Answers
We want to solve for x. Start by getting x by itself on one side.
We can do this by adding 64 to both sides of the equation.
x^3 = 64
Now, to get rid of the 3rd power that x is raised to, we can raise both sides to the 1/3 power
(x^3)^1/3 = 64^1/3
(x^3)^1/3 is the same as x
So x = 64^(1/3) and 64^(1/3) = 4
So x = 4 :)
Related Questions
Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables found in the textbook.)
Answers
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
where
P=amount to be deposited today, to be found
A=amount withdrawn each year=18000
i=Annual interest=9%
n=number of years = 20
Substituting values,
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
[tex]=\frac{18000*((1+0.09)^{20}-1)}{0.09*(1+0.09)^{20}}[/tex]
=164313.82 to the nearest cent
I need help I would really thank whoever answers this for me
Answers
a. 6j - 3 : j = 4
6(4) - 3
24 - 3
21
b. 1/2b + 5 : b = 14
1/2(14) + 5
7 + 5
12
c. 8 + 4k : k = 3.5
8 + 4(3.5)
8 + 14
22
6j - 3 for j = 4.
(6*4) - 3, 24 - 3 = 21.
b.
1/2b + 5 for b = 14
(1/2 * 14) + 5, 7 + 5 = 12
c.
8+4k for k = 3.5
8 + (3.5*4), 8 + 14 = 22
Hope this helps! You could always check these answers on a site called Math-way (without the dash.)
Find the quadratic function whose zeros are 2 and -2 and has maximum value
Answers
y = - a * (x - 2)(x + 2)
y = - a * (x^2 - 4)
a > 0 meaning that a must have a value greater than 0.
• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.
Answers
Final answer:
The given function f(x) = x3 – 5x2 + 9x – 45 has rational roots ±1, ±3, ±5, and ±9.
Explanation:
To determine the number of roots and identify them for the function f(x) = x3 – 5x2 + 9x – 45, we can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation, then p must divide the constant term (in this case, 45) and q must divide the leading coefficient (in this case, 1). By trying all possible combinations of p and q, we can find the rational roots of the equation. In this case, the rational roots are ±1, ±3, ±5, and ±9.
The number of real roots is 1, and it is ( x = 5 ).
To determine the number of roots and identify them for the function[tex]\( f(x) = x^3 - 5x^2 + 9x - 45 \)[/tex], we can use various methods such as the Rational Root Theorem, Descartes' Rule of Signs, or graphing techniques. In this case, since the degree of the polynomial is 3, we know that there will be 3 roots in total.
We'll start by checking for rational roots using the Rational Root Theorem. According to this theorem, if a rational root [tex]\( \frac{p}{q} \)[/tex] exists for the polynomial [tex]\( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), then \( p \)[/tex] is a factor of the constant term [tex]\( a_0 \) and \( q \)[/tex] is a factor of the leading coefficient [tex]\( a_n \)[/tex].
The constant term of [tex]\( f(x) \) is \( -45 \)[/tex]and the leading coefficient is ( 1 ). The factors of ( -45 ) are [tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]. The factors of \( 1 \) are \( \pm 1 \)[tex]\( 1 \) are \( \pm 1 \)[/tex].
By trying all possible combinations of these factors, we can find the rational roots of the polynomial. We'll then use synthetic division or polynomial long division to check if these roots are actually roots of the polynomial.
Let's proceed with the calculations:
1. Possible rational roots:
[tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]
2. Testing these roots using synthetic division or polynomial long division:
Testing [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = (1)^3 - 5(1)^2 + 9(1) - 45 = 1 - 5 + 9 - 45 = -40 \][/tex]
Testing [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = (-1)^3 - 5(-1)^2 + 9(-1) - 45 = -1 - 5 - 9 - 45 = -60 \][/tex]
Testing [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = (3)^3 - 5(3)^2 + 9(3) - 45 = 27 - 45 + 27 - 45 = -36 \][/tex]
Testing [tex]\( x = -3 \)[/tex]:
[tex]\[ f(-3) = (-3)^3 - 5(-3)^2 + 9(-3) - 45 = -27 - 45 - 27 - 45 = -144 \][/tex]
Testing ( x = 5 ):
[tex]\[ f(5) = (5)^3 - 5(5)^2 + 9(5) - 45 = 125 - 125 + 45 - 45 = 0 \][/tex]
[tex]\[ \Rightarrow \text{Root: } x = 5 \][/tex]
Testing ( x = -5 ):
[tex]\[ f(-5) = (-5)^3 - 5(-5)^2 + 9(-5) - 45 = -125 - 125 - 45 - 45 = -340 \][/tex]
Testing ( x = 9 ):
[tex]\[ f(9) = (9)^3 - 5(9)^2 + 9(9) - 45 = 729 - 405 + 81 - 45 = 360 \][/tex]
Testing ( x = -9 ):
[tex]\[ f(-9) = (-9)^3 - 5(-9)^2 + 9(-9) - 45 = -729 - 405 - 81 - 45 = -1260 \][/tex]
Testing ( x = 15 ):
[tex]\[ f(15) = (15)^3 - 5(15)^2 + 9(15) - 45 = 3375 - 1125 + 135 - 45 = 2340 \][/tex]
Testing ( x = -15 ):
[tex]\[ f(-15) = (-15)^3 - 5(-15)^2 + 9(-15) - 45 = -3375 - 1125 - 135 - 45 = -4680 \][/tex]
Testing ( x = 45 ):
[tex]\[ f(45) = (45)^3 - 5(45)^2 + 9(45) - 45 = 91125 - 10125 + 405 - 45 = 81060 \][/tex]
Testing ( x = -45 ):
[tex]\[ f(-45) = (-45)^3 - 5(-45)^2 + 9(-45) - 45 = -91125 - 10125 - 405 - 45 = -102705 \][/tex]
From these tests, we see that ( x = 5 ) is a root of the polynomial. The other roots are irrational or complex.
So, the number of real roots is 1, and it is ( x = 5 ).
1. What is the area of this figure?
Enter your answer in the box.
? cm²
2. What is the measure of angle x?
Enter your answer in the box.
x = °
Answers
Enter your answer in the box.
A = (5x5) + 1/2(4)(5)
A = 25 + 10
A = 35
answer
35 cm²
--------------
2. What is the measure of angle x?
Enter your answer in the box.
x = 90° - 47
x = 43°
Answer:
The area if this figure is 35cm2
Step-by-step explanation:
Find the length of the missing side. The triangle is not drawn to scale.
Answers
x = sqrt(17^2 + 15^2)
x = 8
missing side = 8
For any value of n, list the numbers ln, rn, mn, tn and i in increasing order. (enter your answers as a comma-separated list. enter your answer using the variables rather than numerical values.)
Answers
The correct order is [tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex].
To list the values ln, rn, mn, tn and i in increasing order for any value of n, we need to understand the relationship between these variables.
The variables ln, rn, mn, and tn likely represent different measures, such as left endpoint, right endpoint, midpoint, and trapezoid point in numerical methods, while i often represents the imaginary unit iota in mathematics.
Commonly, if we assume these have increasing values when ordered, they would be listed as:
[tex]l_n[/tex][tex]m_n[/tex][tex]t_n[/tex][tex]r_n[/tex]iTherefore, the values in increasing order are:
[tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex]
What is the weekly wage for a person who works 40 hours at an hourly rate of $9.75?
Answers
Final answer:
To find the weekly wage for someone working 40 hours at an hourly rate of $9.75, multiply the number of hours by the hourly rate, which equals $390.
Explanation:
The weekly wage for a person who works 40 hours at an hourly rate of $9.75 can be calculated by multiplying the number of hours worked per week by the hourly wage. Here's the calculation:
Hourly rate: $9.75Hours worked per week: 40 hoursWeekly wage = Hourly rate × Hours worked per weekWeekly wage = $9.75 × 40Weekly wage = $390Therefore, the answer required for the weekly wage for this person is $390.
6. Alice and Alma have to fill a workbook. Alice has already completed 3 pages and can do 7 pages per hour. Alma has completed 11 pages, but can only work at a rate of 3 pages per hour. Eventually Alice will catch up and the two will be working on the same page. How long will that take? How many pages will each of them have finished?
Answers
Since Alice can do 7 pages per hour, we can represent this part of the equation as 7p. She has already completed 3 pages, so we just add the 3 to the 7p:
7p + 3
Since Alma can do 3 pages per hour, we can represent this part of the equation as 3p. She has already completed 11 pages, so we just add 11 to the 3p:
3p + 11
To determine when both girls will have written the same amount of pages, we set the two equations equal to each other:
7p + 3 = 3p + 11
Then, we solve for p. First, the variables must be on the same side of the equation. We can do this by subtracting 3p from both sides of the equation:
4p + 3 = 11
Next, we must get p by itself. We work towards this by subtracting 3 from both sides of the equation:
4p = 8
Last, we divide both sides by 4. So p = 2.
This means that it will take 2 hours for Alice and Alma to have read the same amount of pages. If we want to know how many pages they will have read, we simply plug the 2 back into each equation:
7p + 3
= 7 ( 2 ) + 3
= 14 + 3
= 17
3p + 11
= 3 ( 2 ) + 11
= 6 +11
= 17
After 2 hours, Alice and Alma will have read the same amount of pages: 17 pages.
TRUE or FALSE?
Two arcs of a circle are congruent if and only if their associated radii are congruent.
Answers
With any given circle, all of the radii will be the same length. So it's guaranteed to have the radii be congruent. This does not lead to arcs of a circle being congruent. If you know that the central angles are the same, then you can say the arcs are congruent. Or if you know the chords are the same length, then you can say the arcs are congruent.
Donte simplified the expression below. mc024-1.jpg What mistake did Donte make? He did not apply the distributive property correctly for 4(1 + 3i). He did not distribute the subtraction sign correctly for 8 – 5i. He added the real number and coefficient of i in 4(1 + 3i). He added the two complex numbers instead of subtracted.
Answers
4(1 + 3i) – (8 – 5i) = –4 + 8i
And the set of options are:
What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.
Answer: option A: he did not apply the distributive property correctly for 4(1 + 3i)
Explanation:
The correct application leads to: 4*1 + 4*3i = 4 + 12i
If you, incorrectly, make 4*1 + 3i, then you get 4 + 3i, and when you subtract (8 - 5i) you get:
4 + 3i - (8 - 5i) = 4 + 3i - 8 + 5i = - 4 + 8i which is what Donte obtained..
Therefore, he applied the distrituvie property incorrectly for 4(1 + 3i)
If "np is greater than or equal to 15" and "n(1-p) is greater than or equal to 15", what is the approximate shape of the sampling distribution of the sample proportion?
Answers
Answer:
The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
If np >= 15 and n(1-p) >= 15
Can be approximated to the normal distribution, with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
So
The sampling distribution of the sample proportion will be approximately normally distributed with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
why does 16 to the power of 0 equal 1?
Answers
hope this helps
Sarah spends 1/6 hour Vacuuming her moms car. She spends four times as long washing the car. Then she spends twice as long waxing the car as she does washing the car. What is the total amount of time Sarah spencer vacuuming washing and waxing her moms car
Answers
Sarah spend 1/6 of an hour vacuuming her mom's car. That means that if we take a whole hour and divide it into 6 equal amounts of time, she spends one of these vacuuming the car. Let's figure out how many minutes that is. One hour is 60 minutes, so dividing an hour into 6 equal amounts of time means each of these is 10 minutes. So, Sarah spends 10 minutes vacuuming her mom's car.
Washing
Sarah spends 4 times as long washing the car as she does vacuuming it. Since she spends 10 minutes vacuuming, that means she spends 4 times that amount (4 x 10 = 40 minutes) washing the car. That is, Sarah spends 40 minutes washing the car.
Waxing
Sarah spends twice as log waxing the car as she does washing it. Since she spends 40 minutes washing, she spends 2 times 40 minutes (2 x 40 = 80) waxing the car. That is, Sarah spends 80 minutes waxing the car.
Total time spent on mom's car
The total time spent on the car is 10 minutes + 40 minutes + 80 minutes. That is 130 minutes. As there are 60 minutes in one hour, we can also express the answer as 2 hours and 10 minutes.
Answer:
C
Step-by-step explanation:
Explain how to rename the fractions using division so they have the same denominator to compare. 4/5 and 6/10
Answers
6/10=3/5
4/5 and 3/5 both have the same denominator
How many ways are there to choose eight coins from a piggy bank containing 100 identical pennies and 80 identical nickels?
Answers
There are 9 ways to choose eight coins from a piggy bank.
Total number of ways =
(Combinations of 8 pennies) + (Combinations of 7 pennies and 1 nickel) + ... + (Combinations of 0 pennies and 8 nickels)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9 ways
Eli earned $98 at his job when he worked for 8 hours. what was his hourly pay rate in dollars per hour hour?Express your answer in simplest form
Answers
$98/8 = $12.25/hour
What is f(2) if the linearization of f(x) at a = 2 is l(x) = 12x + 4?
Answers
.. l(x) ≈ f(a) +f'(a)*(x -a)
Then
.. l(a) = f(a)
f(2) = l(2) = 12*2 +4
f(2) = 28
Simplify the product. (5 − 6)(2 + 7)
Answers
2 + 7 = 9
-1 × 9 = -9
-9 would be the simplified answer.
Hope this helps!
What is the volume of a right circular cylinder with a radius of 3in and a height of 10in
Answers
Answer:
282.6 inches cubed
Step-by-step explanation:
The volume of the cylinder with radius 3 in and height 10 in is
[tex]V=\pi (3^2)(10)= \pi (9)(10)= 90\pi = 90(3.14) = 282.6 in^3[/tex]
Answer:
90 in3
Step-by-step explanation:
From their house to their parents house, the Leightons have to drive 276 miles. if they have already driven 2/3 of the distance, how far have they gone?
Answers
A rectangle is 5 centimeters long and 4 centimeters wide. What is its area?
Answers
In area, you multiply the length times width.
Length = 5
Width = 4
4 x 5 = 20
The rectangle's area is 20.
Hope this helps you.
Have a great day!
How can you tell if the rule you have written for a set of points is correct?
Answers
In order to do that, you take both of the x values and plug them back in to see if you got the desired y value. If you do, it's correct.
For example:
If you had the equation:
y = 2x + 5
and had the points (5,15) and (3,1)
We would check the first coordinates by plugging in the x value:
y = 2(5) + 5
y = 15
Since 15 is our y value, we're correct.
For our next, we can do the same thing, and plug in the x value:
y = 2(3) + 5
y = 6 + 5
y = 11
Since we don't have our desired value, we know we're wrong.
Hope this helps!
In 1999 there were 1647 daily and 7471 weekly newspapers published in the United States, as well as X other kinds of newspapers. The total number of newspapers was 700 greater then seven times the number of other kinds of newspapers. How many newspapers were published in 1999 that were not daily or weekly
I NEED THIS ANSWER !!!! 90 POInTS
Answers
Last year, Rachel opened an investment account with $8200. At the end of the year, the amount in the account had decreased by 7.5%. How much is this decrease in dollars? How much money was in her account at the end of last year? What was the decrease in the amount? WHat was the year-end amount?
Answers
She would have $7585 left in her account at the end of the year.
Y=10x
Graph the function
Answers
since it doesn't say anything after the 10x, the y-intercept is at (0, 0)
A company sells brass and steel machine parts.One shipment contains 3 brass and 10 steel parts and costs $48. A second shipment contains 7 brass and 4 steel parts and costs $54. Find the cost of each type of machine part.
Answers
x--------------> brass cost
y--------------> steel cost
we know that
3x+10y=48
7x+4y=54 -------------------> multiply by -3/7----------> -3x-(12/7)y=-162/7
3x+10y=48
-3x-(12/7)y=-162/7
---------------------------
0x+8.29y=24.86-------------> y=3
3x+10y=48------> 3x+10*3=48----------> x=(48-30)/3=6
the answer is
brass machine parts cost $6
steel machine parts cost $ 3
Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?
Answers
Answer:
HI!
Your spinner has 5 colors, and if you spin it, the probability of landing in each color will be the same ( because the spiner has 5 equal sections).
So for every spin, the probability on landing on each color will be 20%.
If i spin it 200 times, then the 20% of 200 is 0.2*200 = 40.
It means that if you spin it 200 times, then each colour shows 40 times theoretically. The question is: how many times should Alina expect the spinner to land on either purple or orange?
you have 40 for purple and 40 for orange, then the total times that the spinner lands on either purple or orange is 80.
Ms. Maple is a teacher whose salary is $22,570 for this school year, which has 185 days. In Ms. Maple’s school district, substitute teachers are paid $80 per day. If Ms. Maple takes a day off without pay and a substitute teacher is paid to teach her classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Ms. Maple for that day?
Answers
Final answer:
The school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple, calculating by comparing Ms. Maple's daily salary to a substitute teacher's daily rate.
Explanation:
To calculate how much less the school district pays by hiring a substitute teacher instead of paying Ms. Maple for a day, we first need to determine Ms. Maple’s daily salary. This is done by dividing her annual salary by the number of working days in the school year.
Ms. Maple’s daily salary = $22,570 / 185 days = $122 per day.Substitute teacher’s daily salary = $80 per day.The difference between what the school district pays Ms. Maple and what it pays a substitute teacher for one day = Ms. Maple’s daily salary - Substitute teacher’s daily salary = $122 - $80 = $42.Therefore, the school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple.
The area of a circle (A) is given by the formula A=pi*r2
where r is the circle's radius. The formula to find r is . If and , r is centimeters.
Answers
The area of a circle is calculated with the formula A = πr², where pi is the mathematical constant approximately equal to 3.14159 and r represents the circle's radius. Considering significant figures is crucial for maintaining precision, as demonstrated in rounding the calculated area of a circle with radius 1.2 m to 4.5 m², based on the initial data's precision.
Explanation:The area of a circle is calculated using the formula A = πr², where π (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. When calculating the area with a given radius, it's important to consider the significance of figures in your final answer. For instance, if a circle's radius is given as 1.2 meters (with two significant figures), and you calculate the area to be 4.5238934 square meters using a detailed value of pi, you need to round your final answer to maintain the precision of your initial data, resulting in an area of 4.5 m².
It's also valuable to note how ancient civilizations, like the Greeks, approximated mathematics related to circles and how such estimations have evolved into our modern understanding, where the concept of significant figures plays a critical role in ensuring accuracy across varying fields of study and applications.