The answer is <span>She went over by one over six of a cup
</span>
<span>1 cup of that particular chocolate powder has a mass of 128 grams: 1c = 128g
</span><span>64 grams of chocolate powder is x cups.
1c = 128g
x = 64g
1c : 128 g = x : 64g
x = </span>1c : 128 g * 64 g
x = 0.5 c
64 grams of chocolate powder is 0.5 cups = 1/2 cups
<span>She added two over three of a cup of chocolate powder: 2/3 cups
She need to add 1/2 cups: 1/2 = 3/6 cups
She added 2/3 cups: 2/3 = 4/6 cups
So she added 4/6 - 3/6 = 1/6 cups more.
</span>
Option A:
The another name for ∠1 is ∠JLK.
Solution:
How to Label Angles
:
There are two main ways to label angles:
1. Give the angle name by a number or a lower case letters.
2. The second way to name the angle is indicating by the vertex.
Usually the angle is denoted by three letters.
First letter and the second letter denotes the arms of the angle and the middle of the letter denotes the angle (its vertex).
To find the another name for ∠1.
The arms of the angle are LJ and LK and the vertex is L.
So, the name of the angle is ∠JLK.
Middle letter is the actual angle.
Therefore the another name for ∠1 is ∠JLK.
Option A is the correct answer.
Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
x = # of miles
$59.31 = $31 + $0.19x
Subtract $31 from both sides
$28.31 = $0.19x
Divide both sides by $0.19
149 = x
Juan drove 149 miles
Answer:
Slope is 40
Full equation: y=40x-586
Step-by-step explanation:
Slope is y2-y1/x2-x1
14 is x1
-26 is y1
15 is x2
14 is y2
14-(-26)/15-14
40
So the slope is 40
To find the equation
y=40x+b
14=15(40)+b
14=600+b
b=-586
Equation:
y=40x-586
