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3 years ago

What is the product? (5r + 2) (3r -4)

Mathematics

1 answer:

Tanzania [10]3 years ago

7 0

Answer:

15r² - 14x - 8

Step-by-step explanation:

5x * 3x = 15x²
5x * -4 = -20x
2 * 3x = 6x
2 * -4 = -8

Now add your products,

15x² + -20x + 6x + -8 = 15x² - 14x - 8

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3x+30+x=10+2x+5x+2 <br> i need help fast

kupik [55]

Answer:

x=6

Step-by-step explanation:

Group Like Terms:

3x+x+30=10+2x+5x+2

Add similar elements 3x+x=4x:

4x+30=10+2x+5x+2

Add similar elements 2x+5x=7x:

4x+30=10+7x+2

Group like terms:

4x+30=7x+10+2

Add the numbers 10+2=12:

4x+30=7x+12

Subtract 30 from both sides:

4x+30-30=7x+12-30

Simplify:

4x=7x-18

Subtract 7x from both sides:

4x-7x=7x-18-7x

Simplify:

-3x=-18

Divide both sides by -3:

$\frac{-3x}{-3} =\frac{-18}{-3}$

Simplify:

x=6

Hence, the correct answer is 6

4 0

2 years ago

Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back

ankoles [38]

Answer:

The trip normally takes 8 minutes

Step-by-step explanation:

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial speed , v₁, by the boat on the way back = 2 minutes

The increase in speed of the boat by Pilar = 10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than time for the trip, t₁

t₂ = t₁ - 1

Therefore we have;

v₁ × t₁ = v₁×2 + v₂×(t₂-2) = 400

v₁×2 + (v₁ + 10)×(t₂-2) = 400

(v₁ + 10)×t₂ - 20 = 400

But v₁ = 400/t₁ = 400/(t₂ + 1)

Which gives;

(400/(t₂ + 1) + 10)×t₂ - 20 = 400

10×(t₂²+ 36·t₂-2)/(t₂+1) = 400

10·t₂²+ 10·t₂-420 = 0

t₂²+ t₂-42 = 0

(t₂ - 7)(t₂ + 6) = 0

t₂ = 7 minutes or -6 minutes

Given that t₂ is a natural number, we have, t₂ = 7 minutes

Whereby, t₂ = t₁ - 1, we have;

7 = t₁ - 1

t₁ = 1 + 7 = 8 Minutes

The trip normally takes 8 minutes

3 0

3 years ago

In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a re

Mariulka [41]

Step-by-step explanation:

In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades. That leaves 35 cards for everything else.

For the game to be fair, the cost must equal the expected value. The expected value is the sum of each outcome times its probability.

C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)

C = 68/13

C ≈ 5.2308

4 0

2 years ago

A professor wants to award prizes for 1st, 2nd, 3rd, 4th and 5th in the class of 30. In how many ways can the prizes be awarded

aniked [119]

Answer:

$Selection = 17100720\ ways$

Step-by-step explanation:

Given

$Students = 30$

$Positions = 5$ i.e. first to fifth

Required

Determine number of selection

1st position = Any of the 30 students

2nd position = Any of the 29 students

3rd position = Any of the 28 students

4th position = Any of the 27 students

5th position = Any of the 26 students

Number of selection is then calculated as:

$Selection = 30 * 29 * 28 * 27 * 26$

$Selection = 17100720\ ways$

8 0

3 years ago

A marching band is arranged in rows of 7 the first row has 3 band members and each row after the first has 2 more band members t

pav-90 [236]

Answer:

$a_{n}$ = 1+2n and 63

Step-by-step explanation:

the question belongs to arithmetic sequence and $a_{n}$ can be determined by the formula

$a_{n}$ = a1 + d (n-1)

Let " $a_{n}$ " represents the number of band members in the nth row

and 'd' represents the common difference.( as stated each row has 2 more band members than the row before it)

therefore, d=2

'a1' represents first row that has three members. So, a1 = 3

->Rule for nth term will be:

$a_{n}$ = 3 + 2(n-1)

$a_{n}$ = 3 + 2n -2

$a_{n}$ = 1+2n

-> In order to find total number of band members ' $S_{7}$ '

Let $S_{n}$ represent total number in n rows

We'll use the formula, i.e $S_{n}$ = n/1 ( $a_{1}$ + $a_{n}$ )

where, n is the number of terms, $a_{1}$ is the first term and $a_{n}$ is the last term

So,

n=7

$a_{7}$ = 1 + 2(7)= 15

=> $S_{7}$ = 7/2 (3 + 15)

$S_{7}$ = 63

The total number of band members are 63

8 0

3 years ago