Final answer:
To solve the equation ((5x−16)^3−4)^3=216,000, one must apply the rules of exponents and algebraic manipulation step by step, isolating x and using mathematical operations to simplify the expression.
Explanation:
Solving an Equation with Powers
The problem ((5x−16)^3−4)^3=216,000 involves understanding the rules of exponents and algebraic manipulation. When you're dealing with expressions raised to a power, it's important to remember that the power affects everything inside the parentheses, including the number. This is evident in expressions like (5³)* which is equivalent to 5⅜⅓ and results in 5 multiplied by itself 12 times, giving 5⁼.
When approaching the given equation, you would first look to isolate the base of the cube on one side, leading to the cube root to undo the cube power. You would continue simplifying step by step until you isolate x, the variable in question. The key here is to perform operations that counteract the powers and other mathematical operations presented.
In some cases, you might encounter a polynomial long division such as dividing S=9x⁵ +4x⁴ - 5x³ +6x² + 2x - 3 by another polynomial. This requires knowledge of the long division algorithm adapted for polynomials. Each term is divided individually to find the quotient.
help. i don’t understand this at all!!!!!
Baileigh is using a piece of string to hang a painting on the wall. The back of the painting is diagrammed below. 36 cm 36 cm 15 cm 15 cm Note: Figure is not drawn to scale. What is the length of the string? A. 78 centimeters B. 102 centimeters C. 39 centimeters D. 51 centimeters
Kendra used these steps to solve the equation 2x + 5 = 3 + 2(x + 1). Which choice describes the meaning of her result, 5 = 5?
Devon exercised the same amount of time each day for 5 days last week. e His exercise included walking and swimming. e Each day he exercised, he walked for 10 minutes . He exercised for a total of 225 minutes last week. What is the number of minutes Devon swam each of the 5.days last week?
The lengths, in centimeters, of nine earthworms are shown below. 3, 4, 5, 5, 6, 7, 8, 9, 10 What is the median of the data?
reciprocal of 4 and 1/8 fraction
HURRY!!!When are two triangles said to be in perspective?
a.
If the corresponding vertices of two triangles form three lines that intersect in a single point
c.
If the corresponding vertices of four triangles form three lines that intersect in a single point
b.
If the corresponding vertices of three triangles form three lines that intersect in a single point
d.
If the corresponding vertices of two triangles form three lines that intersect in two points.
What is the next number in the following sequence.
0, 1, 1, 2, 3, 5, 8...
a.
9
c.
10
b.
13
d.
11
Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's Age (p) and Winnie's age (w):
p=w+2
p=7w-16
Which is a possible correct method to find Peter's and Winnie's ages?
A. Solve w+2 = 7w-16 to find the value of w
B. Solve p+2 =7p-16 to find the value of p
C. Write the points where the graphs of the equations intersect the x axis
D. Write the points where the graphs of the equations intersect the y axis
Answer:
A. Solve w+2 = 7w-16 to find the value of w.
Step-by-step explanation:
Here p represents the age of Peter and w represents the age of Winnie,
Given,
Peter is 2 years older than Winnie.
⇒ p = w + 2 -----(1)
Also, Peter's age is 16 years less than seven times Winnie's age.
⇒ p = 7w - 16 -----(2),
By equating right sides of equation (1) and (2),
We get,
w + 2 = 7w - 16,
Since, this equation is only in the variable w,
Thus, we can find the value of w with help of the above equation,
After putting this value in either of equation (1) or (2),
We can find the value of p.
Hence, option A is correct.
Note : From equation (1) and (2),
w = p - 2 and [tex]w=\frac{p+16}{7}[/tex]
[tex]\implies p-2=\frac{p+16}{7}[/tex]
⇒ Option B is incorrect.
Now, let x represents w and y represents p in the graph,
Then, the solution will be the intersection point of lines y=x+2 and y=7x-16,
Which is shown below,
⇒ Options C and D are incorrect.
Polygon D is a scaled copy of Polygon C using a scale factor of 6. How many times larger is the area of Polygon D than the area Polygon CCC?
Answer:
Yup...it's 36.
Step-by-step explanation:
A tennis ball bounces so that its initial speed straight upwards is b feet per second. Its height s in feet at time t seconds is given by s = bt − 16t^2 a) Find the velocity v = ds/dt at time t. b) Find the time at which the height of the ball is at its maximum height. c) Find the maximum height. d) Make a graph of v and directly below it a graph of s as a function of time. Be sure to mark the maximum of s and the beginning and end of the bounce.
A prism with a volume of 360 yd³ is scaled down to a volume of 45 yd³. What is the scale factor? Enter your answer, as a decimal or a fraction in simplest form, in the box.
Answer:
The scale factor is equal to [tex]\frac{1}{2}[/tex] or [tex]0.5[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
[tex]z^{3}=\frac{45}{360}= \frac{1}{8}\\ \\z=\sqrt[3]{\frac{1}{8}}\\ \\z=\frac{1}{2}[/tex]
Select the two equations that can be used to solve the following inequality
A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
A. 108π m³
B. 216π m³
C. 972π m³
D. 1296π m³
we are given
radius=r=12m
height=h=9m
now, we can use formula of volume of cylinder
[tex] V=\pi r^2 h [/tex]
now, we can plug values
and we get
[tex] V=\pi (12)^2 *9 [/tex]
we get
[tex] V=1296 \pi m^3 [/tex]
so, the exact volume of the cylinder is [tex] 1296 \pi m^3 [/tex]..........Answer
Answer:
(D)
Step-by-step explanation:
It is given that a cylinder has a radius of 12 m and a height of 9 m. Then,
Volume of the cylinder is given as:
[tex]V={\pi}r^{2}h[/tex]
⇒[tex]V={\pi}(12)^2(9)[/tex]
⇒[tex]V={\pi}(144)(9)[/tex]
⇒[tex]V=1296{\pi}m^3[/tex]
Therefore, the volume of the cylinder is [tex]1296{\pi}m^3[/tex].
Thus, Option D is correct.
If 4 apples and 2 oranges equals $1 and 2 apples and 3 oranges equals $0.70, how much does each apple and each orange cost? (Can you do it step by step)
Write area or perimeter for each situation. Carpeting a floor
Answer:
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
a. Carpeting a floor
To carpet a floor, you need to find the area of it so that we can have an appropriate plan to buy material. Hence, it represented by are
b. Fencing a garden
If you want to fence a garden, we need to know the the total length around it or we can say that is the perimeter of the garden. So this situation is represented by perimeter.
Hope it will find you well.
Julie has read 27 pages out of an 80-page book. What percent of the pages has she read?
PLSSS HELP!!!
What is the exact volume of the sphere?
56.3⎯⎯π ft³
274.625π ft³
366.16⎯⎯π ft³
1464.6⎯⎯π ft³
Answer:
366.16
Step-by-step explanation:
i promise
MULTIPLE CHOICE QUESTION
The product of (SQUARE ROOT SIGN)576 and (SQUARE ROOT SIGN) 684 is
(1) irrational because both factors are irrational
(2) rational because both factors are rational
(3) irrational because one factor is irrational
(4) rational because one factor is rational
Answer:
The given expression is irrational because one factor is irrational
Step-by-step explanation:
Given the expression
[tex](\sqrt{576})(\sqrt{684})[/tex]
we have to find that the product is rational or irrational.
[tex]\sqrt{576}=\sqrt{26\times 26}=26[/tex]
[tex]\sqrt{684}=\sqrt{2 \times 2 \times 3 \times 3 \times 19}=2\times 3\sqrt{19}=6\sqrt{19}[/tex]
[tex]\text{The square root of 19 is irrational }[/tex]
[tex]\text{The square root of 684 is irrational }[/tex]
Hence, the first factor of the expression is rational and the second factor is irrational therefore the product is irrational.
∴ option 3 is correct
The given expression is irrational because one factor is irrational
Answer:
The given expression is irrational because one factor is irrational
Step-by-step explanation:
What is the distance between y = -x+2 and y = -x+4?
Answer:
√2
Step-by-step explanation:
You want the distance between the lines y = -x +2 and y = -x +4.
Distance to a lineThe distance from point (x, y) to line ax +by +c = 0 is given by the formula ...
[tex]d=\dfrac{|ax+by+c|}{\sqrt{a^2+b^2}}[/tex]
ApplicationRewriting the equation of the second line to general form, we have ...
y = -x +4
x +y -4 = 0 . . . . . . . a=1, b=1, c=-4
The equation of the first line is written in slope intercept form, so we can identify the y-intercept as (0, 2). Using this point in the formula for the distance to the second line, we have ...
[tex]d=\dfrac{|1(0)+1(2)-4|}{\sqrt{1^2+1^2}}=\dfrac{|-2|}{\sqrt{2}}=\sqrt{2}[/tex]
The distance between the lines is √2 units.
__
Additional comment
As you can see from the graph, the distance between the lines is the length of the diagonal of a unit square, √2.
How to simplify algebraic expression 8z+4f-6 using z=3 and f=9
Write and graph an equation in two variables that shows the relationship between the time and distance traveled
Answer:
1=1
Step-by-step explanation:
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the sears tower of Chicago is 1450 feet high. a model is 24 inches tall. what is the ratio of the height of the model to the height of the actual sears tower?
** PLEASE HELP!! **
Solve for w.
A.) W= 4k-2b / -5
B.) W= 3k^2- b / -5
C.) W= -3k^2 - b / 5
D.) W= 3k^2 + 2b / -5
The solution for (w) is W= 4k-2b / -5, corresponding to option A.
To solve the equation [tex]\(k = \frac{2b - 5w}{3k}\)[/tex] for (w), we follow these steps:
1. Isolate the term containing (w):
Multiply both sides of the equation by (3k) to eliminate the denominator:
[tex]\[3k^2 = 2b - 5w\][/tex]
2. Isolate (w):
Subtract \(2b\) from both sides of the equation:
[tex]\[3k^2 - 2b = -5w\][/tex]
3. Divide both sides by (-5):
Divide both sides of the equation by (-5) to isolate (w):
[tex]\[w = \frac{3k^2 - 2b}{-5}\][/tex]
Now, let's summarize the answer:
The solution for (w) is given by option:
[tex]\[\boxed{\text{(A) } w = \frac{4k - 2b}{-5}}\][/tex]
GCF and LCM of 3 and 14
Jorge wants to find the most popular way for teens to volunteer in the community. He cannot decide between two methods. Option 1: He will ask every fifth person on each English class roster. Option 2: He will attend a walkathon to ask teen participants about the ways they volunteer. Which statement about the methods is true? Option 1 is biased. Option 2 is biased. Neither is biased. Both are biased.
The statement about the methods is true walkathon to ask teen participants about the ways they volunteer. Then the correct option is B.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Jorge wants to find the most popular way for teens to volunteer in the community. He cannot decide between two methods.
Option 1: He will ask every fifth person on each English class roster. This is a biased one because the best one can be skipped.
Option 2: He will attend a walkathon to ask teen participants about the ways they volunteer. Because all the volunteers participated that can be observed.
The statement about the methods is true walkathon to ask teen participants about the ways they volunteer. Then the correct option is B.
More about the decision-making link is given below.
https://brainly.com/question/3369578
#SPJ6
Value times frequency equals product.
True or False
Answer: The correct answer is true
Step-by-step explanation:
a volleyball reaches its maximum height of 13 feet, 3 seconds after its served. Which of the following quadratics could model the height of the vollyball over time after it is served. Select all that apply.
A: f(x)=2x^2+12x+5
B: f(x)=-2x^2+12x-5
C: f(x)=-2x^2-12x+5
D: f(x)=-2(x-3)^2+13
E: f(x)=-2(x+3)^2+13
Answer:
D.
Step-by-step explanation:
Intuitively it's a volleyball game reaching its maximum height, then we must discard the 1st option because of its parameter a >0, and whenever a>0 the parabola makes a curve, rather different than in a volleyball game.
Also, considering Vertex of this parabola by (-b/2a, -Δ/4a) given the fact that the question says the maximum height.
Taking
y= height in feet
x= time in second
Function Vertex (-b/2a, -Δ/4a)=(-3, -13)
A: f(x)=2x²+12x+5 False
B: f(x)=-2x²+12x-5 Function Vertex (-b/2a, -Δ/4a) = (3,23) False
C: f(x)=-2x²-12x+5 Function Vertex (-b/2a, -Δ/4a) = (-3,23) False
D: f(x)=-2(x-3)²+13 Function Vertex (-b/2a, -Δ/4a) = (3,13) True
E: f(x)=-2(x+3)²+13 Function Vertex (-b/2a, -Δ/4a) =(-3,13) False
The following data represent the flight time (in minutes) of a random sample of seven flights from one city to another city.
287, 270, 260, 266, 257, 264, 258
Compute the range and sample standard deviation of flight time
Answer:
Step-by-step explanation:
A line passes through the point (8, -1) and has a slope of -5/2
Write an equation in slope-intercept form for this line.
Final answer:
To find the slope-intercept form of a line with a given slope of -5/2 that passes through the point (8, -1), we use the point-slope form and then rearrange to get the final equation: y = (-5/2)x + 19.
Explanation:
To write the equation of a line in slope-intercept form (which is y = mx + b), we need to know the slope (m) of the line and the y-intercept (b). In this case, we are given the slope of the line as -5/2 and a point through which the line passes, which is (8, -1). Using the point-slope form, which is y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope, we can substitute the given slope and the coordinates of the given point to derive the slope-intercept form.
The equation starts with y - (-1) = (-5/2)(x - 8). Simplifying the equation, we get:
y + 1 = (-5/2)x + (5/2)*8
y = (-5/2)x + 20 - 1
y = (-5/2)x + 19
So, the equation of the line in slope-intercept form is y = (-5/2)x + 19.
To write an equation in slope-intercept form, substitute the given values of the slope and a point on the line into the equation. The equation of the line passing through the point (8, -1) with a slope of -5/2 is y = -5/2x + 19.
Explanation:To write an equation in slope-intercept form, we need to use the given slope and the coordinates of the point through which the line passes. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We're given that the slope of the line is -5/2, so we can substitute this value for m. We're also given that the line passes through the point (8, -1), so we can substitute these coordinates to find the value of b.
Using the point-slope form of a line, we have y - y1 = m(x - x1). Substituting the given values, we get y - (-1) = -5/2(x - 8). Simplifying, we have y + 1 = -5/2x + 20. Moving the 1 to the other side, we have y = -5/2x + 19. This is the equation of the line in slope-intercept form.
simplify the following expression. 2x-5(2x-7y+3)+(-8)
-8x + 35y - 23 = -1 • (8x - 35y + 23)