Answers
The missing co-ordinate r = 8
(6,9) and (r,-1) are two points on a line whose slope is given as -5.
Slope of a line is the change of y co-ordinates divided by the change in x co-ordinates between two points on a line.
Take (x₁, y₁) = (6,9) and (x₂, y₂) = (r, -1).
The slope of a line is given by,
Slope, m = (y₂-y₁)/ (x₂-x₁)
⇒ -5 = (-1-9)/(r-6)
⇒ -5 = -10/(r-6)
⇒ 1 = 2/(r-6)
⇒ r-6 = 2
⇒ r = 2+6
⇒ r = 8
So the points are (6,9) and (8,-1).
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Related Questions
Please Help me turn vertex form to standard form!!
Answers
Answer:
See below
Step-by-step explanation:
y = -(x-1)^2 +4 Expand R side
y = - ( x^2 -2x+1) + 4
y = -x^2 +2x -1 + 4
y = -x^2 + 2x + 3 a = -1 b = 2 c = 3
A Curve has the equation y=kx^2 +1 And a line has the equation y=kx where
K is a
non-zero
Constant
1)Find the Set
the value of k
for which the
curve and line have no common point.
(1) state the value for which the line is a
tangent to the Curve and for this case, find the coordinates
of the point where the line
touches the curves
Answers
The set of the value for which the curve and line have no common point are is k ∈ (0 , 4).
The value for which the line is a tangent is k = 4.
The coordinates of the point where the line touches the curves is point of tangency = ( 1/2 , 2).
What is tangent?
Tangents in geometry are lines or planes that contact curves or surfaces at points where they are closer to the curve than any other lines or planes drawn through those points.
Given equations in the question:
y = kx² + 1
y = kx
Equating y
kx² + 1 = kx
kx² -kx + 1 = 0
This is Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
D = b²-4ac is called discriminant.
and we know that,
D >0 roots are real and distinct
D =0 roots are real and equal
D < 0 roots are imaginary ( not real ) and different
For no common solution D < 0
For tangent D = 0
so,
kx² -kx + 1 = 0
D = (-k)² - 4k = k² - 4k = k(k - 4)
k(k - 4) < 0
if 0 < k < 4
Hence values of k for which the curve and the line have no common points is k ∈ (0 , 4).
for tangent
k(k - 4) = 0
k is non zero
Hence k = 4
After putting the value of k, given equations are:
y = 4x² + 1
y = 4x
solving these equations to get value of x and y:
4x² + 1 = 4x
4x² - 4x + 1 = 0
(2x - 1)² = 0
x = 1/2
y = 2
Point of tangency = ( 1/2 , 2)
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A figure is rotated 270 degrees counterclockwise about the origin. Then the image is rotated 90 degrees counterclockwise about the origin. Complete the coordinate notation that represents the series of rotations. What can you conclude about the position of the figure after the series of rotations?
If you don't mind, I need the answer ASAP
Answers
The series of rotations are : (x, y) -----> (y, -x) → (y, -x) ----> (x, y).
The total rotation is 360 degrees. So the figure is the original figure itself.
First a figure is rotated 270 degrees counterclockwise about the origin.
A 270 degree counterclockwise rotation is given by the co-ordinate transformation, (x, y) -----> (y, -x)
Then the figure is again rotated 90 degrees counterclockwise about the origin. A 90 degree counterclockwise rotation is given by, (x, y) -----> (-y, x)
So combining with the above transformation, the 90 degree counterclockwise rotation gives, (y, -x) ----> (x, y).
Thus the total rotation transformation is in turn, (x, y) ----> (x, y).
Thus the total rotation in counterclockwise direction about the origin is 360 degrees. So the final figure is the original figure itself.
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PLEASE HELP. Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. 1. Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work. 2. Describe how you would graph this line using the slope-intercept method. Be sure to show all your work. 3. Write the equation in function notation. Explain what the graph of the function represents. Be sure to show all your work. 4. Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology. 5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answers
They are similar because they have the same slope the equation is
y = -2/3x + 531
What is in slope-intercept form?
Given a line's slope and the intercept it makes with the y-axis, one of the mathematical forms used to determine a straight line's equation is called the slope intercept form. The slope intercept form is expressed as y = mx + b, where m is the slope of the straight line and b is the y-intercept.changing 2x+3y=1470 to slope intercept form is solving for y
minus 2x both sides and divide by 3
y = -2/3x + 490
the slope is -2/3
the y intercept is y=490 or the point (0,490)
to graph it, I would start at the origin and go up 490 units on the y axis and put a point there
then go -2 units up (2 down) and 3 to the right and put a point there
then connect the 2 points with a line
in function notation, replace y with f(x) to get
y = -2/3x + 490
graph below
intercepts labeled
2x+3y=1593
they are similar because they have the same slope
the equation is y = -2/3x + 531
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Can I have some help with the question in the attachment. I've done (a) but I think I'm doing (b) wrong
Answers
Answer:
8.33
Step-by-step explanation:
He has to be at work by 10:30, but it takes 20 mins to walk
So, 10:30-20 minutes=10:10
We then look at the arrival time closest to this, which would mean he would arrive at 10.06.
trace this back the bus would gett him at 8:38, but its a 5min walk.
8:38-5 minutes+8.33
hope this helps :)
Miranda did a survey of what time people
get to their office on Monday morning.
The table shows her results for
150 people.
Time
before 7 am
7am to 7:59 am
8am to 8:59 am
9am to 9:59 am
No of people
15
39
75
21
a) What percentage of the people surveyed arrive at their office before 7 am?
Optional working
+
Answer:
b) What percentage of the people surveyed arrive at their office after 7:59 am?
Optional working
Answer:
%
Answers
The percentage of the people surveyed that arrive at their office after 7am is 6.7%.
The percentage of the people surveyed that arrive at their office after 7:59 am is 64%
How to calculate the percentage?From the information, Miranda did a survey of what time people get to their office on Monday morning and the table shows her results.
The number of people that arrived before 7.59am is 15.
The total number of people surveyed will be:
= 15 + 39 + 75 + 21
= 150
The percentage of the people surveyed arrive at their office before 7 am will be:
= 10 / 150
= 6.7%
The percentage of the people surveyed that arrive at their office after 7:59 am will be:
= (75 + 21) / 150.
= 96/150
= 0.64
= 64%
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Answer:
the number of people is 15 so you would do 15/150=10percent
b) 66 percent
Step-by-step explanation:
Simple Interest Round answers to the nearest cent. 1. John is going to invest $100 in an account for 3 years. If the account earns 6% simple interest, how much interest can he expect to earn?
Answers
Given Data:
The initial investment is: P=$100
The total period of investment is: t=3
The annual interest is: 6%.
For the simple interest, the expression to calculate the interest in t years is,
[tex]I=(P\times\frac{r}{100})\times t[/tex]Here r is in percentage.
Substitute known values in the above expression.
[tex]\begin{gathered} I=(100\times\frac{6}{100})\times3 \\ =(6)\times3 \\ =18 \end{gathered}[/tex]Thus, the total intrest for 3 years will be $18.
I need help................
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (1, 7) ← 2 points on the line
m = [tex]\frac{7-1}{1-(-2)}[/tex] = [tex]\frac{6}{1+2}[/tex] = [tex]\frac{6}{3}[/tex] = 2
use either of the 2 points on the line
using (- 2, 1 ) , then
y - 1 = 2(x - (- 2) ) , that is
y - 1 = 2(x + 2) ← equation in point- slope form
An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin
Answers
The percentage 20% of the costs y is given as 0.20y thus the expression which represents the price of the item after the discount is P = y - 0.20y.
What is the percentage?The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.
It is known that x% of something y is given as,
x% of y = (x/100)y
Given that discount of 20% of y
20% of y = (20/100)y
20% of y = 0.20y
Now the final price = initial price - discount
Final price (P) = y - 0.20y
Hence"The percentage 20% of the costs y is given as 0.20y thus the expression which represents the price of the item after the discount is P = y - 0.20y".
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12
Find the horizontal asymptote of f of x equals quantity negative 2 x squared plus 3x plus 5 end quantity over quantity x squared plus 1. (5 points)
y = −2
y = −1
y = 1
y = 2
Answers
The horizontal asymptote is y = -2
The horizontal asymptote is an equation of the form y = k, for some constant k, is a straight line parallel to x-axis.
Horizontal asymptotes are found for rational functions of polynomials when x becomes extremely large, or, as x → ∞.
The function given is, f(x) = (-2x²+3x+5)/(x²+1)
Horizontal asymptote is given by,
y = [tex]\lim_{x \to \infty} \frac{-2x^2+3x+5}{x^2+1}[/tex]
= [tex]\lim_{x \to \infty} \frac{x^2(-2+\frac{3}{x} +\frac{5}{x^2}) }{x^2(1+\frac{1}{x^2}) }[/tex]
= [tex]\lim_{x \to \infty} \frac{(-2+\frac{3}{x} +\frac{5}{x^2}) }{(1+\frac{1}{x^2}) }[/tex]
= -2
So the horizontal asymptote of f(x) is, y = -2
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Answer:
A) y = -2
Step-by-step explanation:
The rules to find the horizontal asymptote (HA) is shown below
Y = A if the numerator and denominator have same highest exponent for example
A^3
B^3
Y = 0 if the numerator have lower exponent and denominator have higher exponent for example
A^1
B^2
None HA if the numerator have higher exponent and denominator have lower exponent for example
A^2
B^1
And the equation shown in the question have same exponent so the answer is -2
PS: please give me brainiest
need someone to answer as soon as possible!
Please please with proof too
Answers
The solutions to the system of equations are x=5, z=1,y=-3
What is system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where each of these equations crosses, are the solutions of systems of equations.A system of equations in algebra consists of two maybe more equations and looks for common answers to the equations.Given equations:
x+y+z=3
3x+(y/3)-2z=12
-5x-6y+3z=-4
Solving by using the substitution method:
[tex]\begin{bmatrix}x+y+z=3\\ 3x+\left(\frac{y}{3}\right)-2z=12\\ -5x-6y+3z=-4\end{bmatrix}[/tex]
Substitute x=3-y-z
[tex]\begin{bmatrix}3\left(3-y-z\right)+\frac{y}{3}-2z=12\\ -5\left(3-y-z\right)-6y+3z=-4\end{bmatrix}[/tex]
Substitute z={8y+9}/{15}
[tex]\begin{bmatrix}-y+8\left(-\frac{8y+9}{15}\right)-15=-4\end{bmatrix}[/tex]
simplify
[tex]\begin{bmatrix}\frac{-79y-72}{15}-15=-4\end{bmatrix}[/tex]
Substitute y=-3
[tex]z=-\frac{8\left(-3\right)+9}{15}[/tex]
z=1
For x=3-y-z
Substitute z=1,y=-3
x=3-(-3)-1
x=5
The solutions to the system of equations are:
x=5, z=1,y=-3
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Solve for s.
19.1 = s − –7.3
s =
Answers
Make sure when you have negatives, most of the time you add parentheses. An example is (-5).
graph this function f(x) = 1/4(x) - 7
Answers
Answer:
This is your graph to the following equation f(x) = 1/4(x) - 7
A perfect score on a test with 25 questions is 100. Each question is worth 4 points. Fred got a score of 68 on the test to write a division sentence using negative numbers where the quotient represents the number of questions Fred answered incorrectly
Answers
The total number of questions that Fred answered incorrectly is 8.
How to express the information?From the information given, a perfect score on a test with 25 questions is 100 and each question is worth 4 points while Fred got a score of 68 on the test.
Therefore, let the number of questions that are got be x.
Based on the information given, this will be:
4 × x = 68
4x = 68
Divide
x = 68 / 4 = 17
The number of questions that he missed will be:
= Total questions - Correct answers.
= 25 - 17.
= 8
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The concession stand are the football games are 288 customers. Those customers, about 77% bought a hot dog. About how many customers buy a hotdog?
Answers
288/100%= 288
2.88x77%= 221
Is a number closer to 0 greater or less than a number more away from 0? (negatives and positives)
Answers
Answer:
A number closer to 0 is generally less than a number more away from 0. When it comes to negative numbers the closer the number to 0, the greater it is.
Step-by-step explanation:
If you need further help please let me know.
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The length of a base of a rectangular prism is 12 dm and the width is 5 dm. What should be the height of the rectangular prism be so that it's volume is smaller than the volume of a cube with a side of 9 dm? (for 30 points) will give you brainlyiest or smthing title
Answers
Answer:
Must be less than 12.15 dm
Step-by-step explanation:
A rectangle is 32ft by 8ft. Stephanie dilated the rectangle and the dimensions of the image were 24ft by 6ft. What was the scale factor used?
Answers
Answer:4
Step-by-step explanation:
image dimension = 24 by 6 feet
preimage dimension = 32 by 8 feet
so 24/6 = 32/8 = 4
scale factor = 4
Elsie is a project manager
in 2016 she earned £2100
in 2017 she was awarded a 3% increase on her monthly salary
given that in 2017 worked 42 hours a week for 45 weeks.
week out her average pay-per-hour of the year
Answers
The average pay-per-hour of the year for Elise will be 13.73 pounds.
How to calculate the average pay?From the information, in 2016 she earned £2100 and in 2017 she was awarded a 3% increase on her monthly salary.
Therefore, the new salary will be:
= 2100 + 3%(2100)
= 2100 + 63
= 2163
Now she worked for 42 hours per week for 45 weeks. This will be:
= 42 × 45
= 1890 hours
Therefore, the total earnings for the year will be:
= 2163 × 12 months
= 25956
The average pay-per-hour of the year will be:
= Total amount / Number of hours
= £25956 / 1890
= £13.73
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Given f(x) = x3 – 2x2 – x + 2, the roots of f(x) are ✔ –1, 1, 2 . Determine the end behavior of f(x).
Answers
Answer:
1, -1 and 2
Step-by-step explanation:
The zeros of the given polynomial function are 1, -1 and 2
Given the polynomial function
First, we need to assume a value of x to check if it will give us zero after substituting:
Assuming x = 1
Since f(1) =0, hence x - 1 is a factor
Dividing x - 1 by the given polynomial function, we will have:
Equating the result to zero
x + 1 = 0 and x - 2 = 0
x = -1 and 2
Hence the zeros of the given polynomial function are 1, -1 and 2
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What number is 40% of 120?
Answers
Answer: 48
Step-by-step explanation:
Convert 40% to a decimal = 0.4
Multiply 0.4 x 120 = 48
Answer:
48
Step-by-step explanation:
40\100×120
=48
( fourth divided by one hundred multiplied by one hundred and twenty is equal to 48)
-3x+7=-x-1
Simplify and solve for the variable
Answers
+3x +3x
7=2x-1
+1 +1
8=2x
8/2
X=4
A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?
Answers
The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
The amount of water initially in the trough = 25 gallons.
The rate of adding water = 11 gallons per minute
Therefore, the total amount (A) of water in x minutes will be,
A = 25 + 11x
The number of minutes to have 80 gallons of water is,
80 = 25 + 11x
11x = 55
x = 5 minutes.
Hence "The equation which is useful to find the amount in gallons of water to the number of minutes since filling started is 25 + 11x therefore, it takes 5 minutes to have 80 gallons of water".
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How do you proof that sqrt(2) is irrational?
I tried this,
p/q = sqrt(2)
p^2/q^2=2
p^2=2q^2
let p = q * sqrt(2) , (equation from top one)
(q*sqrt(2))^2=2q^2
2q^2=2q^2,
q=q
Is anything wrong or does this also prove that sqrt(2) is irrational, if so how?
Answers
Assume √2 is rational, so
√2 = p/q
for some relatively prime integers p,q - meaning we can't reduce p/q any further - and q ≠ 0.
Then
p = √2 q
and squaring both sides gives
p² = 2q²
This tells us that p² is even, so 2 divides p². But if 2 divides p², it must also divide p, since p is a square number. So p = 2r for some integer r, and we have
(2r)² = 2q²
4r² = 2q²
2r² = q²
We're in the same situation as before - 2 divides q², so 2 divides q. Both p and q are thus divisible by 2, but this contradicts our assumption that p and q are relatively prime, which means √2 cannot be expressed as a rational number p/q. Therefore √2 is irrational.
What you've written in your proof is technically correct, but it doesn't help in the irrationality proof.
The points (5, r) and (10, -1) lie on a line with slope 5. Find the missing coordinate r
Answers
Answer: r=-26
Step-by-step explanation:
[tex]\displaystyle\\(5,r)\ \ \ \ (10,1)\ \ \ \ slope \ m=5\\\\\boxed {m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=5\ \ \ \ \ x_2=10\ \ \ \ \ y_1=r\ \ \ \ y_2=-1\ \ \ \ \ m=5\\\\Hence,\\\\5=\frac{-1-r}{10-5} \\\\5=\frac{-1-r}{5}[/tex]
Multiply both parts of the equation by 5:
[tex]5(5)=-1-r\\\\25=-1-r\\\\25+r=-1-r+r\\\\25+r=-1\\\\25+r-25=-1-25\\\\r=-26[/tex]
I need help with this question please
Answers
Answer:
x=-4.5 x=-0.5
y=-1
vertex=-2
How is 9.746 x 10 ^13 written in standard form?
0000000000009746
97,460,000,000,000
9.746000000000000
9,746,000,000,000,000
Answers
hope this helps!! <33
MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO
Answers
The percentage of students that use other means to travel school is 24%
What is method for finding percentage?Percentage is the ratio of the number for which you want to find percentage to the total number with which you want to compare or out of and multiply this ratio with 100.
percentage = (part / whole) ×100
Given that a school has 825 total students.
Percentage of students travelling by car = 20%
Percentage of students travelling by bus = 48%
Percentage of students travelling by bicycle = 8%
Number of students travelling by car = 20% of 825 = (20/100)×825 = 165
Number of students travelling by bus = 48% of 825
= (48/100)×825 = 396
Number of students travelling by bus = 8% of 825 = (8/100)×825 = 66
Number of students travelling by other means = 825-165-396-66 = 198
Therefore, the Percentage of students travelling by other means = (198/825) ×100 = 24%
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The measure of an angle is 78.3°. What is the measure of its complementary angle?
Answers
The complementary angle of the angle is 11.7 degrees
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the complementary angle?The measure of the angle is given as
Angle = 78.3 degrees
Complementary angles add up to 90 degrees
So, we have the other angle to be
Other angle = 90 - 78.3
Evaluate the difference
Other angle = 11.7
Hence, the other angle is 11.7
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Write the fraction 622/1000 in its simplest form
Answers
Answer:
311/55
Step-by-step explanation:
i devided each by 2 and got this then i looked it up and it said this so id k
hope this helped