[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ (-243)^{\frac{1}{5}}\implies \sqrt[5]{(-243)^1}\implies \sqrt[5]{(-3)(-3)(-3)(-3)(-3)} \\\\\\ \sqrt[5]{(-3)^5}\implies -3[/tex]
Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
x = -2+√3i and -2-√3i
Step-by-step explanation:
The formula for the general formula is expressed as;
x = -b±√b²-4ac/2a
Given the expression
x²+4x+7 = 0
a = 1, b = 4 and c = 7
Substitute
x = -4±√4²-4(1)(7)/2(1)
x = -4±√16-28/2
x = -4±√-12/2
x = -4±√4*-3/2
x = -4±2√-3/2
x = -4±2√3i/2
x = -4+2√3i/2 and -4-2√3/2
x = -2+√3i and -2-√3i
The equation x^3-5x=59 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer to one decimal place. You must show all your working. On the same line as your final answer, you must write to "1 decimal place".
Answer:
The answer is "4.3".
Step-by-step explanation:
Given:
[tex]\to x^3 - 5x - 59 = 0[/tex]
When [tex]x = 4.1:[/tex]
[tex]\to f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579[/tex]
When [tex]x= 4.2:[/tex]
[tex]f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912[/tex]
When [tex]x = 4.3:[/tex]
[tex]\to f(4.3) = -0.993[/tex] (closer to 0)
[tex]\to f(4.4) = 4.184[/tex]
It changes the sign so, the root lies in 4.3 and 4.4.When [tex]x = 4.35:[/tex]
[tex]\to f(4.35) = 1.563[/tex]
When the root is closer to 4.3 than 4.4 So, 1.563 is closer to zero than 4.184.
When [tex]x = 4.32:[/tex]
[tex]\to f(4.32) = 0.0216[/tex] close to zero.
So the answer is 4.3 to 1 decimal place.
If p(x) is a polynomial function with p ( 3/4 ) = 0 , which statement is true?
A.The function has a factor of (4x + 3).
B. The function has a factor of (4x – 3).
C. The function has a factor of (3x + 4).
D. The function has a factor of (3x – 4).
If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
If p(x) is a polynomial function with p ( 3/4 ) = 0
Then we need to find which of the given statements are true.
A. The function has a factor of (4x + 3).
If x=3/4 then 4(3/4)+3 which is not equal to zero
B. The function has a factor of (4x – 3).
If x=3/4 then 4(3/4)-3 which is equal to zero
C. The function has a factor of (3x + 4).
If x=3/4 then 3(3/4)+4 which is not equal to zero
D. The function has a factor of (3x – 4).
If x=3/4 then 3(3/4)-4 which is not equal to zero
Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
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A watch increased in price by 4/5. After the increase it was priced at £126. What was the original price of the watch?
A watch increased in price by 4/5 is priced at £126, then the original price of the watch was £100.
We know that the price of the watch increased by 4/5. To find the original price of the watch, we can use the following formula:
original price = new price / (1 + increase percentage)
In this case, the new price of the watch is £126 and the increase rate is 4/5. So we have:
original price(1 + 4/5) = 126
original price = 126 / (1 + 4/5)
original price = 126 / (1+ 0.8)
original price = 126/1.8
original price = 70
So, the original price of the watch was £70.
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Mr. cole is shopping around to find a new gym. Fitness Extreme charges a flat fee of $30 plus $6 per session. Lift for Life charges a flat fee of $50 plus $2 per session. After how many sessions will the two gyms have the same cost?
Answer:
87$
Step-by-step explanation:
How many 8-character passwords consisting of uppercase letters, lowercase letters and digits are there that start and end with the same symbol
Can be cracked within eight hours by the average hacker.
How many 8-character passwords may use both uppercase and lowercase letters?With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.
There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.
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the volume of a cube is 64in squared (2). what’s the length of each side of the cube please help asap
Answer:
4in squared
Step-by-step explanation:
We know that cubes have equal parts all around, and it is basic knowledge for the most part to know 4x4x4 = 64. Therefore, each length must be 4, length, width,and height are all 4.
The measure of the exterior angle of the triangle is
The measure of the exterior angle of the triangle is 139°.
What is an exterior angle theorem?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
From the two given angles are 75° and 64° and exterior angle is 2.
Now, ∠2=75°+64°
∠2=139°
Therefore, the measure of the exterior angle of the triangle is 139°.
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Three Baby penguins and their father were sitting on an iceberg 0.75 meters above the surface of the water. The father dove down 5.7 meters from the iceberg into the water to catch dinner for his kids. What is the father penguin's position relative to the surface of the water? Solve this problem and explain how you solved this problem and came to your answer.
According to the linear regression model, the men’s world record mile run time in 1940 would have been how many seconds?
The men’s world record mile run time in 1940 would have been 10.454 seconds
Here, the equation of the linear function that best fits the data (the line of best fit) is Finishing time = 10.878 - 0.0106(Year after 1900)
Let k be the finishing time in seconds and t be the number of years after 1900
So, the equation of regression line becomes,
k = 10.878 - (0.0106) t
To find the the men’s world record mile run time in 1940 first we find the the number of years (t)
t = 1940 - 1900
t = 40 years
So, the finishig time (k) would be,
k = 10.878 - (0.0106) × 40
k = 10.454 seconds
Therefore, the finishing time was 10.454 seconds
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The data below shows the survey result of 75 randomly selected students.
The school has 1,138 students total. Based on the results of the poll, how many of the school's students should be expected to travel by car? Round your answer to the nearest whole number.
Show your work using the sketch board OR you may insert an image of your work on the following slide.
Chart relating to the question is attached below.
Answer:
349 students
Step-by-step explanation:
Based on the chart given, we can obtain the experimental probability or proportion for the travel plan of 75 students :
Proportion who would be traveling by car :
Number traveling By car / number of samples
p(car) = 23 / 75 = 0.30666
If total number of students = 1138
Using the proportion obtained from the sample, the number of students who would be traveling by car from the population would be :
= 0.30666 * 1138
= 348.98 students
= 349 students
Plz help me with this worksheet, I will give brainliest
Answer:
Step-by-step explanation:
You don't seriously want someone to answer all those problems, do you?
I will tell you that you need to use the Pythagorean theorem, the side relationship in a 30-60-90 and a 45-45-90 triangle. Get off your rear and go for it!!!
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool
The number of units that tile will he need to surround his pool is 19.82units.
this question is of quadratic equation ,
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have,
AB = 4.24 units
BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units.
The number of units that tile will he need to surround his pool is 19.82units.
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Plz, help me with this question!
Answer:
I think D is right, because usually congruent angles have the same angle measure, and there's no answer choice for 1 and 3.
Which statement correctly identifies an asymptote of f (x) = StartFraction 16 x squared minus 35 Over x squared minus 5 EndFraction using limits?
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a vertical asymptote at x = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a horizontal asymptote at y = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a vertical asymptote at x = 16.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Answer:
D
Step-by-step explanation:
Edge
The limit of x approaching infinite of a function gives it's horizontal assymptote. We use this to solve the question, getting the following answer:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Horizontal asymptote:
An horizontal asymptote is the value of y given by:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
In this question:
[tex]f(x) = \frac{16x^2 - 35}{x^2 - 5}[/tex]
The horizontal asymptote is:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5}[/tex]
Considering it is a limit of x going to infinite, we just consider the terms with the highest exponents both in the numerator and in the denominator, so:
[tex]y = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5} = \lim_{x \rightarrow \infty} \frac{16x^2}{x^2} = \lim_{x \rightarrow \infty} 16 = 16[/tex]
Thus, the correct answer is:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
From the graph of the function, given at the end of this answer, you can check that as x goes to infinity, y(green line) approches 16(blue line).
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Jiri's hamster was put on a special diet. Over 5 days, his hamster ate about 0.054 kg of food. About how much food did Jiri's hamster eat in one day?
Answer:
0.0108 kg
Step-by-step explanation:
Jiri is on a special diet
Over 5 days he eats 0.054
Therefore the food consumed in a day can be calculated as follows
5 days= 0.054
1 day= 0.054/5
= 0.0108kg
7m-8=3(2m+4)+m please help
Answer:
m=20
Step-by-step explanation:
Solve the equation:
7m - 8 = 3 ( 2 m + 4)
Multiply 3 and (2m+4)
7m - 8 = 6m + 12
Add 8 to each side
7m = 6m + 20
Subtract 6m from both sides
m = 20
If my answer is incorrect, pls correct me!
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-Chetan K
when you multiply or divide a negative and a negative integer the product will be ? positive or negative?
Answer: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.
When you multiply a negative number by a positive number then the product is always negative
HOPE THIS HELPS
SUKHMANJOT
what number comes next in 18,30,48,72,96
Step-by-step explanation:
the answer is 108 because your counting by 12
Answer:
Hello There!!
Step-by-step explanation:
I believe the answer is 108.
hope this helps,have a great day!!
~Pinky~
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. 3 red marbles and 2 blue marbles What is the best prediction for the number of times that Ellen will draw a blue marble? Choose 1 answer:
The probability best prediction for the number of times that Ellen will draw a blue marble is 200.
Number of blue marbles: 222
Number of red marbles: 333
Total number of marbles: 555
Probability of drawing a blue marble:
222/555
= 0.4
Number of times drawing a blue marble:
300300300 x 0.4
= 120,120,120
Rounded to nearest whole number:
120,120
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is
222/555
= 0.4.
Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.
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It’s supposed to say true or false but can someone help giving brainliest
Answer:
True
Step-by-step explanation:
e^{i\pi} + 1 = 0
Simplifying and therefore meaning that the answer is true.
But in all seriousness 6*3 = 18
6*4a = 24a
So yes it is true :)
Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn
$21 (3 x 7 = 21).
If she works 5 hours, she would earn
$35 (5 x 7 = 35).
If she works 8 hours, she would earn
$56 (8 x 7 = 56).
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If the figure is translated 4 units left what are the coordinates
Answer: (-4,0)
Step-by-step explanation:
Answer: A
Step-by-step explanation:
- Left and right translations affect the x-coordinate
- subtract 4 from the x-coordinate
Read the passage. Bee Stings: The Aftermath You don't have to have a life-threatening allergy to have a negative response to bee stings. Many people experience uncomfortable itching and swelling when stung. But are such reactions merely an annoyance, or might they serve a purpose? Several years ago, researchers who study the immune system wanted to find out. To do this, they injected a group of mice with bee venom. Some of the mice had allergic reactions (such as swelling) to the venom, and others did not. Three weeks later, the researchers injected the same mice with venom for a second time—this time with a dose so large it could be deadly. They found that the mice who had previously had allergic reactions to the venom were much more likely to survive the potentially lethal dose. What is the main idea of the passage?
Researchers found that allergic reactions to bee venom can be as mild as swelling or as severe as death.
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin in the future.
Researchers found that bee venom courses allergic reaction in some mice but not others.
Answer:
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin n the future.
Step-by-step explanation:
I currently have this on IXL & I got it correct.
jacks meeting stared at 2:45 pm and ended at 5:25 pm how long did the meeting last
Jacks meeting lasted for 160 min or 2 hrs 40 min.
What is Time?Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.
Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.
The time for which the meeting lasted can be written as -
{i} = 2:45 pm
{i + 60 minutes} = 3:45 pm
{i + (2 x 60) minutes} = 4:45 pm
{i + (2 x 60 + 40) minutes} = 5:25 pm
{f} = 5 : 25 pm
The meeting lasted for -
2 x 60 + 40
160 minutes
or
2 hours 40 minutes
Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.
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HOW TO DO THIS QUESTION PLEASE
9514 1404 393
Answer:
£6/h
Step-by-step explanation:
Molly is paid £280 for 35 hours' work, so
£280/(35 h) = £8/h
In the next 5 hours, her pay jumps to £350, so she earns at a rate of ...
(£350 -280)/(5 h) = £70/(5 h) = £14/h
The difference in her pay rates is £14/h -£8/h = £6 per hour.
1 Which of the following trinomials can be factored?
A x² + 3x + 3
B x² + 3x - 3
C x² + 3x + 2
D x²-3x - 2
X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0, If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0
What are the trinomial rules?The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.
If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).
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What is the length of the missing leg (in millimeters)
Answer:62
Step-by-step explanation: if you divide 10mm by 8mm you will get the celcius of negative 98mm then count the right angle vice versa and you will get 62
Ok can someone help me with this?
Answer:
1. 14
2. 2.83
3. 6.71
4. 8.77
5. 9.22
6. 5.20
7. 2.45
8. 19
9. I would love to help you with this but I don't know what it means by "circled problems"
Step-by-step explanation:
Answer:
Circle questions 2, 3, 4, 5, 6, 7
Simplified square root:
1. 14
2. 2.8
3. 6.7
4. 8.8
5. 9.2
6. 5.2
7. 2.4
8. 19
Step-by-step explanation:
I'm sure you can do the line plot. It's pretty mandatory.
Question #9:
If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if not then it is irrational.
If you don't understand how to draw a line graph then check the two photos as a guide. Hope it helped :)