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3 years ago

2 The value of y is directly proportional

Mathematics

1 answer:

rusak2 [61]3 years ago

4 0

Answer:

y = 17.5

Step-by-step explanation:

Given that y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition y = 35 when x = 140, then

35 = 140k ( divide both sides by 140 )

0.25 = k

y = 0.25x ← equation of proportion

When x = 70, then

y = 0.25 × 70 = 17.5

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mrs_skeptik [129]

Given:

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

To find:

Which of the lines, if any are perpendicular.

Solution:

If a line passes through two points, then the slope of line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Line a passes through (2, 10) and (4, 13). So, slope of this line is

$m_a=\dfrac{13-10}{4-2}=\dfrac{3}{2}$

Line b passes through (4, 9) and (6, 12). So, slope of this line is

$m_b=\dfrac{12-9}{6-4}=\dfrac{3}{2}$

Line c passes through (2, 10) and (4,9). So, slope of this line is

$m_c=\dfrac{9-10}{4-2}=\dfrac{-1}{2}$

Product of slopes of to perpendicular lines is -1.

$m_a\cdot m_b=\dfrac{3}{2}\times \dfrac{3}{2}=\dfrac{9}{4}\neq -1$

$m_b\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1$

$m_a\cdot m_c=\dfrac{3}{2}\times \dfrac{-1}{2}=\dfrac{-3}{4}\neq -1$

Therefore, any of these lines are not perpendicular to each other.

8 0

3 years ago

J has a loan of $42,350. This loan has a simple interest rate of 8% per year. What is the amount

Aleksandr-060686 [28]

Answer:

6776

Step-by-step explanation:

8℅ = 0.08

0.08 x 42350 = 3388

3388 x 2 = 6776

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3 years ago

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12%

Hitman42 [59]

Answer:

Amount of vinegar. 100% : 20 milliliters

Amount of Italian dressing: 140 milliliters

Step-by-step explanation:

Let's call A the amount of vinegar. 100%

Let's call B the amount of Italian dressing . 12% vinegar

The resulting mixture should have 23% vinegar, and 160 milliliters.

Then we know that the total amount of mixture will be:

$A + B = 160$

Then the total amount of pure antifreeze in the mixture will be:

$A + 0.12B = 0.23 * 160$

$A + 0.12B = 36.8$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

$-A -B = -160$

$A + 0.12B = 36.8$

--------------------------------------

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$B = \frac{-123.2}{-0.88}$

$B = 140\ milliliters$

We substitute the value of B into one of the two equations and solve for A.

$A + 140 = 160$

$A = 20\ milliliters$

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2 years ago