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3 years ago

Solve x2 - 13x + 30 = 0

Mathematics

2 answers:

Svetllana [295]3 years ago

6 0

Answer:

or, x2-(2-15)x +30= 0

or, x2-2x-15x + 30= 0

or,x(x-2)-15(x-2)=0

or, (x-2) (x-15)=0

either, or,

x-2=0 x-15=0

almond37 [142]3 years ago

5 0

Answer:

x2-(10+3)x+30=0

x2-10x-3x+30=0

x(x-10)-3(x-10)=0

(x-10)(x-3)=0

either, or,

x-10=0 x-3=0

x=10 x=3

therefore,x=10,3

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Vladimir79 [104]

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3 years ago

Read 2 more answers

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

Rebeca spent $32.55 for a photo album and three identical candles. The photo album cost $17.50 and the sales tax was $1.55. How

Marina86 [1]

Answer: $4.50 per candle

Step-by-step explanation:

$32.55 - $17.50 - $1.55 = $13.50 for all the candles

To find the price of a single candle we divide our answer by 3

13.50/3 = $4.50

3 0

3 years ago

I golf club charges $10 to join and

Jobisdone [24]

Answer: He could have played more than 3 games.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality.

I golf club charges $10 to join and $5 per game: So, the cost of playing golf is equal to $10 (joining price) plus the product of the number of games played (x) and the price per game (5).

That expression must be higher than 25, since john paid more than $25.

Mathematically speaking

10+ 5 x > 25

Solving for x

5x >25-10

5x >15

x >15/5

x> 3

He could have played more than 3 games, since his cost was higher ( not equal or higher) than 25.

4 0

3 years ago

What is the prime factorization for 180

omeli [17]

Answer:

2*2*3*3*5

Step-by-step explanation:

Factor 180 into prime numbers that multiply together to give 180

180 = 20 *9

= 4*5 * 3*3

= 2*2* 5 * 3*3

Now rewrite them from smallest to largest

2*2*3*3*5

6 0

3 years ago