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Lesechka [4]
2 years ago
15

(04.04 MC)

Mathematics
1 answer:
sp2606 [1]2 years ago
5 0

Answer:

y = x^2/ 60 + 15

=>( x - h)^2 = 4a[ (x^2/6 + 15) - k ].

Step-by-step explanation:

Okay, in order to solve this question very well, one thing we must keep at the back of our mind is that the representation for the equation of a parabola is given as ; y = ax^2 + bx + c.

That is to say; y = ax^2 + bx + c is the equation for a parabola. So, we should be expecting our answer to be in this form.

So, from the question above we are given that "the satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground"

We will make an assumption that the point on the ground is (0,0) and the focus is (0,30). Thus, the vertex (h,k) = (0,15).

The equation that best describes the equation of the satellite is given as;

(x - h)^2 = 4a( y - k). ------------------------(1).

[Note that if (h,k) = (0,15), then, a = 15].

Hence, (x - 0)^2 = (4 × 15) (y - 15).

x^2 = 60(y - 15).

x^2 = 60y - 900.

60y = x^2 + 900.

y = x^2/ 60 + 15.

Hence, we will have;

(x - h)^2 = 4a[ (x^2/6 + 15) - k ].

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Lelechka [254]

Thw answer to your Problem would be A

7 0
3 years ago
SOMEONE HELP PLEASE! ASAP!
Luba_88 [7]
When two lines intersect, the angles across from the intersection (the "X") are congruent (equal), and referred to as "vertical angles."
So by the rule of vertical angles are congruent, we can set them equal:
{x}^{2}  - 6x = 1\div2 \: x + 42 \\  {x}^{2}  - 6x - 1 \div 2 \: x = 42 \\  {x}^{2}  - 6.5x = 42
{x}^{2}  - 6.5x - 42 = 0 \\ multiply \: both\: sides \: by \: 2 \: to \: get \\ rid \: of \: the \: decimal \\ 2({x}^{2}  - 6.5x - 42) = 2(0)
2 {x}^{2}  - 13x - 84 = 0
to factor we need the factors of 84:
1×84, 2×42, 3×28, 4×21, 6×14
Now we need one of those factors ×2 ( from the x^2 term) minus the other factor to equal 13 (the middle term)
it turns out that if we use 4×21: 4×2 = 8
and 21-8 = 13. Woohoo! we got it
So now we have:
2 {x}^{2}  - 13x - 84 = 0 \\ (2x - 21)(x + 4) = 0
Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4

Now we plug in each answer to check:
1) x = 10.5
{x}^{2}  - 6x =  {(10.5)}^{2}  - 6(10.5) \\  = 110.25 - 63 = 47.25
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
47.25 = 47.25
BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
{( - 4)}^{2}  - 6( - 4) = 16 + 24 = 40
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°


6 0
3 years ago
A company has 7 male and 9 female employees, and needs to nominate 2 men and 2 women for the company bowling team. How many diff
lys-0071 [83]

Answer:

The team can be formed in 756 different ways

Step-by-step explanation:

This is a combination problem since we are to select a set of people from a group. Combination has to do with selection.

for example, if r number of object is to be selected from a pool of n objects, this can be done in nCr number of ways.

nCr = \frac{n!}{(n-r)!r!}

Now If A company has 7 male and 9 female employees, and needs to nominate 2 men and 2 women for the company bowling team, then this can be done in the following way;

7C2 * 9C2

7C2 = \frac{7!}{5!2!} \\= \frac{7*6*5!}{5!*2} \\= 7*3\\= 21ways\\\\similarly;\\\\9C2 = \frac{9!}{7!2!}\\9C2= \frac{9*8*7!}{7!*2} \\9C2 = 9*4\\9C2 = 36

7C2 * 9C2 = 21*36

= 756

The team can be formed in 756 different ways

5 0
3 years ago
What is the complement and supplement of 74°?
serious [3.7K]
I think it's 90 degrees
5 0
3 years ago
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E^x is not zero for any finite value of x.

The number of values for which e^x is zero is zero.
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