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olga55 [171]
3 years ago
13

The base of a parallelogram is four times its height. If the area of the parallelogram is 324 cm2, find the base and height.

Mathematics
1 answer:
madam [21]3 years ago
8 0
A = bh
b = 4h
A = 324

324 = 4h * h
324 = 4h^2
324/4 = h^2
81 = h^2
sqrt 81 = h
9 = h

b = 4h
b = 4(9)
b = 36

so the height (h) = 9 cm and the base (b) = 36 cm
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Write an algebraic expression for each statement:
Andrei [34K]

For the given sentences, the algebraic expressions are:

a) N = 110*c - 300

b) N = 12*b

<h3>How to get the algebraic expressions?</h3>

For the first statement:

A 3-digit number, where the tens digit is c, can be written as:

N = 100*a + 10*c + b

Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:

a = c - 3

The ones digit is b, here we know that it is 0, then b = 0.

Replacing that in our number we get:

N = 100*(c - 3) + 10*c = 110*c - 300

N = 110*c - 300

That is the algebraic expression.

b) A two-digit number can be written as:

N = b*10 + a

Where b is the tens digit and a is the ones digit.

Here we know that the units digit is twice as bit as the tens digit, then:

a = 2b

Replacing that we get:

N = b*10 + a = b*10 + 2b = 12*b

N = 12*b

That is the algebraic expression.

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4 0
2 years ago
2-3x=8 what does x equal?
juin [17]
If you would like to solve the equation 2 - 3 * x = 8 for x, you can calculate this using the following steps:

2 - 3 * x = 8
-3 * x = 8 - 2
-3 * x = 6    /(-3)
x = 6 / (-3)
x = -2

Result: x equals to -2.
7 0
3 years ago
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A flare is launched from a life raft with an initial upward velocity of 192 feet per second. How many seconds will it take for t
AVprozaik [17]
So you want height to be 0 so you plug zero into the height and solve from there. You subtract 192 from both sides to get -192=-16tsquared. Then you would divide by -16 and end up with 12 = t^2. Then you find the square root of 12 and get t = 3.464 seconds.
7 0
3 years ago
12. Find the value of x.<br> HELP PLS HELP
xenn [34]

Answer:

x = 16

Step-by-step explanation:

 SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.

The angles opposite to equal sides are equal.

  ⇒  ∠STR  = ∠R

       ∠STR = 4x - 28

Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair

∠STR + ∠STU = 180°    {linear pair}

4x - 28 + 9x = 180

4x + 9x - 28  = 180      {Combine like terms}

       13x- 28 = 180

Add 28 to both the sides

          13x    = 180 + 28

           13x  = 208

Divide both sides by 13

              x = 208/13

  \sf \boxed{x = 16}

8 0
2 years ago
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Given that x = -2 - 3i and y = 4 + 2i , Match The Expressions.
shtirl [24]

Answer:

3y-2x=16+12i

-3x \cdot y=6+48i

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x-y=-6-5i

Step-by-step explanation:

Given:

x=-2-3i

y=4+2i

---

1st problem:

3y-2x

3(4+2i)-2(-2-3i)

Distribute:

12+6i+4+6i

Combine like terms:

16+12i

---

2nd problem:

-3x \cdot y

-3(-2-3i) cdot (4+2i)

-3(-2-3i)(4+2i)

Distribute -3 to first factor:

(6+9i)(4+2i)

Use foil to simplify:

24+12i+36i+18i^2

Replace i^2 with -1:

24+48i-18

Combine like terms:

6+48i

---

3rd problem:

x \cdot 2y

(-2-3i) \cdot 2(4+2i)

Distribute 2 to the second factor:

(-2-3i) \cdot (8+4i)

(-2-3i)(8+4i)

Use foil to simplify:

-16-8i-24i-12i^2

Replace i^2 with -1:

-16-32i+12

Combine like terms:

-4-32i

----

4th problem:

(-2-3i)-(4+2i)

Distribute:

-2-3i-4-2i

Combine like terms:

-2-4-3i-2i

Simplify:

-6-5i

6 0
3 years ago
Read 2 more answers
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