Hello :
<span>2(4w + 8) – 2w + 42 > 78
8w+16-2w+42 </span>> 78......(<span>distributivity × for + )
6w </span>> 20
w > 20/6
Answer:
adi's height = n-t inches
Step-by-step explanation:
from this question
we have Adi to be t inches shorter than sunnee.
sunnee's height = n inches tall
to get adis height, we have to subtract the height difference t from sunnee's height.
the height difference is how many inches by which Adi is shorter = t
adies height = sunnee's height, n - difference in height, t
= <em><u>(</u></em><em><u>n-t)</u></em><em><u> </u></em><em><u>inches</u></em>
<em><u>this </u></em><em><u>expression</u></em><em><u> </u></em><em><u>represents</u></em><em><u> </u></em><em><u>adis</u></em><em><u> height</u></em><em><u> </u></em><em><u>in </u></em><em><u>inches </u></em><em><u>.</u></em>
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
Answer:
a) -1
Step-by-step explanation:
Slope is also known as the gradient
1. assign a value to x and solve for y:
when x = 2, y = 2
when x = 4, y = 0
2. Next, use the equation of a straight line to find the gradient
y = mx + c
y is the y-coordinate, m is the gradient, x is the x-coordinate, c is the point where the line crosses the y-axis, which is found by equating y to 0 and solving for x
so y = mx + c becomes 2 = m*2 + 4, which then becomes 2 = 2m + 4
2m = -2 (take 4 away from 2)
<u>m = -1 </u>
Answer:
The first option is the answer (k = +/- 2 square root of J)
Step-by-step explanation:
Since you need to leave k by itself, You multiply both sides by 4 which will leave you with 4J=k^2. To get rid of the square(^2), you need to square root both sides which will leave k by it self. So now you have 4J inside the square root = k. The last step is to take the square root of 4 (which is + or -2) and put it outside the square root sign, leaving J inside the square root.
