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3 years ago

Simplify the expression 4(x+y) + 3y

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

6 0

Answer:

4x + 7y

Step-by-step explanation:

4(x+y) + 3y

Distribute

4x+ 4y+ 3y

add like terms

4x + 7y

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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule

Sergeeva-Olga [200]

Answer:

First term: 5

Fourth term: 5 1/2

Tenth term: 6 1/2

Step-by-step explanation:

Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:

A(n) = 5 + (n-1) (1/6)

First term:

A(1) = 5 + (1-1) (1/6)

A(1) = 5 + (0) (1/6)

A(1) = 5

Fourth term:

A(4) = 5 + (4-1) (1/6)

A(4) = 5 + (3) (1/6)

A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)

Tenth term:

A(10) = 5 + (10-1) (1/6)

A(10) = 5 + (9) (1/6)

A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)

5 0

3 years ago

There are 10 true-false questions and 20 multiple choice questions from which to choose a five-question quiz how many ways can t

beks73 [17]

Answer:

In 68229 ways can the quiz be selected such that there is atleast three multiple choice questions

Step-by-step explanation:

Given:

Number of True or false questions= 10

Number of multiple choice questions= 20

To Find:

How many ways can 5 questions can be selected if there must be at least three multiple choice questions =?

Solution:

Combination

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

The question States there sholud be ATLEAST 3 multiple choice question,

So, we may have

(3 Multiple choice question and 2 true or false question) or

(4 Multiple choice question and 1 true or false question) or

(5 Multiple choice question and 0 true or false question)

Required Number of ways = (20C3 X10C2) +(20C4 X10C1) + (20C5 X10C0)

Required Number of ways $=(\frac{20!}{20!(20-3)!}\times\frac{10!}{10!(10-2)!})+(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-1)!}) +(\frac{20!}{20!(20-4)!} \times \frac{10!}{10!(10-0)!})$

Required Number of ways = ( 1140 x 42) + (4845 x 10) +(15504 x 1)

Required Number of ways = 47880+48450+15504

Required Number of ways = 68229

3 0

3 years ago

Find the slope of the line through the pair of points.

erastovalidia [21]

Answer:

The answer is A undefined

Step-by-step explanation:

The slope is given by

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

$m=\frac{9-(-13)}{17-17}=\frac{22}{0}$

which is undefined (division by zero)

4 0

3 years ago

The product of x and 6

zubka84 [21]

Answer:

Step-by-step explanation:

5 0

3 years ago

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded.

Mazyrski [523]

Answer:

1/7 (option d) of the sensors on the satellite have been upgraded

Step-by-step explanation:

Each unit contains the same number of non-upgraded sensors

number of non-upgraded sensors for each module (nus)

total number of upgraded sensors on the satellite (tus)

satellite is composed of 30 modular units

total number of non-upgraded sensors on the satellite (tnus):

tnus=30*nus

total number of sensors on the satellite (ts):

ts=tnus+tus = 30*nus + tus (I)

The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite

nus=(1/5)*tus

tus = 5 * nus (II)

Fraction of the sensors on the satellite have been upgraded (FU):

FU = tus/ts

Using I and II

FU= (5* nus)/(30*nus + tus)

FU = (5* nus)/(30*nus + 5 * nus)

FU = (5* nus)/(35*nus)

FU = 1/7

1/7 (option d) of the sensors on the satellite have been upgraded

6 0

3 years ago