Answer:
y= -1x+7
or
y = -1x + b
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(2,5) and (4,3).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (2,5), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=2 and y1=5.
Also, let's call the second point you gave, (4,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=3.
Now, just plug the numbers into the formula for m above, like this:
m=
3 - 5
4 - 2
or...
m=
-2
2
or...
m=-1
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=-1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(2,5). When x of the line is 2, y of the line must be 5.
(4,3). When x of the line is 4, y of the line must be 3.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-1x+b. b is what we want, the -1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (2,5) and (4,3).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(2,5). y=mx+b or 5=-1 × 2+b, or solving for b: b=5-(-1)(2). b=7.
(4,3). y=mx+b or 3=-1 × 4+b, or solving for b: b=3-(-1)(4). b=7.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(2,5) and (4,3)
is
y=-1x+7
Joel purchased an engagement ring with his credit card. His card has an APR of
13.99% and he must pay at least 3% of the balance at the end of each month. If
his carry-over balance for this month is $9,026.74 and he has made no
additional purchases, what would Joel's finance charge be at the end of the
month?
Round your answer to the nearest cent.
Answer:
What is your definition of finance charge?
the interest is $105.24
3% of what he owes (the minimum) is $273.96
Step-by-step explanation:
$9,026.74
+9,026.74 * (.1399/12) = $105.2367438
($9,026.74 + $105.24)*(.03) = $273.96
Answer:
33.19
Step-by-step explanation:
$2846.89
$2846.89 * (.1399/12) = 33.189992583333333333333333333333
Finance Charge is $33.19
Function A is a linear function. Which of the following functions has the same y-intercept as Function A?
Answer:
y = -4x - 5
Step-by-step explanation:
help -------------------------
Answer:
(A) -3 ≤ x ≤ 1
Step-by-step explanation:
The given function is presented as follows;
h(x) = x² - 1
From the given function, the coefficient of the quadratic term is positive, and therefore, the function is U shaped and has a minimum value, with the slope on the interval to the left of h having a negative rate of change;
The minimum value of h(x) is found as follows;
At the minimum of h(x), h'(x) = d(h(x)/dx = d(x² - 1)/dx = 2·x = 0
∴ x = 0/2 = 0 at the minimum
Therefore, the function is symmetrical about the point where x = 0
The average rate of change over an interval is given by the change in 'y' and x-values over the end-point in the interval, which is the slope of a straight line drawn between the points
The average rate of change will be negative where the y-value of the left boundary of the interval is higher than the y-value of the right boundary of the interval, such that the line formed by joining the endpoints of the interval slope downwards from left to right
The distance from the x-value of left boundary of the interval that would have a negative slope from x = 0 will be more than the distance of the x-value of the right boundary of the interval
Therefore, the interval over which h has a negative rate of change is -3 ≤ x ≤ 1
Which of the following rational functions is graphed below?
100
- 10
10
O A. Ax) = 3x=1
X-1
O B. F(x) =
(x - 3)(x + 1)
O C. F(X) =
(x − 3)(x + 1)
O D. F(x) = (x=3**
(+ 1)
Answer:
D
Step-by-step explanation:
D
The correct function of the graph is,
⇒ f (x) = (x - 1) / (x - 3) (x + 1)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function is shown.
Here, The graph is not defined at x = 3, and x = - 1.
Hence, By option;
The correct function of the graph is,
⇒ f (x) = (x - 1) / (x - 3) (x + 1)
Thus, The correct function of the graph is,
⇒ f (x) = (x - 1) / (x - 3) (x + 1)
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Solve for x.
3x + 10
3x +
x = [?]
Answer: x = 28
Step-by-step explanation:
3x+10+3x+2=180
6x+12=180
6x=168
x = 28
Answer:
x=28
Step-by-step explanation:
Since both lines going up are parallel, we can label the angle to the left of the angle with the measure of 3x+10 3x+2. These angles are supplementary as they are on different sides of the same line. This means that:
(3x+10)+(3x+2)=180
6x+12=180
6x=168
x=28
The roots of 7x^2 + x - 5 = 0 are a and b. Compute (a - 4)(b - 4). Thank you!
Answer:
Step-by-step explanation:
a = 7 ; b = 1 ; c = -5
D = b² - 4ac
= 1 - 4*7*(-5)
= 1 + 140
= 141
x =( - b ± √D ) / 2a
= (-1 ± √141)/2*7
= (-1±√141) / 14
[tex]a = \frac{-1+\sqrt{141} }{14}= \frac{-1+11.87}{14}= \frac{10.87}{14}=0.78\\\\b = \frac{-1-\sqrt{141}}{14}= \frac{-1-11.87}{14}= \frac{-12.87}{14}=3.59\\\\\\[/tex]
(a -4 )(b -4) = (0.78 - 4)(-3.59-4) = (-3.22)(-7.59)
= 24.4398
Vhich type of sequence is shown? Check all that apply.
4, 8, 12, 16, ...
The numbers are quickly getting larger, so this is a geometric sequence.
The numbers are slowly getting larger, so this is an arithmetic sequence.
This is an arithmetic sequence because there is a common difference of 4 between each term.
This is a geometric sequence because there is a common ratio of 2 between each term.
Add 4 to the last term to extend this arithmetic sequence.
Multiply the last term by 2 to extend this geometric sequence.
Answer:
This is an arithmetic sequence because there is a common difference of 4 between each term.
Add 4 to the last term to extend this arithmetic sequence
Step-by-step explanation:
The present ages of hero and hero in the ratio 3 is to 4 5 years from now their ratio of their ages will be 4 is 25 find the present ages
Answer:
Presently; Veeru is 15 and Neeru is 20
Step-by-step explanation:
Given
See comment for proper format of question
Let their present ages be x and y
So:
[tex]x : y = 3 : 4[/tex]
5 years time, the ratio will be:
[tex]x + 5: y + 5= 4 : 5[/tex]
Required
Their present ages
Express both ratios as fractions
[tex]x : y = 3 : 4[/tex] becomes
[tex]\frac{x}{y} = \frac{3}{4}[/tex]
and
[tex]x + 5: y + 5= 4 : 5[/tex] becomes
[tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]
Make x the subject in: [tex]\frac{x}{y} = \frac{3}{4}[/tex]
[tex]x = \frac{3}{4}y[/tex]
[tex]x = 0.75y[/tex]
Cross multiply in [tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]
[tex]5(x + 5) = 4(y + 5)[/tex]
Substitute [tex]x = 0.75y[/tex]
[tex]5(0.75y + 5) = 4(y + 5)[/tex]
Open brackets
[tex]3.75y + 25 = 4y + 20[/tex]
Collect like terms
[tex]3.75y -4y = -25 + 20[/tex]
[tex]-0.25y = -5[/tex]
Divide by -0.25
[tex]y = 20[/tex]
Substitute [tex]y = 20[/tex] in [tex]x = 0.75y[/tex]
[tex]x = 0.75 * 20[/tex]
[tex]x = 15[/tex]
Hurry !!Answer each question about the following
geometric series
10
k-1
What is the first term of the series?
a =
S10 - 3(2)k-1
RETRY
k-1
How many terms are in the series?
1
2
9
✓
10
COMPLETE
Answer:
last term is 1536
Value of the geometric series is 3,069
Step-by-step explanation:
took one for the team
There are 10 terms in the geometric series.
And, The first term of the series is, 3
We know that;
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The geometric series is,
⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹
Where, n is from 1 to 10.
Thus, We get;
There are 10 terms in the geometric series.
And, For first term;
Put n = 1;
⇒ S₁₀ = ∑ 3 (2)ⁿ⁻¹
⇒ S₁₀ = ∑ 3 (2)¹⁻¹
⇒ S₁₀ = ∑ 3 (2)⁰
⇒ S₁₀ = ∑ 3 × 1
⇒ S₁₀ = 3
Thus, The first term of the series is, 3
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Please help quickly!
Answer:
the answer is 2.8
Step-by-step explanation:
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
Given:
[tex]\frac{3x}{5} -0.5=1.9[/tex]
Add 0.5 to both sides
[tex]\frac{3x}{5} =2.4[/tex]
Multiply 5 from both sides
[tex]3x=12[/tex]
Divide both sides by 3
[tex]x=4[/tex]
Hope this helps
The equation x ^ 2 - 2x + y ^ 2 - 4y = 20 defines a circle in the xy-coordinate plane What is the radius of the circle?
Answer:
I'll set up the problem and you can do the calculation
Step-by-step explanation:
we need to complete the squares to get the equation in the general form:
[tex] {(x - h)}^{2} + {(y - k) }^{2} = {r}^{2} [/tex]
where h = the x coordinate of the center
k = the y coordinate of the center
r = the radius
so looking at
[tex] {x}^{2} - 2x[/tex]
we can see that if use -1 as the constant we have
[tex] {(x - 1)}^{2} = {x}^{2} - 2x + 1[/tex]
doing the same for y
[tex] {y}^{2} - 4y[/tex]
we can use -2 as the constant (basically you that the s
quare of the y coefficient )
[tex] {(y - 2)}^{2} = {y}^{2} - 4y + 4[/tex]
so now we have to add or subtract the constant on the RHS to see what the square of the radius is according to the general form of the equation at the top
20 +1+4=25
Take the square root and you have the radius
According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences was . The average starting salary for new college graduates in business was (National Association of Colleges and Employers website). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is . Assume that the standard deviation for starting salaries for new college graduates in business is .
Answer:
0.110
0.230
Step-by-step explanation:
Given :
In health :
Average salary, m = 51,541
Standard deviation, s = 11000
In Business :
Average salary, m = 53,901
Standard deviation, s = 15000
Since distribution is approximately normal ;
We can obtain the standardized scores and find the probability ;
Zscore = (x - mean) / standard deviation
Probability of earning salary if atleast $65,000
Health:
P(Z ≥ (65000 - 51541) / 11000) = P(Z ≥ 1.224) = 0.11048 (Z probability calculator)
Business :
P(Z ≥ (65000 - 53901) / 15000) = P(Z ≥ 0.740) = 0.22965 (Z probability calculator)
Hence, the probability of earning a starting salary of atleast $65,000 is :
Health = 0.11048
Business = 0.22965
-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please-4(7j+2=10 please help, please!
Answer:
x=12 . x=-12
Step-by-step explanation:
ONce you do the quadratic equasion than you move on to the solving part and from ther it is easy
What is the quotient represented by the model?
Answer:
0.4
Step-by-step explanation:
If we count up all of the colored squares, we will get 28. And if we count the non-colored squares we will get 72.
Now, we take 28 and we divide it by 72. This will get us 0.3888888. That number rounded up is 0.4.
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
6. A bought 3 3 by 2 kg of wheat and 2 1 by 2kg of rice. Find the total weight of wheat and rice
bought.......
please answer the question proccesfuly.
the answer which is the best I will mark it as braunlist.
Answer:
Step-by-step explanation:544
Answer:
total weight of wheat and rice is 8 kg
Step-by-step explanation:
rice = [tex]3\frac{3}{2}[/tex]
=3*2+3/2
=9/2
wheat = [tex]2\frac{1}{2}[/tex]
=2*2+1/2
=5/2
total weight of wheat and rice = [tex]\frac{7}{2} + \frac{9}{2}[/tex]
since their denominator are same u can add numerators.
=7 +9/2
=16/2
=8
Need help rn please
Geometry
Answer:
Step-by-step explanation:
9). Dimensions of the logo = 4 inch by 6 inch
∵ 12 inches = 1 feet
∴ 1 inch = [tex]\frac{1}{12}[/tex] feet
Therefore, dimensions of the logo (in feet) will be,
[tex]\frac{4}{12}[/tex] feet by [tex]\frac{6}{12}[/tex] feet Or [tex]\frac{1}{3}[/tex] feet by [tex]\frac{1}{2}[/tex] feet
Dimensions of the logo which are 6 times larger than the original one.
Dimensions of the advertisement = [tex]\frac{6}{3}[/tex] feet by [tex]\frac{6}{2}[/tex] feet
= 2 feet by 3 feet
Area of the advertisement = 2 × 3
= 6 feet²
10). By the property of similar polygons,
"Corresponding sides of two similar polygons are proportional"
If the dimensions of two similar polygons are 'x' and 'kx'
Ratio of the perimeter of two polygons = [tex]\frac{\text{Perimeter of the image polygon}}{\text{Perimeter of the original polygon}}[/tex] = k
Ratio of area of two similar polygons = [tex]\frac{\text{Area of the image polygon}}{\text{Area of the original polygon}}[/tex] = k²
Ratio of volumes of two similar polygons = [tex]\frac{\text{Volume of the image polygon}}{\text{Volume of the original polygon}}[/tex] = k³
Help please I’ll give you the brainliest I really got to get this done
Answer:
56
Step-by-step explanation:
pls help my computers about to die lol
Answer:
Elapsed 10 hours and 50 minutes
Step-by-step explanation:
So it's 5:25 pm to 4:15 am.
It goes by 50 mins to get from 5:25 to 6:15.
Now the hours.
It has passed 10 hours to get 6:15 pm to 4;15 am.
A squirrel has a 75% chance of finding food when it is sunny, but only a 25% chance of finding food when it is raining. Suppose there is a 50% chance of rain. What is the probability that a squirrel will find food?
Answer:
The probability is 0.5
Step-by-step explanation:
If there is a 50% chance of rain, then there is also a 50% chance of not rain.
Now let's write all the probabilities:
(just take the percentage and divide it by 100%)
Probability of rain: p = (50%/100%) = 0.5
probabiity for the squirrel to find food when it rains: q = (25%/100%) = 0.25
Then the joint probability, this is, the probability that rains and that the squirrel finds food, is equal to the product of these two probabilities, this is:
P1 = 0.5*0.25 = 0.125
And we also have the case where there is no rain.
Probability that does not rain: p' = (50%/100%) = 0.5
Probability that the squirrel finds food if doesn't rain: q = (75%/100%) = 0.75
The joint probability is:
P2 = 0.5*0.75 = 0.375
The total probability that the squirrel will find food is equal to the sum of the probabilities of the squirrel finding food if there is rain, and the probability of the squirrel finding food if there isn't rain, so the total probability is:
P = P1 + P2 = 0.125 + 0.375 = 0.5
Use log 3 = .477 and log 6 =.778 to approximate the expression. log 2
Answer:
0.301
Step-by-step explanation:
Given that log 3 = .477 and log 6 =.778
Log 2
= log(6/3)
= log 6 - log 3
= 0.778 - 0.477
= 0.301
Hence the value of log 2 is 0.301
What line on a coordinate plane is called the x-axis? Horizontal or Vertical. Please respond as quick as possible
Answer:
it's called the horizontal line
Step-by-step explanation:
also known as y=0
Colin buys a tv for £530.
It depreciates at a rate of 3% per year.
How much will it be worth in 5 years?
Give your answer to the nearest penny where appropriate.
Answer:
£455.13
Step-by-step explanation:
3% = .03
p = 530(1 *- .03)⁵
p = 530(.97)⁵
p = 455.129033621
Rounded
£455.13
The recursive formula to describe a sequence is shown below.
PART A:
State the first four terms of this sequence.
PART B:
Can this sequence be represented using an explicit geometric formula? Justify your answer.
The first four terms of the sequence are 3, 7, 15, and 31. This sequence is represented using an explicit geometric formula.
What is the recursive rule?A rule is defined such that its definition includes itself.
Example:
F(x) = F(x-1) + c
is one such recursive rule.
PART A:
State the first four terms of this sequence.
[tex]a_1 = 3\\\\a_n = 1+ 2a_{n-1}[/tex]
[tex]a_2 = 1+ 2a_{2-1}\\\\a_2 = 1+ 2a_{1}\\\\a_2 = 7\\\\a_3 = 1+ 2a_{2}\\\\a_3 = 15\\\\a_4 = 1+ 2a_{3}\\\\a_4 = 31\\[/tex]
PART B:
This sequence is represented using an explicit geometric formula.
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Please answer quickly, simple geometry
OPTION C IS THE CORRECT ANSWER.
Can someone helpppppppp
Answer:
f(-2) = -3
Step-by-step explanation:
When x = -2 we want the value of y
We use the closed circle value ( open circle does not have a value)
f(-2) = -3
Which of the following graphs represents the equation below?
the graph the represents the equation is C.
Answer:
the answer is a on the image i just did what they said and got it wrong
Step-by-step explanation:
which of the following is the result of the equation below after completing the square and factoring x^2+3x+8=6
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{x^2 + 3x + 8 = 6}[/tex]
[tex]\large\textsf{SUBTRACT 6 to BOTH SIDES}[/tex]
[tex]\mathsf{x^2 + 3x + 8 - 6 = 6 - 6}[/tex]
[tex]\mathsf{8 - 6 = \boxed{\bf 2}}[/tex]
[tex]\mathsf{6 - 6 = \boxed{\bf 0}}[/tex]
[tex]\mathsf{x^2 + 3x + 2 = 0}[/tex]
[tex]\large\textsf{FACTOR the LEFT SIDE OF THE EQUATION}[/tex]
[tex]\mathsf{(x + 1)(x + 2) = 0}[/tex]
[tex]\large\textsf{SET EACH FACTORS to EQUAL 0}[/tex]
[tex]\mathsf{x + 1 = 0 \ OR \ x + 2 = 0}[/tex]
[tex]\large\textsf{SOLVE the EQUATIONS ABOVE and YOU HAVE YOUR x-values}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x = -1 or x = -2}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLEASEEE I nEEED THE ANSWER TnT
NOTE: pls ignore another language just read the english one... ASAP
Answer:
x -1 1 3
y -2 -4 2
Step-by-step explanation:
y=x^2-x-4
when x=-1
y=(-1)^2-(-1)-4
y=1+1-4
y=-2
when x=1
y=(1)^2-(1)-4
y=1-1-4
y=-4
when x=3
y=(3)2-(3)-4
y=9-3-4
y=9-7
y=2
What is the area of the figure shown below, in terms of π ?
(?+?π)square units
if you give me the correct answer then I will mark as brainliest
It's is b cause it is and yeah
Answer:
a
Step-by-step explanation: