Estimate the value of the expression by rounding each number to the given place value. 68 – 29; tens A. 30 B. 35 C. 40 D. 50

n/6 = 10/15

n = 10/15 * 6

n = 10*6 =60,  60/15 = 4

n = 4

Lines r and s are parallel based on the given measure of angles 2 and 6.

Based on the given information, if the measure of angle 2 is 110° and the measure of angle 6 is also 110°, then it can be concluded that lines r and s are parallel. This conclusion is based on the Alternate Interior Angles Theorem, which states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent.

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Answer: 6.121212121212... = 202/33

Step-by-step explanation:

(612 - 6)/99 = 606/99 = 202/33 = 6.12121212121212... ∈ ℚ

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.  

Since 6.121212121212... is a number whose digits are periodic (12) , we can express it as a fraction 202/33, therefore is a rational number ∈ℚ.

[tex]\textit{\textbf{Spymore}}[/tex]

Two lengths within the average range for a ladybug could be 0.2 inches and 0.35 inches, both of which are between the minimum of 0.08 inches and the maximum of 0.4 inches.

The average length of a ladybug can range from 0.08 to 0.4 inch. To find two lengths that are within the given span, we can select any two numbers that fall between these two values. For instance:

These lengths are examples of measurements that would fall within the typical size range of a ladybug.

A. [tex]\[ T = C + G \times P \][/tex]

B. they will spend $748.95 before sales tax.

C. [tex]\[ T = C + G \times P + K \times R \][/tex]  

D. The total cost before sales tax if Homer and Bart purchase one computer, five games, and three extra controllers would be $823.92.

PART A:

Let us define the variables:

- C: Cost of the computer ($499.00)

-  G : Number of games

-  P : Cost of one game ($49.99)

-  T : Total cost before sales tax

The algebraic expression to describe how much they will spend before sales tax based on purchasing the computer and the number of games is:

[tex]\[ T = C + G \times P \][/tex]

PART B:

If they purchase one computer and five games, we substitute G = 5  into the expression:

[tex]\[ T = 499 + 5 \times 49.99 \][/tex]

Now, we can calculate:

[tex]\[ T = 499 + 5 \times 49.99 \]\[ T = 499 + 249.95 \]\[ T = 748.95 \][/tex]

So, they will spend $748.95 before sales tax.

PART C:

Let's define an additional variable:

-  K : Number of extra controllers

-  R: Cost of one extra controller ($24.99)

The algebraic expression to describe how much they spend in total before sales tax when they purchase one computer, any number of games, and any number of extra controllers is:

[tex]\[ T = C + G \times P + K \times R \][/tex]

If they purchase one computer, five games, and three extra controllers, we substitute  G = 5  and  K = 3  into the expression:

[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \][/tex]

PART D:

Now, we can calculate:

[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \]\[ T = 499 + 249.95 + 74.97 \]\[ T = 499 + 324.92 \]\[ T = 823.92 \][/tex]

So, the total cost before sales tax if Homer and Bart purchase one computer, five games, and  three extra controllers would be $823.92.

Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.

Let S represent the number of hours Tom served at the Salvation Army.

Since the total number of hours Tom served is 100, we have,

S + R + M = 100

Substitute R and M with the expressions in terms of S:

S + (S + 19) + (S + 19 + 8) = 100

S + S + 19 + S + 27 = 100
3S + 46 = 100
3S = 54
S = 18

So, Tom served 18 hours at the Salvation Army. Now, we find the hours for the other two charities,

In summary, Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.

Complete question-
Tom performed a total of 100 hours of community service. He served at three charities – Salvation Army, Red Cross and Rescue Mission. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross. Find the number of hours he volunteered at each charity.

Answer:

-24

Step-by-step explanation:

45 + 18 + 27 - 21 - 93 C = -24 Let's use the variable C to represent the change in the balance in Cody's checking account. The easiest way to make the expression is to simply apply the additions and subtractions directly. So let's start with C C "Cody made deposits of $45, $18, and $27 into his checking account." C = 45 + 18 + 27 "He then wrote checks for $21 and $93." C = 45 + 18 + 27 - 21 - 93 So the expression to represent the change to Cody's checking account is C = 45 + 18 + 27 - 21 - 93 Now to simplify it. All you need to do is combine terms together. How far you go is up to you. So let's do it. C = 45 + 18 + 27 - 21 - 93 I'll add together all the deposits. C = (45 + 18 + 27) - 21 - 93 C = 90 - 21 - 93 And I'll combine the checks. C = 90 - 114 So now you can tell at a glance that Cody deposited $90 and wrote checks for $114. But we can make it simpler and combine those as well. So C = -24 And this tells you that Cody's checking account balance is now $24 lower than it was before he started making deposits and writing checks.

Answer:

its A

Step-by-step explanation:

0.4(3b +10) = 19

1.2b + 4 = 19

1.2b = 15

b = 15 / 1.2

b = 12.5