are equal, the the diagonal of the square will be :

XZ² = XY² + WX²

XZ² = 20² + 20²

XZ² = 400 + 400

XZ² = 800

XZ = √800

XZ = 28.28

WY = XZ

WV = 1/2 WY

WV = 1/2 * 28.28

WV = 14.14

6 0

3 years ago

A snowstorm dropped three and two-fifths inches of snow. The next day one and four-fifths inches melted, how much snow was left?

boyakko [2]

Answer:

After the melting there were one and three fifths of snow left.

Step-by-step explanation:

Given that a snowstorm dropped three and two-fifths inches of snow, and the next day one and four-fifths inches melted, the following calculation must be performed to determine how much snow was left:

2/5 = 0.40

4/5 = 0.80

3.40 - 1.80 = X

1.60 = X

0.60 = 3/5

Thus, after the melting there were one and three fifths of snow left.

4 0

3 years ago