Answer:
not correctStep 4: 2x -4Step-by-step explanation:
You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.
SolutionDavid's solution is correct up to Step 4.
At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...
Step 4: (5 -3)x -4 = 2x -4
David's incorrect solution should have been 2x -4.
Which is an equivalent expression for {(5/7)²· (1/3)⁻³}⁻¹ ?
(5/7)² .(1/3)⁻³
(5/7). (1/3)⁻⁴
(7/5)⁻² . (1/3)⁻³
(7/5)² .(1/3)³
Equivalent expression to the given expression [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to
Option d. ( 7 /5)² ( 1/3)³.
As given in the question,
Given expression is equal to :
[ ( 5/7)² ( 1/3)⁻³]⁻¹
Apply law of exponent power to power we get,
( mᵃ nᵇ )ˣ = (m)ᵃˣ × (n )ᵇˣ
( x /y)⁻ᵃ = ( y /x)ᵃ
Here m = 5/ 7, n = 1/3 , a = 2 , b = -3 and x = -1
Equivalent expression of the given expression is:
[ ( 5/7)² ( 1/3)⁻³]⁻¹
= ( 5 / 7 )^(2 × -1) ( 1 / 3)^(-3 × -1)
= ( 5 / 7 )⁻² ( 1 / 3)³
= ( 7 / 5 )²× ( 1 / 3)³
Therefore , equivalent expression of [ ( 5/7)² ( 1/3)⁻³]⁻¹ is equal to the
option d.( 7 /5)² ( 1/3)³.
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I NEEED HELP IM FAILING THIS CLASS WITH A (F) someone pls I’ll give brainliest and tons of points
Answer:
A reflection over the x axis
Step-by-step explanation:
x is the horizontal line we are reflecting one across it to get the other
Function p represents the number of people in the library on a Monday as a function of hours since the library opened. Here is the graph of function p.
Based on the graph and the situation, which domain and range make sense for function p?
A.
Domain: all numbers from 0 to 85. Range: all numbers from 0 to 14.
B.
Domain: whole numbers only from 0 to 14. Range: whole numbers only from 0 to 85.
C.
Domain: all numbers from 0 to 14. Range: whole numbers only from 0 to 85.
D.
Domain: whole numbers only from 0 to 14. Range: all numbers from 0 to 85.
Answer: the correct anserw is A.!
Step-by-step explanation:
Consider function f.
Which statement is true about function f?
A.
The function is continuous.
B.
The domain is all real numbers.
C.
The function is increasing over its entire domain.
D.
As x approaches positive infinity, approaches positive infinity.
The statement B is as x approaches positive infinity f(x) approaches positive infinity is true.
What is the definition of the limit?
A point or level beyond which something does not or may not extend or pass.
We have to check for continuity by evaluating 2ˣ and -x² - 4x + 1
at the breakpoint x = 0
2⁰ is 1 and -x² - 4x + 1 is also 1,
So these two functions approach the same value as x approaches 0.
Now do the same thing with
-x² - 4x + 1 and (1/2)x + 3 at x = 2;
The first comes out to -11 and the second to 4.
Thus, this function is not continuous at x = 2.
We must reject statement A.
for D we have as x increases without bound,
(1/2)x + 3
also increases without bound.
Therefore the statement D is true statement.
Statement C is False,
because the quadratic has a maximum -x² - 4x + 1 has a maximum at
x = -b/[2a],
x = -(-4) / [-2],
x = -2
There are no limitations on the values of the input, x.
A is also a false negative number are in real numbers.
Therefore, the statement B is as x approaches positive infinity f(x) approaches positive infinity is true.
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Answer:
The Answer is B for Edmentum users
Step-by-step explanation:
how do you solve for the y intercept ?
Y Intercept is the point where a line or curve crosses the y-axis of a graph or in other words where x=0.
Knowledge of the y-intercept can be used when graphing lines or when writing an equation in slope-intercept form.
Formula to calculate y-intercept.
We get the y-intercept by using the equation of a straight line which is;
y = mx + b
Where;
m is the gradient of the slope
b is the y-intercept.
We can use the following formula to calculate the y-intercept.
y – a = m ( x – b )
a and b being a point on a line.
Example:
Suppose you have a straight line whose gradient is 3 and a point 2,1, calculate its y-intercept.
Since the y-intercept is when x=0, therefore;
y – 2 = 3 ( x – 1 )
y – 2 = 3x – 1
y = 3x – 1
Therefore, the number that has replaced b is -1, which means that -1 is the y-intercept.
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equation (i), (ii), and (v) are the equivalent.
What is the equivalent expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
We have,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
If we take x =3,
the sums would be true.
for the equation (i) take x = 3,
2 + x = 5
2 + 3 = 5
LHS = RHS = 5
for equation (ii) take x = 3,
x + 1 = 4
3 + 1 = 4
LHS = RHS = 4
for equation (iii) take x = 3,
9 + x = 6
9 + 3 = 6
12 ≠ 6
LHS ≠ RHS
for the equation (iv) take x = 3,
x + (-4) = 7
3 + (-4) = 7
-1 ≠ 7
LHS ≠ RHS
for the equation (v) take x = 3,
-5 + x = -2
-5 + 3 = -2
-2 = -2
LHS = RHS = -2
Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.
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How do I integrate this problem?
[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] = [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.
What do you mean by integration?
The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a collection of little data that cannot be measured separately, the integral is calculated.
The idea of integration has evolved to address the following issues:
once the derivatives of the problem function have been determined.
to determine the region enclosed by a function's graph under specific restrictions.
Given function f(x) = [tex]\frac{4}{x^2+2}[/tex]
[tex]\int\limits\frac{4}{x^2+2} \, dx[/tex]
Substitute u = [tex]\frac{x}{\sqrt{2} }[/tex]
⇒ [tex]\frac{du}{dx} =\frac{1}{\sqrt{2} }[/tex]
⇒ dx = [tex]\sqrt{2}[/tex] du
= [tex]\frac{2^{\frac{5}{2}} }{2u^2+2}du[/tex]
On simplifying
= [tex]2^{\frac{3}{2} }[/tex][tex]\int\limits\frac{1}{u^2+1} \, du[/tex] .........(1)
Now [tex]\int\limits\frac{1}{u^2+1} \, du[/tex] = [tex]tan^{-1} (u)[/tex]
Substitute this value in equation (1)
= [tex]2^{\frac{3}{2} }tan^{-1}(u)[/tex]
Substitute the value of u here
= [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex]
Therefore, [tex]\int\limits\frac{4}{x^2+2} \, dx[/tex] = [tex]2^{\frac{3}{2} }tan^{-1}(\frac{x}{\sqrt{2} })[/tex] + C where C is the integrating constant.
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Which expression is equivalent to 5(x+3)
Answer:
x= -3
Step-by-step explanation:
5x + 15 =0
5x= -15
x= -3
Answer:
x= -3
5x= -15
x = -15/3
x= -3
Jack spends 15 % of his pocket money on sweets and 35 % on magazines. He saves the rest.
Work out how much he spends and saves each week.
Sweets ____p
Magazines £___
Savings £____
Jack spend $15 on sweets
Jack spend $35 on magazines
Jack saves $50
Given,
Jack spends 15 % of his pocket money on sweets and 35 % on magazines.
Jack save the rest ; 100 - (15 + 35) = 100 - 50 = 50%
Here,
If Jack has a pocket money of $100
The money he spends on sweets = 15% of 100 = $15
The money he spends on magazines = 35% of 100 = $35
Then,
The money he saves = 50% of 100 = $50
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Match the equations of perpendicular lines. (You will not use all answer choices on the right.)
The equations of the perpendicular lines are matched as follows:
y = 1/3x + 4 → y = -3x - 4.
y = 2/5x - 7 → y = -5/2x + 7.
y = -5/2x + 8 → y = 2/5x - 6.
y = -2x + 6 → y = 1/2x + 3.
y = 7/5x - 9 → y = -5/7x - 11.
What are the Equations of Perpendicular Lines?If the equations of lines are written in slope-intercept form as y = mx + b, where the slope is the value of m, then the slope of lines that are perpendicular to each other will be negative reciprocal of each other.
For example, if the equation of a line is y = 1/2x + 5, the equation of a line that is perpendicular to it would have a slope of -2.
y = 1/3x + 4 has a slope of 1/3. The negative reciprocal of 1/3 is -3. Therefore, the line that is perpendicular to it would be, y = -3x - 4.
y = 2/5x - 7 has a slope of 2/5. The negative reciprocal of 2/5 is -5/2. Therefore, the line that is perpendicular to it would be, y = -5/2x + 7.
y = -5/2x + 8 has a slope of -5/2. The negative reciprocal of -5/2 is 2/5. Therefore, the line that is perpendicular to it would be, y = 2/5x - 6.
y = -2x + 6 has a slope of -2. The negative reciprocal of -2 is 1/2. Therefore, the line that is perpendicular to it would be, y = 1/2x + 3.
y = 7/5x - 9 has a slope of 7/5. The negative reciprocal of 7/5 is -5/7. Therefore, the line that is perpendicular to it would be, y = -5/7x - 11.
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1.)The half-life of Radium-228 is 5.75 years. What is the annual decay rate? Express the result to four decimal places.
Answer:
Express the annual decay rate as a percentage to two decimal places.
2.) The equation N(t) = 600/ 1 + 59e^−0.7t models the number of people N in a town who have heard a rumor after t days.
How many people started the rumor?
3.) The equation N(t) = 700/1 + 69e−0.8t models the number of people N in a town who have heard a rumor after t days.
To the nearest whole number, how many people will have heard the rumor after 3 days?
1) The annual decay rate of the exponential function is given as follows: 12.94%.
2) The number of people who started the rumor is of 10.
3) The number of people who will have heard the rumor after 3 days is given as follows: 96 people.
How to obtain the measures?For item 1, the format of the exponential function is given as follows:
A(t) = A(0)(1 - r)^t.
In which r represents the annual decay rate.
The half-life of Radium-228 is 5.75 years, hence:
A(5.75) = 0.5A(0).
Thus the annual decay rate of the exponential function is given as follows:
0.5A(0) = A(0)(1 - r)^5.
(1 - r)^5 = 0.5
Applying the fifth root to both sides:
1 - r = (0.5)^(1/5)
1 - r = 0.8706
r = 1 - 0.8706
r = 0.1294 = 12.94%.
Then for items 2 and 3 we just obtain the numeric values.
The number of people who started the rumor is N(0), hence:
N(0) = 600/(1 + 59e^(-0.7 x 0)) = 600/60 = 10 people.
The number of people who heart the rumor after three days is N(3), hence:
N(3) = 700/(1 + 69e^(-0.8 x 3)) = 96 people.
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there are 72 players on 9 teams. How many players are on one team
Answer:
8
Step-by-step explanation:
72 ÷ 9 = 8
Answer:
8
Step-by-step explanation:
72 divided by 9 is 8
the scatter plot and line of best fit below show the length of 12 peoples femur and their height in centimeters. based on the line of best fir, what would be the predicted height for someone with a femur length of 55 cm
The predicted height for someone with a femur length of 55 cm is of:
175 cm.
How to obtain the linear function?The linear function in this problem is obtained using the point-slope format, which is given as follows:
y - y' = m(x - x').
In which:
m is the slope of the linear function.(x',y') are the coordinates of the point.From the image given at the end of the answer, two points on the line are given as follows:
(35, 139) and (40, 151).
Given two points the slope is calculated as the change in y divided by the change in x, hence:
m = (151 - 139)/(40 - 35) = 2.4.
Considering the first point, the definition of the line is given as follows:
y - 139 = 2.4(x - 40).
The predicted height for someone with a femur length of 55 cm is y when x = 55, hence:
y - 139 = 2.4(x - 40).
y - 139 = 2.4(55 - 40)
y = 175 cm.
Missing InformationThe graph of the linear function is given by the image shown at the end of the answer.
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are the following required to file a federal income tax return? MFJ HUSBAND AGE 66 WIFE AGED 60 GROSS INCOME OF $25200
The answer to the Question based on Federal Income Tax return is Yes
What is Federal Income Tax Returm?
It is a kind of tax that people have to pay to government.
Federal Income tax has some of its special conditions also and so is suggested by its name
Solution:
As MJF husband is aged 66 and his Gross income is 25200$ and this amount of money is not very less but infact very high hence there is fixed percentage of tax decided by government per fixed amount of money and MJF husband has to pay that amount of tax to government
Hence answer to the Question is Yes
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I need help asap plssssssss
3 out of 4 cats are orange
Answer:
3 cats are orange and The other 1 is not
Because
Which equation is equivalent to 1/3 (9x+12)+4x+6
Answer:
[tex]7x+10[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}(9x+12)+4x+6 \\ \\ =3x+4+4x+6 \\ \\ =7x+10[/tex]
First correct answer gets brainliest
Given a line with slope = -4 and y-int= (0, 5), write the equation of the line.
Writing the equation algebraically.
Answer:
[tex]y=-4x+5[/tex]
Step-by-step explanation:
The equation of a line with slope [tex]m[/tex] and [tex]y[/tex]-intercept [tex](0,b)[/tex] is [tex]y=mx+b[/tex].
Once i give you brainliest It will be 25 Points!
Answer:
Step-by-step explanation:
First question. Answer is
Does anyone know this?
Answer: i think it's 942,480
Step-by-step explanation:
i just multiplied all of the numbers but i'm probably wrong srry
Answer:
7986m^2
Step-by-step explanation:
140-102=38
area of triangle:
(38*66)/2=1254m^2
area of rectangle:
66*102=6732m^2
total area:
1254+6732=7986m^2
4. Find s if the line through the points (7,3)
and (s, -7) has a slope of -5.
Answer:
s = 9
Step-by-step explanation:
calculate the slope m through the 2 points using the slope formula and equate to - 5
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (s, - 7 )
m = [tex]\frac{-7-3}{s-7}[/tex] = [tex]\frac{-10}{s-7}[/tex]
equate m to slope of - 5
[tex]\frac{-10}{s-7}[/tex] = - 5 ← multiply both sides by s - 7
- 10 = - 5(s - 7) ← divide both sides by - 5
2 = s - 7 ( add 7 to both sides )
9 = s
The Miller family is taking a road trip to visit some relatives. With a full gas tank, the car has a range of 456 miles. Mr. Miller wants to stop to fill up when the range reaches 57 miles remaining. If the car averages 28.5 miles per gallon, then the equation 456 - 28.5g represents how many gallons of gas they will use before they need to fill up. How many gallons of gas will they use before they need to fill up? 57
Answer:
14 gallons
Step-by-step explanation:
456 - 28.5g = 5
28.5g =399
G=14
find the following for the rational function
f (x) =6x²+62-36/x²+3
A. Find the vertical asymptote(s) of f.
B. Find the (x, y) coordinates of any holes in the graph of f.
C. Find the horizontal asymptote(s) of f.
The solution is
A) The vertical asymptote of the function f ( x ) is = -3
B) The holes in the graph of f ( x ) = ( 0 , 6 )
C) The horizontal asymptote of the function f ( x ) is = 6
What are Asymptotes?
An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be f ( x ) = ( 6x² + 6x - 36 ) / ( x² + 3x )
A)
Now , to find the vertical asymptote
To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its denominator equal to zero, and then solve for x values
So , when x² + 3x = 0
x ( x + 3 ) = 0
So , x + 3 = 0
x = 0 is a hole in the graph
x = -3 is the vertical asymptote
B) The hole in the graph is ( 0 , 6 )
C)
Now , to find the horizontal asymptote
If both the polynomials have the same degree, divide the coefficients of the leading terms
So , 6x² and x² are the polynomials having the same degree
So , the coefficients are 6 and 1
y = (leading coefficient of numerator) / (leading coefficient of denominator)
y = 6 is the horizontal asymptote
Hence ,
A) The vertical asymptote of the function f ( x ) is = -3
B) The holes in the graph of f ( x ) = ( 0 , 6 )
C) The horizontal asymptote of the function f ( x ) is = 6
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4. What is the length of b?
b=16
b=24
b=12
b=15
Answer:
b=12
Step-by-step explanation:
The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age. Let l represent Lance's age, and let c represent Chad's age. This situation can be represented by the system l+c=27 and c=2l−6 . Find the age of each person.
The age of Lance and Chad are 7 years and 20 years respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let age of Lance's is = L
Age of Chad's = C
Given that The sum of Lance's and Chad's ages is 27 years. Chad is 6 years younger than twice Lance's age.
The system of equations that represents this situation is;
L + c = 27
C - 6 = 2L
2L - c = -6------ (1)
Therefore,
⇒ ( 2L - c ) + (L + c) = 21
⇒ 3L = 21------- (2)
L = 7
C = 20
Therefore the age of each person;
7 years and 20 years
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What is the slope of the lines
Answer: the slope of the line is 2 or 2/1
Step-by-step explanation:
Find the slope and the y-intercept of the following linear equation. -3x + 2y = 18
Answer:
slope=3/2 y- intercept=9
Answer:
Slope: 3/2
y-intercept: 9
Step-by-step explanation:
Slope-Intercept Form:Slope-Intercept Form is given in the form: [tex]y = mx+b[/tex], where [tex]m = \text{slope and }b=\text{y-intercept}[/tex].
So it's very convenient to have a linear equation in this form to identify the slope and y-intercept. To get into this form, we simply need to isolate the y-value.
Converting to Slope-Intercept Form:We start with the initial equation:
[tex]-3x+2y=18[/tex]
The first step to isolating "y" is to move any terms on the same side as the "y" variable to the other side. So let's move the 3x term to the other side, by adding 3x to both sides.
[tex](-3x+3x)+2y=18+3x\implies 2y=18+3x[/tex]
From here, the only thing that is with the "y" variable is the coefficient. The [tex]2y[/tex] is the same thing as: [tex]2\ *\ y[/tex]. We want to get rid of the 2, which we do by dividing by 2, to cancel out the multiplication by 2.
[tex]\frac{2y}{2} = \frac{18 + 3x}{2} \implies y = \frac{18 + 3x}{2}[/tex]
Now from here we want to distribute the division by 2 as such:
[tex]y = \frac{18 + 3x}{2} \implies y = \frac{3}{2}x + \frac{18}{2} \implies y= \frac{3}{2}x + 9[/tex]
So now we have the equation:
[tex]y= \frac{3}{2}x + 9[/tex]
this is in the slope-intercept form:
[tex]y=mx+b[/tex]
in this form the coefficient of x is the slope, so 3/2 is the slope. The constant is the y-intercept, so 9 is the y-intercept.
Simplifying 6(x+4)2/3x(x+4)
Answer:
[tex]\dfrac{2(x+4)}{x}[/tex] or [tex]2 + \dfrac{8}{x}[/tex]
Step-by-step explanation:
Rewrite the problem as a fraction.
[tex]\dfrac{6(x+4)^2}{3x(x+4)}[/tex]
Then, represent the squared term on the top as two values to make it easier to cancel.
[tex]\dfrac{6(x+4)(x+4)}{3x(x+4)}[/tex]
Now, cancel an x+4 from the top and bottom.
[tex]\dfrac{6(x+4)}{3x}[/tex]
Finally, divide the numerator and denominator by 3.
[tex]\dfrac{2(x+4)}{x}[/tex] or [tex]2 + \dfrac{8}{x}[/tex]
[tex]\bf{\dfrac{6(x+4)2}{3x(x+4)} \iff \ Eliminate \ (x+4).}\\ \\ \bf{That\:is, isolating\:the \ common \ factor \ \dfrac{\not{6}\times2 }{\not{3}x} \ \--\to\dfrac{2\times2}{x}=\dfrac{4}{x} } \\ \\ \boldsymbol{\sf{\dfrac{4}{x} }}\bf{\iff}\boxed{\boxed{\bf{Answer}}}[/tex]
Using the functions s = 13.5h, which statement is true?
The domain of s = 13.5h is (0, 1, 2, 3, 4).
The range of s = 13.5h is (0, 13.5, 27, 40.5, 54).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
s = 13.5h
For h = 0,
s = 0
For h = 1,
s = 13.5
For h = 2,
s = 27
For h = 3,
s = 40.5
For h = 4,
s = 54
Thus,
The domain is (0, 1, 2, 3, 4).
The range is (0, 13.5, 27, 40.5, 54).
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(-14)+(-7) irrational
For the given expression -21 is not a irrational number.
What is irrational number?
In mathematics, all real numbers that are not rational are referred to as irrational numbers. Irrational numbers can't be expressed as the ratio of two integers, in other words.
Any real number that cannot be expressed as the ratio of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, there is no integer or fraction that equals the square root of 2.
Consider the given expression,
(-14) + (-7)
Solving this, we get
(-14) + (-7) = -14 - 7 = -21
Here 21 can be written in the form p/q.
⇒ -21 = -21/1
So, -21 is a rational number.
Hence, -21 is not a irrational number.
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