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3 years ago

Geometry!! can someone help me with #23 please? it would mean a lot thanks :)

Mathematics

1 answer:

Bogdan [553]3 years ago

7 0

Answer:

yes, they are parallel lines in #23

Step-by-step explanation:

the slope of both lines is -1

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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

Assume that 3-month Treasury bills totaling $12 billion were sold in $10,000 denominations at a discount rate of 3.605%

harina [27]

Answer: 55,000,000

this might not be right but hear

6 0

3 years ago

The sum of consecutive numbers is 95. Find the two numbers.

Leviafan [203]

Answer:

47 and 48

Step-by-step explanation:

Consecutive numbers: x and x+1

x + (x + 1) = 95

2x + 1 = 95

2x = 94

x = 47

5 0

3 years ago

Read 2 more answers

Please answer this question now

Papessa [141]

Answer:

1109.12 sq inches is the answer sorry

6 0

3 years ago

Please help quick i get brainliest

IrinaK [193]

Question 1:
If you know that 3 squares equals 7 circles and the squares are being counted by 3, then continue to count the circle by 3 until you get 25 circles.
Example:
3 Squares : 7 circles
4 squares : 10 circles
5 squares : 13 circles
6 squares : 16 circles
7 squares : 19 circles
8 squares : 22 circles
9 squares : 25 circles Add 9 squares to 3 = 12
You will have 12 squares when continues to count all the way to 25 circles.

Question 2:
Just multiply 14 by 28 and you will get your answer. Which is 3. The missing digit's 3. You can then check by doing 392 ÷ 14 to see if you get 28.

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3 years ago