How to find the first 4 terms of a sequence

There are 45 questions on allison's English test. The multiple choice questions are worth 2 points each, and the short answers a

Vladimir [108]

You can solve this problem by creating a system of equations and solving by substitution. This allows you to solve for one of the unknown values (in this case, the number of short answer and number of multiple choice) and you can then solve for both, if you would like.

The two variables in your equations standing in for these missing values represent the number of short answer (s) and the number of multiple choice questions (m).

First create an equation for the number of total questions on the test. The total number of multiple choice and short answer questions is 45:
m + s = 45
Then create an equation with these variables representing the number of points on the test. The point values for each question will be the variable coefficients (numbers that the variables are multiplied by in this problem).
2m + 5s = 120

Now you can take the first equation - since it is simpler, the variables don't have coefficients so it only requires subtraction to get one variable by itself - solve for one of the variables, and substitute the result into the second equation in place of that variable. You will then be able to solve for that variable!

First, solve for m in the first equation by moving the m to one side of the equals sign by itself. It then becomes 45 - s = m

Now put (45-s) into the second equation in place of m.

120 = 2(45-s) + 5s

Distribute the 2(45-s)

120 = 90 - 2s + 5s

Add the "s" expressions together. Subtract 90 from both sides.

30 = 3s

Divide by 3 and find that s = 10

There are 10 short answer questions on the test.

7 0

3 years ago

An air conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to re

blsea [12.9K]

Answer:

$16,000

Step-by-step explanation:

For easier understanding and calculation; we created a table for solving this question.

Destination → Dallas Atlanta Denver Availability

Source

↓

Houston $ 8 $ 12 $ 13 850

Phoenix $ 10 $ 14 $ 8 800

Memphis $ 11 $ 8 $ 14 350

Requirement 800 700 250

Minimum Shipping Cost to Dallas is from Houston and they have 850 air conditioners, Dallas need 800, so ship all required 800 air conditioners from Houston itself

Minimum shipping cost of Atlanta is from Memphis and they have 350 air conditioners, but Atlanta need 700, so ship all the 350 air conditioners that Memphis have to Atlanta

Minimum shipping cost to Denver is from Phoenix and they have 800 air conditioners, but Denver need 250, so ship all the required 250 air conditioners to Denver itself.

Destination → Dallas Atlanta Denver Availability

Source

↓

Houston $ 8 $ 12 $ 13 850

(800)

Phoenix $ 10 $ 14 $ 8 800

(250)

Memphis $ 11 $ 8 $ 14 350

(350)

Requirement 800 700 250

Still Atlanta need 350 air conditioners more, the second minimum shopping cost to Atlanta is from Houston and they have 50 air conditioners left .

So, ship all the 50 air conditioners that Houston have to Atlanta

Also, sent the remaining 300 air conditioners that Atlanta need from Phoenix

Destination → Dallas Atlanta Denver Availability

Source

↓

Houston $ 8 $ 12 $ 13 850

(800) (50)

Phoenix $ 10 $ 14 $ 8 800

(300) (250)

Memphis $ 11 $ 8 $ 14 350

(350)

Requirement 800 700 250

The total cost of shipping = ($ 8 × 800) +( ( $ 12 × 50)+($ 14 × 300) +( $ 8 × 350) ) + ( $ 8 × 250)

= ( $ 6, 400) + $ ( 600 + 4, 200 + 2, 800 ) + $ 2, 000

= $ 16,000

Therefore, the total cost = $ 16,000

7 0

4 years ago

Equation 1:Ax+By=C Equation 2:Dx+Ey=F A, B, C, D, E, and F are non-zero real numbers. Which of the following could replace equat

Sophie [7]

A, B and E.

Adding and multiplying the terms allow them to keep working. However, you must make sure that each variable is changed each time. Not just one as in C and D.

8 0

3 years ago

Write the product as a mixed number: 2 x 2 1/3

inn [45]

Answer:

14/3 or 4.666666667

Step-by-step explanation:

choose 1

8 0

3 years ago

Simplify 9⁴×12³×8/6⁴×4³×54

lawyer [7]

Answer:

don't post irrelevant questions check in the same place

Step-by-step explanation:

meem/jbb-qoqh-xcs

8 0

3 years ago

Read 2 more answers