slope = - 2, midpoint = (2, - 2 )
the slope m is calculated using the ' gradient formula '
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )
m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2
calculate midpoint using midpoint formula
{[tex]\frac{1}{2}[/tex] (4 + 0 ), [tex]\frac{1}{2}[/tex] (- 6 + 2 )] = (2, - 2 )
gradient of perpendicular bisector = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
equation in slope-intercept form is
y = mx + c ( m is slope and c the y-intercept )
partial equation is y = [tex]\frac{1}{2}[/tex] x + c
to find c substitute ( 2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 in slope-intercept form
Answer:
-2
(2,-2)
1/2
y=(1/2)x-3
Step-by-step explanation:
It’s correct on edge.
There were 70 birds in a tree. One year later, the number oIn 2013, there were 70 birds in a tree. One year later, the number of birds decreased by 30%. How many birds were in the tree in 2014?F birds decreased by 30%. How many birds were in the tree in 2014?
GEOMETRY HELP , thank you doe helping me , the question is in the below
The answer to your problem is Substitution (A) due to y being 4.
Compare using an inequality symbol 54.045 and 54.405
The two of the given numbers 54.045 and 54.405 can be compared using the inequality as 54.045 < 54.405.
Given two numbers 54.045 and 54.405. If the two numbers are plotted on the graph as shown below, it can be clearly seen that 54.045 comes before 54.405 on positive axis.
Therefore, 54.045 is smaller than 54.405. So ‘<’ smaller than inequality symbol will be used in between 54.045 and 54.405.
Hence, the correct representation of the comparison is 54.045 < 54.405.
Learn more about Inequality here:
https://brainly.com/question/28823603
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would the correct answer be 4? photo attached.
The answer is B. 2
Hope it helps
Please help me with this question
For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.
To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.
Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.
Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.
Answer: Third option
Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was −170 feet. Then she continued to hike down for another 20 minutes at a different rate. Her change in elevation for this part of the hike was −220 feet. During which portion of the hike was her rate of change in elevation greater? Complete the explanation
Answer: First portion is greater than second portion.
Step-by-step explanation:
Time taken to hiked down a trail = 10 minutes
Change in elevation = (-) 170 feet
Speed is given by
[tex]Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}[/tex]
Similarly,
Time taken to hiked down a trail = 20 minutes
Change in elevation = (-)220 feet
Speed is given by
[tex]Speed=\frac{Distance}{Time}[/tex]
[tex]Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}[/tex]
So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.
As 17 feet per minutes is greater than 11 feet per minutes.
what is y=8/5(x-9)+16 in slope intercept form
y = 8/5( x - 9 ) + 16
8/5 = 1.6
y = 1.6x - 14.4 + 16
y = 1.6x + 1.6
The slope is therefore 1.6 and
The y-intercept is 1.6
How to express exponential equation, 3^c = 27 , as a logarithmic equation
If you consider the logarithm base 3 of both sides, you have
[tex] \log_3(3^c) = \log_3(27) [/tex]
You can use a rule of logarithms that allow you to turn exponents into multiplicative factors:
[tex] \log_a(b^c) = c\log_a(b) [/tex]
So the equation becomes
[tex] c\log_3(3)=\log_3(27) [/tex]
Now, by definition, you have
[tex] \log_a(b)=c \iff a^c=b [/tex]
So, you have
[tex] \log_3(3)=x \iff 3^x=3 \iff x = 1,\quad \log_3(27)=y \iff 3^y=27\iff y=3 [/tex]
So, the equation becomes
[tex] 1\cdot c = 3 \iff c=3 [/tex]
[tex]log_{3}[/tex]27 = c
using the law of logs : [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
given [tex]3^{c}[/tex] = 27 then
[tex]log_{3}[/tex] 27 = c
A web designer charges a $200 fee plus $50 per hour to build a website. Which equation represents the total cost, y, to a customer based on the number of hours, x, it takes to buld the website? A. y = 50x − 200 B. y = 250x C. y = 200x + 50 D. y = 50x + 200
D. y = 50x + 200 is your answer
Which angles shown in the drawing are supplementary
Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = hours.
Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:
1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes
Then add the time the bus traveled:
4 hours 9 minutes + 20 minutes = 4 hours 29 minutes
Answer:
4 hours and 29 mins
Step-by-step explanation:
How do you solve 3/2x-4=16
[tex]\frac{3}{2}x[/tex] - 4 = 16
[tex]\frac{3}{2}x[/tex] = 20 added 4 to both sides
3x = 40 multiplied both sides by 2
x = [tex]\frac{40}{3}[/tex] divided both sides by 3
Answer: x = [tex]\frac{40}{3}[/tex]
(k+1)(5k+1) I need to find the product
the answer is 5k^2+6k+1
What is the value of x?
Enter your answer in the box.
x =
Keep in mind both of these angles are equal to each other meaning the equation will have a = So...
4x+7=5(x-4)
Now multiply 5 to x and 4
4x+7=5x-20
Now subtract 4x from 5x
7=1x-20
Now add 20 to both sides
27=x
So x=27
Holly bought blank CD's and spent $34.57.What is that amount rounded to the nearest dollar?.
Answer:
$35
Step-by-step explanation:
Rounding to the nearest dollar which would be 4 so in that case you would use the 5 in .57 and because 5 is a large number it would make the 4 into a five thus making it $35. Hope this helped :)
Myra is evaluating the expression –31.7 + 4.5x, when x = 2.1.
–31.7 + 4.5(2.1)
–27.2(2.1)
–57.12
What was Myra’s error?
Myra should have multiplied -31.7 and 2.1 first.
Myra should have multiplied 4.5 and 2.1 first.
Myra should have subtracted -27.2 and 2.1 first.
Myra should have added -31.7 and 2.1 first.
–31.7 + 4.5x, when x = 2.1.
-31.7 + 4.5(2.1)
-31.7 + 9.45
Myra should have multiplied 4.5 and 2.1 first.
Answer:
B.Myra should have multiplied 4.5 and 2.1 first.
Step-by-step explanation:
We are given that Myra is evaluating the expression
-31.7+4.5 x when x=21.
We have to find the error in Myra's calculation
When x=2.1
-31.7+4.5(2.1)
-31.7+9.45
=-22.25
By using DMAS rule
D=Divide
M=Multiply
A=Addition
S=Subtraction
But Myra first add -3.7 to 4.5 then multiply
Hence, Myra should have multiplied 4.5 and 2.1 first instead of add.
Answer:B.Myra should have multiplied 4.5 and 2.1 first.
The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression.
The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.
The expression shown is an exponential expression. An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does. A represents the initial value, in this case-the initial number of bacteria. B represents the growth rate. When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion. In this case, a=57, and b=0.31.
Hope this makes sense!
There are 21 groups of 3 in a room. How many people are there. I need an equation
Julio cubes a number and then takes the cube root of the result.He ends up with 20.What number did julio start with
Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.
If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.
What is the value of f(3) when f(x) = 4x + 1
Here is the equation:
[tex]f(x)=4x+1[/tex]
You need to find f(3). To do that, substitute all the x's with 3:
[tex]f(x)=4x+1 \rightarrow f(3)=4\times3 + 1[/tex]
The first thing you need to do is multiply 4 by 3. Multiply:
[tex]4 \times 3 = 12[/tex]
Here is your new equation:
[tex]f(3)=12+1[/tex]
To get your answer, you need to add 12 and 1. Add:
[tex]12+1 = 13[/tex]
That means:
[tex]\bf f(3)=13[/tex]
If you have any questions, feel free to ask in the comments! :)
F(x)= 4x+1
To find f(3) you substitute it into x.
F(3)= 4(3)+1
F(3)=12+1
F(3)=13
you are biking at a speed of 18 miles per hour you are 3 miles behind your friends who is biking at a speed of 12 miles per hour how amount of time it catch up to your friend
Find the x-coordinate where the graph of the function f(x) = e(–sinx) has a slope of 0
pie
pie/4
pie/2
none of these
[tex]y = e^{-sin(x)}[/tex]
[tex]y' = -e^{-sin(x)}(cos(x))[/tex]
[tex]0 = -e^{-sin(x)}(cos(x))[/tex]
When is cos (x) = 0? at 90° (aka π/2)
Answer: [tex]\frac{\pi}{2}[/tex]
Answer: Hello there!
We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.
This is equivalent to see when f'(x) = 0
where f'(x) is the derivative of f(x)
Then the first step is derivate the function f(x)
if we have a function of the form g(h(x)), his derivate is:
g'(h(x))*h'(x)
In our case, g(x) = exp(x) and h(x) = - sin(x)
then f'(x) = exp(-sin(x))*(-cos(x))
Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.
cos(90°) = 0, and 90° is equivalent to pi/2
Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0
this means that the function f(x) has a slope of 0 in the point x = pi/2
What is the y-intercept of 6x+ 12y= 60?
A. 5
B. 10
C .60
What is the slope of the line that contains the points (1, −1) and (−2, 8)?
A. −3
B. 7 over 3 negative
C. 1 over 3 negative
Which two units of measure below are longer than a meter?
centimeter
kilometer
millimeter
heptometer
K is the midpoint of segment HL . H has coordinates (1, -7 ) , and K has coordinates(-9, 3 ). Find the coordinates of other end point L.
The coordinates of the other endpoint L are (-19, 13).
If K is the midpoint of segment HL, we can use the midpoint formula to find the coordinates of point L.
The midpoint formula states that if you have the coordinates of two endpoints of a line segment and the coordinates of the midpoint, you can find the missing endpoint.
Let's denote the coordinates of point L as (x, y).
The midpoint formula is:
Midpoint =[tex]\(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\)[/tex]
Given:
Coordinates of K = (-9, 3)
Coordinates of H = (1, -7)
Let (x, y) be the coordinates of point L.
Using the midpoint formula for x-coordinates:
[tex]\(\frac{{1 + x}}{2} = -9\)[/tex]
Solving for x:
[tex]\(1 + x = -18\)[/tex]
[tex]\(x = -19\)[/tex]
Using the midpoint formula for y-coordinates:
[tex]\(\frac{{-7 + y}}{2} = 3\)[/tex]
Solving for y:
[tex]\(-7 + y = 6\)[/tex]
[tex]\(y = 13\)[/tex]
Therefore, the coordinates of the other endpoint L are (-19, 13).
Given f(x) = ax – b, what is f-1(x)?
A) x+b/a
B) 1/ax-b
C) 1/ax+b
ANSWER
The correct answer is A
[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]
EXPLANATION
Given [tex]f(x)=ax-b[/tex].
We can find the inverse by taking the steps.
1. Let [tex]y=ax-b[/tex]
2. Interchange x and y
[tex]x=ay-b[/tex]
3. Make y the subject
[tex]x+b=ay[/tex]
[tex]\frac{x+b}{a}=y[/tex]
The new function we got now is the inverse of f(x)
[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]
x + b/a Replace f(x) with y, interchange x and y and solve for y.
What is the equation and the solution to 136 divided by 3
How can u solve this by graphing ?
*(Answer)*= (2,1)
*(Information)*= There is an attachment of the graph
Write a variable expressi on for *10 divided by the sum of y and 4
Answer:
x = 10 / (y + 4)
Step-by-step explanation:
Erin has $45,688 in sales. If her commission rate Is 2.9% , what is the amount of her commission?
Answer:
The amount of her commission is $1,324.952
Step-by-step explanation:
1. You have the following information given in the problem above:
- Erin has $45,688 in sales.
- Erin's commission rate is 2.9% (0.029).
2. Therefore, to solve this exercise you must multiply the commission rate by her sales, as following:
[tex](45,688)(0.029)=1,324.952[/tex] dollars