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4 years ago

Which is the equation in slope-intercept form for the line that passes through (3, 7) and is perpendicular to 3x-5y=8

Mathematics

1 answer:

Natalija [7]4 years ago

5 0

Answer:

Step-by-step explanation:

Perpendicular lines have slopes which are the negative reciprocal of each other. To find the slope, convert 3x-5y=8 into y=mx+b form.

3x-5y=8

-5y = -3x +8

y = 3/5 x - 8/5

The slope is 3/5 so its perpendicular slope is -5/3. Write the equation of this line through the point (3,7) using point slope form. Then simplify into y=mx+b form.

$y-y_1=m(x-x_1)\\y-7 = -\frac{5}{3}(x-3)\\y-7=-\frac{5}{3}x + 5\\y = -\frac{5}{3}x+12$

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Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels, what percent of b

Ulleksa [173]

Answer:

The number of plain bagels are 18 and it is 75% of the total bagels .

The amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

Step-by-step explanation:

Formula

$Percentage = \frac{Part\ value\times 100}{Total\ value}$

As given

Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels .

As one dozens contains 12 items .

Thus

Total number of bagels bought by Jen = 2 × 12

= 24

Let us assume that the x be the scalar multiple of sesame bagels and plain bagels .

Number of sesame bagels = 1x

Number of plain bagels = 3x

Than the equation becomes

x + 3x = 24

4x = 24

$x = \frac{24}{4}$

x = 6

Thus

Number of plain bagels = 3 × 6

= 18

Part value = 18

Total value = 24

Putting all the values in the formula

$Percentage = \frac{18\times 100}{24}$

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As given

Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram.

Part value = 0.53 grams

Total value = 0.65 grams

Putting all the values in the formula

$Percentage = \frac{0.53\times 100}{0.65}$

$Percentage = \frac{5300}{65}$

Percentage = 81.5 %

Therefore the amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

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