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3 years ago

Determine if the two figures are congruent and explain your answer using transformations.

Mathematics

1 answer:

Vinvika [58]3 years ago

4 0

Answer:

Step-by-step explanation:

By observation we see that the sides:

DC = HG

CB = GF

BA = FE and DA = HE so the 2 figures are congruent.

If we reflect EFGH in the y-axis we see that the point F (4, 1( moves to (-4,1)

and the point E moves from (2, 0) o (-2, 0) and the other 2 points points move in a similar fashion.

If we then move the whole figure up 1 unit then 1 to the right EFGH completely occupies the same area as ABCD confirming they are congruent.

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Find the sum. (9 + 7n) +(-3+ 4c) + (2 + 5m)

irga5000 [103]

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3 years ago

Write the equation: One half of a number decreased by 4 is 2

AnnyKZ [126]

Answer:

Step-by-step explanation:

decrease means subtracted

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4 years ago

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:

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

Verification:

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

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

it takes tom 4 hours to build a fence. If he hires jack to help him, together they can do the job in just 3 hours. If jack built

Butoxors [25]

Tom:
time to build a fence= 4 hours; rate =1/4 job/hr.

tom &jack
time to build a fence = 3 hrs.; rate = 1/3 job/hr

Jack :
time to build a fence= x hrs ; rate = 1/x job/hr

1/4 + 1/x = 1/3
3x + 12 = 4x
x=12 hrs. (Time for jack to build a fence )

5 0

4 years ago

Read 2 more answers

Peter’s Pants Palace advertises the following sale: Shirts are 1/2 off the original price; pants are 1/3 off the original price;

svetoff [14.1K]

Answer:

10$, 11$

Step-by-step explanation:

40/4 = 10$

33/3 = 11$

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3 years ago