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2 years ago

If 9: x= x4, then x=

Mathematics

1 answer:

Furkat [3]2 years ago

3 0

Answer:

x = ±6

Step-by-step explanation:

9 : x = x : 4

9/x = x/4

Cross multiply.

x² = 9 × 4

x² = 36

x = ±√36

x = ±6

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

A population of 1,000 squirrels lives on a rectangle-shaped farm plot that is 25 feet long by 10 feet wide what is the populatio

Lemur [1.5K]

First, find the area of the plot:
25*10=250

1000/250 is 4

the population density is 4 squirrels per square foot.

5 0

3 years ago

Liam, Sarah and Emily shared some money in the ratio 3:6:8

tino4ka555 [31]

Hdndhdjhdbhsjdwkdbdjdjdd

3 0

3 years ago

X^2+4y^2=36 the lenght of the major axis is?

musickatia [10]

Answer:

Step-by-step explanation:

x² + 4y² = 36

divide by constant

x²/36 + y²/9 = 1

x²/6² + y²/3² = 1

6>3, so length of major axis is 2×6 = 12

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3 years ago

Jasmine's cell phone company charges her $35 an month for phone service plus 0.50 for each text message.How many text messages d

VashaNatasha [74]

Jasmine sent 17 texts. 0.50×34=17

17=35=52

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3 years ago