Answer:
(–5, –7)
Step-by-step explanation:
From the question given above, the following data were obtained:
Slope = 9/5
Coordinate 1 = (–10, –16)
x₁ = –10
y₁ = –16
Coordinate 2 = (x₂, y₂)
Next, we shall determine the change in x and y coordinate. This can be obtained as follow:
Slope = change in y–coordinate / change in x–coordinate
Slope = Δy / Δx
Slope = 9/5
9/5 = Δy / Δx
Thus,
Δy = 9
Δx = 5
Next, we shall determine the second coordinates as follow:
Δy = y₂ – y₁
Δx = x₂ – x₁
For x–coordinate:
x₁ = –10
Δx = 5
Δx = x₂ – x₁
5 = x₂ – (–10)
5 = x₂ + 10
Collect like terms
x₂ = 5 – 10
x₂ = – 5
For y–coordinate:
y₁ = –16
Δy = 9
Δy = y₂ – y₁
9 = y₂ – (–16)
9 = y₂ + 16
Collect like terms
y₂ = 9 – 16
y₂ = – 7
Coordinate 2 = (x₂, y₂)
Coordinate 2 = (–5, –7)
Answer:
The 95% confidence interval based on this sample is =
[6.41, 7.79]
Step-by-step explanation:
The formula for Confidence Interval =
Mean ± z × standard deviation/√n
Sample mean = 7.1 hours
Standard deviation = 5 hours
n = 200 students
z = 95% confidence interval z score
= 1.96
C.I = 7.1 ± 1.96 × 5/√200
C.I = 7.1 ± 0.693
Hence, Confidence Interval
= 7.1 - 0.693
= 6.407
Approximately = 6.41
= 7.1 + 0.693
= 7.793
Approximately = 7.79
Therefore, the 95% confidence interval based on this sample is
[6.41, 7.79]
3 divided by 10 is 0.3
2 divided by 5 is 0.4.
They are not equivalent.
The number of matinee movies attended is 4.
The number of a evening show movies attended is 2.
<u>Step-by-step explanation:</u>
- Let x represent the number of matinee movies attended.
- Let y represent the number of evening show movies attended.
- Alejandro went to see a total of 6 movies.
Therefore, from the given data the equation can be framed as :
⇒ x + y = 6 ----------(1)
- The cost of a matinee is $7.
- The cost of an evening show is $12.
- Alejandro spent a total of $52.
Therefore, from the given data the equation can be framed as :
⇒ 7x + `12y = 52 ---------(2)
<u>To solve the equations for x and y values :</u>
Mulitply eq (1) and by 7 and subtract eq (2) from eq (1),
7x + 7y = 42
- <u>(7x + 12y = 52)</u>
<u> - 5y = - 10 </u>
⇒ y = 10/5
⇒ y = 2
The number of a evening show movies attended is 2.
Substitute y=2 in eq (1),
⇒ x+2 = 6
⇒ x = 6-2
⇒ x = 4
The number of matinee movies attended is 4.
Answer:
x³ + 7x² - 6x - 72
Step-by-step explanation:
Given
(x + 6)(x + 4)(x - 3) ← expand the second and third factor, that is
(x + 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) + 4(x - 3) ← distribute both parenthesis
= x² - 3x + 4x - 12 ← collect like terms
= x² + x - 12
Now multiply this by (x + 6) in the same way
(x + 6)(x² + x - 12)
= x(x² + x - 12) + 6(x² + x - 12) ← distribute both parenthesis
= x³ + x² - 12x + 6x² + 6x - 72 ← collect like terms
= x³ + 7x² - 6x - 72
