An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of the given expression can be done as,
[tex]\dfrac{5x}{x^2-1} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{x^2-1^2} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{(x+1)(x-1)} \times \dfrac{x+1}{x^2}\\\\= \dfrac{5}{(x-1)x}[/tex]
Hence, the simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).
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:D
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Answer:
tan(theta) = 3/4
A wheelchair ramp with a length of 82 inches has a horizontal distance of 80 inches. What is the ramps vertical distance?
For a wheelchair ramp with a length of 82 inches has a horizontal distance of 80 inches is mathematically given as
v = 18inches
What is the ramp's vertical distance?Generally, the equation for vertical distance is mathematically given as
r^2 = h^2 + v^2
(82)^2 = (80)^2 +v^2
6724 = 6400 + v^2
v^2 = 6724-6400
v^2 = 324
v = [tex]\sqrt{324}[/tex]
v = 18inches
In conclusion, the ramp's vertical distance is
v = 18inches
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Which equation represents the line that is parallel to y= 2 and passes through (-1,-6)?
А.x= -1
B.X= 2
C. y=-6
D.y= 2x - 4
Answer:
y = -6
Step-by-step explanation:
Lines that are parallel have the same slope
y= 2 means that it is a horizontal line
The parallel line must be in the same form
y=
We want it through the point (-1,-6)
y = -6
What is the square root of 5?
Answer:
2.2360679775
used a calculator
Step-by-step explanation:
In 2012, the population of a city was 6.63 million. The exponential growth rate was 3.01% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 11 million?
d) Find the doubling time.
Answer:
So first we need to determine what the exponential growth function would look like. Exponential growth functions look like [tex]P(t) = P_0*e^{r*t}[/tex] and in our case [tex]P_0[/tex] would be the initial population which is 6.63 million. R is the next variable that we need to fill out which is the rate of change which in our case is 3.01% or 0.0301.
This is how our function should look now [tex]P(t)=6.63*e^{0.0301*t}[/tex]
Moving onto part b, we need to estimate the population of the city in 2018 which 6 years from 2012 and we plug that into t and solve.
[tex]P(t) = 6.63 * e^{0.0301*6}[/tex]
[tex]P(t) = 6.63*e^{0.1806}[/tex]
[tex]P(t) = 6.63 *1.1979[/tex]
[tex]P(t) = 7.9423\ million[/tex]
Moving onto part c, we need to find when the population of the city will be 11 million which will be done by setting P(t) to 11 million and solving for t.
[tex]11 = 6.63*e^{0.0301*t}[/tex]
[tex]\frac{11}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}[/tex]
[tex]1.659=e^{0.0301*t}[/tex]
[tex]ln(1.659)=ln(e^{0.0301*t})[/tex]
[tex]\frac{0.506}{0.0301}=\frac{0.0301*t}{0.0301}[/tex]
[tex]16.818\ years = t[/tex]
Moving onto part d, we need to find the doubling time. This will be similar to the previous part but we will be finding the time it takes to double our population. So instead of putting 11 million for P(t) we put 6.63 * 2 in there which is 13.26.
[tex]13.26 = 6.63*e^{0.0301*t}[/tex]
[tex]\frac{13.26}{6.63} = \frac{6.63*e^{0.0301*t}}{6.63}[/tex]
[tex]2=e^{0.0301*t}[/tex]
[tex]ln(2)=ln(e^{0.0301*t})[/tex]
[tex]\frac{0.693}{0.0301}=\frac{0.0301*t}{0.0301}[/tex]
[tex]23.028\ years = t[/tex]
Hope this helps! Let me know if you have any questions
Find the slope of (-4,3) (-3,4)
Answer:
y = x + 7
Step-by-step explanation:
The area of a rectangular recreation area is 45 square miles.
The width is 5 miles.
a. Find the length
B. Find the perimeter
Answer: a. 9 miles b. 28 miles
Step-by-step explanation:
PART A:
Area = Length x Width
Therefore, 5 times some number = 45.
To solve this, use division - 45/5 = 9 miles
PART B:
Perimeter = L + L + W + W
You know width is 5 miles and length is 9 miles.
5+5+9+9 = 28 miles.
If x < 5, then which of the following must be true?
- x < 5
- x > -5
- x > 5
- x < -5
Let's check the options :
[tex] - x < 5[/tex]
Divide both sieds by - 1
[tex] \frac{ - x}{ - 1} > \frac{ 5}{ - 1} \\ [/tex]
[tex]x > - 5[/tex]
False
_____________________________________________
[tex] - x > - 5[/tex]
Divide both sides by - 1
[tex] \frac{ - x}{ - 1} < \frac{ - 5}{ - 1} \\ [/tex]
[tex]x < 5[/tex]
True
_____________________________________________
Divide both sides by - 1
[tex] \frac{ - x}{ - 1} < \frac{5}{ - 1} \\ [/tex]
[tex]x < - 5[/tex]
False
_____________________________________________
[tex] - x < - 5[/tex]
Divide both sides by - 1
[tex] \frac{ - x}{ - 1} > \frac{ - 5}{ - 1} \\ [/tex]
[tex]x > 5[/tex]
False
solve the equation 3x-2=13
Answer:
add 2 to 13 thats 15 divided by 3 is 5
Step-by-step explanation:
Hannah is 16 years younger than Ericka. In 5 years Ericka will be twice as old as Hannah. How old is each
Answer:11 and 27
Step-by-step explanation:
11+16=27 and they are 16 years apart and because it says 5 years 27+5=32 and if you add 5 to 11 you get 16 and 16+16=32
can someone help me here
NONSENSE=REPORT
topic: Inscribed Angles and Intercepted Arc
Answer:
Step-by-step explanation:
5(b + 6) - 3b I need help TwT
Answer:
its 2b+30 bc you can't find b in this case
Step-by-step explanation:
Please help me on this!
Answer:
Answer is in attachment
Pls Mark brainliest :)
What is the volume of this rectangular pyramid?
7 mm
9 mm
9 mm
cubic millimeters
Paula earned 56% on her science test. If she got 14 problems correct, then how many questions were on the test?
A cloth mill produces 3746 meters of cloth in a day. how much cloth will it produce in 285 days
Answer:
1,067,610 cloth will be produced in 285 days
Step-by-step explanation:
- 3746 meters of cloth in a day
- in 285 days
3746 x 285 = 1,067,610
A(x)=x(10-x)
When is A(x) at its maximum? Explain
Or show how you know.
Answer:
A(x) is at its maximum at x = 5, or (5, 25)
Step-by-step explanation:
Putting A(x)=x(10-x) back into its standard form gives A(x) = -x^2 + 10x. The equation to find the x value in vertices in these types of functions is -b / 2a, the letters pertaining to the coefficients. In this case, this graph would have a maximum at -(10)/2(-1), or -10/-2 = 5 --> Thus, when x=5, the downwards facing graph is at its maximum
(Might not be important but another method to solve:)
Take the derivative of the function A(x) = x(10-x) and set it equal to 0 to find the x value of all vertices. In this case, A'(x) = -2x + 10,
-2x + 10 = 0
-2x = -10
x = 5
A(x) is at its maximum at x=5 because it is when A'(x), the derivative, is equal to 0 and thus has a flat slope (or vertex)
Answer:
(5, 25)
Step-by-step explanation:
A(x) is a parabola meaning the max point would be called the vertex
Expand A(x)
[tex]x(10 - x) = 10x - x^{2}\\x^{2} -10x[/tex]
The vertex point is (h, k)
To find h:
[tex]h =- \frac{-b}{2a} \\b = -10\\a = 1\\h = - \frac{-10}{2(1)} \\h = - \frac{-10}{2} \\h = 5[/tex]a and b are from the equation [tex]ax^{2} + bx[/tex]
To find k, plug in h values:
[tex]k = \\f(5) = 5^{2} - 10(5)\\f(5) = 25[/tex]
vertex = (h, k) = (5, 25)
graph attached as well for a visual
The circle has a Circumference of a 9.42units. What is the area of the square? Use 3.14
The area of a square is the square of its side. The area of the square is 2.2477 units².
What is the area of a square?The area of a square is the square of its side. It is given by the formula,
Area of the square = a²
Given the circumference of the circle is 9.42 units. Therefore, the radius of the circle can be written as,
Circumference of the circle = 2πr
[tex]\rm9.42\ units= 2\pi r\\\\r = \dfrac{9.42}{2\pi}\ units[/tex]
Now, as the side of the square is equal to the radius of the circle, therefore, the area of the circle will be equal to,
Area of the circle = a² = r²
[tex]\rm \text{Area of the circle }= (\dfrac{9.42}{2\pi})^2[/tex]
[tex]\rm = \times \dfrac{9.42}{2\pi} \times \dfrac{9.42}{2\pi}\\\\ = 2.2477\ units^2[/tex]
Hence, the area of the square is 2.2477 units².
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You have 10 shirts, 4 pairs of pants, and 3 pairs of shoes. How many outfits can you create?
Answer:
120 different outfits.
Step-by-step explanation:
10x4=40
40x3=
120
Ella's Jewelry box contains 20 earrings 4 blue 6 green 2 red and 8 white. she took one earning from the box and than replaced it. She recorded results in the table shown below
Color Number of times picked from jewelry box
blue 14
green 8
red 16
white 12
What's the theoretical possibility of choosing a red earring?(fraction and percent)
What's the Experimental possibility of choosing a red earring?(fraction and percent)
What's the theoretical possibility of choosing a blue earring?(fraction and percent)
What's the Experimental possibility of choosing a blue earring?(fraction and percent)
The theoretical possibility of choosing a red earring is 1/10, 10%.
The experimental possibility of choosing a red earring is 8/25, 32%
The theoretical possibility of choosing a blue earring is 1/5, 20%.
The experimental possibility of choosing a blue earring is 7/15 or 28%.
What are the probabilities?
Theoretical probability determines the chances that a random event would happen.
Theoretical probability = number of the earing in the box / total number of earrings
Red earrings = 2/20 = 1/10 = 10%
Blue earrings = 4/20 = 1/5 = 20%
Experimental probability is based on the result of an experiment that has been carried out multiples times
Experimental probability = number of times the earing was chosen / number of time the experiment was conducted
The experimental possibility of choosing a red earring= 16/50
= 8/25, 32%
The experimental possibility of choosing a blue earring = 14/50 = 7/25 = 28%
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Factor -1/4 out of -1/2x - 5/4y
The factor from the provided expression of the variable x and y is taken out. The resultant expression is -1/4(2x-5y).
What is a factor of equation?The factor of a equation is the terms or number which is common in all the terms of the that equation.
The first term of the equation is,
-1/2x
Multiply with 2 in numerator and denominator of this term as,
-2/4x
(-1/4)2x
Now the second term of the equation is,
-5/4y
Rewrite this term as,
(-1/4)5y
Thus, the expression become,
1/2x - 5/4y
(-1/4)2x- (-1/4)5y
-1/4(2x-5y)
Hence, the factor from the provided expression of the variable x and y is taken out. The resultant expression is -1/4(2x-5y).
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3 The owners intend to store machinery in the undercover storage. Do you think this is wise? Explain.
The owners intend to store machinery in the undercover storage is a wise idea as it will not be exposed to too much sunlight or water damage.
What is seem as a machinery?Machinery is known to be any kind of mechanical, electrical, or electronic tool that has been set up to carryout some basic function.
Note that The owners intend to store machinery in the undercover storage is a wise idea as it will not be exposed to too much sunlight or water damage and as such it is advisable only in some cases.
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Help me
Solves multi-step equation
119=7(2e+7)
Answer:
e=+5
Step-by-step explanation:
119=7(2e+7)
We move all terms to the left:
119-(7(2e+7))=0
We calculate terms in parentheses: -(7(2e+7)), so:
7(2e+7)
We multiply parentheses
14e+49
Back to the equation:
-(14e+49)
We get rid of parentheses
-14e-49+119=0
We add all the numbers together, and all the variables
-14e+70=0
We move all terms containing e to the left, all other terms to the right
-14e=-70
e=-70/-14
e=+5
Step-by-step explanation:
the other answer is right but it seems a bit overly complicated how the result was achieved.
119 = 7(2e + 7)
119 = 14e + 49
70 = 14e
e = 70/14 = 5
that's really it.
What are the coordinates of the vertex of the parabola described by the
equation below?
y = 4(x + 7)2 - 2
Answer:
(−7,−2)
Step-by-step explanation:
Use the vertex form, y=a(x−h)2+k, to determine the values of a, h, and k.
a=4
h=−7
k=−2
(−7,−2)
please help me evaluate 3|-4|
Answer:
12
Step-by-step explanation:
[tex]3|-4| = 3(4) = 12[/tex]
Answer:
[tex] | - 4| = 4 \\ 3 \times 4 = 12[/tex]
please help me with this
Answer:
x=12m
Step-by-step explanation:
44 divide by 3 2/3 = 12
-4(7+v)=28
Please answer this with how you got the answer.
Answer:
v = -14
Step-by-step explanation:
» Solution
Step 1: Distribute the -4 to the terms inside the parantheses.
[tex](-4)(7)+(-4)(v)=28[/tex] [tex]-28-4v=28[/tex] [tex]-4v-28=28[/tex]Step 2: Add 28 to both sides.
[tex]-4v-28+28=28+28[/tex] [tex]-4v=56[/tex]Step 3: Divide both sides by -4.
[tex]-4v/-4=56/-4[/tex] [tex]v=-14[/tex]Therefore, v = -14.
You must be at least 5 ft tall to ride the roller coaster? write an inequality that represents this statement
Answer:
5ft > can ride the roller coaster??
Step-by-step explanation:
im not 100% sure what u mean
In a data set with a normal distribution, the mean is 59 and the standard deviation is 3.
Part A
About what percent of the data lie between 53 and 62?
Part B
Complete: About 95% of the data lie between ______ and ________.
Answer:
Part A: 81.5%
Part B: About 95% of the data lie between 53 and 65.
Step-by-step explanation:
Note: the percentages marked in red and blue never change
For Part A, we add the percentages that are between 53 and 62. So, 34% + 34% + 13.5% which is 81.5%
For Part B, we can look at this graph and seen that 95% of this data set lies between 53 and 65
Hope this is correct and of help!
The function h(x) = (x + 3)2 + 2. How is the graph of h(x) translated from the parent graph of a
quadratic function, f(x) = xº? Select all that apply.
The graph of h(x) is shifted 3 units to the right of the parent graph.
O The graph of h(x) is shifted 2 units up from the parent graph.
The graph of h(x) is vertically compressed by a factor of
The graph of h(x) is a reflection of the parent graph.
The graph of h(x) has a different y-intercept from the parent graph.
Both graphs have two x intercepts.
The Answers are B,C, and E
I got this by graphing the function of h(x) and the parent function f(x) on the same graph and analogizing the shifts of h(x) from the parent graph f(x). Also the function included two different y-intercepts.
