MATHEMATICS HIGH SCHOOL

If you have 6 pieces of plywoodthat are 4'x8', how many total
1xl pieces can you get out if
you use all of them?

Answers

Answer 1

Answer:

Answer:192

Step-by-step explanation:

Calculate the area l*w or s*s

Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here

4*8=32/1=32*6=192

Answer 2

Answer:

Final answer:

You can get a total of 192 pieces of 1'x1' plywood from six 4'x8' pieces.

Explanation:

To find the total number of 1'x1' pieces that can be cut from the 4'x8' plywood pieces, we need to find the total area of plywood available and then divide it by the area of the desired pieces.

First, calculate the area of one piece of plywood: 4 feet x 8 feet = 32 square feet.

Since there are 6 pieces, the total area of plywood is 6 x 32 square feet = 192 square feet.

Since each 1'x1' piece has an area of 1 square foot, you can get 192 1'x1' piecesout of all the plywood.

Learn more about Area Calculation here:

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.Amy is an installer for the telephone company. She earns $10 per hour. How much does she earn in 40 hours?
a population decrease from 404 million to 288 million .which of the following is the percent decrease of the population

on sara's computer, 3/8 of the hard drive is files. Of the files, 1/6 are games . What part of the hard drive is games?

Answers

$\frac38 \cdot \frac16=\frac3{48}=\frac1{16}$

$\frac38\ \cdot\ \frac16=\frac18\ \cdot\ \frac12=(1)/(16)$

1/3 of something = 3

Answers

1/3 of 9 = 3

$1/3*9 \n =1/3*9/1 \n =9/3 \n=3$

$(1)/(3)x=3\n x=9$

Which expression gives the solutions of -5+2x^2=-6x

Answers

Answer:

The solutions are

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

Step-by-step explanation:

we have

$-5+2x^(2) =-6x$

rewrite the quadratic equation

$2x^(2)+6x-5=0$

The formula to solve a quadratic equation of the form $ax^(2) +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}$

in this problem we have

$2x^(2)+6x-5=0$

$a=2\nb=6\nc=-5$

substitute in the formula

$x=\frac{-6(+/-)\sqrt{6^(2)-4(2)(-5)}} {2(2)}$

$x=\frac{-6(+/-)√(76)} {4}$

$x=\frac{-6(+/-)2√(19)} {4}$

$x1=(-6+2√(19))/(4)$

$x2=\frac{-6-2√(19)} {4}$

-5 + 2x² = -6x
rearrange the equation to the form ax² + bx + c = 0

=> 2x² + 6x - 5

use the quadratic formula to solve for the value(s) of x $-b ± \sqrt{ (b^(2) - 4ac)/(2a) }$

=> $-6 ± \sqrt{ (6^(2) - 4(2)(-5))/(2(2)) }$

=> $-6 ± \sqrt{ (36 - (-40))/(4) }$

=> $-6 ± \sqrt{ (76)/(4) }$

∴ x = $-6 + √( 19) }$ OR x = $-6 - √(19)$

x = - 1.64 ; x = - 10.36

The monthly utility bills in a city are normally distributed with a mean of $121 and a standard deviation of $23. Find the probability that a randomly selected utility bill is between $110 and $130.

Answers

Answer:

Step-by-step explanation:

Applying the formula for normal distribution,

z = (x - u)/s

Where u = mean

s = standard deviation

x = the monthly utility bill in dollars

From the information given,

s = 23

u = 121

The probability that a randomly selected utility bill is between $110 and $130 is expressed as

P(110 lesser than or equal to x lesser than or equal to 130)

For 110

z1 = (110 - 121)/23 = - 11/23

z1 = - 0.4783

Looking at the normal distribution table,

The corresponding z score is 0.3192

For 130

z2 = (130 - 121)/23 = 9/23

z2 = 0.391

Looking at the normal distribution table,

The corresponding z score is 0.65173

P(110 lesser than or equal to x lesser than or equal to 130) = 0.65173 - 0.3192 = 0.33253

If f(x) = 4x − 6 and g(x) = 6x − 4, what is f · g?

Answers

Answer:

f · g = 24x² - 52x + 24

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Expand by FOIL
Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4x - 6

g(x) = 6x - 4

Step 2: Find f · g

Substitute in function values: f · g = (4x - 6)(6x - 4)
Expand [FOIL]: f · g = 24x² - 16x - 36x + 24
[Subtraction] Combine like terms: f · g = 24x² - 52x + 24

Find the product of (x − 3)2.
x2 + 6x + 9
x2 − 9
x2 − 6x + 9
x2 + 9

Answers

(x-3)² ⇒ (x-3)(x-3)

(x-3)(x-3) = x(x-3) -3(x-3) ⇒ x² - 3x - 3x + 9 ⇒ x² - 6x + 9

The 3rd option is the correct answer. x² - 6x + 9

Answer:

$\large\boxed{x^2-6x+9}$

Step-by-step explanation:

$(x-3)^2\n\n\bold{METHOD\ 1}\n\n(x-3)^2=(x-3)(x-3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\n\n=(x)(x)+(x)(-3)+(-3)(x)+(-3)(-3)\n\n=x^2-3x-3x+9\qquad\text{combine like terms}\n\n=x^2-6x+9\n\n\bold{METHOD\ 2}\n\n(x-3)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\n\n=x^2-2(x)(3)+3^2\n\n=x^2-6x+9$