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3 years ago

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Madison and Ella are painting their bedroom walls pink. The clerk at the home store calculated that they would need two gallons

of paint to cover their walls. They have 3/8 gallon of red paint and 1 5/12 gallons of white paint that they want to mix together to make pink. Will they have enough to cover the walls after they mix the red and white paint together

1 answer:

Elza [17]3 years ago

5 0

Answer:

Madison and Ella do not have enough paint to cover the walls after they mix the red and white paint together.

Step-by-step explanation:

Volume of red paint = $\frac{3}{8} gallon$

Volume of white paint = $1\frac{5}{12} gallon=\frac{17}{12} gallon$

Total volume of pink paint by mixing red and white :

$\frac{3}{8} gallon+\frac{17}{12} gallon$

$=\frac{3\times 12+17\times 8}{8\times 12}=\frac{172}{96}=\frac{43}{24} gal$

$\frac{43}{24} gallon\approx 1.79 gallon$

Volume of total paint required by them as calculated by clerk = 2 gallons

$2 gallons>\frac{43}{24}$

So, this means that Madison and Ella do not have enough paint to cover the walls after they mix the red and white paint together.

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<u>QUESTION 2a</u>

We want to find the area of the given right angle triangle.

We use the formula

$Area=\frac{1}{2}\times base\times height$

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<u>QUESTION 2b</u>

The given diagram is a rectangle.

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$Area=length \times width$

The length of the rectangle is $l=7cm$ and the width of the rectangle is $w=ycm$ .

We substitute the values to obtain the area to be

$Area=7 \times y$

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$Area=7y$

<u>QUESTION 2c.</u>

The given diagram is a rectangle.

The area of a rectangle is given by the formula

$Area=length \times width$

The length of the rectangle is $l=2x cm$ and the width of the rectangle is $w=4 cm$ .

We substitute the values to obtain the area to be

$Area=2x \times 4$

The expression for the area is

$Area=8x$

<u>QUESTION 2d</u>

The given diagram is a square.

The area of a square is given by,

$Area=l^2$ .

where $l=b m$ is the length of one side.

The expression for the area is

$Area=b^2 m^2$

<u>QUESTION 2e</u>

The given diagram is an isosceles triangle.

The area of this triangle can be found using the formula,

$Area=\frac{1}{2}\times base\times height$ .

The height of the triangle is $4cm$ .

The base of the triangle is $6a cm$ .

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$Area=\frac{1}{2}\times 6a \times 4cm^2$

$Area=12a cm^2$

<u>QUESTION 3a</u>

Perimeter is the distance around the figure.

Let P be the perimeter, then

$P=x+x+x+x$

The expression for the perimeter is

$P=4x mm$

<u>QUESTION 3b</u>

The given figure is a rectangle.

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$P=L+B+L+B$

This simplifies to

$P=2L+2B$

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$P=2(L+B)$

<u>QUESTION 3c</u>

The given figure is a parallelogram.

Perimeter is the distance around the parallelogram

$Perimeter=3q+P+3q+P$

This simplifies to,

$Perimeter=6q+2P$

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$Perimeter=2(3q+P)$

<u>QUESTION 3d</u>

The given figure is a rhombus.

The perimeter is the distance around the whole figure.

Let P be the perimeter. Then

$P=5b+5b+5b+5b$

This simplifies to,

$P=20b mm$

<u>QUESTION 3e</u>

The given figure is an equilateral triangle.

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$P=3x+2x+4x+5-1+1$

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<u>QUESTION 3h</u>

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The perimeter is the distance around the whole trapezium.

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$P=m+(n-1)+(2m-3)+(n+3)$

We group like terms to get,

$P=m+2m+n+n-3+3-1$

We simplify to get,

$P=3m+2n-1$ mm

QUESTION 3i

The figure is an isosceles triangle.

We add all the distance around the figure to obtain the perimeter.

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Then $P=(2a-b)+(a+2b)+(a+2b)$

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$P=2a+a+a-b+2b+2b$

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$P=4a+3b$ mm.

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The given figure is a square.

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We substitute this value to obtain;

$Area=(2m)^2$

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$Area=l\times w$ .

where $l=5a cm$ is the length of the rectangle and $w=6cm$ is the width of the rectangle.

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$Area =5a \times 6$

$Area =30a cm^2$

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$Area=l\times w$ .

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We substitute the values into the formula to get,

$Area =7y \times 2x$

The expression for the area is

$Area =14xy cm^2$

QUESTION 4d

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$Area =3p^2 cm^2$

See attachment for the continuation

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3 years ago

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