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Nitella [24]
3 years ago
8

What solution do 2x2 - 13x + 21 = 0 and 2x2 + 9x - 56 = 0 have in common? Round your answer to the nearest tenth if necessary.

Mathematics
1 answer:
lys-0071 [83]3 years ago
4 0
So if we want to know the common solution(s) to a system of 2 equations, So we can just set both equations equal to each other and solve for the x value(s). That’s where I start below;

2x^2-13x+21 = 2x^2+9x-56
2x^2 cancels out and moving everything to one side and anything with an x variable to the other side we have then;
-22x=-77
22x=77 by cancelling the negative signs
x=77/22 therefore x=7/2 or 3.5

Hope this helps you. Any questions please ask.
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An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a stan
weqwewe [10]

Answer:

The proportion of children that have an index of at least 110 is 0.0478.

Step-by-step explanation:

The given distribution has a mean of 90 and a standard deviation of 12.

Therefore mean, \mu = 90 and standard deviation, \sigma = 12.

It is given to find the proportion of children having an index of at least 110.

We can take the variable to be analysed to be x = 110.

Therefore we have to find p(x < 110), which is left tailed.

Using the formula for z which is p( Z < \frac{x - \mu}{\sigma}) we get p(Z < \frac{110 - 90}{12} = 1.67).

So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)

Using the Z - table we can calculate p(Z < 1.67)  = 0.9522.

Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478

Therefore the proportion of children that have an index of at least 110 is 0.0478

8 0
3 years ago
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pentagon [3]
I know you have 1 and 3 right but I'm sorry about not knowing the rest.
8 0
3 years ago
Yolanda spends 8/23 hours per month playing soccer. Approximately how many hours does she play soccer in a year
Novosadov [1.4K]
Given:
8 2/3 hours per month
12 months in a year.

Number of hours she play soccer in a year.

8 2/3 must be converted to improper fraction.

((8*3)+2)/3 = 26/3

26/3 * 12 = (26 * 12)/3 = 312/3 = 104 

Yolanda spends 104 hours in a year playing soccer.
5 0
3 years ago
Read 2 more answers
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Ilya [14]
Let the actual distance be x mile.
1/4 inch = 1/2 mile
9/2 inch = x mile
(9/2)/(1/4)=x/(1/2)
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the actual distance is 9 mile.
8 0
2 years ago
Evaluate P(5, 2)<br><br> 20<br> 60<br> 240<br> 10
vesna_86 [32]

P(5,2) =  n! /(n-r)!

n = 5, r = 2:

= (5 x 4 x 3 x 2 x 1 ) /  3 x 2 x 1

Cancel out common factors:

= 5 x 4 = 20

The answer is 20.

3 0
3 years ago
Read 2 more answers
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