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3 years ago

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The sum of two numbers is 40. If the larger is divided by the smaller, the quotient is 5 and the remainder is 4. Find the number

.

1 answer:

solmaris [256]3 years ago

6 0

Answer:

numbers are 33 and 7

Step-by-step explanation:

x+y=40

4y+5+y=40

5y+5=40

5y=35

y=7

x=4y+5=4(7)+5=28+5=33

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What size is the television screen shown in the illustration? Find if 20 in. and 15 in. ?

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Choose the option that best answers the question.The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If Angl

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Answer:

The correct option is 1.

Step-by-step explanation:

Given information: The coordinates of a right angled triangle ABC are A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6). Angle ABC = 90°.

It means AB and BC are legs of the right angled triangle ABC.

Side AB lies on the y-axis because the x-coordinate of both A and B is 0.

Two legs are perpendicular to each other. So, BC must be parallel to x-axis and the y-coordinate of both B and C is must be same.

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$4a-2a=5+6$

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Divide both sides by 2.

$a=\frac{11}{2}$

The value of a is 2. So the coordinates of triangle ABC are

$B(0,4a-5)=B(0,4(\frac{11}{2})-5)\Rightarrow B(0,17)$

$C(2a+1,2a+6)=C(2(\frac{11}{2})+1,2(\frac{11}{2})+6)\Rightarrow C(12,17)$

The area of a triangle is

$Area=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The area of triangle ABC is

$Area=\frac{1}{2}|0(17-17)+0(17-0)+12(0-17)|$

$Area=\frac{1}{2}|12(-17)|$

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$Area=\frac{1}{2}(204)$

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The area of triangle ABC is 102. Therefore the correct option is 1.

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