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2 years ago

12

Terry is making 5 hat and scarf sets. Each scarf requires 3 yards of material and each hat requires 18 inches of material. How m

any feet of material does he need for all 5 hat and scarf sets?

1 answer:

Delvig [45]2 years ago

4 0

5*18 = 90
5*3= 15

90+15= 105

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0.75 is what percent of 37.75

jarptica [38.1K]

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3 years ago

What is the equation of the quadratic graph with a focus of (4,3) and a directrix of y=-6

Rufina [12.5K]

Answer:

f(x) = (1/18)x^2 - (4/9)x - 65/18

Step-by-step explanation:

Since the focus (4,3) is higher up than is the directrix y = -6, the vertex is between y = -6 and y = 3, halfway between these values, to be exact: y = -3/2. Thus, the y-coordinate of the vertex is (-6 + 3/2), or -4.5. The x-coordinate of the vertex is 4, which comes from that 4 in (4,3). Thus, the vertex is (4, -4.5) or (4, -4 1/2).

The standard equation for a vertical parabola with vertex at (h,k) is:

4p(y-k) = (x-h)^2, where p is the distance between vertex and focus or between vertex and directrix. In this case p = 4.5. Thus, the equation of this quadratic is 4(4.5)(y - [-4.5]) = (x - 4)^2, or

18(y+4.5) = (x-4)^2, or y+4.5 = (1/18)(x-4)^2.

Let's expand this and rewrite the result as a quadratic equation in standard form y = ax^2 + bx + c:

y + 4.5 = (1/18)(x^2 - 8x + 16). Multiplying all terms by 18 to remove both fractions, we get:

18y + 81 = x^2 - 8x + 16. Rearranging these terms, we get:

18y = x^2 - 8x + 16 - 81, or

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5 0

3 years ago

Read 2 more answers

Kyle gave 2/7 of his money to his wife and spent 4/5 of the remainder. If he had $300 left, how much money did he have at first?

densk [106]

Answer:

$5,250

Step-by-step explanation:

2/7x - [4/5(2/7x)] = 300

2/7x - 8/35x = 300

10/35x = 8/35x = 300

2/35x = 300

2x = 10500

x = 5250

6 0

3 years ago

Is a number decreased by three squared nonlinear or linear

Dennis_Churaev [7]

Answer:

A number decreased by three squad is a nonlinear.

Step-by-step explanation:

6 0

4 years ago

Given that cos θ = –12∕13 and θ is in quadrant III, find csc θ.

Trava [24]

Answer:

A

Step-by-step explanation:

We are given:

$\displaystyle \cos(\theta)=-\frac{12}{13},\,\theta\in\text{QIII}$

Since cosine is the ratio of the adjacent side over the hypotenuse, this means that the opposite side is (we can ignore negatives for now):

$o=\sqrt{13^2-12^2}=\sqrt{25}=5$

So, the opposite side is 5, the adjacent side is 12, and the hypotenuse is 13.

And since θ is in QIII, sine/cosecant is negative, cosine/secant is negative, and tangent/cotangent is positive.

Cosecant is given by the hypotenuse over the opposite side. Thus:

$\displaystyle \csc(\theta)=\frac{13}{5}$

Since θ is in QIII, cosecant must be negative:

$\displaystyle \csc(\theta)=-\frac{13}{5}$

Our answer is A.

7 0

3 years ago

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