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Lelu [443]
3 years ago
5

Use the quadratic formula to find the exact solutions of x2 - 5x - 2 = 0.

Mathematics
1 answer:
Fudgin [204]3 years ago
6 0

Step-by-step explanation:

{x}^{2}  - 5x - 2 = 0 \\ a = 1 \: and \: b =  - 5 \: and \: c =  - 2 \\ x =  \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a}  \\ x =  \frac{ - ( - 5)± \sqrt{ {( - 5)}^{2}  - (4 \times 1 \times  - 2)} }{(2 \times 1)}  \\ x =  \frac{5± \sqrt{33} }{2}  \\ either : x =  \frac{5 +  \sqrt{33} }{2} \:  or \:  \frac{5 -  \sqrt{33} }{2}  \\ x = 5.4 \: or \:  - 0.4

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A boy throws a ball into the air. The equation h=−16t^2+23t+4 models the path of the ball, where h is the height (in feet) of th
lina2011 [118]

Answer:

0.72secs

Step-by-step explanation:

Given the height of the ball in air modeled by the equation:

h=−16t²+23t+4

Required

Total time it spent in the air

To get this we need to calculate its time at the maximum height

At the maximum height,

v = dh/dt = 0

-32t + 23 = 0

-32t = -23

t = 23/32

t = 0.72secs

<em>Hence the total time it spend in the air will be 0.72secs</em>

8 0
3 years ago
Y is inversely proportional to x.
Inessa [10]

Answer:

1. xy = 63

2. y = 3

Step-by-step explanation:

Given

Variation: inverse Proportion

y = 7, x = 9

Required

- Write an equation connecting y and x

- Find y when x = 21

Given that thee variation is inversely proportional;

This implies that

y\ \alpha\ \frac{1}{x}

Convert variation to equation

y\ = \frac{k}{x} ----------- Equation 1

Where k is the constant of variation

Substitute 7 for y and 9 for x in equation 1

7 = \frac{k}{9}

Multiply both sides by 9

9 * 7 = 9 * \frac{k}{9}

63 = k

Substitute 63 for k in equation 1

y = \frac{63}{x}

Multiply both sides by x

x * y = \frac{63}{x} * x

xy = 63

Hence, the equation connecting x and y is xy = 63

Solving for when x = 21

Substitute 21 for x in the above equation

21 * y = 63

Divide both sides by 21

\frac{21 * y}{21} = \frac{63}{21}

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4 0
3 years ago
What is the solution of the equation 9^2x=6? Round your answer to the nearest ten-thousandth.
sammy [17]

Answer:

0.4077

Step-by-step explanation:

It's important to use parenthesis to avoid confusion.

9^(2x) = 6

Use exponent properties:

(9^2)^x = 6

81^x = 6

Take log of both sides

ln(81^x) = ln(6)

Use log properties:

x ln(81) = ln(6)

Solve for x:

x = ln(6) / ln(81)

x ≈ 0.4077

4 0
3 years ago
Solve the polygon for x
wariber [46]
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\\ \rm\Rrightarrow 5(10x+15)+2(14x)+6x-3=1080

\\ \rm\Rrightarrow 50x+75+28x+6x-3=1080

\\ \rm\Rrightarrow 84x+72=1080

\\ \rm\Rrightarrow 84x=1008

\\ \rm\Rrightarrow x=1008/84

\\ \rm\Rrightarrow x= 12

4 0
3 years ago
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otez555 [7]
Answer: The probability that 3 or more of the next 5 customers will order chocolate is 30%.  3/10

Sandy conducted her own experiment to answer this question. She observed what groups of 5 customers ordered. In her experiment, 30% of the time at least 3 of the customers ordered chocolate.

The fraction 30% is 3/10.
7 0
3 years ago
Read 2 more answers
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