Given line: y =3x - 7
Slope-intercept form is y = mx + b where m is slope and b is the y intercept
To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)
the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]
This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]
This is the current formula you found:
[tex]y=\frac{-1}{3} x + b[/tex]
To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b
-1 = [tex]\frac{-1}{3}[/tex](2) + b
-1 = [tex]\frac{-2}{3}[/tex] + b
[tex]\frac{-1}{3}[/tex] = b
That means that the equation perpendicular to y = 3x - 7 is...
y = [tex]\frac{-1}{3} x - \frac{1}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y =3x - 7
Step-by-step explanation:
Graph y = √x + 2 and y = 3x on the same set of coordinate axes. Use the graphs to find the exact solutions to the equation √x + 2 = 3x. Then, find the solutions using an algebraic method.
Answer:
x = 1
Step-by-step explanation:
The graph is shown below. The solution is x = 1.
___
√x +2 = 3x . . . . given
√x = 3x -2 . . . . . subtract 2
x = 9x^2 -12x +4 . . . . square both sides
9x^2 -13x +4 = 0 . . . . subtract x to put in standard form
(x -1)(9x -4) = 0 . . . . . factor the quadratic
x = 1 . . . or . . . x = 4/9 . . . . values of x that make the factors zero
The "solution" x = 4/9 is extraneous, in that it does not satisfy the equation. It would correspond to the intersection of the line with the negative branch of the square root function. That is, it does satisfy -√x +2 = 3x.
The solution is x=1.
Explain how to write an equation that represents this scenario
Answer:
1 ticket equals to $2.50. Since x number of tickets are sold, the total amount raised will be $2.50 multiply by x, which is 2.5x. Since y represents the total amount of money raised, 2.5x equals to y
The composition of a function and its inverse is always __________.
Answer:
Answer:
X
The given statement is true.
Step-by-step explanation:
An inverse function can be defined as a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa, i.e., f(x) = y if and only if g(y) = x.
Examples are x+2 and x-2
WE get f(x) = x+2
Apply g(x) = g(f(x))=g(x+2)
=x+2-2=x
Thus by applying composiiton g f or fg in any order we get the answer as x
THis is the property of any inverse function
Step-by-step explanation:
Answer:
X
Step-by-step explanation:
It was corrected on E2020.
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
8 12, 15
10, 24, 26
12, 20, 25
15.18 20
Which logarithmic equation is equivalent to the exponential equation below? e^a=55
(You will receive 34 points)
Answer:
The answer is B.
e^a=55
Taking log on both sides,
lne^a = ln 55
a lne= ln55
a= ln55.
The value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).
What is Logarithm?
A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
What is the value of [tex]e^a = 55[/tex]?We solve the value of this expression using the basic logarithm,
[tex]\rm{log_ab=c[/tex]
Similarly,
[tex]\rm{log_e55=a[/tex]
we know that the log base of exponent is natural log, therefore,
[tex]\rm ln\ 55=a[/tex]
Therefore, the value of the expression [tex]e^a = 55[/tex] in the logarithmic equation is equivalent to (ln 55=a).
Learn more about Logarithm:
https://brainly.com/question/163125
What is an imaginary number
Answer:
An imaginary number is a number that does not exist pretty much. It is usually written as "i", and, when squared = -1. However, you cannot root -1 to get a number, so i is the term that is given to be the answer.
Note:
i² = -1
~
Which shows how to find the value of this expression when X=-2 and Y = 5?
(3x3y=272
31-216
(-2)4
21954
Answer:
Option 1 is correct
Step-by-step explanation:
Given expression is:
[tex](3x^3y^{-2})^2\\[/tex]
Putting the values
[tex]= [3 (-2)^3 (5)^{-2}]^2\\We\ have\ to\ make\ the\ powers\ positive\\= [{\frac{3(-2)^3}{5^{2}} }]^2\\= \frac{[{3(-2)^3}]^2}{(5^2)^2} \\Applying\ outer\ power\\= \frac{3^2(-2)^6}{5^4} \\[/tex]
Hence option one is correct ..
Can someone plz give me the answer for this question?
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = [tex]e^{2x}[/tex] - 4
let f(x) = y
y = [tex]e^{2x}[/tex] - 4
Switch x and y and solve for y, that is
x = [tex]e^{2y}[/tex] - 4 ( add 4 to both sides )
x + 4 = [tex]e^{2y}[/tex]
Take the ln of both sides
ln(x + 4) = ln [tex]e^{2y}[/tex] = 2y [tex]ln_{e}[/tex] = 2y
Divide both sides by 2
y = [tex]\frac{ln(x+4)}{2}[/tex], that is
[tex]f^{-1}[/tex] (x) = [tex]\frac{ln(x+4)}{2}[/tex]
What is 70% of 30?
7
15
20
21
Answer:
D. 21
Step-by-step explanation:
Hope I helped!
Your answer is for this question is 21
1.) To find 70% percent of 30 you simply multiply both. To do that you gotta first change the percent into a decimal by moving the point two types to the left.
70 = 70.0
2.) As you can see we change the percent into a decimal.
70% = .70
3.) Now we can multiply 30 by .70 which will give us an answer of 21.
Hope this helps!!!
Please Mark as Brainliest!!!
camille purchased 4.2 pounds of gummy worms for $1.75 per pound and 3.6 pounds of jelly beans for $2.25 per pound. how much did she spend for the candy? F. $15.45. G. $14.45. H. $15.25. I. $14.35.
Answer:
$15.45 (Answer F)
Step-by-step explanation:
Total expenditure was ($1.75/lb)(4.2 lb) + ($2.25/lb)(3.6 lb) = $15.45
The map below shows the location of 3 houses where you had to do lawn work today. Your truck gets 8 miles per gallon of gasoline, so you chose the shortest route from your house to the jobs and then back home, as shown below. If gas costs $1.52 per gallon, what was the total cost of the gas that you used today?
Answer:
$3.80
Step-by-step explanation:
We are given a graph showing the location of 3 houses where you had to do lawn work today, with the distances from your house.
Given that one truck gets 8 miles per gallon of gasoline and gas costs $1.52 per gallon, we are to find the total cost of the gas used.
Total distance = 7 + 3 + 4 + 6 = 20 miles
Gallons of gas used = 20 / 8 = 2.5
Total cost of gas used = 2.5 * 1.52 = $3.80
Two lines perpendicular to the same plane are?
• A. coinciding lines
• B. equivalent
• C. parallel lines
• D. congruent lines
us
Answer:
C. parallel lines
Explanation:
If two straight lines be at right angles to the same plane, the straight lines would be parallel.
Jayne is studying urban planning and finds that her town is decreasing in population by 3% each year. The population of her town is changing by a constant rate.True or False?
What are the solutions for x when y is equal to 0 in the following quadratic
function?
y = x ^+ 6x +12
OA) X = 3 or x = 4
OB) x= -3 or x = 4
OC) x= 3 or x = 4
OD) x= -3 or x = 4
O E) no solution
Answer:
The correct answer option is E) No solution.
Step-by-step explanation:
We are given the following quadratic equation which we are to solve for x when the value of y is 0:
[tex]y = x ^2+ 6x +12[/tex]
[tex]x ^2+ 6x +12=0[/tex]
Using the quadratic formula since there are no factors:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac }}{2a}[/tex]
Substituting the values in the formula to get:
[tex]x=\frac{-6 \pm \sqrt{6^2-4(1)(12) }}{2(1)}[/tex]
[tex]x=-3+\sqrt{3}i[/tex] or [tex]x=-3-\sqrt{3}i[/tex]
There are no real number solutions to this quadratic equation.
Two numbers have a sum of 24, and 7 times the first number minus the second number is equal to 16. What is the smaller number?
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = y
x + y = 24
7x - y = 16 Add these two equations
8x = 40 Divide by 8
8x/8 = 40/8
x = 5
The smaller number will be 5
================
5 + y = 24
y = 19
==================
Proof
7*5 - 19 = 16
35 - 19 = 16
According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 - 33x2 – 12x + 20.
Which is an actual root of f(x)?
a) -5/2
b) -2
c) 1
d) 10/3
Answer:
a) -5/2.
Step-by-step explanation:
Try substituting (-5/2) into f(x):
6(-5/2)^4 + 5(-5/2)^3 - 33(-5/2)^2 - 12(-5/2) + 20
= 234.375 + -78.125 - 206.25 + 30 + 20
= 0.
So it is -5/2.
Answer:
a) [tex]x= -5/2[/tex]
Step-by-step explanation:
We substitute in the function the values given in the options to confirm whether they are roots or not
a) [tex]x= -5/2[/tex]
the function will be:
[tex]f(-\frac{5}{2} )=6(-\frac{5}{2} )^4 + 5(-\frac{5}{2} )^3-33(-\frac{5}{2} )^2-12(-\frac{5}{2})+20[/tex]
simplifying:
[tex]f(-\frac{5}{2} )=6(\frac{625}{16} )-5(\frac{125}{8} )-33(\frac{25}{4} )+30+20[/tex]
[tex]f(-\frac{5}{2} )=234.375-78.125-206.25+50\\f(-\frac{5}{2} )=0\\\\[/tex]
since the function when [tex]x= -5/2[/tex] is equal to zero, this is an actual root of f(x).
Does anyone know the solution and answer to this question please ??!
Answer:
C
Step-by-step explanation:
Given the similarity ratio, then the
linear ratio of sides = linear ratio of perimeters.
Hence
ratio of perimeters = [tex]\frac{9}{4}[/tex]
what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83
Answer:
35
Step-by-step explanation:
We know that the general formula for arithmetic sequence is
a_n=a_0+(n-1)d
Using the general formula, we can make equations for 6th term and 9th term
a_6=a_0+(6-1)d
a_6=a_0+5d
101=a_0+5d Eqn 1
For 9th term
a_9=a_0+(9-1)d
a_9=a_0+8d
83=a_0+5d Eqn 2
Subtracting equation 2 from equation 1
101-83=a_0+5d-(a_0+8d)
18=a_0+5d-a_0-8d
18=-3d
d= -6
Putting d=-6 in Eqn 1, we get:
101=a_0+5(-6)
101=a_0-30
a_0=101+30
a_0=131
Now that we have values of a_0, and d we can find the 17th term
a_17=a_0+(17-1)d
=131+(16)(-6)
=131-96
=35
So the 17th term is 35 ..
HURRY can a triangle can be constructed with angles measuring 115°,55°, and 20°? yes or no
Answer:
no
Step-by-step explanation:
The sum of the angles of a triangle must add to 180 degrees
115+55+20 = 190
This is not equal to 180 so it is not a triangle.
Answer:
No
Step-by-step explanation:
115°,55°, and 20° = 190° degrees and a triangle can only be 180° .
Rewrite the rational exponent as a radical expression. 3 to the 2 over 3 power, to the 1 over 6 power
Pleaseeeeee Helppppp ;)
Answer:
the ninth root of 3
Step-by-step explanation:
3 to the 2 over 3 power, to the 1 over 6 power rewritten as a radical expression is ''the ninth root of 3''.
Hope this helps!
Answer:
kk
Step-by-step explanation:
If m∠A = (3x-6)° and m∠B = (x + 9)°, find the m∠D.
A) 32°
B) 39°
C) 41°
D) 49°
E) None of the above
Because line BD goes through the center of the circle Angle A is a right angle which equals 90 degrees.
Set the equation for A to equal 90 and solve for x:
3x-6 = 90
Add 6 to each side:
3x = 96
Divide both sides by 3:
x = 32
Now we have a value for x , use that to solve for angle b:
B = x +9 = 32 + 9 = 41 degrees.
Now we know A and B, we can solve for D.
The three inside angles of a triangle need to equal 180.
D = 180 - 90 - 41 = 49 degrees.
The answer is D) 49
complete the table for the given rule. rule: y=2x
Answer:
x | y
-2| -4
-1 | -2
0 |0
1 | 2
2 | 4
Step-by-step explanation:
Find the factored form of
-7y - y2 = 0
Answer:
-y(7+y) =0
Step-by-step explanation:
-7y - y^2 = 0
Factor out a -y
-y(7+y) =0
Using the zero product property
-y =0 and 7+y =0
y=0 7-7+y = 0-7
y=0 y = -7
What is the square root of a^3 and b^4 expressed in simplified form?
Answer:
(a)(b²)√a
Step-by-step explanation:
√(a³b⁴)
Root both variables. Note that pairs of the same variables can be brought out of the root.
√(a³) = √(a * a * a) = a√a
√(b⁴) = √(b * b * b * b) = b²
(a)(b²)√a is your answer.
which of the following values of X is not in the domain of f(x)=x+3/x-7
The value of x that is not in the domain is x = 7.
which of the following values of X is not in the domain of f(x)?
Remember that in math we can't divide by zero, so any value that makes the denominator equal to zero can't be in the domain.
Here the rational function is:
f(x) = (x + 3)/(x - 7)
When x = 7, the denominator becomes zero, so x = 7 is not in the domain.
CAN YOU PLEASE HEP ME WITH THIS ONE THIS IS TIMED PLEASE! Amy has 35 tiles of the same shape and size in a box. The colors of and amounts of the tiles are shown below:
12 red tiles
8 yellow tiles
15 pink tiles
Without looking in the box, Amy takes out a tile at random. She then replaces the tile and takes out another tile from the box. What is the probability that Amy takes out a yellow tile in both draws?
8 over 35 multiplied by 7 over 34 equal 56 over 1190
8 over 35 multiplied by 8 over 35 equal 64 over 1225
8 over 35 plus 7 over 34 equal 517 over 1190
8 over 35 plus 8 over 35 equal 560 over 1225
Answer:
B) 8 over 35 plus 8 over 35 equal 64 over 1225
Step-by-step explanation:
There are 8 yellow tiles out of 35 tiles.
Its not A because she replaces.
Its not C or D because you would only add when it says and
Answer:
8 over 35 multiplied by 8 over 35 equal 64 over 1225
Step-by-step explanation:
I got it right on my test. Give the other person brainliest.
50 points please with explanation
Answer:
no it is not a function
Step-by-step explanation:
it has no sequence and in order for a table to be a function it needs a sequence. look at X it goes from 1, 5, 7, then back down to 2 it has no correlation.
Answer:
no its not a function and ill explain why
Step-by-step explanation:
it has no sequenceand in order for a table to be a functionit needs a sequence. look at Xit goes from 1, 5, 7, then back down to 2 it has no correlation.
first operation to solve 2x + 3 = 11
Answer:
subtract 3 from both sides
Step-by-step explanation:
Given
2x + 3 = 11 ( subtract 3 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
Help me please algebra 2 PLEASSEEEEE!!!
Answer:
29.74 degrees.
Step-by-step explanation:
Tan(theta) = opposite / adjcent.
opposite = 8
adjacent = 14
Tan(theta) = 8/14
Tan(theta) = 0.5714
theta = tan^-1(0.5714)
theta = 29.74 degrees
solve x - 3 = 7
3 - 3 = 7
x - 3 ___ = 7 ____
x ___ = ___
x = ___
Hi,
x - 3 = 7
x = 7 + 3
x = 10