Jeremy has two pieces of what one is 90 inches and the other is 72 inches he want to cut the pieces of wood in the smaller pieces to the all the pieces are the same length if you wants the pieces to be as long as possible and doesn't want to have any lumber left over how long should each piece me how many total pieces of lumber will he have
find the complex roots of x^3+1=0
[tex]\text{Use:}\ a^3-b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex] x^3+1=0\\\\x^3+1^3=0\\\\(x+1)(x^2-(x)(1)+1^2)=0\\\\(x+1)(x^2-x+1)=0\iff x+1=0\ \vee\ x^2-x+1=0\\\\x+1=0\to x=-1\in\mathbb{R}-real\ solution\\\\x^2-x+1=0\\\\x^2-2\cdot x\cdot0.5+1=0\\\\\underbrace{x^2-2\cdot x\cdot0.5+0.5^2}_{(a-b)=a^2-2ab+b^2}-0.5^2+1=0\\\\(x-0.5)^2-0.25+1=0\\\\(x-0.5)^2+0.75=0\ \ \ |-0.75\\\\(x-0.5)^2=-0.75\iff x-0.5=\pm\sqrt{-0.75}\ \ \ |+0.5\\\\x=0.5-i\sqrt{0.75}\ \vee\ x=0.5+i\sqrt{0.75}\\\\x=\dfrac{1}{2}-i\sqrt{\dfrac{3}{4}}\ \vee\ x=\dfrac{1}{2}+i\sqrt{\dfrac{3}{4}} [/tex]
[tex]\boxed{x=\dfrac{1-i\sqrt3}{2}\ \vee\ x=\dfrac{1+i\sqrt3}{2}}[/tex]
[tex]\text{in standard form:}\ \boxed{x=\dfrac{1}{2}-\dfrac{\sqrt3}{2}i\ \vee\ x=\dfrac{1}{2}+\dfrac{\sqrt3}{2}i}[/tex]
candy buys 20 ounces of mixed nuts .she puts an equal number of ounces in each of 3 bags .how many ounces of nuts will be in each bag?write the answer as a whole number and a fraction.
Answer:
[tex]6\frac{2}{3}[/tex]
Step-by-step explanation:
Candy buys 20 ounces of mixed nuts.
She puts an equal number of ounces in each 3 bags.
In each bag she can put = [tex]\frac{20}{3}[/tex]
= [tex]6\frac{2}{3}[/tex]
She can put [tex]6\frac{2}{3}[/tex] ounces of nuts in each bag.
the 2 points are reflections of each other across the x-or y-axis identify the axis help me please
Me. Simpson drove 105 miles in 2 1/2 hour what was mr. Simpson speed in miles per hour
divide total miles driven by time:
105 miles / 2.5 hours = 42 miles per hour
Jumlah panjang dan lebar suatu persegi panjang adalah 32cm. Sedangkan luasnya adalah 240cm. Tentukan (a) panjang dan lebarnya (b) kelilingnya dan (c) panjang diagonal persegi panjang
P and L : 12 and 20 cm
Perimeter : 64 cm
Diagonal = 4√34
Further explanationThe playground is a rectangular shape. There are several properties possessed by rectangular shapes, namely:
• 1. each angle is equal and is a right angle
• 2. the diagonals intersect and divide each other equally
• 3. sides facing the same length
There are two rectangular shapes namely square and rectangle
Square if all sides are the same length
The formula used in rectangular is:
• 1.Area
Rectangle
[tex]\large{\boxed{\bold{Area=w\:\times\:l}}}[/tex]
w = width
l = length
Square
[tex]\large{\boxed{\bold{area=a^2}}}[/tex]
a = length of side
• 2. perimeter
Rectangle
[tex]\large{\boxed{\bold{perimeter=2\times(w+l)}}}[/tex]
w = width
l = length
Square
[tex]\large{\boxed{\bold{perimeter=4\times\:a}}}[/tex]
a = length of side
P+L = 32 cm
Area = 240 cm²
Then
P = 32-L
Area = (32-L) x L
Area =32L-L²
240 = 32L-L²
-L²+32L-240=0
L²-32L+240 = 0
(L-12)(L-20)=0
L = 12 or L = 20
Then =P= 20 or 12
B)Perimeter= 2 x (P +L) = 2 x (12+20) = 64 cm
C) Diagonal
Phytagoras :
[tex]\rm diagonal=\sqrt{20^2+12^2}\\\\diagonal=\sqrt{400+144}\\\\diagonal=\sqrt{544}=4\sqrt{34}[/tex]
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Solve the equation for w
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If P(A) = 0.5, P(B) = 0.3, and P(A or B) = 0.6, find P(A and B)
The length of a rectangle is 6 1/2 inches and the width is 3 3/4 inches. What is the ratio, using whole numbers, of the length to the width?
The ratio, using whole numbers of the length to the width is [tex]\frac{26}{15}[/tex]
Given the following data:
Length of a rectangle = [tex]6\frac{1}{2}[/tex] inches.Width of a rectangle = [tex]3\frac{3}{4}[/tex] inches.To calculate the ratio, using whole numbers of the length to the width:
What is ratio?Ratio can be defined as a mathematical expression that is used to denote the proportion of two (2) or more quantities with respect to one another.
How to calculate the ratio.First of all, we would convert the mixed fraction to a proper fraction as follows:
For the length:
[tex]6\frac{1}{2}=\frac{13}{2}[/tex]
For the width:
[tex]3\frac{3}{4}=\frac{15}{4}[/tex]
Now, we can calculate the ratio, using whole numbers of the length to the width:
[tex]Ratio = \frac{length}{width} \\\\Ratio = \frac{\frac{13}{2} }{\frac{15}{4} } \\\\Ratio = \frac{13}{2} \times \frac{4}{15} \\\\Ratio =\frac{26}{15}[/tex]
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A function is created to represent the miles per gallon your car gets. What restrictions would be made to the domain ?
A. The domain were only include integers.
B. The domain will only include positive integers.
C. The domain would include all real numbers.
D. The domain would only include positive numbers.
Option: D is the correct answer.
D. The domain would only include positive numbers.
Step-by-step explanation:Domain of a function--
It is the set of all the x-values or the values of the independent values for which the function is defined.
Here the function is used to represent the miles per gallon your car gets.
i.e. the independent variable is the number of gallons the car gets.
and the dependent variables is the number of miles covered by the car.
As the number of gallons of the car can't be negative or zero , it could be any positive number.
Hence, the domain would include any positive number.
Please help I don’t understand.I need to know if it is a linear function and how to write it in standard form. :)
Josh spends 40 cents of every dollar on snacks,14 cents out of every dollar on school supplies and saves the rest. If Josh earns 32.00 per week, how much does he Dave per week
Josh saves $14.72 per week from his $32.00 earnings after spending on snacks and school supplies.
The student is asking about how much Josh saves per week after spending on snacks and school supplies from his earnings. Josh spends 40 cents of every dollar on snacks and 14 cents of every dollar on school supplies, which totals 54 cents on expenditures out of every dollar he earns. To calculate his savings, we subtract this total expense from the dollar:
1 dollar - 0.54 dollars (expenses) = 0.46 dollars saved.
To find out how much Josh saves from his weekly earnings of $32.00, we multiply his savings rate per dollar by his total earnings:
$32.00 x 0.46 = $14.72 per week saved.
Write a translation rule that maps point D(7,-3) onto point D'(2,5).
Which of the following numbers has 5 in the ten thousands place A. 652,341. B. 562, 341. C. 462,541. D. 265,401
ratio 5 to 15 in a fraction lowest term
You bought a large container of fruit punch. The label on the container says there are 128 fluid ounces of fruit punch in the container. How many cups is that?
The phone company charges 10 cents to connect a call for one minute, and 8 cents per minute after that. How long could you talk on the phone for $1?
What is the product 5/10.10/3
An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.
a. How much has the angelfish grown?
b. An inch is 1/12 of a foot. How much has the angelfish grown in feet?
40 points!
The angelfish has grown by 5/6 inches, which is equivalent to 5/72 feet when converted.
The question asks how much an angelfish has grown both in inches and in feet.
Part A: Growth in Inches
The angelfish was originally 1 1/2 inches long and grew to 2 1/3 inches. To calculate the growth, subtract the original length from the current length:
2 1/3 inches (current length) - 1 1/2 inches (original length) = 7/3 inches - 3/2 inches
To subtract, convert to a common denominator (6 in this case): 7/3 becomes 14/6 and 3/2 becomes 9/6,
14/6 - 9/6 = 5/6 inches
So the angelfish has grown by 5/6 inches.
Part B: Growth in Feet
Since 1 inch is 1/12 of a foot, to calculate the growth in feet, multiply the growth in inches by the conversion factor:
5/6 inches * (1 foot/12 inches) = (5/6) * (1/12)
Multiplying these fractions, we get 5/72 feet, which is the growth in feet.
The sum of 3 consecutive odd numbers is 183. What is the second number in this sequence?
183/3 = 61 which is the middle odd number
you would then take the odd number below 61 and the odd number above 61 to equal 183
59 +61 +63 = 183
Find two consecutive even integers whose sum is -50. Which of the following equations could be used to solve the problem? 2x = -50 2x + 1 = -50 2x + 2 = -50 x2 + 1= -50
consecutive even integers are 2 apart
so they are x and x+2
their sum is x+x+2
the sum is -50
so x+x+2=-50 would be the equation
we can simplify it to get 2x+2=-50
the answer is the 3rd option
what integer divided by six, less eighteen, is negative twenty-two?
What is the value of x?
Enter your answer in the box.
Find the value of x so that the figures have the same area.
25ft, x-6 ft
x ft, 15ft
How do you simplify using the laws of exponents?
Can you show me an example pleaseee
https://youtu.be/6ieqoMb0kWI
Watch this video hope this helps you.
Express each ratio as a fraction in simplest form:
0.3 km to 500 m
Answer: 3/5
Step-by-step explanation:
The ratio shows how many times a number is contained in another. To express the ratio as a fraction in its lowest term, we convert 0.3km to metre.
1000 metre makes 1 kilometers. Therefore,
0.3km = 0.3 × 1000 = 300 metre
0.3 km to 500m= 300m to 500m
300m : 500m = 300/500
Reducing to its lowest term, 100 is a common factor.
300/500 = (100×3) / (100×5)
= 3/5.
Multiply. 5⋅2/3 Enter your answer as an improper fraction, in simplified form, in the box
Answer:
[tex]\frac{10}{3}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]5.\frac{2}{3}[/tex]
We have to multiply and find answer in improper fraction in simplified form
In order to find the answer we will multiply nominator by nominator denominator remain same.
[tex]5\cdot \frac{2}{3}=\frac{10}{3}[/tex]
It is improper fraction and simplified from .
Answer:[tex]\frac{10}{3}[/tex]
Simplify: -5/4 divided by 2 3/5
If y=3-x what is y if x =-4
The formula A=1w is used to calculate the area A of a rectangle surface using the length(l) and the width (w) of the surface which formula could be used to find W in terms of A and L
David is buying a new car for $21,349 he plans to make a down payment of 3000 if he's to make a monthly payments of $352 for the next five years what APR has he paid