Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
(9)
Here (h, k) = (3, - 2), thus
y = a(x - 3)² - 2
To find a substitute (2, 3) into the equation
3 = a(2 - 3)² - 2 ( add 2 to both sides )
5 = a(- 1)² = a , then
y = 5(x - 3)² - 2 ← in vertex form
y = 5(x² - 6x + 9) - 2
= 5x² - 30x + 45 - 2
y = 5x² - 30x + 43 ← in standard form
(10)
Here (h, k) = (2, - 5), thus
y = a(x - 2)² - 5
To find a substitute (5, 4) into the equation
4 = a(5 - 2)² - 5 ( add 5 to both sides )
9 = a(- 3)² = 9a ( divide both sides by 9 )
a = 1
y = (x - 2)² - 5 ← in vertex form
y = x² - 4x + 4 - 5
y = x² - 4x - 1 ← in standard form
Hi there!
Question 1:
For this, we are taking away 1/4 yards of spring from 7/8 yards. This is essentially just subtracting 1/4 from 7/8. This then gives us the equation:

Now, to subtract these, we want to make it so the denominators are the same, or the numbers on the lower half are the same. (One way to explain why this is true is:
). Now, to make it so the denominators are the same, we can multiply the second fraction, 1/4, by 2/2 as 2/2 is essentially 1, and multiplying by 1 will get the same result, just with a denominator switched in this case. Doing this, we get:


Now, subtracting the numerators, we get:
yards of string will remain.
Question 2:
For this, we are combining these two thicknesses, and thus we add 1/4 to 7/12. This gives us the equation:

Now, we again want to make it so the denominators are the same. (Here's a similar proof but for addition this time:
). Now, to make the denominators the same, we can multiply the first fraction, 1/4, by 3/3 (also equivalent to 1). Doing this, we get:


, which is equivalent to (dividing both the top and the bottom by 2)
inches.
Hope this helps!
Answer:
3 dress shirts and 3 T-shirts
4 dress shirts and 1 T-shirt
Step-by-step explanation:
You must spend at least $93 and no more than $100.
2 dress shirts: $42 + 5 T-shirts: $60 = $102 too much money
2 dress shirts: $42 + 4 T-shirts: $48 = $90 too much money left
3 dress shirts: $63 + 3 T-shirts: $36 = $99 this works
4 dress shirts: $84 + 1 T-shirt: $12 = $96 this works
5 dress shirts: $105 too much money
Answer:
3 dress shirts and 3 T-shirts
4 dress shirts and 1 T-shirt
Answer:
B
Step-by-step explanation:
Range is y-values, hun which is the second number in each of the ordered pairs. And when you list ranges(y) or domains(x) you do it from least to greatest which is why it goes from negatives to positives in numerical order rather than the order given in the problem.
Answer:
its really easy just multiply
Step-by-step explanation:
multiply everything together