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vodka [1.7K]
2 years ago
12

For the cyclic quadrilateral ABCD, which statement is true? A) The sum measure of ∠A and ∠B equals 180°. B) The sum measure of ∠

A and ∠D equals 180°. C) The sum measure of ∠B and ∠D equals 180°. D) The sum measure of ∠C and ∠D equals 180°.

Mathematics
2 answers:
xz_007 [3.2K]2 years ago
7 0

Answer:

C

Step-by-step explanation:

kifflom [539]2 years ago
6 0
See the picture attached to better understand the problem

we know that
A quadrilateral is called Cyclic quadrilateral <span>if its all vertices lie on the circle.
</span><span>The opposite angles of a Cyclic - quadrilateral are supplementary
</span>so
∠A+∠C=180°
and
∠B+∠D=180°

therefore
the answer is
<span>C) The sum measure of ∠B and ∠D equals 180°</span>

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Question 21

Let's complete the square

y = 3x^2 + 6x + 5

y-5 = 3x^2 + 6x

y - 5 = 3(x^2 + 2x)

y - 5 = 3(x^2 + 2x + 1 - 1)

y - 5 = 3(x^2+2x+1) - 3

y - 5 = 3(x+1)^2 - 3

y = 3(x+1)^2 - 3 + 5

y = 3(x+1)^2 + 2

Answer: Choice D

============================================

Question 22

Through trial and error you should find that choice D is the answer

Basically you plug in each of the given answer choices and see which results in a true statement.

For instance, with choice A we have

y < -4(x+1)^2 - 3

-7 < -4(0+1)^2 - 3

-7 < -7

which is false, so we eliminate choice A

Choice D is the answer because

y < -4(x+1)^2 - 3

-9 < -4(-2+1)^2 - 3

-9 < -7

which is true since -9 is to the left of -7 on the number line.

============================================

Question 25

Answer: Choice B

Explanation:

The quantity (x-4)^2 is always positive regardless of what you pick for x. This is because we are squaring the (x-4). Squaring a negative leads to a positive. Eg: (-4)^2 = 16

Adding on a positive to (x-4)^2 makes the result even more positive. Therefore (x-4)^2 + 1 > 0 is true for any real number x.

Visually this means all solutions of y > (x-4)^2 + 1 reside in quadrants 1 and 2, which are above the x axis.

5 0
2 years ago
How much does 4 5/7 kg of candy cost if 5/6 kg costs $7.50
Aliun [14]

Answer:

It costs $42.43

Step-by-step explanation:

Lets explain how to solve the problem

- The cost of \frac{5}{6} kilogram of candy is $7.5

- We need to find the cost of 4\frac{5}{7} kilogram

We  can use the ratio to find the answer

======= Dollar   :    Kilogram

======= 7.5        :    \frac{5}{6}

=======  c           :    4\frac{5}{7}  

By using cross multiplication

∴ c × \frac{5}{6} = 7.5 × 4\frac{5}{7}

∵ 4\frac{5}{7} = \frac{4*7+5}{7}

∴ 4\frac{5}{7} = \frac{33}{7}

∴ c × \frac{5}{6} = 7.5 × \frac{33}{7}

∴ c × \frac{5}{6} = \frac{495}{14}

Divide both sides by \frac{5}{6}

∴ c = \frac{495}{14} ÷ \frac{5}{6}

Change the division sign to multiplication sign and reciprocal the

fraction after the division sign

∴ c = \frac{495}{14} × \frac{6}{5}

∴ c = \frac{297}{7} = 42.43 dollars

∵ c represents the cost of 4\frac{5}{7} kg

∴ It costs $42.43

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