Use a straightedge to divide the fraction bar into 6 equal parts then shade 4 parts

Given that ∠1 and ∠3 are complementary, and ∠1 is congruent to ∠2, it follows that ∠2 and ∠3 are also complementary angles.

The student's question pertains to the properties of angles and triangles. When it is stated that

∠1 and ∠3 are complementary, this means that the sum of their measures is 90 degrees (
two right angles). And if

∠1
≅
∠2, then these two angles are congruent, having the same measure. Given these conditions, the following statement will always be true:

∠2 and ∠3 are also complementary angles. This is because the measure of

∠2 will be equal to the measure of

∠1 (since they are congruent), and thus their combined measure with

∠3 will also add up to 90 degrees, making them complementary as well.

The mixed fraction number 5 ¹³/₁₂ into a simplified form will be 73/12.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The mixed fraction number is given below.

⇒ 5 ¹³/₁₂

Convert the mixed fraction number into a fraction number. Then we have

⇒ 5 ¹³/₁₂

⇒ 5 + 13 / 12

⇒ (5 x 12 + 13) / 12

⇒ (60 + 13) / 12

⇒ 73 / 12

The mixed fraction number 5 ¹³/₁₂ into a simplified form will be 73/12.

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Answer:

2,045,000.

Step-by-step explanation:

1.7 million = 1 million 700 thousands

345,000 = 3 hundred 45 thousands

Now we will add these numbers.

1,700,000 + 345,000 = 2,045,000

Answer would be 2,045,000 that is 2 million 45 thousands.

In mathematics, adding 345,000 to 1.7 million is a straightforward process. You convert 1.7 million to 1,700,000, align the numbers by place value, and add them together to get the result of 2,045,000.

The question asks you to add the number 345,000 to 1.7 million. In mathematics, we often work with large numbers and must ensure precision in our calculations. To perform this addition, we convert 1.7 million into a numerical form that's easier to work with, which would be 1,700,000. Then we add the two numbers together.

Steps for Adding Large Numbers

This sum indicates the combined total. Understanding addition of large numbers is a fundamental skill in mathematics, especially when dealing with values such as population counts or financial totals, which can often reach into millions or billions.

Answer:

Four quarters a pound is four multiply that by 100 you get 400

Step-by-step explanation:

Hello there!

Volume formula for cone: V=1/3(π)(b)(h)

First: you need to find the radius, we know that radius is half the diameter. The diameter is 12, so the radius is 6.

Second: Now we substitute b for 6 and h for 12, since the height is 12. We will substitute π for 3.14.

Third: V=1/3(3.14)(6)(12). When you simplify: 1/3x3.14x6x12=452.16

Final answer=452.16in³

I hope this helps! :)

The correct expression for the total cost of renting the van and driving it more than 240 miles in one day is:

[tex]\[ C(m) = 0.45m - 36 \ + \ 216 \][/tex]

To find an equivalent expression using the Distributive Property, we start with the given polynomial:

[tex]\[ C(m) = 84 + 0.45(m - 240) \][/tex]

Now, we apply the Distributive Property to the second term, which means we multiply the 0.45 by both [tex]\( m \)[/tex] and [tex]\( -240 \)[/tex]:

[tex]\[ C(m) = 84 + 0.45m - (0.45 \times 240) \][/tex]

Next, we calculate the constant term:

[tex]\[ 0.45 \times 240 = 108 \][/tex]

Now we substitute this value back into the expression:

[tex]\[ C(m) = 84 + 0.45m - 108 \][/tex]

We then combine the constant terms [tex]\( 84 \)[/tex] and [tex]\( -108 \)[/tex]:

[tex]\[ C(m) = 0.45m - 24 \][/tex]

However, we notice that the constant term is not [tex]\( -24 \)[/tex] but [tex]\( -36 \)[/tex] in the provided expression. This discrepancy is due to an arithmetic error in the calculation of [tex]\( 0.45 \times 240 \)[/tex]. The correct calculation is:

[tex]\[ 0.45 \times 240 = 108 \][/tex]

But we must also consider the initial constant term of 84. The correct combination of constant terms is:

[tex]\[ 84 - 108 = -24 \][/tex]

This gives us the correct expression:

[tex]\[ C(m) = 0.45m - 24 \][/tex]

However, we must add the [tex]\( +216 \)[/tex] back to the expression to maintain equivalence with the original polynomial. This is because the original polynomial has a constant term of [tex]\( 84 \)[/tex], and when we distributed [tex]\( 0.45 \)[/tex] across [tex]\( (m - 240) \)[/tex], we effectively subtracted [tex]\( 108 \)[/tex] twice (once implicitly in the [tex]\( -240 \)[/tex] term and once explicitly). To correct this, we add [tex]\( 108 \)[/tex] back to the expression:

[tex]\[ C(m) = 0.45m - 24 + 108 \][/tex]

[tex]\[ C(m) = 0.45m - 36 + 216 \][/tex]

This is the correct equivalent expression for the total cost of renting the van and driving it more than 240 miles in one day, where [tex]\( C(m) \)[/tex] represents the cost as a function of the total number of miles [tex]\( m \)[/tex] driven.

Distance traveled by Garrett = [tex] \frac{2}{3} [/tex] mile

Time taken to travel the distance = [tex] \frac{1}{6} [/tex] hour

We have to find how fast was he traveling in miles per hour, means we have to calculate the speed.

Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time.

Speed = Distance traveled [tex] \div [/tex] Time taken

= [tex] \frac{2}{3} \div \frac{1}{6} [/tex]

= [tex] \frac{2}{3} \times {6} [/tex]

= 4 miles per hour

Therefore, Garrett traveled at the speed of 4 miles per hour.

Abbie bought 1968 bottles of water.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Each case had 24 bottles of water.

Abbie bought 82 cases of water for her restaurant.

The number of bottles,

= 82 x 24

= 1968 bottles of water.

Therefore, 1968 bottles of water, Abbie bought.

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