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ki77a [65]
3 years ago
13

11. A certain alloy contains 14.25% nickel. How much nickel is there in a piece weighing 375 pounds?Round your answer to the nea

rest hundredth.
A. 112.49 pounds
B. 12.24 pounds
C. 53.44 pounds
D. 78.92 pounds

12. Theresa worked 9 hours on Monday and 7 hours on Wednesday. Her total pay was $116.00. What is her rate per hour?
A. $16.57
B. $8.29
C. $7.25
D. $12.89
Mathematics
2 answers:
Andrej [43]3 years ago
3 0
11. 375x0.1425 = 53.475 (53.44 to 2 d.p.)

12. 116 / (9+7) = $7.25
      Total payment / Hours spent working = Money per hour

Alika [10]3 years ago
3 0
Theresa worked 9 hours on Monday and 7 hours on Wednesday. Her total pay was $116.00. What is her rate per hour?    <span>$12.89</span>
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If D is midpoint of side BC of triangle ABC. P and Q are points lying respectively on side AB and AC such that DP is parallel to
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See proof below

Step-by-step explanation:

Assume triangle ABC to have vertices at;

A(2,-1), B(2,-7) and C(6,-7)

D is midpoint of BC, thus D is at (4,-7)

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Plot the points on a graph tool and join the points to view the sketch.

To prove area of triangle CPQ is 1/4 area of ABC will be;

Find area ABC and CPQ then compare the areas.

Apply the distance formula to find the length of sides of the triangles then find the areas.

The distance formula is;

d=\sqrt{x_2-x_1)^2+(y_2-y_1)^2}

Length of side AB from the sketch is;

AB=\sqrt{(2-2)^2+(-7--1)^2} =\sqrt{-6^2} =\sqrt{36} =6units

Length of side BC will be;

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1/2 *base length*height ------because it is a right-triangle

1/2*4*6=12 square units

Find the lengths of all sides of triangle CPQ

Length of side PQ is half that of side BC thus PQ=2 units

Length of side PC is;

PC=\sqrt{(6-2)^2+(-7--4)^2} =\sqrt{4^2+-3^2} =\sqrt{16+9} =\sqrt{25} =5units

Length of side QC will be;

QC=\sqrt{(6-4)^2+(-7--4)^2} =\sqrt{2^2+-3^3} =\sqrt{4+9} =\sqrt{13}

QC= √13 = 3.6 units

Find area of triangle CPQ given all sides by applying the Heron's formula for area of triangle which is;

A=√s(s-a)(s-b)(s-c)  where;

A=area of the triangle

s= half the perimeter of the triangle

a=side PQ = 2 units

b=side PC = 5 units

c= side QC = 3.6 units

Finding the perimeter of triangle CPQ will be;

P=sum of all sides

P=2+5+3.6 =10.6 units

s=10.6/2 = 5.3

Area of the triangle CPQ will be;

A=\sqrt{5.3(5.3-2)(5.3-5)(5.3-3.6)} \\A=\sqrt{5.3(3.3)(0.3)(1.7)} \\A=\sqrt{8.9} =2.98

A=3.0 (1 decimal place)

Compare the areas;

Area of triangle ABC=12 square units

Area of triangle CPQ = 3 square units

Area of triangle CPQ / Area of triangle ABC = 3/12 =1/4

Thus you have proved that area of triangle CPQ is 1/4 th area of triangle ABC because 1/4 *12 =3

Learn More

Area of a triangle ;brainly.com/question/14869984

The Heron's formula : brainly.com/question/10713495

Keywords: midpoint, triangle, sides, parallel, prove , area, equal

#LearnwithBrainly

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