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horrorfan [7]
1 year ago
7

1. 1/3 - 7/8rewrite the complex fraction as a division expressionshow the complex fraction in simplest form. 2. The lions won 35

out of 40 games this season. What fraction of the games did the lions win? Write your answer in simplest form.Write a decimal and a percent equivalent to the fraction of games the lions won.3. Stephanie had $325.48 in her checking account. She made deposits of $28.35 and $78.88A. How much money was in Stephanie's account after the deposits? B. Stephanie also wrote one check for $107.85. How much money is in her account now?4. Mr. and Mrs Thomas are planning to build a fence around their garden. They are comparing different measurements for their plans. (Plan A: Posts are 4 1/4 feet in length. Posts must be installed 7/8 feet below ground level.)(Plan B: Posts are 6 3/4 feet in length. Posts must be installed 1 and 1/2 feet below ground level.)A. What will be the height of the fence in Plan A?B. What will be the height of the fence in Plan B?C. Which fence would be taller and by how much?D. Mr and Mrs Thomas decide to go with Plan A. Their total bill is $356.88. If they pay 220 in cash and charge the remainder, How much did they charge??
Mathematics
1 answer:
Svet_ta [14]1 year ago
7 0

1. 1/3 - 7/8

rewrite the complex fraction as a division expression

show the complex fraction in simplest form.

step 1

we have

\begin{gathered} \frac{1}{3}-\frac{7}{8} \\  \end{gathered}

Multiply the first term by 8/8

so

(1/3)*(8/8)=8/24

Multiply the second term by 3/3

(7/8)*(3/3)=21/24

step 2

substitute in the original expression

8/24 -21/24

the fractions have the same denominator

so

(8-21)/24

-13/24

therefore

the answer is

-13/24

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Finger [1]

Answer:

<em>Fencing required = 1586 m</em>

Step-by-step explanation:

The given statements can be thought of a triangle \triangle ABC as shown in the diagram attached.

A be the 1st vertex, B be the 2nd vertex and C be the 3rd vertex.

Distance between 1st and 2nd vertex, AB = 435 m

Distance between 2nd and 3rd vertex, AC = 656 m

\angle A =49^\circ

To find:

Fencing required for the triangular field.

Solution:

Here, we know two sides of a triangle and the angle between them.

To find the fencing or perimeter of the triangle, we need the third side.

Let us use <em>Cosine Rule </em>to find the third side.

Formula for cosine rule:

cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

\Rightarrow cos 49^\circ = \dfrac{656^{2}+435^{2}-BC^{2}}{2\times 435\times 656}\\\Rightarrow BC^2 = 430336+189225-2 (435)(656)cos49^\circ\\\Rightarrow BC^2 = 430336+189225-570720\times cos49^\circ\\\Rightarrow BC^2 =619561-570720\times cos49^\circ\\\Rightarrow BC \approx 495\ m

Perimeter of the triangle = Sum of three sides = AB + BC + AC

Perimeter of the triangle = 435 + 495 + 656 = <em>1586 m</em>

<em></em>

<em>Fencing required = 1586 m</em>

4 0
3 years ago
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