Answer:
The answer to the first question is: 9 4/21
The answer to the second question is: B.) 24 14/27
I hope this helps you! :D
Answer and step-by-step explanation:
5. To arrange it, find its value first:
4 - 6 = -2
-4 + 6 = 2
-4 - 6 = -10
So to arrange it from the least to greatest, it would be:
-10 , -2, 2 = c => a => b
8. To know which one have the least solution, calculate all of it first:
a. x + 5 = 13
Subtract both side by 5
x = 13 - 5
x = 8
b. -6x = -30
Divide both side by -6
-6x / -6 = -30/-6
x = 5
c. x / 4 = 18
x = 18 * 4
x = 72
d. x - 2 = -11
x = -11 + 2
x = -9
So d. have the least value (-9)
9. a. 10x - 4x = 6x
b. -15n + 3n = -12n
c. 7.5y + 1.6y = 9.1y
d. m + 4 - 2m = m - 2m + 4 = -m + 4
10. Student B are the students who invole in both piano and the band (As you can see it is in the middle of the diagram and it located in both circle (diagrams) so it would be both
Student G is the student who in the band because they only located in the band circle (diagram)
Hope those would help you :3
Student
Answer:
D. is the correct option
Step-by-step explanation:
There is a total of 5 people, so we can either split the pizza cost into 5, or into 10 and multiply by 2 (since each guest ate 2 slices) We'll do the first option since it's simpler.
$17.49 ÷ 5 = 3.489 or rounded up to $3.50
Next, we'll add $1.19 to $3.59 which equals $4.69
Hope this helps!
It’s SAS. Hope I helped sorry if I got it wrong
Answer:
- 20. The vertex is (2/3, 14/3) | p = 3, q = -2/3 and r = 14/3
- 21. 20x² + 2x - 3 = 0
Step-by-step explanation:
20.
<h3>Given</h3>
<h3>To find</h3>
- The least value of the y and the corresponding value of x
- Constants p, q and r such that 3x² - 4x + 6 = p(x + q)² + r
<h3>Solution</h3>
The given is the parabola with positive a coefficient, so it opens up and the minimum point its vertex.
<u>The vertex has x = -b/2a and corresponding y- coordinate is found below: </u>
- x = - (- 4)/2*3 = 2/3, and
- y = 3(2/3)² - 4(2/3) + 6 = 4/3 - 8/3 + 6 = 14/3
- So the vertex is (2/3, 14/3)
<u>The vertex form of the line has the equation:</u>
- y = a(x - h)² + k, where (h, k) is the vertex
<u>Plugging in the values:</u>
<u>Comparing with p(x + q)² + r, to find out that:</u>
- p = 3, q = -2/3 and r = 14/3
=====================================
21.
(i) α and β are the roots of: ax² + bx + c = 0
<u>Show that:</u>
- α + β = -b/a and αβ = c/a
<h3>Solution</h3>
<u>Knowing the roots, put the equation as:</u>
- (x - α)(x - β) = 0
- x² - αx - βx + αβ = 0
- x² - (α+β)x + αβ = 0
<u>Comparing this with the standard form:</u>
<u>Divide by </u><u>a</u><u> to make the constants of x² same:</u>
<u>Now comparing the constants:</u>
- - (α+β) = b/a ⇒ α+β = - b/a
- αβ = c/a
--------------------------------------------
(ii)
<h3>Given</h3>
- α and β are the roots of: 3x² - x - 5 = 0
<h3>To Find </h3>
- The equation with roots 1/2α and 1/2β
<h3>Solution</h3>
<u>The sum and the product of the roots:</u>
- α + β = -b/a = 1/3
- αβ = c/a = -5/3
<u>The equation is:</u>
- (x - 1/2α)(x - 1/2β) = 0
- x² - (1/2α + 1/2β)x + 1/(2α)(2β) = 0
- x² - (α + β)/(2αβ)x + 1/4αβ = 0
- x² - (1/3)/(2(-5/3))x + 1/(4(-5/3)) = 0
- x² + 1/10x - 3/20 = 0
- 20x² + 2x - 3 = 0