Vertical angles are congruent, so their measures are equal.
Set the angle measures equal and solve for x.
2x + 2 = 3x - 52
-x = -54
x = 54
___________
| |
| 54 |
|__________|
The answer is inside a box.
Using a system of equations, it is found that Gina got 22 questions correct in the test.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
- Variable x: Number of questions she got correct.
- Variable y: Number of questions she got wrong.
The test has 30 questions, hence:
x + y = 30 -> y = 30 - x.
She scored 152 points, hence, considering the value of each question:
8x - 3y = 152.
Since y = 30 - x:
8x - 3(30 - x) = 152
11x = 242
x = 242/11
x = 22
Gina got 22 questions correct in the test.
More can be learned about a system of equations at brainly.com/question/24342899
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Answer:
22 3/4 ft
Step-by-step explanation:
The diagram seems to show a 6 1/2 ft person casting a 9 ft shadow at the same time a flagpole is casting a 31 1/2 ft shadow. You want the height of the flagpole.
<h3>Proportion</h3>
Shadow lengths are presumed proportional to the height of the object making them. This means ...
h/(31 1/2) = (6 1/2)/9 . . . . . all lengths in feet
Multiplying by 31 1/2, we get ...
h = (31 1/2)(6 1/2)/9 = (819/4)/9 = 91/4
h = 22 3/4 . . . . ft
The flagpole is 22 3/4 feet tall.
Answer:
Step-by-step explanation:
The quadratic formula would be the following...
where the original quadratic equation would be represented as follows
Using this information and the information provided in the image we can plug in the quadratic equation values in the image to form the quadratic formula.
That would be the correct order for the values.
- 4 w - 4 = - 24
- 4w = - 20
w = 5
