1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
otez555 [7]
3 years ago
5

The length of a rectangle is three times its width. If the area of the rectangle is 192 ft^2, find its perimeter

Mathematics
2 answers:
allochka39001 [22]3 years ago
6 0
Lets x = width
length = 3x

A = length times width
A = x * 3x
192 = 3x^2
192/3 = x^2
64 = x^2
8 = x

so width = 8
length = 3x = 3(8) = 24

P = 2(L + W)
P = 2(24 + 8)
P = 2(32)
P = 64

answer
P = 64 feet
Blababa [14]3 years ago
3 0
Answer: 64 feet.

Explanation:
Perimeter formula: 2l + 2w
Area formula: l•w
Length = 3w
Area = 192 ft^{2}
192 = (3w) • w 
192 = 3w^{2}
192 ÷ 3 = 3w^{2} ÷ 3
64 = w^{2} 
\sqrt{64} = \sqrt{ w^{2} }
8 = w 

Width = 8
Length = 3(8) = 24 
Perimeter = 2(24) + 2(8) = 64 feet.

You might be interested in
Solve for t. You must write your answer in fully simplified form. <br> −19= 7t
Olenka [21]

Answer: dot know srry

Step-by-step explanation:

8 0
2 years ago
What is the equation of a line that is parallel to y=2/3x-7 and passes through (12,2)?
Ganezh [65]

Answer:

<h2>The answer is option A</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

From the question the original line is

y = 2/3x - 7

Comparing with the general equation above

Slope = 2/3

Since the lines are parallel their slope are also the same

Slope of parallel line = 2/3

So the equation of the line using point

(12 , 2 ) and slope 2/3 is

y - 2 =  \frac{2}{3} (x - 12) \\ y - 2 =  \frac{2}{3} x - 8 \\ y =  \frac{2}{3} x - 8 + 2

We have the final answer as

y =  \frac{2}{3} x - 6 \\

Hope this helps you

5 0
3 years ago
Read 2 more answers
Mr.George divided his money in the ratio 2:6 between Evan and ricky.Evan got the smaller amount of $420. How much did ricky rece
Gemiola [76]
Ratios are like fractions in the way that you can simplify them if they have common factors.
we can simplify this ratio to 
1:3
that means that the bigger part got 3 times the amount of the smaller part. The problem says that Evan got the smaller amount, so if we multiply the smaller amount by 3 we should and will get the bigger amount. It says that $420 is the smaller part.
420*3=1260
so the bigger amount of money is $1260
So, because Ricky got the bigger part of Mr. George's money, he must have received
$1260<span />
6 0
3 years ago
2. <br> Find m∠F.<br><br> a.30°<br><br> b.60°<br><br> c.15°<br><br> d.10°
Juliette [100K]

Answer:

Step-by-step explanation:

\sf Sin \ F = \dfrac{Opposite \ of \ angle \ F}{hypotenuse}

       = \dfrac{9}{18}\\\\= 0.5

    F = Sin^{-1} \ (0.5)\\

        = 30°

4 0
2 years ago
Math<br><br><br><br> pls help!!<br><br><br><br><br><br> answers?
statuscvo [17]

Answer: Choice B) Infinitely many solutions

  • one solution: x = 8, y = -7/2, z = 0
  • another solution: x = -12, y = 13/2, z = 10

=======================================================

Explanation:

Here's the starting original augmented matrix.

\left[\begin{array}{ccc|c}  1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\-4 & 0 & -8 & -32\\\end{array}\right]

We'll multiply everything in row 3 (abbreviated R3) by the value -1/4 or -0.25, which will make that -4 in the first column turn into a 1.

We use this notation to indicate what's going on: (-1/4)*R3 \to R3

That notation says "multiply everything in R3 by -1/4, then replace the old R3 with the new corresponding values".

So we have this next step:

\left[\begin{array}{ccc|c}  1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\1 & 0 & 2 & 8\\\end{array}\right]\begin{array}{l}  \ \\\ \\(-1/4)*R3 \to R3\\\end{array}

Notice that the new R3 is perfectly identical to R1.

So we can subtract rows R1 and R3, and replace R3 with the result of nothing but 0's

\left[\begin{array}{ccc|c}  1 & 0 & 2 & 8\\5 & 1 & 9 & 73/2\\0 & 0 & 0 & 0\\\end{array}\right]\begin{array}{l}  \ \\\ \\R3-R1 \to R3\\\end{array}

Whenever you get an entire row of 0's, it <u>always</u> means there are infinitely many solutions.

-------------------

Now let's handle the second row. That 5 needs to turn into a 0. We can multiply R1 by 5, and subtract that from R2.

So we need to compute 5*R1-R2 and have that replace R2.

\left[\begin{array}{ccc|c}  1 & 0 & 2 & 8\\0 & 1 & -1 & -7/2\\0 & 0 & 0 & 0\\\end{array}\right]\begin{array}{l}  \ \\5*R1-R2 \to R2\ \\\ \\\end{array}

Notice that in the third column of R2, we have 9-5*2 = 9-10 = -1. So we have -1 replace the 9. In the fourth column of R2, we have 73/2 - 5*8 = -7/2. So the -7/2 replaces the 73/2.

--------------------

At this point, the augmented matrix is in RREF form. RREF stands for Reduced Row Echelon Form. It seems a bit odd that the "F" of "RREF" stands for "form" even though we say "form" right after "RREF", but I digress.

Because the matrix is in RREF form, this means R1 and R2 lead to these equations:

R1 : 1x+0y+2z = 8\\ R2: 0z+1y-1z = -7/2

which simplify to

R1: x+2z = 8\\R2: y-z = -7/2

Let's get the z terms to each side like so:

x+2z = 8\\x = -2z+8\\\text{ and }\\y-z = -7/2\\y = z-7/2\\

Therefore, all of the solutions are of the form (x,y,z) = (-2z+8, z-7/2, z) where z is any real number.

If z is allowed to be any real number, then we can simply pick any number we want to replace it. We consider z to be the "free variable", in that it's free to be whatever it wants. The values of x and y will depend on what we pick for z.

So the concept of "infinitely many solutions" doesn't exactly mean we can pick just <em>any</em> triple for x,y,z (admittedly it would be nice to randomly pick any 3 numbers off the top of my head and be done right away). Instead, we can pick anything we want for z, and whatever we picked, will directly determine x and y. The x and y are locked into place so to speak.

Let's say we picked z = 0.

That would lead to...

x = -2z+8\\x = -2(0)+8\\x = 8\\\text{ and }\\y = z-7/2\\y = 0-7/2\\y = -7/2\\

So z = 0 would lead to x = 8 and y = -7/2

Rearranging the items in alphabetical order gets us:

x = 8, y = -7/2, z = 0

We have one solution of (x,y,z) = (8, -7/2, 0)

Now let's say we picked z = 10

x = -2z+8\\x = -2(10)+8\\x = -12\\\text{ and }\\y = z-7/2\\y = 10-7/2\\y = 13/2\\

So we have x = -12, y = -13/2, z = 10

Another solution is (x,y,z) = (-12, 13/2, 10)

There's nothing special about z = 0 or z = 10. You can pick any two real numbers you want for z. Just be sure to recalculate the x and y values of course.

To verify each solution, you'll need to plug them back into the original equations formed by the original augmented matrix. After simplifying, you should get the same thing on both sides.

8 0
2 years ago
Other questions:
  • A square painting has a length of 62 cm. What is the area of the painting?
    14·2 answers
  • given the functions f(x)=x^3-11x^2 40x-48 what one the following is a factor of f(x)? answer choices: a: x 16 b:x 4 c:x-16 d:x-3
    14·1 answer
  • 9% rounded to the nearest whole number
    7·2 answers
  • Find the Measure of side C
    12·1 answer
  • The football and soccer teams at Juan's middle school are selling movie tickets. He wants to determine the average
    9·1 answer
  • Please help me answer these.
    13·1 answer
  • The interior angles formed by the sides of a hexagon have measures that sum to 720°.
    7·1 answer
  • Picture 1272837373773
    15·1 answer
  • Solve for A, find the exact value of each expression below.
    7·1 answer
  • Write the equation of a line that is parallel to y=1/2x+4 and goes thru the point(-3,4)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!