Write an equation of the line that passes through the pair of points (5, 8) and
(9, 16).
Answers
Answer:
D: y = 2x - 2
Step-by-step explanation:
1. [tex]\frac{16-8}{9-5}[/tex] = 2
2. y = 2x + b
3. Insert the points into the equation: 8 = 10 + b
4. b = -2
5. y = 2x - 2
=======================================================
Explanation:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (16-8)/(9-5)
m = 8/4
m = 2
Then use this slope, along with another point such as (x,y) = (5,8) to find b
y = mx+b
8 = 2*5+b
8 = 10+b
8-10 = b
-2 = b
b = -2
Or you could use the other point (x,y) = (9,16)
y = mx+b
16 = 2*9+b
16 = 18+b
16-18 = b
-2 = b
b = -2
Either way, we get the same y intercept.
So because m = 2 is the slope and b = -2 is the y intercept, we go from y = mx+b to y = 2x-2
-------------------
To help verify the answer, note how plugging x = 5 leads us to...
y = 2x-2
y = 2*5 - 2
y = 10-2
y = 8
So x = 5 and y = 8 pair up together. This verifies (5,8) is on the line.
Through similar steps, you should find that the input x = 9 leads to the output y = 16. So that would confirm (9,16) is also on the line, and fully confirm the answer.
Related Questions
Find the area of a triangle as a mixed number.
Answers
Answer:
I believe the answer is 4 37/50!
Please show work. The way that you solve for surface area and vol confuse me.
Answers
Answer:
search up the formula
Step-by-step explanation:
In the data set shown below, what is the value of the quartiles?
{4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
A. Q1 = 4.6; Q2 = 5.5; Q3 = 5.95
B. Q1 = 4.7; Q2 = 5.5; Q3 = 6
C. Q1 = 4.7; Q2 = 5.5; Q3 = 5.9
D. Q1 = 4.6; Q2 = 5.5; Q3 = 5.92
Answers
Answer:
A. Q1 = 4.6; Q2 = 5.5; Q3 = 5.95
Step-by-step explanation:
{4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
First find the median or the 2nd quartile
There are 9 data points so the middle is the 5th
4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
Q2 = 5.5
Now looking at the data on the left, we need to find the middle, which is Q1 or the first quartile
4.3, 4.5 , 4.7, 5,
It is between 4.5 and 4.7 so we average
(4.5+4.7)/2 = 9.2/2 = 4.6
Q1 is 4.6
We do the same for the data on the right, which is the third quartile or Q3
5.7, 5.9, 6, 6.1
(5.9+6)/2 = 11.9/2 = 5.95
Q3 = 5.95
Answer: IT'S A !!
Step-by-step explanation:
Which expression describes this graph?
A. x -5
B. x -5
C. x < -5
D. x > -5
Answers
Answer:
C
Step-by-step explanation:
The equation that described the graph is x<-5
Question 6 a-c if plz show ALL STEPS like LITERALLY EVERYTHING
Answers
9514 1404 393
Answer:
a) quadrant III
b) 4π/3, -2π/3
c) (1/2, (√3)/2)
d) ((√3)/2, -1/2
Step-by-step explanation:
a) The attachment shows the point P and the numbering of the quadrants (in Roman numerals). Point P lies in quadrant III.
__
b) Measured counterclockwise, the angle to point P is 240° or 4π/3 radians. Measured clockwise, the angle is -120° or -2π/3 radians. In the diagram, these are shown in green and purple, respectively.
__
c) Adding π/2 to the angle 4π/3 or -2π/3 brings it to 11π/6, or -π/6. This point is marked as P' (blue) on the diagram. The coordinate transformation for π/2 radians CCW rotation is ...
(x, y) ⇒ (-y, x)
P(-1/2, -√3/2) ⇒ P'(√3/2, -1/2)
In terms of trig functions, the coordinates of the rotated point are ...
P'(cos(-π/6), sin(-π/6)) = P'(√3/2, -1/2)
__
d) Adding or subtracting π radians to/from the angle moves it directly opposite the origin. Both coordinates change sign. This point is P'' (red) on the diagram.
Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.
Answers
Answer:
A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Step-by-step explanation:
Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.
Bod and coa are _____ angles
Answers
Answer:
opposite angles
Step-by-step explanation:
They are formed in the intersection of lines AD and BD.
Answer:
opposite angles
Step-by-step explanation:
they are formed in the intersection of lines AD and BD. two figures are called similar if they have same shape however have different size.
Someone please help me with this
Answers
Answer:
Step-by-step explanation:
Năm báo cáo:
- Tồn cuối năm: trong kho: 800 sp; gửi bán: 1200sp
- Số lượng sản xuất: 10.000 sp
- Giá bán: 100.000 đồng/sp
Năm kế hoạch:
- Dự kiến số lượng sản xuất tăng 10%
- Tồn cuối năm: tăng 10% so với năm báo cáo
- Giá bán: 95.000 đồng/sp
- Giá vốn 1 sp: 79.500 đồng (tăng 6% so với năm báo cáo)
Yêu cầu:
1/ Tính doanh thu năm kế hoạch
2/ Tính giá vốn hàng bán năm kế hoạch (FIFO)
Answers
Answer:
THE ANSWER IS
What is the mean of the following list of extra credit points earned on a statistics test?
10,8,18,17,7
Answers
Answer:
12
Step-by-step explanation:
Given the data :
X : 10,8,18,17,7
The mean value of scores obtained can be obtained thus :
Mean = ΣX / n
n = sample size = 5
Mean = ΣX / n = (10+8+18+17+7) / 5
Mean = 60 / 5 = 12
i need help ON THIS PLS
Answers
Answer:
No, because the ratio of pay to hours is not the same for each pair of value.
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
Answers
9514 1404 393
Answer:
Tn = -4n² +40n +36
Step-by-step explanation:
A graphing calculator readily performs the quadratic regression, yielding the formula ...
Tn = -4n² +40n +36
__
The first and second differences of the given sequence terms are ...
28, 20, 12 and -8, -8
The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:
-4, -16, -36, -64
Subtracting these values from the original sequence gives the linear sequence ...
76, 116, 156, 196
which has first term 76 and common difference 40. The equation for the n-th term of this is ...
an = 76 +40(n -1) = 36 +40n
Adding this linear sequence to the sequence of squared terms, we get ...
Tn = -4n² +40n +36
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
Answers
9514 1404 393
Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answers
Answer:
280.8997
Step-by-step explanation:
cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15
= 280.8997
Total surface area of prism is 280.890cm²
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.
The term "surface area" is sometimes used to refer to "total surface area".
Find the sector angle in radians
α = 25× (π/180)
α = (25π)/(180) rad
Find the area of the prism:
A = 2×15×5 + 15×15×α + 5×15×α
A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)
A = 280.890cm²
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Which expression is equivalent to
-32 3/5
-8
-3/325
3/325
1/8
Answers
Answer:
[tex]-32^\frac{3}{5} = -8[/tex]
Step-by-step explanation:
Given
[tex]-32^\frac{3}{5}[/tex]
Required
The equivalent expression
We have:
[tex]-32^\frac{3}{5}[/tex]
Rewrite as:
[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]
Expand
[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]
Remove bracket
[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]
[tex]-32^\frac{3}{5} = -2^3[/tex]
[tex]-32^\frac{3}{5} = -8[/tex]
find the missing side length in the image below
Answers
Answer:
3/6=?/10
Step-by-step explanation:
multiply by together. ?=5
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answers
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
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A sports centre has a seating capacity of 600. Seventy-five percent of the seats are occupied. How many seats are unoccupied?
Answers
Answer:
150 are unoccupied
Step-by-step explanation:
If 75% are occupied, then 100% -75% = 25% are unoccupied
600 *25%
600 *.25
150
150 are unoccupied
Answer:
150
Step-by-step explanation:
100% - 75% = 25%
25% of seats unoccupied
hence,
number of seats unoccupied = 25/100 * 600 = 150
The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry? A. x = 0 B. x = 2 C. x = 6 D. x = -2
Answers
9514 1404 393
Answer:
B. x = 2
Step-by-step explanation:
The graph is symmetrical about the vertical line through its vertex. The x-value of that vertex is 2, so the line of symmetry is ...
x = 2
find all the missing measurement
Answers
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
In this diagram,which equation could prove to be true in order to conclude that the lines are parallel?
Answers
Answer:
b/a = c/d (first option)
Step-by-step explanation:
Two lines:
f(x) = a*x +b
g(x) = m*x + s
are parallel if m = a, and s ≠ b.
So the lines must have the same slope and different y-intercept.
For the graphed lines is obvious that the y-intercepts are different, so let's look at the slopes.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
So now let's look to our lines.
The top one, passes through (-a, 0) and (0, b)
Then its slope is:
a₁ = (b - 0)/(0 - (-a)) = b/a
The bottom line passes through the points (0, -c) and (d, 0)
Then the slope will be:
m₁ = (0 - (-c))/(d - 0) = c/d
Then the lines will be only parallel if the slopes are equal, which means that we must have
b/a = c/d
The correct option is the first one.
. Using the identity (a + b)² = (a² + 2ab + b²), evaluate 112²
Answers
[tex]\\ \sf\longmapsto 112^2[/tex]
[tex]\\ \sf\longmapsto (100+12)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(12)+12^2[/tex]
[tex]\\ \sf\longmapsto 10000+2400+144[/tex]
[tex]\\ \sf\longmapsto 12400+144[/tex]
[tex]\\ \sf\longmapsto 12544[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛112²
⇛(100 + 12)²
⇛(100)² + 2 × 100 × 12 + (12)²
⇛10000 + 2400 + 144
⇛12400 + 144
⇛12544
If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum
Answers
9514 1404 393
Answer:
d) 10.38%
Step-by-step explanation:
The multiplier for four quarters of quarterly compounding is ...
(1 +10%/4)^4 = 1.025^4 = 1.103812890625
This is about 1 + 10.38%.
The effective rate of interest is about 10.38% per annum.
a) Express the prime number 31 as the difference of two squares? 31 =
Answers
Answer:
31 = 16²-15²
Step-by-step explanation:
16² = 256
15² = 225
256 - 225 = 31
match the polynomial with its correct name
Answers
Answer
Attach a file for us to see the problem
Step-by-step explanation:
If P(x): x < |2x|. b) What is the value of ∃x P(x)?
Answers
Answer:
true
Step-by-step explanation:
because some of x if x=3 then 3<6 is true
01:15:51 Differential equation of the family of circles touching the y-axis at origin is
Answers
Step-by-step explanation:
Correct option is
B
x
2
−y
2
+2xy
dx
dy
=0
The system of circles touching Y axis at origin will have centres on X axis. Let (a,0) be the centre of a circle. Then the radius of the circle should be a units, since the circle should touch Y axis at origin.
Equation of a circle with centre at (a,0) and radius a
(x─a)²+(y─0)²=a²
That is,
x²+y²─2ax=0 ─────► (1)
The above equation represents the family of circles touching Y axis at origin. Here 'a' is an arbitrary constant.
In order to find the differential equation of system of circles touching Y axis at origin, eliminate the the arbitrary constant from equation(1)
Differentiating equation(1) with respect to x,
2x+2ydy/dx─2a=0
or
2a=2(x+ydy/dx)
Replacing '2a' of equation(1) with the above expression, you get
x²+y²─2(x+ydy/dx)(x)=0
That is,
─x²+y²─2xydy/dx=0
or
x²─y²+2xydy/dx=0
Express as index form
log 2 64 = 6
Answers
Answer:
hsv s deutsche ki bhar ke dekhte hai mera gham na
Simplify this expression.
6 + 8 ÷ 2
3
7
10
12
Answers
Explanation:
Using PEMDAS, subtract first, then add the quotient.
6+(8/2)
6+4
10
A cyclist rides her bike at a speed of 30 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 2
minutes? Do not round your answers,
Answers
Step-by-step explanation:
The answer is mentioned above.
