We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.
Their measures are given as:
∠UVW = x - 10
∠XYZ = 4x - 10
Adding these, we have:
(x - 10) + (4x - 10) = 90
Simplifying:
5x - 20 = 90
Adding 20 to both sides:
5x = 110
Dividing by 5:
x = 22
Substituting back:
∠UVW = 22 - 10 = 12°
∠XYZ = 4(22) - 10 = 78°
Therefore, the values are:
x = 22°
∠UVW = 12°
∠XYZ = 78°
<span>5.7 liters of a 5% solution combined with 4.3 liters of a 40% solution.
To begin, define the problem with formulas.
x Represents the liters of the 5% solution utilized.
10-x Represents the liters of the 40% solution used.
This forms an equation: 5% of x plus 40% of (10-x) equals 20% of 10.
0.05x + 0.40(10-x) = 0.20 * 10
Now, distribute the 0.40 coefficient.
0.05x + 4.0 - 0.40x = 0.20 * 10
Next, combine the terms.
4.0 - 0.35x = 2.0
Add 0.35x to each side.
4.0 = 2.0 + 0.35x
Subtract 2 from both sides.
2.0 = 0.35x
Lastly, divide both sides by 0.35.
5.7 = x
Thus, 5.7 liters of a 5% solution is required. To determine the volume of the 40% solution, subtract from 10.
10.0 - 5.7 = 4.3</span>
Answer:
No solution
Step-by-step explanation:
Given: 
and 
Handle each inequality separately.
Utilizing the subtraction property of inequalities
and
Utilizing the addition property of inequalities
Thus, the solution to the combined inequality is the overlap of both solutions.
Refer to the attached image for the number line representation.
No solution
Answer:
Please refer to the explanation
Step-by-step explanation:
Given that:
Sarah, Jose, and you all reside on the same street:
The distance between you and Jose is 5 blocks
The distance between Jose and Sarah is 2 blocks
Calculating the distance (b) between you and Sarah:
Since it is not specified if Sarah is closer to you or to Jose;
Thus;
Distance b from you to Sarah will be:
(The distance to Jose ± the distance to Sarah)
b = (5 ± 2)
b = (5 + 2) or (5 - 2)
b = 7 blocks or 3 blocks
A proportion maintains a consistent ratio m/d
If m = 0.75d, then the m/d ratio translates to (0.75d)/d = 0.75
In this case, the ratio can be expressed as (.75d-2)/d = 0.75 - (2/d).
Thus, it is not proportional.
