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3 years ago

Triangle Congruence theorems

Mathematics

1 answer:

Hunter-Best [27]3 years ago

5 0

Triangle Congruence Theorems

Use the triangle congruence theorems below to prove that two triangles are congruent if:
Three sides of one triangle are congruent to three sides of another triangle (SSS: side side side)
Two sides and the angle in between are congruent to the corresponding parts of another triangle (SAS: side angle side)
Two angles and the side in between are congruent to the corresponding parts of another triangle (ASA: angle side angle)
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle (AAS: angle angle side)
The hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle (HL: hypotenuse leg)

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One number is 4 times another number. The sum of their reciprocals is 5. What are the two numbers?

ivann1987 [24]

Answer:

The two number are:

$y=1,\:x=\frac{1}{4}$

Step-by-step explanation:

Let 'x' be the first number

let 'y' be the second number

Given that one number is 4 times another number, the first equation is

$y = 4x$

Next, the sum of their reciprocals is 5, so

$\frac{1}{x}+\frac{1}{y}=5$

Now, we have the system of equations

$\begin{bmatrix}y=4x\\ \frac{1}{x}+\frac{1}{y}=5\end{bmatrix}$

Let us solve the system of equations

$\begin{bmatrix}y=4x\\ \frac{1}{x}+\frac{1}{y}=5\end{bmatrix}$

substitute y = 4x in the equation $\frac{1}{x}+\frac{1}{y}=5$

$\frac{1}{x}+\frac{1}{4x}=5$

Least Common Multiple of x, 4x: 4x

Adjust fractions based on L.C.M

$\frac{4}{4x}+\frac{1}{4x}=5$

$\frac{4+1}{4x}=5$

$\:\frac{5}{4x}=5$

Multiply both sides by 4x

$\frac{5}{4x}\cdot \:4x=5\cdot \:4x$

Simplify

$5=20x$

switch sides

$20x=5$

Divide both sides by 20

$\frac{20x}{20}=\frac{5}{20}$

Simplify

$x=\frac{1}{4}$

For y = 4x, substitute $x=\frac{1}{4}$

$y = 4x$

$y=4\cdot \frac{1}{4}$

$y=1$

Therefore, the two number are:

$y=1,\:x=\frac{1}{4}$

<u>Verification:</u>

$\frac{1}{x}+\frac{1}{y}=5$

substituting $y=1,\:x=\frac{1}{4}$

$\:\frac{1}{\frac{1}{4}}+\frac{1}{1}=\:5\:\:$

$4+1=5$

$5 = 5$

L.H.S = R.H.S

and

$y = 4x$

substituting $y=1,\:x=\frac{1}{4}$

$y\:=\:4\left(\frac{1}{4}\right)$

$y=1$

8 0

3 years ago

Help me please! i forgot how you do this!!

Arte-miy333 [17]

Answer:

Step-by-step explanation:

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3 years ago

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Please help and explain. I need help with 16,17,20

zzz [600]

16. LCM is 21
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The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.

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