<u>Given</u>:
Given that the triangles ABD and CAD are similar.
The length of AB is 12.
The length of BD is x.
The length of AC is 27.
We need to determine the value of x.
<u>Value of x:</u>
Let us use the leg rule to determine the value of x.
Thus, we have;

Substituting the values, we get;

Cross multiplying, we get;


Dividing both sides by 27, we have;

Thus, the value of x is 
Hence, Option D is the correct answer.
The range of the function is {-34, -2, -20}
<h3>How to determine the range?</h3>
The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
Read more about range at:
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Answer:
(12,-6)
Step-by-step explanation:
we have
----> inequality A
---> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
<u><em>Verify each point</em></u>
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B
case 1) (0,-1)
Inequality A

----> is true
Inequality B

----> is not true
therefore
The ordered pair is not a solution of the system
case 2) (0,3)
Inequality A

----> is true
Inequality B

----> is not true
therefore
The ordered pair is not a solution of the system
case 3) (-6,-6)
Inequality A

----> is true
Inequality B

----> is not true
therefore
The ordered pair is not a solution of the system
case 4) (12,-6)
Inequality A

----> is true
Inequality B

----> is true
therefore
The ordered pair is a solution of the system (makes true both inequalities)
Answer:
A
Step-by-step explanation:
A. is the only correct solution to this question because you can also see that if we take 8 and divide this by 32 we get 1/4, so we know it is true.
33 photos in a 4x to 7x ratio
4x + 7x = 33
11x = 33
x = 3
33 photos can be put in a 4(3) to 7(3) ratio
which is a 12 to 21 ratio
so 12 photos on one side, and 21 on the other side to get the ratio of 4 to 7
Note:
<span>a(b) = ab = a x b = a times b</span>