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Aloiza [94]
3 years ago
6

Given: ∠A and ∠B are complementary angles.

Mathematics
1 answer:
Eddi Din [679]3 years ago
7 0

Answer:

 - For the statement -3x=24, the reason is: <em>Subtraction property of Equality</em>

- For the statement x=-8, the reason is: <em>Division property of Equality.</em>

- For the statement m\angle B=-6(-8)-39, the reason is: <em>Substitution property of Equality.</em>

Step-by-step explanation:

The missing pictures are attached.

We must remember that:

- The Subtraction property of Equality states that:

If\ a=b,\ then\ a+c=b+c

- The Division property of Equality states that:

If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}

- The Substitution property of Equality states that:

 If\ a=b,\ then\ b\ can\ replace\ a

Knowing this properties we can identify the missing reasons that correctly complete the proof.

 - For the statement -3x=24, the reason is:

Subtraction property of Equality

(Because it is obtained by subtracting  66 from both sides of -3x+66=90)

- For the statement x=-8, the reason is:

Division property of Equality

(Because it is obtained by dividing both sides of  -3x=24 by -3)

- For the statement m\angle B=-6(-8)-39, the reason is:

Substitution property of Equality

(Because it is obtained by substituting the value of "x" into   m\angle B=-6x-39)

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Answer:

A = 15000(1.02)^4t ; $33,120.59

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1 year ago
4/5 gallon of water divided by 4 bottles what fraction of a gallon is in each bottle
Vinvika [58]

Answer:

1/5 gallon of water in each bottle

Step-by-step explain:

4/5 = 0.8

0.8/4 = 0.2 or 1/5 gallons

3 0
3 years ago
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches. Which is the slant h
Nikitich [7]

Answer: 5 inches


Step-by-step explanation:

Given: Volume of clay = 48 cubic inches

If we make a solid square right pyramid with a base edge a= 6 inches.

Then its base area = a^2=6^2=36\ inches^2

we know that volume of square right pyramid=\frac{1}{3}\times\ a^2h

Therefore, volume of square right pyramid made by all of clay=\frac{1}{3}\times\ a^2h=48 cubic inches

\Rightarrow\frac{1}{3}\times\ (36)\times\ h=48\\\Rightarrow12h=48\\\Rightarrow\ h=4\ inches.....\text{[Divide 12 on both sides]}

Now, slant height l=\sqrt{(\frac{a}{2})^2+h^2}

\\\Rightarrow\ l=\sqrt{3^2+4^2}\\\Rightarrow\ l=\sqrt{9+16}\\\rightarrow\ l=\sqrt{25}\\\Rightarrow\ l=5

The slant height of the pyramid if Helen uses all the clay=5 inches

5 0
2 years ago
Read 2 more answers
Use the diagram to complete the statement.<br><br><br><br> CF =
kondor19780726 [428]

Answer:

∠ECF = 37°

Step-by-step explanation:

∠ACG = 37°   because it is a complementary angle to 53° (37° + 53° = 90°)

∠ECF = 37° because it is a vertical angle to 37°

4 0
3 years ago
Combine and simplify the following radical expression <br><br> ASAP ASAP ASAP ASAP
Montano1993 [528]

Answer:

\sqrt[3]{3}

Step-by-step explanation:

Our expression is: \frac{1}{3} \sqrt[3]{81}.

Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or 3^3*3. Put this in for 81:

\sqrt[3]{81} =\sqrt[3]{3^3*3}=\sqrt[3]{3^3} *\sqrt[3]{3}

We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:

\sqrt[3]{3^3} *\sqrt[3]{3}=3\sqrt[3]{3}

Now, let's multiply this by 1/3, as shown in the original problem:

\frac{1}{3}* 3\sqrt[3]{3}=\sqrt[3]{3}

Thus, the answer is \sqrt[3]{3}.

<em>~ an aesthetics lover</em>

6 0
3 years ago
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