Part B if u want part A too

The product of two consecutive odd intergers is 1 less than four times thier sum. Find the two integers.

seraphim [82]

Consecutive odd integers are 2 apart
they are x and x+2
the product (x times (x+2)) is 1 less than 4 times their sum

x(x+2)=-1+4(x+x+2)
$x^2+2x=-1+4(2x+2)$
$x^2+2x=-1+8x+8$
$x^2+2x=8x+7 minus (8x+7) from both sides [tex]x^2-6x-7=0$
factor
what numbers multliply to get -7 and add to get -6?
-7 and 1
(x-7)(x+1)=0
set equal to 0
x-7=0
x=7

x+1=0
x=-1

so the x can be 7 or -1
the other number (x+2) can be 7 or 1

test each

7 and 9
7(9)=-1+4(7+9)
63=-1+4(16)
63=-1+64
63=63
true

-1 and 1
-1(1)=-1+4(-1+1)
-1=-1+4(0)
-1=-1+0
-1=-1
true

the 2 integers can be 7 and 9 or -1 and 1 (both pairs of numbers work)

3 0

3 years ago

3. In an auditorium, 1/6 of the students are fifth graders, 1/3 are fourth graders, and 1/4 of the remaining students are second

Katen [24]

12

<h3>Further explanation</h3>

<u>Given:</u>

In an auditorium,

$\frac{1}{6}$ of the students are fifth graders,
$\frac{1}{3}$ are fourth graders, and
$\frac{1}{4}$ of the remaining students are second graders.

There are 96 students in the auditorium.

<u>Question:</u>

How many second graders are there?

<u>The Process:</u>

The least common multiple (LCM) of 3 and 6 is 6.

Let us draw the diagram of all students.

$96 \div 6 \ units = 16 \rightarrow \boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16}\boxed{16} = 96 \ students$

$\frac{1}{6}$ of the students are fifth graders, or 1 of 6 units above, that is $\boxed{16} = 16 \ students$
$\frac{1}{3} = \frac{2}{6}$ are fourth graders, or 2 of 6 units above, that is $\boxed{16}\boxed{16} = 32 \ students$

The remainder is 6 units - (1 unit + 2 units) = 3 units, that is $\boxed{16}\boxed{16}\boxed{16} = 48 \ students$ . Or, 96 - 16 - 32 = 48 students.

$\frac{1}{4}$ of the remaining students are second graders.

Let us count how many second graders are there.

$\boxed{ \ \frac{1}{4} \times 48 \ students = ? \ }$

Thus, there are 12 second-graders in the auditorium.

- - - - - - - - - -

Quick Steps

$\boxed{ \ \frac{1}{4} \times \bigg(1 - \frac{1}{6} - \frac{1}{3} \bigg) \times 96 = ? \ }$

$\boxed{ \ = \frac{1}{4} \times \bigg(\frac{6}{6} - \frac{1}{6} - \frac{2}{6} \bigg) \times 96 \ }$

$\boxed{ \ = \frac{1}{4} \times \frac{3}{6} \times 96 \ }$

$\boxed{ \ = \frac{3}{24} \times 96 \ }$

We crossed out 24 and 96.

$\boxed{ \ = 3 \times 4 \ }$

$\boxed{\boxed{ \ = 12 \ students \ }}$

<h3>Learn more</h3>

How long did it take Charlotte to finish the word search brainly.com/question/8561495
What fraction of all Sarah's photos is of her friends brainly.com/question/1020296
Create and solve a story problem about two friends and their weekly allowance brainly.com/question/2968321

Keywords: In an auditorium, 1/6 of the students, fifth graders, 1/3, fourth, 1/4, the remaining students, second, 96, how many, second graders

3 0

3 years ago

Read 2 more answers

Can some one just tell me if these are right? If not can I have the answers?

-Dominant- [34]

Yes you have them correct

6 0

3 years ago

What is -5(3-2g) equal

klio [65]

Answer:

Simplified the expression

− 15 + 10 g

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. What is the volume of the roof to the ne

Lubov Fominskaja [6]

The volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

<h3>How to find the volume of the composite figures?</h3>

To find the volume of the composite figures, follow the steps listed below:,

Separate the figure.
Calculate the volume of each figure by which the composite figure is made of.
Add the volume of all the individual figures to get the total volume of composite figures.

A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. The volume of the roof is:

$V=\dfrac{1}{3}(\text{length x width x height})\\V=\dfrac{1}{3}40\times40\times20\\V\approx10667\rm\; ft^3$

The volume of the room is:

V=length x width x height

V=40 x 40 x 30

V=48000 ft³

The volume of the entire house, including the roof, is,

V=10667+48000

V=58667 ft³

Thus, the volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.

Learn more about the volume of composite figures here;

brainly.com/question/1205683

#SPJ1

7 0

1 year ago