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padilas [110]
3 years ago
13

What is the product of the 2 solutions of the equation x^2+3x-21=0

Mathematics
1 answer:
Advocard [28]3 years ago
3 0
X²+3x-21=0

1) we solve this square equation:
x=[-3⁺₋√(9+84)] / 2=(-3⁺₋√93)/2
We have two solutions:
x₁=(-3-√93)/2
x₂=(-3+√93)/2

2) we compute the product of the 2 solutions found.
[(-3-√93)/2][(-3+√93)/2] =(-3-√93)(-3+√93) / 4=
=(9-93)/4=-84/4=-21

Answer: the product of the 2 solutions of this equation is -21
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A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.An orange hot-air balloon is 160 fee
Serhud [2]

ANSWER

Find out the how long will the Yellow balloon be higher than the orange balloon.

To proof

Now  the diagram is given below

As given

A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.

i.e height of the yellow baloon off the ground  = 100 feet

rising at rate = 8 feet per second.

.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second.

i.e height of the orange baloon off the ground  = 160 feet

rising at rate = 5feet per second.

Formula

Relative\ velocity = \frac{Relative\ Distance}{Relative\ time}

Relative velocity =  rising rate of yellow balloon -   rising rate of orange balloon

= 8 -5

= 3 feet per second

Relative distance =  height of the yellow baloon off the ground -  height of the orange baloon off the ground

= 160 -100

= 60 feet

put in the formula

= \frac{60}{3}

= 20 second

after  20 second Yellow balloon will be higher than the orange balloon.

Hence proved

8 0
3 years ago
What is the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice?
maria [59]
In a throw of 2 fair dice, there are 6*6=36 equiprobability outcomes.

To get a sum of 5, there are 4 ways, (1,4),(2,3),(3,2),(4,1) with probability of 4/36=1/9

To get at least one 5, there are 6+6-1=11 outcomes (note (5,5) has been counted in both, so subtracted from sum).  The probability is 11/36

Since the two events are mutually exclusive (once we have a five, the sum can no longer be 5), we can add the probabilities to get the probability of one event or the other.

P(sum of 5 OR at least one 5)=1/9+11/36=4/36+11/36=15/36=5/9
4 0
3 years ago
What is the inverse function of f(x) = 25x-3?
Harrizon [31]

Answer:

The answer is

<h2>{f}^{ - 1} (x) =  \frac{x +3 }{25}</h2>

Step-by-step explanation:

f(x) = 25x - 3

To find the inverse of f(x) , equate f(x) to y

That's

y = f(x)

We have

y = 25x - 3

Next interchange the terms that's x becomes y and y becomes x

x = 25y - 3

<u>Next solve for y</u>

Move 3 to the other side of the equation

That's

25y = x +  3

<u>Divide both sides by 25</u>

\frac{25y}{25}  =  \frac{x + 3}{25}

We have the final answer as

{f}^{ - 1} (x) =  \frac{x +3 }{25}

Hope this helps you

5 0
3 years ago
What mixed numbers are equivalent to −1. 5/6 ​ and ​ ​ −1. 7/9 ​ and use the LCD? Enter your answers in the box. if it helps the
Vlada [557]

Answer: -1.5/6 = -1/4; -1.7/9 = -17/90


Step-by-step explanation: Yeah, I'm not exactly sure what the problem is asking for, but this how I interpreted it. Use the LCD of the fractions -1.5/6 and -1.7/9 to find equivalent fractions with integer numerators and denominators.

For me, LCD doesn't help with solving the problem that much.

But anyways, the first fraction, -1.5, can be turned in an integer if you multiply the entire fraction by 2. So the result would be -3/12. You can simplify this to -1/4.

The second fraction, when multiplied by 10 yields -17/90. 17 is a prime number and is not a factor of 90, thus the equivalent fraction of -1.7/9 is 17/90.

Hope this helped.



8 0
3 years ago
Read 2 more answers
Pls help asap MIDSEGMENTS
Kay [80]

Answer:

56 degrees

Step-by-step explanation:

The midsegment is parallel to a side and the other side is a transversal. Using the Corresponding Angles Theorem, you get that m<1=56 degrees

4 0
2 years ago
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