Determine the equation with roots -4 and 2 and goes through (6, 20)
Answers
Answer:
y = x² + x - 4
Step-by-step explanation:
Given roots x = a and x = b, then the factors are
(x - a) and (x - b)
The function is then the product of the factors
y = a(x - a)(x - b) ← where a is a multiplier
Given roots are x = - 4 and x = 2 then the factors are
(x - (- 4)) and (x - 2), that is (x + 4) and (x - 2), thus
y = a(x + 4)(x - 2)
To find a substitute (6, 20) into the function
20 = a(6 + 4)(6 - 2) = a(10)(4) = 40a ( divide both sides by 40 ), thus
a = =
y = (x + 4)(x - 2) ← expand factors
= (x² + 2x - 8) ← distribute
y = x² + x - 4
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What to the third power equals 729
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45 pennies
9 nickels
1 quarter and 2 dimes
1 quarter, 1 dime, and 2 nickels
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Answers
600 / 50 = 12
So you would have to play for 12 hours to reach 1000 points
Answers
Answer:
V ≈ 2011 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = area of base × perpendicular height
V = πr²h ( r is the radius and h the height )
Here r = 8 and h = 10, thus
V = π × 8² × 10
= π × 64 × 10 = 640π ≈ 2011 cm³ ( to nearest whole number )
a. Is the ratio of quarters to dimes still 5:3?
b. If so, illustrate with an example. If not, give a counter-example.
3. You are 13 years old, and your cousin is 19 years old. As you grow older, is your age proportional to your cousin's age? Explain your reasoning
Answers
Answer:
1. The relation is proportional.
2. The ratio of quarters and to dimes will not remain 5 : 3.
3. y = 6 + x, Hence, not proportional.
Step-by-step explanation:
1. I can do 90 sit-ups in 2 minutes and my friend can do 135 sit-ups in 3 minutes.
If we consider t as the time in minutes and n as the number of sit-ups, then we can write (2,90) and (3,135) as two ordered pairs.
So, the relation between t and n will be
⇒ n = 45t
Therefore, the relation is proportional.
2. The initial ratio of quarters to dimes was 5:3. If I add the same number of quarters and dimes to it then,
a) The ratio of quarters and dimes will not still be 5 : 3.
b) Let, the number of quarters was 5 then the number of dimes was 3. {As the ratio was 5 : 3}
Now, we add 3 new quarters and 3 new dimes in the collection. then, finally, the number of quarters will be (5 + 3) = 8 and the number of dimes will become (3 + 3) = 6.
Therefore, the new ratio will become 8 : 6 = 4 : 3 which is not equal to 5 : 3.
3. I am 13 years old, and my cousin is 19 years old.
So, if my age is given by x and that of my cousin is y, then
y - x = 19 - 13
⇒ y - x = 6
⇒ y = 6 + x
This relation will continue as the year passes. So, the relation is not proportional as the relation is not like y = kx. (Answer)
Answers
Answer:
Step-by-step explanation:
Step by step explanation