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Karo-lina-s [1.5K]
3 years ago
13

The parallelograms have a combined area of 3 1/7 square yards. The height of each parallelogram is 1 2/7 yards. How long is the

base of each parallelogram? What is the area of the smallest rectangle of wall that the mirror could fit on?
Mathematics
1 answer:
Naily [24]3 years ago
8 0

Answer:

a) How long is the base of each parallelogram?

1 2/9 yards.

b) What is the area of the smallest rectangle of wall that the mirror could fit on?

3 Square yards

Step-by-step explanation:

The parallelograms have a combined area of 3 1/7 square yards. The height of each parallelogram is 1 2/7 yards.

Step 1

We find the area of each of the parallelogram

This is calculated as:

Combined area of the parallelograms ÷ 2

= 3 1/7 square yards ÷ 2

= 22/7 square yards ÷ 2

= 22/7 square yards × 1/2

= 11/7 square yards

= 1 4/7 square yards.

Step 2

How long is the base of each parallelogram?

The height of each parallelogram is 1 2/7 yards.

Area of parallelogram = Base × Height

Base of each parallelogram = Area of each parallelogram/Height of each parallelogram

= 1 4/7 square yards ÷ 1 2/7 yards

= 11/7 square yards ÷ 9/7 yards

= 11/7 square yards × 7/9 yards

= 11/9 yards

= 1 2/9 yards.

Step 3

What is the area of the smallest rectangle of wall that the mirror could fit on?

Area of a rectangle = Length × Width

Length =(Base of parallelogram × 2)

Width = Base of parallelogram = 1 2/9 yards = 11/9 yards

Length = 1 2/9 yards × 2

= 11/9 × 2 = 22/9 yards

Area of rectangle = 11/9 × 22/9

= 242/81 square yards

= 2.987654321 square yards

Approximately = 3 Square yards

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The ratio of blue cars to red cars in a garage is 9:7. If there are 49 red cars in the garage then how many blue cars must be in
m_a_m_a [10]

Answer:

Blue cars, B = 63 cars

Step-by-step explanation:

Let the blue cars be B.

Let the red cars be R.

Given the following data;

Ratio of B:R = 9:7 = 9 + 7 = 16

Red cars, R = 49

To find the number of blue cars;

First of all, we would determine the total number of cars using the expression;

R = 7/16 * x = 49

7x = 49 * 16

7x = 784

x = 112 cars

Now, we can find the number of blue cars;

B = 9/16 * 112

B = 1008/16

Blue cars, B = 63 cars

3 0
3 years ago
Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$
horrorfan [7]

Answer:

A +B+C+D  = 3 is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

A+B+C+D = ? if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under \sqrt (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \   (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, A +B+C+D = 5+6-10+2 = \bold3

5 0
3 years ago
The figures are similar. Find x.
Luda [366]

Answer:x=16.5

Step-by-step explanation:

22divided by 4 is 5.5

5.5 times 3 is 16.5

4 0
3 years ago
Help me answer 2/9 divided by 1/6
Zigmanuir [339]

1.33333

Step-by-step explanation:

Don't worry it checks out.

3 0
3 years ago
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Help plz!!!!!!!!!!!!!
trapecia [35]

Answer:

i believe the relative max coordinate is (2,4)

relative min is (-2,0) and (4,0)

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