Answer:
See below.
Step-by-step explanation:
First one is 18 liters.
Second is false.
Third is 24 pints.
1) B.
2) A.
3) A.
4) True.
5) B.
-hope it helps
Find the slope for the two lines and state that they are equal (condition for parallel lines)
Slope of line AB
[y2 - y1] / [x2 - x1]
Slope of line CD
[y4 - y3] / [x4 - x3]
Condition
[y2 - y1] / [x2 - x1] = [y4 - y3] / [x4 - x3]
Volume of the box= <span>56 cubic inches
let x is the length, then
width =</span><span>2 inches shorter than its length = x - 2
</span>height = <span>3 inches taller than its length = x+3
Volume = length x width x height
56 = x x (x-2) x (x+3)
56 = (x</span>² -2x)(x+3)
56 = x³ +3x² -2x² - 6x
56 = x³ + x² -6x
x³+x²-6x-56 = 0
using the rational root theorem and factoring the polynomial;
(x-4)(x² +5x +14) = 0
from here;
x-4 = 0
x = 4
So, length = 4 inches
width = x - 2 = 4 -2 = 2 inches
length = x + 3 = 4 + 3 = 7 inches
volume = l x w x h = 4 x 2 x 7 = 56
Answer:
The area of triangle DEF is
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its heights is proportional and this ratio is called the scale factor and the ratio of its areas is equal to the scale factor squared
step 1
Find the scale factor
Let
z ----> the scale factor
----> ratio of its heights
step 2
Find the area of triangle DEF
Let
z ----> the scale factor
x ----> the area of triangle DEF
y ----> the area of triangle ABC
so
we have
substitute and solve for x
The equation for the function is
Explanation:
The equation for the function that passes through the points and
The equation of the line that passes through the points and is given by
where m is the slope and it can be determined using the formula,
Substituting the values of x and y in the slope formula, we have,
Simplifying, we get,
Thus, the slope is m=1.
Substituting the values in the equation , we have,
Multiplying the terms within the bracket,
Adding on both sides of the equation,
Thus, the equation for the function is