For the linear function f(x) = -2x+1 , find the following
a. Slope and Y-intercept.
b. Is the function increasing, decreasing, or constant, justify your answer.
c. Graph the function, label x, and y-intercepts.
Answers
Given:
The function is:
[tex]f(x)=-2x+1[/tex]
To find:
a. Slope and Y-intercept.
b. Is the function increasing, decreasing, or constant, justify your answer.
c. Graph the function, label x, and y-intercepts.
Solution:
a. We have,
[tex]f(x)=-2x+1[/tex] ...(i)
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=-2,b=1[/tex]
Therefore, the slope of the line is -2 and the y-intercept is 1.
b. If the slope of a linear function is negative, then the function is decreasing.
If the slope of a linear function is positive, then the function is increasing.
If the slope of a linear function is 0, then the function is constant.
The slope of the linear function is negative.
Therefore, the function is decreasing.
c. We have,
[tex]f(x)=-2x+1[/tex]
At [tex]x=0[/tex], we get
[tex]f(0)=-2(0)+1[/tex]
[tex]f(0)=1[/tex]
So, the y-intercept is at (0,1).
At [tex]f(x)=0[/tex], we get
[tex]0=-2x+1[/tex]
[tex]2x=1[/tex]
[tex]x=\dfrac{1}{2}[/tex]
[tex]x=0.5[/tex]
So, the x-intercept is at [tex]\left(0.5,0\right)[/tex].
Plot the points [tex](0,1), \left(0.5,0\right)[/tex] and connect them by a straight line as shown below:
Related Questions
Un estudiante debe recorrer dos tercios de kilómetro para llegar al colegio, si avanza medio kilómetro en bus y lo demás a pie ¿Cuánto le falta caminar?
Answers
Answer:
Al estudiante le falta caminar [tex]\frac{1}{3}[/tex] de kilómetro.
Step-by-step explanation:
Un estudiante debe recorrer dos tercios de kilómetro para llegar al colegio. Dos tercios equivale a la fracción [tex]\frac{2}{3}[/tex] .
El estudiante avanza medio kilómetro en bus. Un medio equivale a la fracción [tex]\frac{1}{2}[/tex], por lo tanto un medio es la mitad de una cantidad. Para calcular la distancia recorrida en bus se realiza la siguiente multiplicación:
[tex]\frac{1}{2} *\frac{2}{3}[/tex]
Resolviendo:
[tex]\frac{1}{2} *\frac{2}{3} =\frac{1*2}{2*3} =\frac{2}{6} =\frac{1}{3}[/tex]
Entonces, la distancia recorrida en bus es [tex]\frac{1}{3}[/tex] de kilómetro.
Para calcular la distancia recorrida a pie se calcula la diferencia entre la distancia total a recorrer por el estudiante y la distancia recorrida en bus. Esto es:
[tex]\frac{2}{3} - \frac{1}{3}[/tex]
Resolviendo:
[tex]\frac{2}{3} - \frac{1}{3}=\frac{2-1}{3} =\frac{1}{3}[/tex]
Al estudiante le falta caminar [tex]\frac{1}{3}[/tex] de kilómetro.
WILL MARK BRAINLIEST!!!
Jamie is going on a trip to visit her grandparents. The airline allows each suitcase to hold 50 pounds. She has already packed clothes and other things that weigh a total of 26 pounds. The inequality p + 26 ≤ 50 can be used to see how much more she can pack in the suitcase.
Why is this problem written as an inequality instead of an equation?
Answers
Answer:
Because the airline allows each suitcase to hold up to 50 pounds, and it doesn't force them to hold exactly 50 pounds
Answer:
Step-by-step explanation:
b/c she doesn't have to have exactly 50 pounds, she can have any were from 0 to 50 pounds in each suit case. They are not going to charge her more, if she only brings 49 pounds :DDDD It's the same charge up to and including 50 pounds. If she brings 51 pounds then maybe she would get charged more :P But not for 50 pounds or less . :) Make sense?
Select the values that make the inequality n > -8 true.
(Numbers written in order from least to greatest going across.)
Answers
Answer:
9
Step-by-step explanation:
I'm somewhat confused I think you're forgot to put so more information
The value that makes the inequality n > -8 true will be -2. Thus, the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below:
n > -8
The value of n is greater than -9. Then the value that makes the inequality n > -8 true will be -2.
Thus, the correct option is A.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
The missing options are given below.
a) - 2
b) - 9
c) - 10
d) - 20
4. Find the roots of the equation 30x – 45 = 5x? by factoring.
Answers
Answer:
[tex]x = 1\frac{4}{5}[/tex]
Step-by-step explanation:
Factor and set each factor equal to zero.
Answer:
Step-by-step explanation:
30x-45=5x
30x-5x=45
25x=45
x=45/25
x=9/5
Find the area of the figure F2 cm
2 cm
5 cm
5 cm
Answers
Answer:
the answer would be 20cm^2 i took a quiz.
Step-by-step explanation:
Which statement is true? 1. Parallelism are frameworks 2. A square is always a rhombus 3.A rhombus is always a square 4. A rectangle is a trapezoid
Answers
Answer:
2
Step-by-step explanation:
A square is a quadrilateral with four equal sides.
Characteristics of a square includes:
• The diagonals bisect each other at 90°.
• Opposite sides parallel and of equal length
• The four angles of a square are equal.
A rhombus is a four sides quadrilateral with the four sides equal in length
The area of a rhombus =
where p and q are the two diagonals
Volume of a pyramid = 1/3 x ( length base x height)
True or False
3 is a factor of n(n + 2)(n − 1) by mathematical induction.
Explain why.
Answers
true true true true true true true
Answer:
false
Step-by-step explanation:
3(3+2)(3-1) is not =0
The factor of n(n+2)(n-1) = 1
On a map, 1 inch equals miles. Two houses are inches apart on the map. What is the actual distance between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios.
Answers
Answer:
The actual distance between the houses is 18.9 miles.
Step-by-step explanation:
The exact question is as follows :
Given - On a map, 1 inch equals 5.4 miles. Two houses are 3.5 inches apart on the map.
To find - What is the actual distance between the houses?
Solution -
Given that,
1 inch = 5.4 miles
⇒3.5 inches = 3.5 × 5.4 miles
= 18.9 miles
∴ we get
The actual distance between the houses is 18.9 miles.
A garden hose is leaking 1 liter of water every 1/8 hour. How many liters of water will it leak in 3 ¾ hours? *
Answers
Therefore, 1/8 of 60 is 7.5, meaning, 1 litre of water is leaked every 7.5 minutes.
3¾ hours is 60 x 3 + 60/4
= 180 + 15
= 195 minutes
As 3 ¾ hours is 195 minutes and 1 litre is leaked every 7.5 minutes, we have to divide 195 by 7.5.
195/7.5 = 26
Therefore, the garden hose will leak 26 litres in 3 ¾ hours.
Ani was told to write the number four and eight hundredths. She wrote 4.8. Was Ani correct or incorrect
Answers
Kathy has a circular hot tub in her backyard with a radius of 5.5 feet. She wants to place a decorative border around the circumference of the hot tub. If the border costs $6.70 per foot, how much will the border for the hot tub cost?
Answers
Simplify: -10m + 2m4 – 13m – 20m4
Answers
Answer:
-23m-18m^4
Step-by-step explanation:
-10m+2m^4-13m-20m^4
(-10m+-13m)+(2m^4-20m^4)
-23m+-18m^4
-23m-18m^4
If this helps please mark as brainliest
I NEED HELP PLEASE IT WOULD HELP ME ALOT
Answers
Answer:
Step-by-step explanation:
21 is the side opposite the angle you want.
67 is the hypotenuse. Those two sides define the Sin
Sin(theta) = opposite / hypotenuse
Sin(theta) = 21 / 67
Sin(theta) = .313432
theta or x = sin-1(0.313432)
x = 18.27
Sorry, I must have hit the wrong key the first time.
Answer:
18.27˚
Step-by-step explanation:
What is the range for 42 42 52 53 58 58 61
Answers
Answer:
range would be 19
Step-by-step explanation:
Answer:
I have to say -282
Step-by-step explanation:
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
3.2/.8=
help pls
also the steps to doing it.
Answers
Answer:
4
Step-by-step explanation:
I don't really know how to show the steps, but one of the easiest ways to do this is to see how many times 0.8 goes into 3.2. So 0.8 + 0.8 + 0.8 +0.8 = 3.2 So 3.2/0.8 is 4
Or you can multiply the numerator and denominator by 10, which keeps the value of the fraction but gets rid of pesky decimals: 32/8 this should be fairly straight forward and a key reason to memorize your times tables. 8*4=32
PLS HELP ILL GIVE BRAINLIEST
Answers
Answer:
answer is 8
Step-by-step explanation:
take Lcm of 8 and 32
Answer:
8
Step-by-step explanation:
There are 12 sixth graders, 11 seventh
graders, and 13 eighth graders on a
soccer team. The coach randomly selects
one student to collect all of the soccer
balls. In how many ways can choosing
not an eighth grader occur?
Answers
Answer: 1
Step-by-step explanation:
because there not the only ones on the team
What is the equation of the line that passes through the points (4,-1 ) and (-7,4 )?
Answers
Answer:
[tex] \large{ \tt{❃ \: STEP- BY - STEP \: EXPLANATION}} : [/tex]
Let the equation of line passes through the points A ( 4 , - 1 ) and B ( - 7 , 4 ) . Let A ( 4 , -1 ) be ( x₁ , y₁ ) & B ( - 7 , 4 ) be ( x₂ , y₂ )[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]
Using two - point form of the equation of straight line , we have :[tex] \boxed{ \large{ \bf{❀ \: y -y _{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1}} (x - x_{1)}}}}[/tex]
- Plug the values :
[tex] \large{ \bf{⇢ \: y - ( - 1) = \frac{4 - ( - 1)}{ - 7 - 4}(x - 4) }}[/tex]
[tex] \large{ \bf{⇢y + 1 = \frac{4 + 1}{ - 11} (x - 4)}}[/tex]
[tex] \large{ \bf{⇢ \: y + 1 = - \frac{5}{11} (x - 4)}}[/tex]
[tex] \large{ \bf{⇢y + 1 = - \frac{5}{11}x + \frac{20}{11} }}[/tex]
[tex] \large{ \bf{⇢y + 1 = \frac{ - 5x + 20}{11} }}[/tex]
[tex] \large{ \bf{⇢11(y + 1) = - 5x + 20}}[/tex]
[tex] \large{ \bf{⇢11y + 11 = - 5x + 20}}[/tex]
[tex] \large{ \bf{⇢5x + 11y + 11 - 20 = 0}}[/tex]
[tex] ⇢ \boxed{\large{ \bold{\bf{5x + 11y - 9 = 0}}}}[/tex]
♕ Hence , 5x + 11y - 9 = 0 is the required equation of the line.✺ The two most important days in your life are the day you are born and the day you find out why ! ♪
♡ Hope I helped! ツ
☪ Have a wonderful day / evening ! ☼
# StayInAndExplore ! ☂
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A car wash detailed 288 cars in 8 hours. At what rate did the car wash detail cars in cars per hour?
A.
34 cars per hour
B.
37 cars per hour
C.
36 cars per hour
D.
35 cars per hour
Answers
Answer:
a
Step-by-step explanation:
The perimeter of a triangular park is (16x + 3) feet. Two of the sides are 5x - 1 and 2x + 5. What is the missing length?
Answers
Answer:
9x - 1
Step-by-step explanation:
A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees
Area of a triangle = 1/2 x base x height
the perimeter of a triangle = sum of the side lengths
missing length = perimeter - sum of the two sides
sum of the two sides = (5x -1) + (2x + 5) = 7x + 4
missing length = 16x + 3 - (7x + 4) = 9x-1
Y
х
B В
The transformation below is applied
to AXYZ
(XY) → (0.5x, 0.5y)
What are the coordinates of point X"?
0 62.0.5)
(0.5,-2)
(2.0.5)
0 1.2, 0.5)
Answers
Answer:
(-2, 0.5) first
Step-by-step explanation:
X (-4, 1) → X' (-4*0.5, 1*0.5)
X'(-2, .5)
i hate copy and pastes
Answers
Answer:
why they're so helpful
Step-by-step explanation:
Answer:
Me too it so much wooooorrrrkkk
Step-by-step explanation:
pleasee helppp i have 15 assignments to finish plus a final exam in 4 hours !!
Answers
f(x) = square root of (-7 + 2) - 6
f(x) =square root of (-5) - 6
f(x) = 2.236 = 2.2 - 6
f(x) = -3.8
F(x) = √x+2 -6
F(x) = √7+2 -6
F(x) = 3-6
F(x) = -3
The diagram shows different forms of thermal energy transfer.
What do the flames below the pot represent?
Answers
Did I get this right ?
Answers
Answer:
square root of 15 is the answer
Step-by-step explanation:
What are the possible vaules of x it (4x-5)2=49?
Answers
[tex]\boxed{The\:value\:of\:x\:is\:7.375.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex](4x - 5)2 = 49 \\ ⇢8x - 10 = 49 \\⇢8x = 49 + 10 \\ ⇢8x = 59 \\ ⇢x = \frac{59}{8} \\ ⇢x = 7.375[/tex]
Therefore, the value of x is 7.375.
[tex]{ \bf{ \underbrace{To\:verify :}}}[/tex]
[tex](4x - 5)2 = 49 \\ ⇢(4 \times 7.375 - 5)2 = 49 \\ ⇢(29 .5 - 5)2 = 49 \\ ⇢24.5 \times 2 = 49 \\ ⇢49 = 49 \\ ⇢ L.H.S.=R. H. S[/tex]
Hence verifed.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
14.How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating at 5
km/hr2?
Answers
Answer:
8.8
Step-by-step explanation:
Calculate the volume of the composite solid.
Answers
Answer:
about 33.52 in^3
Step-by-step explanation:
Volume of composite figure = volume of cone + volume of hemisphere
Volume of a cone = 1/3(nr^2h)
n = 3.14
r = radius
h = height
1/3 x 3.14 x 2^2 x 4 = 16.74 inches^3
volume of a hemisphere = (2/3) x (n) x (r^3)
n = 3.14
r = radius
2/3 x 3.14 x 2^3 = 16.74 inches^3
16.74 inches^3 + 16.74 inches^3 = 33.49
hi, can you please show me the solution on this one?
How many different batting orders can a coach make from the 9 players?
362,880
9
40,320
i'll give brainliest if you're right! thanks in advance..
Answers
Answer:
362,880
Step-by-step explanation:
Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.
PLS HELP I WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
[tex]6 {x}^{2} {y}^{3} - 2x + 10 \\ when \: x = 5 \: y = - 3 \\ 6( {5})\: ^{2} ( { - 3})^{3} - 2(5) + 10 \\ 6 (25)( - 27) - 10 + 10 \\ = - 4050[/tex]