The graph below represents which system of inequalities?
1 answer:
Answer:
The system of inequalities is
Step-by-step explanation:
step 1
Find the equation of the solid line that goes through the points negative 3, 0, negative 4, negative 1
Let
A(-3,0),B(-4,-1)
Find the slope
m=(-1-0)/(-4+3)
m=-1/-1=1
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=1
point A(-3,0)
substitute
y-0=(1)(x+3)
y=x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
step 2
Find the equation of the solid line that goes through the points 1, 1, 2, negative 1
Let
C(1,1),D(2,-1)
Find the slope
m=(-1-1)/(2-1)
m=-2/1=-2
The equation of the line into point slope form is equal to
y-y1=m(x-x1)
we have
m=-2
point C(1,1)
substitute
y-1=(-2)(x-1)
y=-2x+2+1
y=-2x+3
The solution is the shaded area below the solid line
therefore
The equation of the first inequality is equal to
therefore
The system of inequalities is
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Answer:
a₁ = - 24
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 2a₅ , then
a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )
- a₁ - 2d = 0 → (1)
The sum to n terms of an AP is
=
[ 2a₁ + (n - 1)d ]
Given = 84 , then
(2a₁ + 6d) = 84
3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )
2a₁ + 6d = 24 → (2)
Thus we have 2 equations
- a₁ - 2d = 0 → (1)
2a₁ + 6d = 24 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate d
- 3a₁ - 6d = 0 → (3)
Add (2) and (3) term by term to eliminate d
- a₁ = 24 ( multiply both sides by - 1 )
a₁ = - 24
Answer:
x = ± 5
Step-by-step explanation:
x² - 25 = 0 ( add 25 to both sides )
x² = 25 ( take square root of both sides )
x = ± = ± 5
That is x = - 5, x = 5
Using conditional probability, it is found that there is a 0.8462 = 84.62% probability that a woman who gets a positive test result is truly pregnant.
<h3>What is Conditional Probability?</h3>Conditional probability is the probability of one event happening, considering a previous event. The formula is:
In which
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, the events are:
- Event A: Positive test result.
- Event B: Pregnant.
The probability of a positive test result is composed by:
- 99% of 10%(truly pregnant).
- 2% of 90%(not pregnant).
Hence:
The probability of both a positive test result and pregnancy is:
Hence, the conditional probability is:
0.8462 = 84.62% probability that a woman who gets a positive test result is truly pregnant.
You can learn more about conditional probability at brainly.com/question/14398287