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Shalnov [3]
3 years ago
9

The sum of two integers is 9 and the sum of their squares is 53. Find the integers.

Mathematics
1 answer:
Schach [20]3 years ago
6 0
X + y = 9 Subtract x from both sides.
y = 9 - x

x^2 + y^2 = 53
x^2 + (9 - x)^2 = 53 Remove the brackets.
x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.
2x^2 - 18x + 81 = 53 Subtract 53 from both sides.
2x^2 - 18x + 81 - 53 = 0
2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.
2(x^2 - 9x + 14) = 0
2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it.
x - 2 = 0
x =  2
x - 7 = 0
x = 7
If x = 2 then y = 7
If x = 7 then y = 2
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Find the Y-coordinate of point P that lies 1/3 along segment RS, where R (-7, -2) and S (2, 4).
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Given that the point P lies 1/3 along the segment RS as shown below:

To find the y coordinate of the point P, since the point P lies on 1/3 along the segment RS, we have

\begin{gathered} RP:PS \\ \Rightarrow\frac{1}{3}:\frac{2}{3} \\ thus,\text{ we have} \\ 1:2 \end{gathered}

Using the section formula expressed as

[\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}]

In this case,

\begin{gathered} m=1 \\ n=2 \end{gathered}

where

\begin{gathered} x_1=-7 \\ y_1=-2 \\ x_2=2 \\ y_2=4 \end{gathered}

Thus, by substitution, we have

\begin{gathered} [\frac{1(2)+2(-7)}{1+2},\frac{1(4)+2(-2)}{1+2}] \\ \Rightarrow[\frac{2-14}{3},\frac{4-4}{3}] \\ =[-4,\text{ 0\rbrack} \end{gathered}

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0

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1 year ago
The amount of water consumed each day by a healthy adult follows a normal distribution with a mean of 1.30 liters. A health camp
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Answer:

H0: μ ≤ 1.30

H1: μ > 1.30

|Test statistic | > 1.833 ; Reject H0

Test statistic = 3.11

Yes

Pvalue = 0.006

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H0: μ ≤ 1.30

H1: μ > 1.30

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Standard deviation, s = 0.187 (calculator)

Decison rule :

|Test statistic | > TCritical ; reject H0

df = n - 1 = 10 - 1 = 9

Tcritical(0.05; 9) = 1.833

|Test statistic | > 1.833 ; Reject H0

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(xbar - μ) ÷ (s/√(n))

(1.484 - 1.30) ÷ (0.187/√(10))

0.184 / 0.0591345

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Since ;

|Test statistic | > TCritical ; We reject H0 and conclude that water consumption has increased

Pvalue estimate using the Pvalue calculator :

Pvalue = 0.006

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