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olchik [2.2K]
3 years ago
14

Answer quickly please

Mathematics
2 answers:
Alex3 years ago
4 0

Answer:

x=6

Step-by-step explanation:

......................

vitfil [10]3 years ago
3 0

Answer:

x=6

Step-by-step explanation:

7x+2y = 48

Let y = 3

7x +2(3) = 48

7x+6 = 48

Subtract 6 from each side

7x+6-6 = 48-6

7x = 42

Divide each side by 7

7x/7 = 42/7

x = 6

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A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per
pishuonlain [190]

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

y=a(t-h)^2+k

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

y=ax^2+bx+c

then the x-coordinate of the vertex is

h=-\frac{b}{2a}

Now in our case b = 32 and a = -16; therefore,

h=\frac{-32}{2(16)}=1

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

k=-16(1)+32(1)+96=112

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

h(t)=a(t-1)^2+112

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

h(0)=-16(0)^2+32(0)+96=96

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

96=a(0-1)^2+11296=a+112

subtracting 112 from both sides gives

a=-16

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

h(t)=0.

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

-16\left(t-1\right)^2+112=0

Now subtracting 112 from both sides gives

-16(t-1)^2=-112

Dividing both sides by -16 gives

(t-1)^2=\frac{-112}{-16}(t-1)^2=7

taking the square root of both sides gives

t-1=\pm\sqrt{7}

adding 1 to both sides gives

t=\pm\sqrt{7}+1

Hence, the two solutions we get are

t=\sqrt{7}+1=3.6t=-\sqrt{7}+1=-1.6

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

3 0
1 year ago
The heights of american men aged 18 to 24 are approximately normally distributed with a mean of 68 inches and standard deviation
Rudik [331]
A normal distribution is symmetrical about the mean. Therefore half of all young men are shorter than 68 inches.
7 0
3 years ago
Read 2 more answers
Ratio as a fraction 8 to 14
grigory [225]
8/14, which can be reduced to 4/7 by dividing 8 by 2 and 14 by 2

So, your answer is 4/7

Hope I helped!

Let me know if you need anything else!

~ Zoe
3 0
3 years ago
An insurance office has 65 employees. If 39 of the employees have cellular​ phones, what portion of the employees do not have ce
Vsevolod [243]
65-39=26 so 26 employess dont have cellular phones. So 26/65 or in simplified form 2/5
7 0
2 years ago
Read 2 more answers
Need help with 35 thank you so much!!
Yakvenalex [24]

If a pentagon is regular, then all of the sides are the same length. This means that

5x-4=2x+11 \iff 5x-2x = 11+4 \iff 3x=15 \iff x = 5

So, if x=5, the lengths of the sides evaluate to

5x-4 = 25-4=21,\quad 2x+11=10+11=21

So, all the sides of the pentagon are 21 units long, and AB is 21 units long as well, because all sides are the same length.

3 0
3 years ago
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