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3 years ago

graph the line that passes through the point (0, -3) and is perpendicular to another line whose slope is 2

Mathematics

1 answer:

Nadya [2.5K]3 years ago

4 0

Answer:

y = -1/2x -3

Step-by-step explanation:

The line perpendicular to one with a slope of 2 will have a slope that is the negative reciprocal of 2, that is, -1/2. The given point is the y-intercept of the required line, so we can write its equation directly in slope-intercept form:

y = mx + b

where m is the slope (-1/2), and b is the y-intercept (-3). Your line is ...

y = -1/2x -3

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A) For ΔJKL use the Triangle Proportionality Theorem to solve for x.

scoray [572]

Answer:

Part a) The value of x is 10

Part b) The perimeter of triangle JKL is $79\ units$

Step-by-step explanation:

Part a) Find the value of x

we know that

The <u>Triangle Proportionality Theorem,</u> states that if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally

$\frac{3x-5}{3x-5+10}=\frac{28-8}{28}\\ \\\frac{3x-5}{3x+5}=\frac{20}{28} \\ \\(3x-5)(28)=(3x+5)(20) \\ \\84x-140=60x+100\\ \\84x-60x=140+100\\ \\24x=240\\ \\x=10$

Part b) we know that

The perimeter of triangle JKL is equal to

$P=JK+KL+JL$

substitute the values

$P=(3x+5)+28+16=3x+49$

substitute the value of x

$P=3(10)+49=79\ units$

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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4 years ago

For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. H

Ostrovityanka [42]

Answer:

The number of possible dinner specials are 4368.

Step-by-step explanation:

The number of dinner specials = 5

They include appetizer, a salad, an entree, a side dish, and a dessert.

Possible items to choose from = 16.

They are 1. Appetizer Chicken strips, 2. Shrimp cocktail, 3. Buffalo wings, 4. Potato skins, 5. Salad Garden, 6. Caesar Entree T-bone steak, 7. Pot roast, 8. Lamb Side dish Corn, 9. Rice, 10. French fries, 11. Baked potato, 12. Pinto beans, 13. Dessert Chocolate cake, 14. Brownies, 15. Ice cream, 16. Apple pie

This is a combination problem requiring a combination solution with the following formula and steps:

C (n, r) =? C (n, r) = ?

n choose r

n (objects) = 16

r (sample) = 5

C (n, r) =? C (n, r) = ?

C (n, r) =C (14,5) C (n, r) =C (16,5)

=16! (5! (16−5)!) =16! (5! (16−5)!)

= 4368

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3 years ago