Answers
Answer:
f₁(x) = -3x + 2
f₂(x) = x - 4
f₃(x) = x + 8
f₄(x) = -2x - 6
f₅(x) = -3x
Step-by-step explanation:
1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)
Let the equation of the blue line is,
y = mx + b
Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{8-2}{-2-0}[/tex]
m = -3
Y-intercept 'b' = 2
Therefore, equation of the line will be,
y = -3x + 2
Linear function representing the line will be,
f₁(x) = -3x + 2
2). Let the equation of the red line passing through (0, -4) and (2, -2) is,
y = mx + b
Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{-4+2}{0-2}[/tex]
m = 1
y-intercept 'b' = -4
Therefore, the linear function will be,
f₂(x) = x - 4
3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,
y = mx + b
Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]
m = 1
y-intercept 'b' = 8
Therefore, linear function will be,
f₃(x) = x + 8
4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,
y = mx + b
Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]
m = -2
y-intercept of the line 'b' = -6
Therefore, function representing the line will be,
f₄(x) = -2x - 6
5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,
y = mx + b
Since the line is passing through origin, y-intercept 'b' = 0
Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]
m = -3
Therefore, equation of the linear function will be,
f₅(x) = -3x
Related Questions
A rectangular playing field is twice as long as it is broad. If its area is 0.5294km2, find in Km, the perimeter of the field.
Answers
let Length be [tex] l [/tex] be $b$ ,
given : $l=2b$
and area, $lb=0.5294$
put $l=2b$ in equation of area,
$2b^2=0.5294 \implies b^2=0.2647 \implies b=0.5144$
and $l=1.0288$
perimeter =$2(l+b)=3.0864$ km
The perimeter of the field will be equal to 3.0864 km.
What is a perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. The perimeter of the rectangle is the sum of all the sides of the rectangle.
It is given that a rectangular playing field is twice as long as it is broad. If its area is 0.5294 square km.
The perimeter of the field will be calculated as below:-
let Length be b
l=2b
l x b=0.5294
Put l=2b in the equation of area,
2b²=0.5294
b² =0.2647
b=0.5144 and l=1.0288
The perimeter will be calculated as:-
perimeter =2(l+b)=3.0864 km
Therefore, the perimeter of the field will be equal to 3.0864 km.
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darious buys a bottle of chemical solution that contains 70% alcohol. the bottle contains 500 ml of solution. how many ml of alcohol r in the solution
Answers
Answer:
350 ml of alcohol
Step-by-step explanation:
70% = 70/100 = 0.7
70% of 500 ml is:
500*0.7 = 350 ml
there are:
350 ml of alcohol
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 20
3 10
5 0
7 -10
Initial value: 20, rate of change: 10
Initial value: 30, rate of change: 10
Initial value: 25, rate of change: -5
Initial value: 20, rate of change: -10
Answers
Answer:
Initial Value: 25, Rate of change -5.
First. Lets find the rate of change.
y2-y1/x2-x1 = m
We have A(1,20) B(3,10)
10-20/3-1=-5
m=-5(Rate of change)
Now let's find the initial value using slope-point form.
y-y₁=m(x-x₁)
y-20=-5(x-1)
=-5x+5+20
=-5x+25
The initial value is the value of y when the value of x is equal to 0. (Also the Y-Intercept)
Initial Value = -5(0)+25
=25
PLS ANSWER I WILL GIVE BRAINLIST AND A THANK YOU!!!! :)
Answers
Answer:
THE OTHER ANSWER IS WRONG
Step-by-step explanation:
90=20+6x-2
92=20+6x
72=6x
12=x
Hope this helps!
what is the x intercept for y=(2x(x-3))/(x-1). ?
my answer sheet says it is supposed to be -0.5
Answers
Answer:
( 0,0) and (3,0)
Step-by-step explanation:
y=(2x(x-3))/(x-1)
Set y = 0
0 =(2x(x-3))/(x-1)
Multiply each side by x-1, which makes x not equal to 1
0 =(2x(x-3))
Using the zero product property
2x=0 x-3 =0
x=0 x= 3
The x intercepts are x=0 x= 3
( 0,0) and (3,0)
The growth of a population of mountain lions can be described by the function f(x) = 500(1.015)^x, where x is the number of years after the first census. How do the mathematical domain and range compare to the reasonable domain and range? Check all that apply. Thank you!
Answers
Answer:
B E
Step-by-step explanation:
Answer:
B. The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0.
E. The mathematical range has a minimum value greater than 0, while the reasonable range is limited to whole numbers and has a minimum value greater than or equal to 500.
Step-by-step explanation:
Edge 2021
1.Solve by factorization method: x+1/x=11 1/11 2.Comment on the nature of roots for 4x^2-5=2(〖x+1)〗^2-7 plz, help...
Answers
Answer:
The equation
[tex]4\,x^2-5=2\,(x+1)^2-7[/tex]
can be solved by first expanding all indicated operations, and later when the constant terms disappear, by factoring out 2x , leaving the equation as a product of two factors equal zero, from which it is easy to extract the roots. See below.
Step-by-step explanation:
When solving for x in the following expression, and using factoring to apply at the end the zero product theorem:
[tex]4\,x^2-5=2\,(x+1)^2-7\\4\,x^2-5=2\,(x^2+2x+1)-7\\4\,x^2-5=2\,x^2+4\,x+2-7\\4\,x^2-5=2\.x^2+4\,x-5\\4\,x^2=2\,x^2+4\,x\\4\,x^2-2\,x^2-4\,x=0\\2\,x^2-4\,x=0\\2\,x\,(x-2)=0[/tex]
We observe that for the last product, to get a zero, x has to be zero (making the first factor zero), or x has to be "2" making the binomial factor zero.
Joshua remembered he had a coupon in his pocket that would take and additional 30%off the price of the shirts. Calculate the new total cost of the shirts including a sales tax of 6.5%
Answers
Answer:
New cost of the shirt=$39.028416
Step-by-step explanation:
Target is having a Back to School sale where all polo shirts are discounted by 20%. Joshua wants to buy five shirts: two cost $10.98 each, one costs $11.50, and two others cost $15.99 each. Joshua remembered he had a coupon in his pocket that would take an additional 30% of the shirts. Which choice represents the new total cost of the shirts including the sales tax of 6.5%
Solution
Two shirts cost=$10.98 each
One shirt cost=$11.50
Two shirts cost=$15.99 each
Total cost of shirts=(2*$10.98 + $11.50 + 2*$15.99)
=$21.96 + $11.50 + $31.98
=$65.44
All polo shirts are discounted by 20%
It means he would pay 100%-20% of the total cost
100%-20%=80%
Discounted price=$65.44 * 80%
=$65.44 * 0.8
=$52.352
He has a coupon of 30% off the shirt
100% -30%=70%
=$52.352*70%
=$52.352 * 0.7
=$36.6464
Plus Sales tax of 6.5%
6.5% of $36.6464
=0.065* $36.6464
=$2.382016
New cost of the shirt=$36.6464 + $2.382016
=$39.028416
PLEASE HELP, GIVING 55 POINTS IF YOU ANSWER (08.03/08.05 MC) A pair of equations is shown below: y = 3x − 5 y = 6x − 8 Part A: Explain how you will solve the pair of equations by substitution or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)
Answers
Answer:
A. (1, -2)
B. the lines intersect at the solution point: (1, -2).
Step-by-step explanation:
A. The equations can be solve by substitution by using the y-expression provided by one of them to substitute for y in the other.
This gives ...
3x -5 = 6x -8
Adding 8-3x to both sides, we get ...
3 = 3x
Dividing both sides by 3 gives ...
1 = x
Substituting this value into the first equation, we can find y:
y = 3(1) -5 = -2
The solution is (x, y) = (1, -2).
__
B. The lines intersect at the solution point, the point that satisfies both equations simultaneously. That point is (1, -2).
Msr walkers class set up an online fund with a goal to raise 1280
Answers
Answer: is brainly broken for u too??
Step-by-step explanation:
Please help me understand this. Thank you! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows the Number of Weeks on x-axis and Number of Songs Left to Download on the y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answers
Answer:
Rate of Change/Slope = -20
Equation: y= -20x +100
Step-by-step explanation:
A. We know the rate of change is also known as the slope. If we used the slope formula to find the slope we can find the Rate of Change.
[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]
B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'
(0,100)
(100)=-20(0) + b
b = 100
Since we know the slope and the b value we can write the equation:\
y = -20x +100
The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :
Slope = - 20y = -20x + 100Slope = Rise / Run Rise = (y2 - y1) = (0 - 100) = - 100Run = (x2 - x1) = (5 - 0) = 5Slope = - 100 / 5 = - 20
General form of a slope - intercept relation :
y = bx + cThe intercept, c can be calculated thus:
100 = - 20(0) + c
100 = 0 + c
c = 100
Hence, the slope - intercept equation will be y = - 20x + 100
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Bernita and Derek each plot a number on a number line. the numbers are unique but have the same absolute value. the sum of the absolute values of the numbers is 50. what are the two numbers
Answers
Answer:
-25, 25
Step-by-step explanation:
Since the numbers have the same absolute value and the sum of their absolute values is 50, they both must have an absolute value of 50/2 = 25.
Unique numbers with the same absolute value will have opposite signs.
The numbers are -25 and 25.
please help :) (1) We went to the Museum of Natural Science to see the new gem exhibit. (2) The display included and showed minerals from all over the world. (3) The most impressive part of the show was the extensive display of diamonds and other precious stones. Which revision makes one of the sentences more concise? A. Sentence 1: Delete the word “gem.” B. Sentence 2: Delete the phrase “and showed.” C. Sentence 3: Change “impressive” to “interesting.” D. Sentence 3: Change “show” to “exhibit.”
Answers
Answer
B. Sentence 2: Because included, and showed is the exact same thing so B
Step-by-step explanation:
Answer:
just so other guy can have brainlest
Step-by-step explanation:
The population of fruit flies tripled every day and the population today is 200 fruit flies.
a) Write an equation modeling the growth in the population of fruit flies.
b) What was the population of fruit flies 3 days ago?
Answers
Answer:
Equation = 600nNumber of fruit flies after 3 days = 1800 fruit fliesStep-by-step explanation:
Given:
Number of fruit flies = 200
Rate of growth = 3 times per day
Find:
A . Equation
B . Number of fruit flies after 3 days
Computation:
A . Equation = 3n(200)
Equation = 600n
B. Number of fruit flies after 3 days
Number of fruit flies after 3 days = 600(3).
Number of fruit flies after 3 days = 1800 fruit flies
An_ is the set of numbers that include negative numbers
and the subset of_ numbers (...-3, -2, -1, 0, 1, 2, 3...). Also
described as positive numbers and their opposites and zero.
Blank 1:
Blank 2:
Answers
Answer:
Integer, rational
Step-by-step explanation:
An integer is normally described as a positive and their opposites and zero. The explaination for blank 2 is a rational number because a rational number can also be an integer and a whole number. Hope this helps!
Answer:
Step-by-step explanation:
The answer is integer. Integer are whole numbers that are either positive or negative including 0.
Please help me I promise I will mark brainliest, I need an answer asap!!!!!!!! please hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! f(x) = 3x + 9, g(x) = 5x^2 Find (f + g)(x). A). -5x^2 + 3x + 9 B). Quantity three x plus 9 divided by five x squared. C). 15x^3 + 45x D). 5x^2 + 3x + 9
Answers
Answer:
D
Step-by-step explanation:
(f+g)(x) = f(x) + g(x)
=3x + 9 + 5x²
=5x² + 3x + 9
What is the slope of the line below (1, -2) (4, -2)
Answers
Answer:
0
Step-by-step explanation:
We can use the slope formula to find the slope
m = (y2-y1)/(x2-x1)
= ( -2 - -2)/( 4 -1)
= (-2+2)/( 4-1)
= 0/3
= 0
Answer:
Slope =0Step-by-step explanation:
[tex](1, -2) , (4, -2)\\m = ?\\x_1 =1\\y_1 =-2\\x_2 =4\\y_2 =-2\\\\m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{-2-(-2)}{4-1} \\m = \frac{-2+2}{3}\\ m = \frac{0}{3}\\ m = 0[/tex]
Choose all answers that apply
A -x + (-x) = 0
B x - (-x) = 0
C none of the above
Answers
Answer:
c
Step-by-step explanation:
none of the above
C none of the above
because x-(-x)=x+x=2xand
-x+(-x)= -x-x=-2x
so answer is 'C' none of the above
20. A pool holds 1440 CUBIC feet of water, the aty
charges $). 15 per cubic meter of water
used now, much will it cost to fill the pool?
Answers
Complete question :
A pool holds 1440 cubic feet of water, the city charges $1.75 per cubic meter of water used.
How much will it cost to fill the pool?
Answer:
$71.36
Step-by-step explanation:
Amount charged per cubic meter = $1. 75
Total volume of pool = 1440 ft^3
Using the conversion unit chart :
1 cubic meter = 35.3147 cubic foot
Then we can express the capacity of water held by the pool in cubic metre.
If 1 cubic meter = 35.3147 cubic foot
Then ;
y cubic meter = 1440 cubic foot
y = 1440/35.3147
y = 40.776220 cubic meter
Thus;
Cost of filling the pool will be;
$1.75 × 40.776220
= $71.358386
= $71.36
Write 37 99 as a decimal. A) 0.037 B) 0.37 C) 0.37 D) 3.73 (ALSO there are 2 of the .37 in the problem so im not sure what i have to do)
Answers
Answer:
Step 1: Address input parameters & values.
Input parameters & values:
The fraction number = 37/99
Step 2: Write it as a decimal
37/99 = 0.3737
0.3737 is the decimal representation for 37/99
Answer is 0.3737 repeating.
Hope this helps! Plz mark brainliest! ☜(ﾟヮﾟ☜)
Two numbers are in ratio 3 by 2 and their difference is 5 find numbers
Answers
Answer:
15,10
Step-by-step explanation:
let the numbers be 3x and 2x
3x-2x=5
x=5
∴ numbers are 3×5,2×5
or 15,10
Please help me with this problem. I will give brainliest!
Answers
Answer:
centre = (11, 0 ), radius = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - h)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
(x - 11)² + y² = 9 ← in standard form
with (h, k ) = (11, 0 ) and r² = 9 ⇒ r = [tex]\sqrt{9}[/tex] = 3
centre = (11, 0 ) and r = 3
A family has four children. What is the probability that two children are girls and two are boys? Assume the the probability of having a boy (or a girl) is 50%.
Answers
Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.
The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.
The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.
Clinton is having a coin drive. Each class has a goal of 600 pennies.Layla has already collected 338 pennies. How many more pennies does Layla need to collect to reach their goal. PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINLIEST PLEASE AND EXPLAIN HOW YOU GOT YOUR ANSWER
Answers
Answer:
262 pennies
Step-by-step explanation:
If Layla already has 388 pennies and she needs 600 pennies total, all she needs to do is is take the amount she already has away from 600:
Which equation does NOT graph a line? A) y = 5 B) y = -3x3 C) y = 2/3 x D) y = −8x That 3 in b is an exponent btw
Answers
Answer:b
Step-by-step explanation:
Rocket science
Factor completely, then place the answer in the proper location on the grid. 6x2 - 3x - 30
Answers
Answer:
3(2x-5)(x+2)
Step-by-step explanation:
Factor out the 3.
3(2x²-x-10)
Factor the remaining.
3(2x-5)(x+2)
(I don‘t know what grid they’re talking about.)
Dubai Mall and Deira City Centre are equidistant from Wafi Mall. Considering Wafi Mall as origin, the position of Deira City Centre is ( 0,7). If the ordinate of the position of Dubai Mall is zero, then write the coordinates of the position of Dubai Mall.
Answers
they're equidistant, so distance should be equal.
distance of City centre is [tex]\sqrt{0^2+7^2}=7[/tex]
distance of mall is simply $x$. (ordinate is 0, means the point is on x axis , and that's the distance from origin)
thus, $$x=7$$
Jayden is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after t hours?
Answers
Answer:
a. 8 gallons
b. (11-0.75t) gallons
Step-by-step explanation:
a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.
We proceed as follows;
Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours
Mathematically, that would be 0.75 * 4 = 3 gallon
Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.
That would be; 11 - 3 = 8 gallons
b. Like above, we want to know the amount of fuel left after t hours.
Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t
Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.
Mathematically, that would be 11- 0.75t
Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?
Answers
Answer: [tex]64.3=\frac{1}{3}(B)(7)[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} Bh[/tex]
B is the area of the base
h is the height of the cone
[tex]V=64.3 cm^3[/tex]
[tex]h=7cm[/tex]
[tex]64.3=\frac{1}{3}(B)(7)[/tex]
[tex]192.9=(B)(7)[/tex]
[tex]B=192.9/(7)[/tex]
[tex]=27.56cm^2[/tex]
Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 41.9mg. The population standard deviation in all cans is 5.2mg. You suspect that there is more than 40mg of sodium per can. Find the z-score.
Answers
Answer:
Z - score = 2.83
Step-by-step explanation:
Given the following :
Number of samples (N) = 60
Sample mean (x) = 41.9mg
Population mean (μ) = 40mg
Population standard deviation (sd) = 5.2
Using the relation :
Z = (x - μ) / (sd / √N)
Z = (41.9 - 40) / (5.2 / √60)
Z = 1.9 / (5.2 / 7.7459666)
Z = 1.9 / 0.6713171
Z = 2.8302570
Therefore, the z-score = 2.83
