Answers
To find the domain of the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we need to consider the values of x for which the expression is defined.
First, we need to consider the square root term, sqrt(5x^2-8x). The square root of a number is only defined for nonnegative values, so we need to find the values of x for which 5x^2-8x is nonnegative. We can do this by setting 5x^2-8x equal to 0 and solving for x:
5x^2-8x=0
5x(x-8)=0
We can see that x=0 and x=8 are the solutions to this equation. Since the square root of a negative number is not defined, the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is only defined for x values that are greater than or equal to 0 and less than or equal to 8. This means that the domain of the expression is x ∈ [0, 8].
To solve the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we can start by isolating one of the exponential terms on one side of the equation. Let's isolate the term 2^(sqrt(5x^2-8x)):
24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x))
22^(2sqrt(5x^2-8x)+1)=332^(sqrt(5x^2-8x))
2^(2sqrt(5x^2-8x)+1)=16.52^(sqrt(5x^2-8x))
2sqrt(5x^2-8x)+1=4.5+sqrt(5x^2-8x)
sqrt(5x^2-8x)=3.5
5x^2-8x=12.25
5x^2-8x-12.25=0
We can use the quadratic formula to solve this equation for x:
x = (-(-8) ± sqrt((-8)^2 - 45(-12.25))) / (2*5)
x = (8 ± sqrt(64 + 97)) / 10
x = (8 ± sqrt(161)) / 10
x = (8 ± sqrt(289)) / 10
x = (8 ± 17) / 10
x = -9/10 or 25/10
Since x must be greater than or equal to 0 and less than or equal to 8, the only solution that is within the domain of the expression is x=25/10, or x=2.5.
Therefore, the solution to the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is x=2.5.
what do you mean by domain of a function?
The domain of a function is the set of all input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function as an argument, or input, and produce a valid output
For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since the function is defined for any value of x. However, some functions may not be defined for certain values of x. For example, the function g(x) = 1/x is not defined for x=0 because division by zero is not allowed. In this case, the domain of the function g(x) would be all real numbers except for x=0.
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Related Questions
What is this equal to: (3*2)+6
Answers
Answer:
12
Step-by-step explanation:
(3x2) + 6
6 + 6 = 12
Answer:
12
Step-by-step explanation:
3 × 2 is 6
6 + 6 is 12
thus answer is 12
describe the zeros & multiplicity of the function f(x)=2x^3+4x^2-8x-16
Answers
The zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.
What is Cubic equation?
Cubic equations are polynomials of degree3. That means the maximum degree of polynomial is three.
And the standard form of cubic equation is;
f(x) = ax³ + bx² +cx +d, where a, b, c and d are constant coefficients a ≠ 0.
Given that the expression
f(x) = 2x³ + 4x² - 8x - 16
Now we find the roots or zeroes of equation;
for that we will try hit and trial method,
let x = 2
f(x) = 2 (8) - 4 (4) - 8(2) -16
f(x) = 0
That means (x-2) is one of roots of cubic equation.
Now to find other roots of the cubic equation, we will simplify the cubic expression
f(x) = 2x² (x-2) + 8x (x-2) + 8 (x-2)
f(x) = (x-2) (2x²+ 8x + 8)
Now we will find the roots of quadratic equation (2x²+ 8x + 8).
let g(x) = (2x²+ 8x + 8).
factors of quadratic equation is (x+2) and (x+2).
Therefore the zeroes of the expression f(x) = 2x³ + 4x² - 8x - 16 are (x-2), (x+2) and (x+2). And multiplicity of x = -2 is 2.
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Please help me. This is my last question and I have no more points left.
The coordinate plane below shows the location of rectangle TUVW.
rectangle TUVW is to be dilated by a factor of 3, with the center of dilation at the point (1,0). drag and drop the the correct answers into each box.
Answers
Step-by-step explanation:
i just answered this question. how often did you post it ?
Let f(x)=\sqrt(3x-9) and g(x)=3x^(2)-9
A) what is the inverse of function f?
b) is f an inverse of g? Please show all work
Answers
A) The inverse of f(x) is f⁻¹(x) = (x² + 9)/3 and B) f is not an inverse of g.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, f(x) = [tex]\sqrt{3x - 9}[/tex].
y = [tex]\sqrt{3x - 9}[/tex].
y² = 3x - 9.
3x = y² + 9.
x = (y² + 9)/3.
y = (x² + 9)/3.
f⁻¹(x) = (x² + 9)/3 and g(x) = 3x² - 9, so f is not an inverse of g.
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4 2/3 - 3 3/8 + 4 3/5
Answers
Answer:
18.475?
Step-by-step explanation:
Find h in the parallelogram shown.
Answers
Answer: the answer is 4
Step-by-step explanation:
8. What is the equation of the function shown in the graph?
Yaxs
B.
C.
y=-3x
y=3x
y= x
y=-3x
Xanl
Answers
The equation of the given function is y = -1/3 x. By using the points through which the line passing through, we can find its equation. Option A is correct.
What is the formula for finding the equation of a line passing through two points?The equation of the line passing through two points such as (x1, y1) and (x2, y2) is
y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)
Calculation:From the given graph, the line is passing through the points (0, 0), (-3, 1), and (3, -1).
The equation of the line passing through (-3, 1) and (3, -1) is
y - y1 = [(y2 - y1)/(x2 - x1)] × (x - x1)
⇒ y - 1 = (-1 - 1)/(3 + 3) × (x + 3)
⇒ y - 1 = -2/6 (x + 3)
⇒ y - 1 = -1/3 (x + 3)
⇒ 3y - 3 = -x - 3
⇒ 3y = -x
⇒ y = -1/3 x
So, option A is correct.
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I'm needing some help please with the graph
Answers
Answer:
If you are having trouble understanding the graph, it may be helpful to break it down into smaller pieces. Start by looking at each axis and what it represents. Then, look at each data point and see how it relates to the axes. Finally, look at the overall shape of the graph and what it is trying to tell you. If you are still having trouble understanding the graph, you may want to reach out to someone who is knowledgeable about graphs or data analysis for assistance.
Step-by-step explanation:
Please help me
Solve the answer
Arc QR =
Arc RS =
Answers
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
The value of ARC QR is 48
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
The value of ARC RS is 96
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
Therefore the value of ARC QR is 48° and ARC RS is 96°
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Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
Answers
The required time will be 12.9 years.
What is compound interest?
The interest charged on a loan or deposit is referred to as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest.
Given, P = $1700
I = $500
A = P + I = 1700 + 500 = $2200
r = 2% = 0.02
compounded quarterly, n = 4
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
or, 2200 = 1700(1+ (0.02/4))^(4t)
or, 1.294 = 1.005^4t
or, t = 12.9 years
Hence, the required time will be 12.9 years.
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Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional
questions.
Online Content: Site 1
One of the advantages to an employer of paying employees piece rate or commission is that the employee is paid based solely on
their performance. What is one disadvantage of this type of pay?
BIUS X, X²
ΕΞΩ
I
B
T
Answers
The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.
What is piece rate?Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.
Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.
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14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.
Answers
The least possible height of AB is 3.650 m.
What is a word problem?
A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.
For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.
Given, CD=2.6 m, BD=12 m
From the figure,
or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]
or, tan 5 [tex]\leq \frac{AB - 2.6}{12}[/tex]
When AB be least, then
[tex]\frac{AB - 2.6}{12}[/tex] = tan 5
or, AB = (12*tan 5) + 2.6
or, AB = 3.650 m
Hence, the least possible height of the AB is 3.650 m.
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PLEASE HELPPP!!!
The admission fee at the museum is 8.50 for children and 12.50 for adults on a certain day, a total of 240 people entered the museum and 2400$ was collected.
Use the variable c to represent children and the variable a to represent the adult
Answers
Answer:
Below
Step-by-step explanation:
a + c = 240 re-arrange to c = 240-a
revenue from child tix = 8.50 ( 240-a)
revenue from adult tix = 12.50 a summed, the revenues = 2400
8.5(240-a) + 12.5 a = 2400
2040 - 8.5 a + 12.5 a = 2400
4.5 a = 360
a = 80 tix then c = 240 - a = 160 tix
Look at the number line below.
A number line labeled from 0 to 3 with tick marks every one-tenth unit. Tick marks 0, 1, 2, and 3 are labeled. There is a dot at the third tick mark to the right of 2.
Identify the point on the number line and write it as both a fraction and a decimal.
Fraction:
Decimal:
Answers
Answer:
fraction 23/10 that's 2 ³/10
decimal 2.3
which model can be used to find 4/5 divided by 1/10
Answers
Apply the fraction rule model can be used to find 4/5 divided by 1/10.
What is fraction rule?
For fractions to be added or subtracted, their denominators must match (the bottom value). the same denominators are used for addition and subtraction. It only requires adding or subtracting the numerators if the denominators are already equal.
[tex]$\frac{\frac{4}{5}}{\frac{1}{10}}$[/tex]
Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]
[tex]$=\frac{4 \cdot 10}{5 \cdot 1}$[/tex]
Cancel [tex]$\frac{4 \cdot 10}{5 \cdot 1}: 8$[/tex]
=8
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Karen sold 15 hand-made bracelets, earning a total profit of $71.25. She plans to make 25 bracelets for her city’s arts and crafts market. If she sells all 25 bracelets, how much profit can Karen expect to earn?
Answers
Answer: $118.75
Step-by-step explanation: first to see how much one bracelet is, you have to do 71.25/15=4.75. one bracelet is $4.75. so now we multiply 4.75 by 25 to see how much 25 bracelets cost. 4.75x25=118.75. so, if Karen seems all of her bracelets, she can expect to make $118.75.
If BD bisects AC and AC bisects BD, is AABE^ ACDE? Explain.
Yes; the triangles are congruent by SSS.
Yes; the triangles are congruent by ASA.
Yes; the triangles are congruent by SAS
NO; the triangles are not congruent.
Answers
Yes; the triangles are congruent by SAS.
What is triangle ?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
AC and BD bisects one another
AE = CE --- Side
and
BE = DE --- Side
When both lines bisect one another, they form a pair of vertical angles and
When we apply the theorem of vertical angles to this, we have that:
∠AEB = ∠CED --- Angle
At this point, we have established:
Two sides of ABE and CDE are congruent and One angle in each of ABE and CDE are also congruent
Hence, the triangles are congruent by SAS.
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how do i find the inverse of f(x)=[tex]\sqrt[3]{5x+5}[/tex]
Answers
The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
What is inverse of function?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).Change y in for the f(x) :
y = ∛5x + 5
Switch the x and y
x³ = 5y + 5
x³ - 5 = 5y
y = ( x³ - 5 ) / 5
f⁻¹ = ( x³ - 5 ) / 5
Hence, The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
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Identify the terms coefficients and constant 6m + 8+4+3m
Answers
Answer:
Below
Step-by-step explanation:
6m + 8+4+3m <==== 6 and 3 are coefficients 8 and 4 are constants
9m + 12 <===== 9 is a coefficient 12 is a constant
Answer:
The coefficients are 6 and 3
The constants are 8 and 4
Step-by-step explanation:
coefficients are the numbers before the letters.
Constants do not have letters.
help me please thank youuuu
Answers
Answer:
g(x)= -x^2 - 3
Step-by-step explanation:
We know the vertex is (0, -3) and the parabola is opening downward that means the a value has to be negative. And if you know the transformation that -3 moves the parabola down by 3 units as f(x) represents the parent function y= x^2
What is the total number of units (in millions) of electricity produced
each year based on the current extraction rates of coal from all
mines combined assuming all mines have an endless supply of
coal?
Answers
Answer:
Just by multiplying the extraction by the output per kilo for each mine and then summing it. The question asks to express it in millions and you have 8.2 million units
Step-by-step explanation:
Hope it helps
a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe
Answers
2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2
HELPME Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour.
Answers
Explanation: 3 times 3.75= 11.25
11.25 times 2= 22.5
Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)
Answers
1. Find the slope of the two points. 6-(-7) is 13 and -1 -(-2) is 1, so the slope is 13/1.
2. Write the equation in point slope form.
y - y1 = m(x - x1)
y - 6 = 13(x -(-1)
3. Use distributive property.
y - 6 = 13x + 13
4. Add 6 to both sides.
y = 13x + 18
Hope this helps
Five consecutive numbers add up to a total of 35. What is the highest of these numbers
A. 6
B. 7
C. 8
D. 9
E. 10
Answers
Answer:
9
Step-by-step explanation:
5,6,7,8,9
A unicorn is racing a chinchilla. The chinchilla is one hundred feet a head of the unicorn
and running at a rate of 5.75 feet per second. The unicorn is running at a rate of 30 feet
per second. Write an inequality that shows when the unicorn gets ahead of the
chinchilla.
Answers
The inequality that shows when the unicorn gets ahead of the chinchilla is 30s > 100 + 5.75s.
What is the inequality that shows when the unicorn gets ahead?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of seconds be represented by s.
The chinchilla is one hundred feet a head of the unicorn and running at a rate of 5.75 feet per second. This will be 100 + 5.75s.
The unicorn is running at a rate of 30 feet
per second. This will be 30s
The inequality will be 30s > 100 + 5.75s.
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Kaitlin the trainer has two solo workout plans that she offers her clients: plan A and plan B each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 8 who did plan b on Saturday there were 5 clients who did plan A and 2 who did plan b Kaitlin trained her friday clients for a total of 7 hours and her Saturday clients for a total of 6 hours how long does each of the workout plans last
Answers
Let A be the length of plan A in hours and B be the length of plan B in hours. We can set up the following system of equations to represent the given information:
3A + 8B = 7
5A + 2B = 6
Solving this system of equations using elimination, we find that A = 0.6 hours and B = 0.4 hours.
Therefore, plan A lasts 0.6 hours and plan B lasts 0.4 hours.
The length and width of two sides of a rectangle are consecutive odd integers. The area of the rectangle is 143 square units.
Find the dimensions of the rectangle.
The width of the rectangle is blank and length is blank
Answers
The dimensions of the rectangle are 70.5 by 72.5 units.
What is a dimension?
A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.
Solution Explained:
Given,
Area = 143 unit^2
A/Q,
Let length be x and width be x + 2.
So, Area = l X w
143 = x + x + 2
143 = 2x + 2
x = (143 - 2)/2
x = 70.5
So width = x + 2 = 70.5 + 2 = 72.5
So, the dimensions are 70.5 by 72.5
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A bag contains five white balls and three black balls. Your goal is to draw two white balls.
(a) You simultaneously draw two balls at random. What is the probability that they are both white?
(b) You simultaneously draw two balls at random. Once you have drawn two balls, you put back any black balls, and redraw so that you again have two drawn balls. What is the probability that you now have two white balls? (Include the probability that you chose two white balls on the first draw.)
Answers
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A pack contains five white balls and three torpedoes. You want to draw two white balls.
Total events = 5 + 3
Total events = 8
You all the while drawing two balls aimlessly. Then the probability that they are both white is given as,
P = 5 / 8
P = 0.625
You all the while drawing two balls aimlessly. Whenever you have drawn two balls, you set back any debases, and redraw with the goal that you again have two drawn balls. Then the probability is given as,
P = [(3/8) x (5/8)] + [(3/8) x (5/8) x (4/7)]
P = (15 / 64) + (60 / 448)
P = 0.3683
The probability is the first and the second case will be 0.625 and 0.3683, respectively.
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If you make $31.65 in 8 hours, how much in total?
Answers
Answer:
$253.20
Step-by-step explanation: