Answer:
Step-by-step explanation:18x−2(3x+1)=5x−16
18x+(−2)(3x)+(−2)(1)=5x+−16
18x+−6x+−2=5x+−16
(18x+−6x)+(−2)=5x−16
12x+−2=5x−16
12x−2=5x−16
Step 2: Subtract 5x from both sides.
12x−2−5x=5x−16−5x
7x−2=−16
Step 3: Add 2 to both sides.
7x−2+2=−16+2
7x=−14
Step 4: Divide both sides by 7.
7x
7
=
−14
7
x=−2
Answer:
x=−2
Answer:
Dimensions are;
2.5 inches height
Base: 10 inches by 10 inches
Max volume; 250 Sq.in
Step-by-step explanation:
Let each side of the square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60
Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
The lowest common multiple of 3, 5, and 7 is 105, so
that's the smallest number that has those prime factors.
Every multiple of 105 is another one:
210, 315, 420, etc.
So is (105) times (any multiple of 3 or 5 or 7):
(x 3, 6, 9) 315, 630, 945, etc.
(x 5, 10, 15) 525, 1050, 1575, etc.
(x 7, 14, 21) 735, 1470, 2205, etc.
Same side interior
Alternate exterior
Same side interior
Alternate exterior
Alternate interior
(In order)
Since the angles are complementary, they add to 90°. So we can write the equation:
x represents the first angle, and 4x represents the second
x+4x=90
5x=90
x=18
So the first angle is 18° and the second is 72° (18*4)
Hope this helps