Is this congruent by SSS, SAS, AAS, ASA??

If five times the smaller of two numbers is subtracted from twice the larger the result is 16 if the larger is increased by thre

Rudiy27

Answer:

Smaller Number = 10

Larger Number = 33

Step-by-step explanation:

Let the smaller number be "x" and the larger number be "y"

5 TIMES smaller is SUBTRACTED from TWICE larger, the result is 16, we can write:

2y - 5x = 16

and

Larger increased by 3 TIMES SMALLER, result is 63, so we can write:

y + 3x = 63

We can write this in terms of x, as:

y = 63 - 3x

Now we put this in equation 1 and solve for x first:

2y - 5x = 16

$2(63 - 3x) - 5x = 16\\126-6x-5x=16\\11x=110\\x=10$

Now,

y = 63 - 3x

y = 63 - 3(10)

y = 63 - 30

y = 33

Smaller Number = 10

Larger Number = 33

8 0

3 years ago

If a sequence is recursively defined by f(0)=5 and f(n+1)=-4f(n)+2 for n greater than or equal to 0. Find f(3) ?

Angelina_Jolie [31]

Answer:

The correct answer is f(3) = -294

Step-by-step explanation:

To find f(3), we have to find f(1) and f(2)

It is given that,

f(0)=5 and f(n+1)=-4f(n)+2

To find f(1)

using given information,

f(1) = -4f(0) + 2 = -4*5 + 2 = -20 +2 = -18

To find f(2)

f(2) = -4f(1) + 2 = -4*-18 + 2 = 72 + 2 = 74

To find f(3)

f(3) =-4f(2) + 2 = -4*74 + 2 =-296 + 2 = -294

Therefore the value of f(3) = -294

6 0

3 years ago

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.

hodyreva [135]

Any point with coordinates (x, y) reflected across the y-axis is going to have the opposite x value that it did before.
You should be able to find the coordinates yourself for part a. (you didn't provide the original ones so I can't help you there)
Here is the "rule" for a reflection across the y-axis:
$(x,\ y)\rightarrow(-x,\ y)$
And when we go 1 unit to the right and 2 down, that's the same as
$(x,\ y)\rightarrow(x+1,\ y-2)$

Combining those into one rule is pretty simple, Use our result for the first in the second and we would get $(-x+1,\ y-2)$ , so the rule is
$\boxed{(x,\ y)\rightarrow(-x+1,\ y-2)$ .
Part A is asking for the coordinates after the reflection (x, y) ⇒ (-x, y).
Part C is asking for the coordinates after the full translation ⇒ (-x+1, y-2)

8 0

4 years ago

Maria invested $4,000 at 3.5% simple interest. She left the principal invested for 57 months. Robert invested $3,500 at 8.5% sim

Alex_Xolod [135]

Answer:

Maria have $123,75 more total money than Robert at the end of their investments.

Step-by-step explanation:

To calculate the simple interest we should multiply the Initial invest, with the interest without percentage and the time in years.

As the time is in months we have to divide it by 12 so we have the mesure of time in years, then the interest for each of the investments will be:

Maria

Invest = $4,000 Interest = 3.5/100=0.035 Time = 57/12 = 4.75

Simple Interest = 4,000 x 0.035 x 4.75 = $665

Total money at the end of the invest = $4,000 + $665 = $4,665

Robert

Invest = $3,500 Interest = 8.5/100=0.085 Time = 42/12 = 3.5

Simple Interest = 3,500 x 0.085 x 3.5 = $1,041.25

Total money at the end of the invest = $3,500 + $1,041.25 = $4,541.25

Now we have to subtract the total money of Robert from the total money of Maria to know how much money did she got over Robert after their invests

$4,665 - $4,541.25 = $123.75

At the end of the invest, Maria got $123,75 more than Robert

8 0

3 years ago

john's dad gave him 8 3/4 pieces of wood. he used 4 2/3 pieces to make a bird house. his friend david then asked for 1 1/2 piece

Serjik [45]

Ok so this all about subtracting fractions this is what you want to do:

you can change 8 3/4 and 4 2/3 to have the same value and deominator
8 3/4 = 8 9/12(multiply both sides by 3)
4 2/3 = 4 8/12(multiply both sides by 4)
you do this because 12 is divisible by 3 and 4

then, subtract 4 8/12 from 8 9/12 because John is using some of the wood his dad gave him.
then subtract once again, taking 11/2 away from your difference.
again match the deominator of 11/2 to the deominator of your difference which should be 12. another divisible of 12 is 2 and 6.
11/2 = 66/12 = 5 6/12(multiply both the top and bottom by 6)
and start subtracting.

so John should have -1 5/12(?) wood left

3 0

3 years ago