Answer:
These lines will be perpendicular when m = ³⁄₂
Step-by-step explanation:
Two lines are perpendicular when the product of their gradients equal to -1. So:
m₁ * m₂ = -1
Let's get the first equation in gradient-intercept form (same as equation two).
2x + 3y = 4
3y = -2x + 4
y = -⅔x + ⁴⁄₃
We know the first gradient, and now we can find the gradient of the second line (which when multiplied will result in -1 as these lines are perpendicular). So:
-⅔ * m₂ = -1
m₂ = ³⁄₂
Answer: 1. {-2, -3} 2. {-5, 5} 3. {-3, 5}
<u>Step-by-step explanation:</u>
1) First, factor the equation by finding two numbers whose product is 6 and sum is 5. Then apply the Zero Product Property by setting each product equal to zero and solving for m.
m² + 5m + 6 = 0
∧
1 + 6 = 7
2 + 3 = 5 This works!
(x + 2)(x + 3) = 0
x + 2 = 0 x + 3 = 0
x = -2 x = -3
2) Factor out the GCF of 5. Notice the remaining factor is the difference of squares (because the middle term is missing and the first and last terms are perfect squares. Then apply the Zero Product Property by setting each product equal to zero and solving for p.
5p² - 125 = 0
5(p² - 25) = 0
5(p +5)(p - 5) = 0
5 ≠ 0 p+ 5 = 0 p - 5 = 0
p = -5 p = 5
3) Factor out the GCF of 2. Factor the equation by finding two numbers whose product is -15 and sum is -2. Then apply the Zero Product Property by setting each product equal to zero and solving for x.
2x² - 4x - 30 = 0
2(x² - 2 - 15) = 0
∧
1 - 15 = -14
3 - 5 = -2 This works!
(x + 3)(x - 5) = 0
x + 3 = 0 x - 5 = 0
x = -3 x = 5
***************************************************
You are allowed a maximum of 3 questions.
Try #4 and #5 on your own. If you still need help with them, please create a new question and post them.
Answer:
The answer is below
Step-by-step explanation:
A shop contained some refrigerators and televisions. The total number is 800, and 45% of them were refrigerators. If 60% of refrigerators were sold and 65% of televisions were sold last week. How many fewer refrigerators were sold than televisions?
Solution:
The number of refrigerators = 45% of 800 = 0.45 * 800 = 360 refrigerators.
The number of televisions = 800 - 360 = 440 televisions.
number of refrigerators sold = 60% of 360 = 0.6 * 360 = 216 refrigerators
number of televisions sold = 65% of 440 = 0.65 * 440 = 286 televisions
The number of fewer refrigerators that were sold than televisions = 286 - 216 = 70
Answer: P(4) = 0.097
<u>Step-by-step explanation:</u>
Answer:
50 black, 40 blue, and 20 red.
