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3 years ago

What is the solution to this linear system?

Mathematics

1 answer:

andrew-mc [135]3 years ago

6 0

Answer:

C) (14, 8, 10)

Step-by-step explanation:

the values in the parentheses go in order of the letters in the first equation

all you have to do is plug in the values

p+q+r=32. (14)+(8)+(10)=32

p-r=4. (14)-(10)=4

2p+q=36. 2(14)+(8)=36

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You invest $5000 in an account at 5.5% per year simple interest. How much will you have in the account at the beginning of the 6

NeX [460]

Answer:

The amount in the account in the beginning of the 6th year is $6375 .

Step-by-step explanation:

Formula

$Simple\ interest = \frac{Principle\times Rate\ times Time}{100}$

As given

You invest $5000 in an account at 5.5% per year simple interest.

Principle = $ 5000

Rate = 5.5 %

Time = 5 years

(As calculate amount in the account for beginning of 6th year.)

Putting all the values in the formula

$Simple\ interest = \frac{5000\times 5.5\times 5}{100}$

$Simple\ interest = 50\times 5.5\times 5$

Simple interest = $ 1375

Amount = Principle + Simple interest

Putting values in the above formula

Amount = $5000 + $1375

Amount = $ 6375

Therefore the amount in the account in the beginning of the 6th year is $ 6375 .

8 0

3 years ago

The length of a rectangle is eight more than twice its width. The perimeter is 96 feet. Find the dimensions of the rectangle

Debora [2.8K]

Answer:

The width of the rectangle is 14'8", and the length is 33'4"

Step-by-step explanation:

We're given two pieces of information:

The length is eight more than twice the width:

$l = 2w + 4$

The perimeter is 96 feet:

$p = 96$

We also need to apply one more piece of information that is not provided here, and that is the relationship between the perimeter of a rectangle, and it's length and width:

$p = 2l + 2w$

We can solve for w by plugging the other two values into the last:

$p = 2w + 2l\\96 = 2w + 2(2w + 4)\\96 = 2w + 4w + 8\\88 = 6w\\3w = 44\\w = \frac{44}{3}\\w = 14\frac{2}{3}$

Now we can find the length by plugging w into the first equation:

$l = 2w + 4\\l = 2(14\frac{2}{3}) + 4\\l = 29\frac{1}{3} + 4\\l = 33\frac{1}{3}$

One third of a foot is four inches, so the width is 14'8" and the length is 33'4"

To make sure our answer is correct, we should plug those numbers back into the area equation and see if we're right:

$p = 2l + 2w\\p = 2(33\frac{1}{3}) + 2(14\frac{2}{3})\\p = 66\frac{2}{3} + 29\frac{1}{3}\\p = 96$

So we know our answer's correct

8 0

2 years ago

The graph of f(x)=cos(x) is transformed to a new function, g(x) , by stretching it horizontally by a factor of 4 and shifting it

SpyIntel [72]

The equation of the new function is $g(x)= cos4 x+1$

Explanation:

The Parent function is $f(x)=cos x$

We need to determine the new function g(x) using the transformation by stretching the f(x) horizontally by a factor of 4 and shifting it 1 unit up.

The function transformation formula is given by

$f(x)=a \cos b(x-c)+d$

Where a stretches the function vertically

b compresses or stretches it horizontally,

c shifts the function left or right

d shifts the function up or down

Since, it is given that the function stretches horizontally by a factor of 4 and shifting it 1 unit up.

Hence, $b=4$ and $d=1$

Substituting these values in the formula, we have,

$g(x)=cos4x+1$

Thus, the equation of the new function is $g(x)= cos4 x+1$

8 0

3 years ago

You buy a container of cat litter for $11.50 and a bag of cat food for x dollars. The total purchase is $16.80, which includes 5

NARA [144]

Answer:

4.46

Step-by-step explanation:

(11.5 + x) + 5% = 16.8

11.5 + x = 16.8 - 5%

x = (16.8 - 5% ) - 11.5

x = 15.96 - 11.5

x = 4.46

5 0

3 years ago

Read 2 more answers

The complement of an angle is 81° what is the measure of the angle

Fiesta28 [93]

9°, complementary angles always add up to 90°

5 0

3 years ago