The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
What is Linear Function?
A straight line on the coordinate plane is represented by a linear function.
The linear function formulas are:
y = mx + b (slope-intercept form)y−y1 = m(x−x1) (point-slope form)Ax + By = C (standard form)xa+yb = 1 (intercept form)Here, we have
The given functions are f(0)=2 and f(3) = -1
For f(0) = 2
Coordinate: (0,2)
y-intercept, c: 2
For f(3) = -1
Coordinate: (3,-1)
gradient or slope, m when x₁ = 0, y₁ = 2, x₂ = 3, y₂ = -1
=( y₂-y₁)/(x₂-x₁)
= ( -1 -2)/(3 - 0)
= -3/3
= -1
The linear equation is in the slope-intercept form, y=mx+c
f(x) = -x+2, where -1 is the slope and 2 is the y-intercept.
Hence, The linear function f with the given values f(0) = 2, f(3) = -1 is f(x) = -x + 2.
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Vertex of f(x) = |2x + 3
The vertex of the equation given as .f(x) = |2x + 3| is (-3, 0)
What is the vertex?The vertex of a function or an equation is the minimum or the maximum point on the function
How to determine the vertex of the graph?From the question, we have the equation of the function to be
f(x) = |2x + 3|
The above function is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is represented as
Vertex = (h, k)
By definition, a graph that has a vertex would have an obvious maximum or minimum point on it
By comparing the equations f(x) = a|x - h| + k and f(x) = |2x + 3| to determine the vertex, we have
(h, k) = (-3, 0)
This means that
Vertex = (-3, 0)
Hence, the vertex of the equation is (-3, 0)
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I NEED HELP ME PLEASE!!!
Answer:
I hope this is right
TG = 34 TG=34 inches
From the figure
PQR is a triangle
PS, QT are medians of the triangle
G is the centroid
Step 1: Calculate the segment of the median (TG = ? )
We know that
Each median is divided into segments with a 2:1 ratio by the triangle centroid.
\therefore \frac{TG}{GQ} = \frac{2}{1} ∴
GQ/TG = 1/2
TG = 2 GQ TG=2GQ
TG = 2 * 17 TG=2∗17
TG = 34 TG=34
Hence, segment of the median TG = 34 inches
help again for a friend
The required equation of slope is y = x/2 + 6
Given : y = 3x + 6
this is of the form y = mx + c
thus on comparing we get
the slope or m = 3
And the y intercept = 0, 6
It is also given that we have to find the equation of the slope which passes through the point ( -2, 5 )
thus the two points are:
( -2, 5 ) and ( 0,6 )
Thus the slope or m = y2 - y1/ x2 - x1
=> m = 6 - 5 / - ( -2 )
m = 1/ 2
Thus the equation of the slope is
y - y₁ = m ( x - x₁ )
₁Substituting the value of m from above we get
y - 5 = 1/2 ( x + 2 )
this implies 2y - 10 = x + 2
x - 2y = - 12
or we can also write this as
y = x/2 + 6
Refer to the graph given below for further understanding.
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1/2 : 2/3 = X:1
[1 mark]
The value of X for the given equation is X = 3/4.
What are the ratio and proportion?A percentage is the equality of two ratios, while a ratio is the divisional comparison of two numbers. As well as being written as x: y or x/y, ratios are sometimes expressed as x is to y.
A proportional equation declares that two ratios are similar on a comparative basis. A ratio means that x is to y as z is to w and is represented as x: y: z: w. Since w and y are not equal in this situation, x/y = z/w.
The given equation is
1/2 : 2/3 = X:1
We can rewrite it as
(1/2)/ (2/3) = X
X = 1/2 × 3/2
X= 3/4
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Write 22 as a percentage of 58
Give your answer correct to the nearest whole number.
Answer:
38%
Step-by-step explanation:
22 ÷ 58 = 0.3793...
Ans × 100 = 37.93%
As a whole number = 38%
Need help. I also need to show my work
The factors of the expression (x³ - 6x² + 3x + 10) are (x + 1), (x - 2), and (x - 5).
We are given a mathematical expression. The expression is cubic in nature. We need to find the factors of the algebraic expression. Let the expression be represented by the variable "E". The expression consists of three terms. Hence, the expression is trinomial. The expression is given below.
E = x³ - 6x² + 3x + 10
One of the factors in the expression is already given. The given factor is (x + 1).
Now we will perform the long division method on the expression to break it into the given factor and a quadratic expression.
E = (x + 1)(x² - 7x + 10)
Now we will factorise the quadratic expression.
E = (x + 1)[x² - 2x - 5x + 10]
E = (x + 1)[x(x - 2) - 5(x - 2)]
E = (x + 1)(x - 2)(x - 5)
We cannot simplify and factorise the expression any further.
Hence, the factors of the expression are (x + 1), (x - 2), and (x - 5).
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Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. How much did
Mrs. Smith pay for 30 muffins?
Explain your answer
a) $3
b) $10
c) $15
d) $30
Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 , the correct option is (a) and (d) .
In the question ,
it is given that
the equation is (6x+2)/3 = 2 - (3x+14)
solving the brackets on the right side of the equation ,
(6x+2)/3 = 2 - 3x - 14
(6x+2)/3 = -3x - 12 ....option(a)
On Cross Multiplying , we get
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36 ....option(d)
Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 .
The given question is incomplete , the complete question is
Using Simplification , Select all equations that are equivalent to
(6x+2)/3 = 2 - (3x+14)
(a) (6x+2)/3 = -3x-12
(b) (6x+2) = 2 - (3x+14)
(c) 2x + 2/3 = 2 - (3x+14)
(d) 6x+2 = -9x-36
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HELP MEEE PLEASEEEEEE
Answer:
Length YZ is about 16.2 cm (to the first decimal place)
Step-by-step explanation:
In order to find the lenth YZ we need to know the the Pythagorean theorem which is a²+b²=c² (or leg² + leg² = hypothnose)
For this problem let a = line segment XY, let b = YZ and let your hypothnose (c) to be ZX
Substitute your known values in the equation so we know a = 5 cm and c = 17 cm so we can apply it in our equation 5²+ b² = 17² Square your known values in this case 5² and 17² which is 25 and 289 respectively. The equation is now 25+b²=289 Do the inverse operation to Isolate you unknown variable which is b. We do this by subtracting 25 on both sides after doing so the equation is now b²= 264 Square root both sides of the equation the point is to get rid of the squared part of b². After doing so your answer is b = 16.2480768093Round to the first decimal place the two remains the same so the final answer is 16.2 cmat a university, the probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12. find the probability that the student takes statistics given that he or she is a business major
The probability that the student takes statistics given that he or she is a business major is 0.04.
Define probability.The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
Given,
The probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12
Students who have taken both:
P( statistics ∩ business) = 0.036
Only a statistics major:
P( statistics/ business) = 0.9
P( student is business major)
P ( statistics / business) ÷ P( statistics/ business)
0.036/0.9
0.04
The probability that the student takes statistics given that he or she is a business major is 0.04.
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An engineering technician makes $25 an hour for the first 40 hours she works
during a week and $32 an hour for each hour over 40 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
O A. y=
O C. y =
(25x
132(x-40)+1000
OB. y=-
OD. y=
[25x
132x+1000
(25x
(32(x-40)
(25x
132x
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
x> 40
0≤x≤ 40
X> 40
SUBMIT
The Piecewise Function be
25x when x < 40
y =
1000+32(x-40) when x > 40
Given, an engineering technician makes $25 an hour for the first 40 hours she works.
and $32 an hour for each hour over 40 hours.
Let the number of hours be x and her total weekly pay in dollars be, y
then the piecewise function,
25x when x < 40
y =
1000+32(x-40) when x > 40
Hence, the piecewise function be
25x when x < 40
y =
1000+32(x-40) when x > 40
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in a certain year, 13,839 professional train pushers are diagnosed with carpal tunnel. the top cities for such diagnoses are tokyo with 2,551, osaka with 3,049, and kyoto with 1,436. if a professional train pusher recently diagnosed with carpal tunnel is randomly selected, what is the probability that they are from somewhere other than tokyo, kyoto or osaka?
Probability that the professional other than Tokyo, Kyoto or Osaka is 6803/13839.
Total number of professional train pushers who are diagnosed with carpal tunnel is 13839
Number such professional from Tokyo = 2551
Number such professional from Osaka = 3049
Number such professional from Kyoto = 1436
So, number such professional from other than these three cities = 13839 - (2551+3049+1436) = 6803
Hence the probability that the professional other than Tokyo, Kyoto or Osaka is = 6803/13839
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it is given that I = PRT/100
express P in terms of I, R and T
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's express P (principle) in terms of I, R and T
[tex]\qquad \sf \dashrightarrow \: I= \dfrac{PRT}{100} [/tex]
[tex]\qquad \sf \dashrightarrow \: PRT = I \sdot 100[/tex]
[tex]\qquad \sf \dashrightarrow \: P = \dfrac{I \sdot 100}{RT} [/tex]
and that's it ~
P can be expressed in terms of I, R, T as P=100×I / (R×T)
Given equation
I=PRT/100
100 × I = PRT
100 × I / RT = P
P = 100 × I / RT
This formula is used to calculate Simple Interest, where P= Principal, I= Intrest to be Calculated. R= Annual rate of interest, T= Time (in years). Here one will shift the 100 from the denominator and multiply with the I next we will move the rate and time from the numerator to the denominator. The equation we now get will be in terms of I, R, and T and one can find the Principal using this equation.
I hope this answer helps.
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Against the Wind a small plane flew 858 miles in 2 hours and 10 minutes the return trip only took 1 hour and 50 minutes what was the speed of the wind?what was the speed of the plane in still air?
Let the speed of the small plane be 'R'.
Let the speed of the wind be 'S'.
Plane's time against wind = 2 hours and 10 minutes = 13/6 hours.
Plane's time with wind = 1 hour and 50 minutes = 11/6 hours
Use formula;
Distance = speed x time
Against the wind:
858 = (13/6) (R-S) = (13/6) R - (13/6)S
With wind:
858 = (11/6)(R + S) = (11/6)R + (11/6)S
Multiplies each by 6.
5148 = 13R - 13S
5148 = 11R + 11S
Use elimination method
56628 = 143R - 143S (multiplies by 11)
66924 = 143R + 143S (multiplies by 13)
Further solving;
123552 = 276R
R = 432 miles/ hr. (speed of small plane )
And, S = 36 miles/ hr. (speed of wind)
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Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 28.45°. What is the measure of ∠P?
28.45°
75.775°
121.55°
151.55°
Step-by-step explanation:
the sum of all angles in a triangle is ALWAYS 180°.
and by using the word "congruent" : for angles that only means they are equally large.
we know the third angle.
so,
180 = P + Q + R = 2×P + 28.45
(because P = Q)
2×P = 151.55
P = Q = 151.55 / 2 = 75.775°
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function . (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C : Determine the average rate of change between day 2 and day 4. Show your work (4 points )
Step-by-step explanation:
A
it is an exponential function.
for a linear function the charge rate would have to be constant between any pair of data points.
the change rate is
( f ( interval end ) - f ( interval begin ) ) /
( interval end - interval begin )
between (1, 2) and (2, 4) we have a charge rate of
(4 - 2) / (2 - 1) = 2
between e.g. (3, 8) and (4, 16) we have a charge rate of
(16 - 8) / (4 - 3) = 8
the change rate is therefore not constant, and it is not a linear function.
B
we see
x1 = 1, y1 = 2
x2 = x1 + 1, y2 = y1×2
x3 = x2 + 1, y3 = y2×2
we get the impression that
xn = xn-1 + 1 = x1 + (n - 1)
yn = yn-1 × 2 = y1 × 2^n
so, while going linearly along the x-axis, y increases by the powers of 2.
the function is then
f(x) = 2^x
C
the change rate between station 2 and 4 (NOT day 2 and 4) is
(16 - 4) / (4 - 2) = 12/2 = 6
Step 1 5x + 9 = 2x - 3
Step 2 3x + 9 = -3
Step 3 3x = -12
Step 4 x = -4
What operation did he perform to get from step 1 to step 2
Answer:
He subtracted a term of [tex]2x[/tex] from both sides of the equation.
Please help me please help me
Answer:
the answer Is 6 .........
Compare the following fraction 8/14 and 4/7
Answer:
These fractions are equivalent, with 4/7 being the simplest form of both.
Step-by-step explanation:
8/14 can be simplified to 4/7 also by dividing both sides by two :)
The sides of a triangle are in the form of consecutive even integers. If its perimeter is 48cm, find the
measure of each side.
Answer:
The sides of the triangle would be 14, 16, and 18.
Step-by-step explanation:
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May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
What number is 763 less than 850.08?
Answer:
87.08.
850.08 - 763 = 87.08.
Please help geomatry 9th grade
The statements that are a result of corresponding parts of congruent triangles being congruent are:
EFGH has four congruent sidesDiagonal FH is perpendicular to side FEAngle FEH is congruent to angle FGHWhat is an isosceles triangle?An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;
Equilateral triangleRight angle triangleScalene triangleFrom the figure;
Sides EFGH are congruent, that is, equal
Since Sides EFGH are congruent, it can not be a rectangle, it is a square.
Triangle FGH and FEH are both isosceles triangle.
Diagonal FH bisects triangle FGH and FEH
So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.
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Solve |2x - 3| < 7.
Answer:
5 or (-2,5)
Step-by-step explanation:
|2x-3|<7
2x-3<7
2x=10
x=5
Answer:
x < 5
Step-by-step explanation:
Add 3 to both sides of the equation. This is to balance the equation.2x - 3 + 3 < 7 + 3
Now, add 7 and 3.7 + 3 = 10
Add -3 and positive 3.-3 + 3 = 0
= 2x + 0
= 2x
Now, the problem becomes,2x < 10
Divide by 22x/2 < 10/2
Divide by 2: 10/210/2 = 5
Divide by 2: 2x2x/2 = 2/2
= x (We assume x = 1)
Divide both numbers= 5/1
= 5
Therefore,
x < 5
Hope this helps!
a fair coin is tossed 28 times. what is the probability that at most 25 tails occur? a) 0.99998628 b) 0.00000152 c) 0.99999848 d) 0.00001220 e) 0.01001372 f) none of the above.
The probability that at most 25 tails occur is 0.99999848.
We know that,
P(x = x) = ⁿCₓ × pˣ × [tex]q^{n-x}[/tex]
p = probability of success = 0.5
n = number of trials = 28
q = 1 - p = 0.5
The probability of the tail occurring at most 25 times can be written as
P(X ≤ 25) = P (X = 0) + P(X = 1) + ..... + P(X = 25)
Using a binomial probability calculator,
P(X ≤ 25) = 0.99999848
Therefore the probability that at most 25 tails occur is 0.99999848
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Please help
At the beginning of spring, London planted a small sunflower in her backyard. The sunflower's height in inches,
h
h, after
w
w weeks, is given by the equation
h
=
4
w
+
15
h=4w+15. What could the number 4 represent in the equation
The change in the sunflower's height for every one additional week.
The sunflower's height after one week.
The sunflower's final height
The sunflower's height after 0 weeks.
I need help like asap !!!
only numbers and decimal points
a classroom of children has 18 boys and 19 girls in which five students are chosen at random to do presentations. what is the probability that more boys than girls are chosen? a) 0.1334 b) 0.4731 c) 0.0197 d) 0.4535 e) 0.3398 f) none of the above.
The probability that more boys than girls are chosen is 0.4731. So option b is correct.
Combination:
The act of combining or the state of being combined. A number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.
Here it is given that there are 18 boys and 19 girls and 5 students are chosen.
We have to find the probability that more boys than girls are chosen.
Probability = [tex]C^{5} _{18}[/tex] + [tex]C^{4}_{18} C^{1} _{19}[/tex] + [tex]C^{3} _{18} C^{2} _{19}[/tex] / [tex]C^{5}x_{37}[/tex]
= 8568 + 58140 + 139536 / 435897
≈ 0.4731
Therefore the probability is 0.4731.
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
sara has 20 sweets
12 liquorice sweets , 5 mint sweets and 3 humbugs.
sara takes two random sweets
work out probability that the two sweets will not be the same
If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.
How to find the probability?Probability of getting two of each sweet:
P( Liquorice) = (12/20)×(11/19)
P (Liquorice) =132/380
P (mints) =(5/20)×(4/19)
P (mints) =20/380
P (Humbugs) =(3/20)×(2/19)
P (Humbugs) =6/380
Probability that two sweets will be the same
P(same) =132/380+20/380+6/380
P(same) =158/380
Hence,
Probability that two sweets will not be the same
P(not same) = 1- (158/380)
P(not same) =380 -158 /380
P(not same) = 222 /380
P(not same) =111 /190
Therefore the probability is 111/190.
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Sophia earned $36 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The ratio when Sophia earned $36 at her job when she worked for 4 hours is 1:9.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
From the information, Sophia earned $36 at her job when she worked for 4 hours.
The equivalent ratio to illustrate the information will be:
= 4 / 36
= 1/9
= 1:9
Note that the coordinates point weren't given in the question.
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