Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
Oy-5= {(x-1)
Oy- z = 5(x-1)
O y-1 = {(x+5)
O y-1= 5(x-1)
Answers
Answer:
C
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
here m = [tex]\frac{1}{2}[/tex] and (a, b) = (5, 1), so
y - 1 = [tex]\frac{1}{2}[/tex](x - 5)
The equation that represents a line that passes through (5, 1) and has a slope of 1/2 is; C: y - 1 = ¹/₂(x - 5)
What is the Equation of the Line?The formula for equation of a line in point- slope form is expressed as;
y - b = m(x - a)
where;
m is the slope of line
(a, b) is a coordinate point on the line
In this question, we are given;
m = 1/2 and (a, b) = (5, 1)
Thus equation of the line is;
y - 1 = ¹/₂(x - 5)
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Related Questions
(100 Points)last one i promise lol
Answers
Answer:
40.35
Step-by-step explanation:
First find the discount
97 * 60%
97 *.6 = 58.2
Subtract the discount to find the new price
97-58.20 =38.80
Next find the tax
38.80 * 4%
38.80 * .04
1.55
We add the tax to the sales price
38.8+1.55
40.35
Neil started a stamp collection with 12 stamps. Every week , he adds 4 more stamps to the collection. Which function? F represents the relationship between the number of stamps (s) and the number of weeks (w)
Answers
Answer:
[tex]s=4w+12[/tex]
Step-by-step explanation:
Let
s -----> the number of stamps
w ----> the number of weeks
we know that
The linear equation that represent this situation is
[tex]s=4w+12[/tex] ----> equation of the line into slope intercept form
where
the slope m is equal to [tex]m=4\ stamps/week[/tex]
the y-intercept b is equal to [tex]b=12\ stamps[/tex] ---> (the initial value)
which graph represents the given linear function 4x+2Y=3
Answers
Answer:
B
Step-by-step explanation:
4x + 2y = 3
(send 2y to the right and 3 to the left)
4x - 3 = -2y
(divide everything by -2)
(4x)/(-2) - 3/(-2) = y
So now we have a function which is like
y = ax + c
c = the y value of intersection point of the equation and the y-axis
a = amount of increase in y values per x value
so in this example:
(4x/(-2)) = (4/(-2))x -> a = 4/(-2) = -2
and
c = -3/-2 = 3/2
So the graph that we're searching for is increasing (-2) y values (so decreasing 2 y values) per 1 x value and has an intersection with the y-axis where y = 3/2
What type of data is best represented by a bar graph?
A. Data that are compared using bars
B. Parts of a total amount
C. Each response shown by an X or a dot
D. Change in data over time
Answers
A bar graph is most suitable for comparing data across different categories or groups, as each bar corresponds to a particular group and the height or length of the bar shows the quantity of data for that group.
Explanation:The type of data that is best represented by a bar graph is generally data that is being compared across different categories or groups, which corresponds to option A. This is because each bar in a bar graph represents a particular group or category, and the height or length of the bar corresponds to the quantity of data for that group. For example, if you conducted a survey to find out the favorite fruit of students in a class and the choices were apples, bananas, oranges, and grapes, a bar graph would be a suitable way to present this categorical data.
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Determine 8th term in the
geometric sequence whose first
term is -10 and whose common
ratio is 2.
Answers
Answer:
- 1280
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
here a₁ = - 10 and r = 2, hence
[tex]a_{8}[/tex] = - 10 × [tex]2^{7}[/tex] = - 10 × 128 = - 1280
What is the percent of change from 35 to 62? round to the nearest percent.
Answers
In order to change from 35 to 62, we have to add 27. So, the question becomes: which percentage of 35 is 27?
To answer this question, we set this simple equation
[tex]27 = 35\cdot\dfrac{x}{100}[/tex]
And solving for x we have
[tex]x = \dfrac{2700}{35} \approx 77.14[/tex]
So, if you change from 35 to 62, you have an increase of about 77%
The percentage change is 77.14%
The following information can be gotten from the question:
Old number = 35
New number = 62
Increase in number = 62 - 35 = 27
Percentage change will be:
= (Increase in number / Old number) × 100
= 27/35 × 100
= 2700/35
= 77.14%
In conclusion, the percentage change is 77.14%
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Which data sets have outliers? Check all that apply.
14, 21, 24, 25, 27, 32, 35
15, 30, 35, 41, 44, 50, 78
16, 32, 38, 39, 41, 42, 58
17, 23, 28, 31, 39, 45, 75
18, 30, 34, 38, 43, 45, 68
Answers
Answer:
the answer is c and e
Step-by-step explanation:
just took it
The datasets that have outliers are (c) 16, 32, 38, 39, 41, 42, 58, (d) 17, 23, 28, 31, 39, 45, 75 and (e) 18, 30, 34, 38, 43, 45, 68
What are data sets?Data sets are simply collections of related data elements
What are outliers?Outliers are data elements that are relatively far from other data elements in the dataset
If a value is too small or too high from other elements, then the dataset has an outlier
By the method of observation, we can conclude that the following datasets have outliers
16, 32, 38, 39, 41, 42, 5817, 23, 28, 31, 39, 45, 7518, 30, 34, 38, 43, 45, 68Hence, the datasets that have outliers are (c), (d) and (e)
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Which expression is equivalent to (2x2 + 4x - 7)(x-3)?
ОО
O A. x(2x2 + 4x - 7) - 3
O B. -3x(2x2 + 4x - 7)
O c. x/2x2 + 4x + 7) + 3(2x2 + 4x - 7)
O D. (2x2 + 4x - 7)(x) + (2x2 + 4x 7)(-3)
Answers
Answer:
D
Step-by-step explanation:
It isn't the most efficient way to solve the problem, but the other 3 are incorrect.
expression (2 x 2 + 4 x - 7)(x) + (2 x 2 + 4 x 7)(-3) is equivalent to (2 x 2 + 4 x - 7)(x-3).
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y if x is given.
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The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use? When Harold wrote his equation, the point he used was (7, 3). When Harold wrote his equation, the point he used was (0, 7). When Harold wrote his equation, the point he used was (7, 0). When Harold wrote his equation, the point he used was (3, 7).
Answers
Answer:
When Harold wrote his equation, the point he used was (7, 0) ⇒ the third answer
Step-by-step explanation:
* Lets look to the equation to find the correct answer
- He used the point-slope form is y – y1 = m(x – x1), where m is the
slope of the line , (x1 , y1) are the coordinates of the point which
the line passes through it and (x , y) are the coordinates of any
general point on the line
- Lets solve the problem
- Harold correctly wrote the equation y = 3(x – 7)
∵ y - y1 = m (x - x1)
∵ y = 3 (x - 7)
- By comparing between the two equations
∴ y1 = 0
∴ m = 3
∴ x1 = 7
- He used the point (x1 , y1)
∴ Harold used the point (7 , 0) to write the equation
∴ The answer is when Harold wrote his equation, the point he used
was (7, 0)
ANSWER
When Harold wrote his equation, the point he used was (7, 0).
EXPLANATION
The point-slope form is given as
[tex]y-y_1=m(x-x_1)[/tex]
The equation Harold wrote correctly is:
[tex]y = 3(x - 7)[/tex]
This is the same as:
[tex]y - 0= 3(x - 7)[/tex]
Comparing to point-slope form, we have
[tex]x_1=7 \: \: and \: \: y_1=0[/tex]
Hence the point is (7,0)
When Harold wrote his equation, the point he used was (7, 0).
What us the slope of the line (-7,2) and (5,8)
Answers
Final answer:
The slope of the line passing through the points (-7,2) and (5,8) is calculated using the slope formula and is found to be 0.5.
Explanation:
The student asked about the slope of the line passing through two points, (-7,2) and (5,8). To find the slope, one should use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values from the points, we have m = (8 - 2) / (5 - (-7)) = 6 / 12 = 0.5. Therefore, the slope of the line is 0.5.
x2 - 15x + 56
factor
Answers
Answer:
(x - 7)(x - 8)
Step-by-step explanation:
To factorise the quadratic
Consider the factors of the constant term (+ 56) which sum to give the coefficient of the x- term (- 15)
The factors are - 7 and - 8, since
- 7 × - 8 = + 56 and - 7 - 8 = - 15, hence
x² - 15x + 56 = (x - 7)(x - 8)
Hi! I need help with this problem.
Answers
Answer:
B 70
Step-by-step explanation:
7 |H| + 4 G
H = -6 and G = 7
| H| = 6
7*6 + 4*7
42+28
70
The weight of the paper clip is 1.0025 grams. Find the number of significant digits in the measurement
Answers
Answer: There are 5 sig figs in 1.0025
Step-by-step explanation:
With significant figures, any number other then 0 is a significant figure. The two zeros are significant because they are followed by more numbers. If the number was 1.000, there would only be one sig fig.
Hope this helps!
A camera manufacturer spends $1,800 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $18
each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50
cameras per day, what would their daily profit be?
Answers
Amount of money spent per day = $1800
Cost of overhead expenses per day for labor and materials = $9
Selling price of each camera = $18
a. Let us assume the number of cameras manufactured per day = x dollars
Then
Cost of cameras sold in 1 day = 18x
So
18x = 1800 + 9x
18x - 9x = 1800
9x = 1800
x = 200
From the above deduction, we can conclude that the number cameras sold per day is 200
b. Daily selling amount of 250 cameras = 250 * 18
= 4500 dollars
Daily manufacturing price of 250 cameras = 1800 + (9 * 250)
= 4050 dollars
Then
Daily profit = 4500 - 4050
= 450 dollars
Which relation is a function?
Mn
Answers
The top right one, because for every argument there is only one corresponding value.
prove that tan2A is equal to 2tanA/1-tan^2A
Answers
[tex]\tan(2\alpha)=\dfrac{2\tan \alpha }{1-\tan^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha}}{1-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha}{\cos^2\alpha}-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha-\sin^2 \alpha}{\cos^2\alpha}}[/tex]
[tex]\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha}{\cos\alpha} \cdot\dfrac{\cos^2\alpha}{\cos^2\alpha-\sin^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha\cos\alpha}{\cos^2\alpha-\sin^2 \alpha} \\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\sin(2\alpha)}{\cos(2\alpha)}[/tex]
Answer:
See below.
Step-by-step explanation:
tan 2A = sin 2A / cos 2A
= 2 sinA cosA / (cos^2A - sin^2A)
Now divide top and bottom of the fraction by cos^2 A:
2 sinA cosA cos^2A sin^2 A
------------------- / ----------- - -------------
cos^2A cos^2 A cos^2 A
= 2 tan A / 1 - tan^2A).
Convert this decimal into its fractional
form, simplified completely.
0.700
Answers
Hello There!
I Provided Steps In The Image Attached.
Have A Great Day!
find the equation in standard form , of the line passing through points (2,-3) and (4,2)
Answers
The form of linear equation that describes line is:
[tex]y=sx+n[/tex]
First we must calculate the slope.
[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]
Now it looks a bit more like this:
[tex]y=\dfrac{5}{2}x+n[/tex]
All we need now is to put in y and x from one point doesn't matter which. I'll pick A.
The equation now looks like this:
[tex]-3=\dfrac{5}{2}\cdot2+n[/tex]
Solve for n.
[tex]
-3=5+n \\
n=-8
[/tex]
And finally write the equation.
[tex]f(x)=\dfrac{5}{2}x-8[/tex]
Hope this helps.
r3t40
when simplified, which of the following expressions has a coefficent of -3?
A) -2m + 5m
B) 2m + 5m
C) 5m - 2m
D) -5m + 2m
Can i get an explanation too?
Answers
-5m+2m= -3m
A coefficient is the numerical value in front of the variable, in this case the letter m is the variable. All this means is no matter what the value of m is, it is always multiplied by -3 in this instance. And the variable just represents something you are using an equation to solve for its value. Hope this helps. Any questions please feel free to ask me. Thanks.
Answer: The answer is: -5m + 2m
Step-by-step explanation:
Because -5 + 2 equals -3
Hope it helps
God bless you guy!
The lines shown below are parallel.if the green line has a slope of -2,what is the slope of the red line?
Answers
Answer:
-2
Step-by-step explanation:
If the lines are parallel, the slopes are the same.
Since the green line has a slope of -2, the red line has a slope of -2
When lines are parallel, the slopes of the lines will be equal to one another.
When lines are perpendicular they have negative reciprocal slopes, and the product of their slopes will equal -1.
I need to know how to find x
Answers
First calculate the diameter of circle.
[tex]d=8+4=12[/tex]
Now we know that diameter is equal for any two points on the arc of a circle lying opposite to each other.
[tex]12=x+4[/tex]
Now just simply solve for x.
[tex]
12=x+4 \\
12-4=x+4-4 \\
\boxed{x=8} \\
[/tex]
Hope this helps.
r3t40
What is (f+g)(x)
f(x)=-x^2-3
g(x)=3x
Answers
Answer:
[tex]\large\boxed{(f+g)(x)=-x^2+3x-3}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-x^2-3\\\\g(x)=3x\\\\\text{Substitute:}\\\\(f+g)(x)=(-x^2-3)+(3x)=-x^2+3x-3[/tex]
What is the inverse of the function f(x) = 4x + 8?
h(x) = x – 2
h(x) = x + 2
h(x) = x – 2
h(x) = x + 2
Answers
To find the inverse of an equation just switch the places of the x and y, then solve for y like so...
(keep in mind that f(x) means the same thing as y)
original equation:
y = 4x + 8
switching x and y:
x = 4y + 8
x - 8 = 4y
[tex]\frac{1}{4}x[/tex] - 2 = y
Hope this helped!
~Just a girl in love with Shawn Mendes
3x+1÷9=2×-3÷8 solve the equation
Answers
Answer:
x = -35/72
Step-by-step explanation:
3x + 1/9 = 2x - 3/8
x = -3/8 - 1/9
x = -35/72
3x - y = 2
y = x - 1
When the expression x - 1 is substituted into the first equation for y, the resulting equation is
Answers
Answer:
see explanation
Step-by-step explanation:
Given
3x - y = 2
Substitute y = x - 1 into the equation
3x - (x - 1) = 2
3x - x + 1 = 2 ← simplify left side
2x + 1 = 2 ← required equation after substitution
Given.
3x - y = 2
Substitute x - 1 for variable y.
3x - x - 1 = 2 ← Resulting equation
60. George made a payment of $37.50 on a
bill of $73.94. How much did he still owe?
Answers
George still owes $36.44 after making a payment of $37.50 on his original bill of $73.94. This is calculated by subtracting the payment from the original bill amount.
Explanation:George made a payment of $37.50 on a bill of $73.94. To determine how much he still owes, we subtract the payment he made from the original bill.
Original bill: $73.94
Payment made: $37.50
To calculate the remaining balance:
Subtract the payment made from the original bill: $73.94 - $37.50.This equals $36.44.Therefore, George still owes $36.44 on his bill.
The length of a picture is 22.75 inches shorter than twice the width. If the perimeter is 116.5 inches, find the dimensions
Answers
Answer:
Step-by-step explanation:93.75
Follow below steps;
To solve for the dimensions of the picture whose length is 22.75 inches shorter than twice the width and has a perimeter of 116.5 inches, we first need to set up equations based on the given information.
Step 1: Set up the equations
Let w represent the width of the picture. Then, the length will be 2w - 22.75 inches.
Since the perimeter of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width, we can substitute the expressions for length and width to get the perimeter equation:
116.5 = 2(2w - 22.75) + 2w
Step 2: Solve for width
Expanding the perimeter equation we get:
116.5 = 4w - 45.5 + 2w
Combining like terms:
116.5 = 6w - 45.5
Adding 45.5 to both sides:
116.5 + 45.5 = 6w
162 = 6w
Divide both sides by 6 to find w:
w = 162 / 6
w = 27 inches
Step 3: Find the length
Now we calculate the length using the width (w = 27):
Length = 2w - 22.75
Length = 2(27) - 22.75
Length = 54 - 22.75
Length = 31.25 inches
So, the dimensions of the picture are a width of 27 inches and a length of 31.25 inches.
. Which points are on the graph of the function rule f(x) = 10 - 4x?
(2, -18), (0, -10), (-2,-2)
(-2, 18), (0, 10), (2, 2)
(18, -2), (10,0), (2, 2)
(-18, 2), (-10,0), (-2,-2)
Answers
Answer:
(-2, 18), (0, 10), (2, 2)
Step-by-step explanation:
All you do is plug each coordinate into the equation to confirm the authentication.
I am joyous to assist you anytime.
Answer:
(-2, 18), (0, 10), (2, 2)
Step-by-step explanation:
You're welcome ;)
What value of x is in the solution set of 9(2x + 1) < 9x – 18?
–4
–3
–2
–1
Answers
Answer:
-4Step-by-step explanation:
[tex]9(2x+1)<9x-18\qquad\text{divide both sides by 9}\\\\2x+1<x-2\qquad\text{subtract 1 from both sides}\\\\2x<x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\x<-3\\\\-4<-3[/tex]
The product of 4 and a number is 3 less than the number. what is the number?
Answers
Answer:
the number is -1
Step-by-step explanation:
Turn this into an equation. 4x = x-3
subtracting x from both sides gives
3x=-3
so x = -1
Hope this helps!