Arnie is mixing red and yellow paints to make two different shades of orange. To make 1 cup of dark orange paint, he needs 7 ounces of red paint and 1 ounce of yellow paint. To make 2 cups of light orange paint, he needs 13 ounces of yellow paint and 3 ounces of red paint. Answer parts a and b.

Arnie has enough red paint

Step-by-step explanation:

step 1

Find out the number of ounces of red paint needed to make 3 cups of dark orange paint

Let

x > number of ounces of red paint

y > number of ounces of yellow paint

z > cups of dark orange

we know that

\frac{x}{z}=\frac{7}{1}\ \frac{ounces\ red\ paint}{cups\ dark\ orange}

z

x

=

1

7

cups dark orange

ounces red paint

so

For z=3 cups

substitute and solve for x

\frac{x}{3}=\frac{7}{1}

3

x

=

1

7

x=21\ ounces\ of\ red\ paintx=21 ounces of red paint

step 2

Find out the number of ounces of red paint needed to make 3 cups of light orange paint

Let

x > number of ounces of red paint

y > number of ounces of yellow paint

z > cups of light orange

we know that

\frac{x}{z}=\frac{3}{2}\ \frac{ounces\ red\ paint}{cups\ light\ orange}

z

x

=

2

3

cups light orange

ounces red paint

so

For z=3 cups

substitute and solve for x

\frac{x}{3}=\frac{3}{2}

3

x

=

2

3

x=4.5\ ounces\ of\ red\ paintx=4.5 ounces of red paint

step 3

Adds the ounces of red paint

21+4.5=25.5\ ounces\ of\ red\ paint21+4.5=25.5 ounces of red paint

25.5\ ounces < 32\ ounces25.5 ounces<32 ounces

therefore

Arnie has enough red paint

answer: ask

step-by-step explanation:

d .tv

step-by-step explanation:

the side tv is included in both triangles.   this means it corresponds to itself in the transformation.

this is justified by using the reflexive property, which states that anything is congruent to itself.