Answer:
1. value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice
2. evaluates at x = -1; remainder is -11 . . . . first choice
Step-by-step explanation:
Dividing f(x) by (x -a) gives ...
f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r
If we multiply this expression by (x -a), we see ...
f(x) = (x -a)g(x) +r
so
f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a
f(a) = 0 +r
f(a) = r . . . . . . . . . a statement of the remainder theorem
If r=0, then x-a is a factor of f(x) = (x-a)g(x).
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1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.
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2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.
Find x and y intercept and plot
set x to zero and find y
set y to zero and find x
tada, 2 points
if x=0, then y=-4
if y=0, then x=-16
we havee the points
(0,-4) and (-16,0)
or
y=-1/4x-4
The answer is (7, -26) for The second endpoint.
We'll call the midpoint M. In order to find this, we must first note that to find a midpoint we need to take the average of the endpoints. To do this we add them together and then divide by 2. So, using that, we can write a formula and solve for each part of the k coordinates. We'll start with just x values.
(Ux + Vx)/2 = Mx
(Vx + 3)/2 = 5
Vx + 3 = 10
Vx = 7
And now we do the same thing for y values
(Uy + Vy)/2 = My
(Vy + 6)/2 = -10
Vy + 6 = -20
Vy = -26
This gives us the final point of (7, -26)
Answer:
37°
Step-by-step explanation:
we're going to use cosine rule In calculating for the value of angle A
note that cosine rule can be used when two sides are given with an included angle . from the diagram above, the two sides given are side AB and side AC and the included angle is A
Hence cosine rule
a^2 = AB^2+AC^2 - 2AB×AC Cos A
3.2^2= 2.1^2+4.6^2-2×2.1×4.6COSA
10.24 =4.41+21.16- 19.32 COSA
10.24 = 25.57-19.32COSA
10.24-25.57= -19.32COSA
-15.33= -19.32COSA
dividing bothsides by - 19.32
COSA= -15.33/19.32
COA= 0.79347826
A = COS^-1 (0.79347826)
A= 37.488
A= 37°
<h2>hope this helps!!</h2>
Let's say our first integer is "a".
how to get the next consecutive EVEN integer? well, just add or subtract 2 from it, therefore, the second consecutive integer will be "a + 2".
and the next after that, will then be (a + 2) + 2, or "a + 4".
so those are are 3 integers, a a + 2 a+4
notice that, from any even or odd integer, if you hop twice either forwards or backwards, you'll land on another even or odd integer respectively.
2 + 2 is 4, or 8 + 2 is 10 some even ones
3 + 2 is 5, or 13 + 2 is 15, some odd ones
![\bf \stackrel{\textit{3 times the first}}{3a}~~=~~\stackrel{\textit{26 less than twice the sum of the others}}{2[~(a+2)+(a+4)~]~~~-26} \\\\\\ 3a=2[~2a+6~]-26\implies 3a=4a+12-26\implies 3a=4a-14 \\\\\\ 0=a-14\implies 14=a](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7B3%20times%20the%20first%7D%7D%7B3a%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7B26%20less%20than%20twice%20the%20sum%20of%20the%20others%7D%7D%7B2%5B~%28a%2B2%29%2B%28a%2B4%29~%5D~~~-26%7D%0A%5C%5C%5C%5C%5C%5C%0A3a%3D2%5B~2a%2B6~%5D-26%5Cimplies%203a%3D4a%2B12-26%5Cimplies%203a%3D4a-14%0A%5C%5C%5C%5C%5C%5C%0A0%3Da-14%5Cimplies%2014%3Da)
what are the other two consecutive integers? well, a + 2 and a + 4.
