Hopefully this helps, and sorry I didn't do 8 I'm limited on time
Answer:
I think this is what is wanted
Step-by-step explanation:
We have these opposite pairs
- 9.2 and -9.2
- 2.9 and -2.9
- 1.4 and -1.4
- 4.1 and -4.1
So all we're doing is matching each positive number with its negative version. In terms of a visual, the opposite of a number is mirrored over 0 on the number line. So for instance, the opposite of 2 is -2, with each being two units away from 0 on the number line.
Answer:
The value of DC is 66.34.
Step-by-step explanation:
The triangles ABC and DCA are right angled triangles.
The straight line AC is a bisector for angles C and A.
The measure of ∠C is 30°.
Then the measure of angles BCA and ACD will be 15° each.
The measure of angle DAB is 150°.
Then the measure of angles DAC and BAC will be 75° each.
Now consider the right angled triangle ABC.
The measure of side AC is:
![AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}](https://tex.z-dn.net/?f=AC%5E%7B2%7D%3DAB%5E%7B2%7D%2BBC%5E%7B2%7D%5C%5CAC%3D%5Csqrt%7BAB%5E%7B2%7D%2BBC%5E%7B2%7D%7D%5C%5C%3D%5Csqrt%7B4%5E%7B2%7D%2B%2810%5Csqrt%7B3%7D%29%5E%7B2%7D%7D%5C%5C%3D%5Csqrt%7B316%7D)
Consider the right angled triangle DCA.
The angle DAC measure 75°.
Using the trigonometric identities compute the value of Perpendicular DC as follows:
![tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34](https://tex.z-dn.net/?f=tan%5C%2075%5E%7Bo%7D%3D%5Cfrac%7BDC%7D%7B%5Csqrt%7B316%7D%7D%5C%5C%5C%5CDC%3D3.732%5Ctimes%5Csqrt%7B316%7D%5C%5C%5C%5CDC%3D66.34)
Thus, the value of DC is 66.34.
Answer: D) All real numbers greater than or equal to -4.
Explanation:
The lowest point occurs when y = -4, which is where the vertex is located.
The range consists of y values such that y = -4 or y > -4. We can shorten that last sentence to say
. So y is greater than or equal to -4.
As you can probably tell, the range is the set of all possible outputs of a function.