There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
Answer:
<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>
Step-by-step explanation:





Complete Question
A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
Answer:
The 95% confidence interval is 
No, the confidence interval includes 0.25, so the true percentage could easily equal 25%
Step-by-step explanation:
From the question we are told that
The total sample size is 
The number of offspring that is yellow peas is 
The number of offspring that is green peas is
The sample proportion for offspring that are yellow peas is mathematically evaluated as

Given the the confidence level is 95% then the level of significance is mathematically represented as


The critical value of
from the normal distribution table is

Generally the margin of error is mathematically evaluated as

=> 
=> 
The 95% confidence interval is mathematically represented as

=> 
=> 
Answer:
<u>1. Nora and Lila be on the same page of the book after 6 days and a half.</u>
<u>2. Nora and Lila be on the page 180.</u>
Step-by-step explanation:
1. Let's check the information given to resolve the question:
Current page of the novel that Nora is reading now = 128
Pages per day Nora reads = 8
Current page of the novel that Lila is reading now = 102
Pages per day Lila reads = 12
Days ahead for Nora and Lila will be on the same page = x
2. After how many days of reading will Nora and Lila be on the same page of the book?
128 + 8x = 102 + 12x
8x - 12x = 102 - 128 (Subtracting 12x and 128 at both sides)
-4x = -26
x = 6.5
<u>Nora and Lila be on the same page of the book after 6 days and a half.</u>
<u>3.</u> What page will they be on?
Nora : 128 + 8 (6.5) = 128 + 52 = 180
Lila : 102 + 12 (6.5) = 102 + 78 = 180
<u>Nora and Lila be on the page 180</u>
<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>
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- A polygon with 10 sides ( Decagon )
⠀
<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>
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- The value of one of the exterior angles
⠀
<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>
⠀

⠀
<u>Solution</u><u> </u><u>:</u><u>-</u>
⠀
Putting the given values, we get,
⠀

Thus, the value of the exterior angles of a Decagon is 36°.
⠀
