Answer:
-6
Step-by-step explanation:
add -3n and -4n= -7n
add 17 to 25
-7n=42
n=-6
Answer:
P and Q are two points on the line x-y+1=0 and are at a distant of 5 units from the origin. Find the area of triangle POQ.
Step-by-step explanation:
P and Q are the intersection points of
x-y+1 = 0 and the circle x^2 + y^2 = 25
sub y = x+1 into the circle
x^2 + (x+1)^2 = 25
x^2 + x^2 + 2x + 1 - 25 = 0
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = 3 or x = -4
y = 4 or y = -3
so P(3,4) and Q(-4,3) are our two points
Height of triangle.
h = |0 - 0 + 1|/√2 = 1/√2
PQ = √( (-7)^2 + 1^2) = √50 = 5√2
area POQ = (1/2)(1/√2)(5√2) = 5/2 square units
hope this helped
Answer:
<h2>The x-interecepts are 5.6 and -1.4, approximately.</h2>
Step-by-step explanation:
The given equation is

Where
,
and
, let's use the quadratic formula

Therefore, the x-interecepts are 5.6 and -1.4, approximately.
Answer:
Roland is right, he can be 95% sure that average gas prices have gone up since the same time last year.
Step-by-step explanation:
Let μ be average gas price around Syracuse.
Then hypotheses are:
μ = $2.68
μ > $2.68
Then test statistic can be calculated as:
z=
where
- X is the Roland's calculated average gas prices of 50 gas stations ($2.74)
- M is the average average gas prices in the entire of Syracuse last year
- s is the standard deviation ($0.11)
Then z=
≈ 3.86
Since P-value of test statistic ≈ 0.00006 <0.05 (significance level), we can reject the null hypothesis.