========================================================
Explanation:
Plug in x = -1 to find that
f(x) = 2|x-1|
f(-1) = 2|-1-1|
f(-1) = 2|-2|
f(-1) = 2*(2)
f(-1) = 4
If you repeat for x = 1, you should find that f(1) = 0
--------
Now use the average rate of change formula below. Effectively, we're using the slope formula more or less.
[tex]m = \frac{f(b)-f(a)}{b-a}\\\\m = \frac{f(1)-f(-1)}{1-(-1)}\\\\m = \frac{0-4}{1+1}\\\\m = \frac{-4}{2}\\\\m = -2\\\\[/tex]
The average rate of change on this interval is -2
This is the same as finding the slope through the points (-1, 4) and (1, 0).
Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line. Estimate how far the hurdles are from one another. Do not include units (meters) in your answer. Round your answer to the nearest whole meter. plzzzzzzzzzzzzzzz help
Answer:
7.5 metres
Step-by-step explanation:
According to the Question,
Given,Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line.Thus, the distance from the first hurdle to eighth hurdles is 80-(12+15.5) = 52.5m
Now, we have 8 Hurdle but the distance between each hurdle is equally divided in 7 parts . (Please find the diagram in Attachment)
So, 52.5 /7 ⇔ 7.5m far the hurdles are from one another.
Write an equation for the data shown in each table.
Answer:
1) f(x) = 500·(1.1)ˣ
2) f(x) = 500·(0.9)ˣ
Step-by-step explanation:
1) The given values in the table are;
x; 0, 1, 2, 3
f(x); 500, 550, 605, 665.5
By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;
550/500 = 11/10 = 1.1 = 605/550 = 665.5/605
From which we have;
The values of f(x) are in a geometric progression
The nth of a geometric progression = a·rⁿ
The common ratio, r = 1.1
The first term, a = 500
The number of terms, n = x
Therefore, xth term, f(x) = a×(r)ˣ
Substituting the values gives;
The equation for the data shown in the table is f(x) = 500·(1.1)ˣ
2) The given table of values is presented as follows;
x; 0, 1, 2, 3
f(x); 500, 450, 405, 364.5
The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405
The terms of f(x) are in a geometric progression
The first term. a = 500
The common ratio, r = 9/10 = 0.9
The nth term of a geometric progression, G.P. = a·rⁿ
By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;
The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.
someone please help, I need it, show all work.
Sadia works at a theatre selling popcorn. Large boxes of popcorn sell
for $5.00 and small boxes of popcorn sell for $3.00. During her shift
last night, she sold 60 boxes of popcorn. Her receipts totalled $260,
not including taxes. Determine the number of large and small
popcorn boxes she sold last night.
Answer:
its 55 not 60
Step-by-step explanation:
just divide 260 by 5 and 3
The required number of large and small popcorn boxes sold are 40 and 20 respectively.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the number of the large box be x and the small box is y.
According to the question,
5x + 3y = 260 - - - - - - -(1)
x + y = 60
x = 60 - y - - - - - - - - (2)
Put the value of equation, (2) in equation 1
5 (60 - y) + 3y = 260
300 - 5y + 3y = 260
2y = 40
y = 20
Now,
x = 60 - 20
x = 40
Thus, the required number of large and small popcorn boxes sold are 40 and 20 respectively.
Learn more about arithmetic here:
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The sides of a triangle are 4, 7, and 10. The triangle is dilated by a scale factor of 3 to create a
new triangle. Find the perimeter of the new triangle.
A
21 units
B
63 units
30 units
D
25 units
Answer:
B 63 units
Step-by-step explanation:
Dilatation is an increase of shape , a larger imagine , the dilatation is 3 so times each side by three and add them all up
12. The length and width of a rectangle are in the ratio 7:3. If the perimeter is 62cm calculate: (1) the width (ii) the length of a diagonal to the nearest centimetre. (iii) the area of the rectangle.
Answer:
Step-by-step explanation:
Length = 7x
Width = 3x
Perimeter = 2L + 2W
Part A
2*7x + 2*3x = 62
14x + 6x = 62
20x = 62
x = 62/20
x = 3.1
Length = 3.1 * 7 21.7
Width = 3.1 *3 9.3
Width = 9.3
Part B
Use the Pythagorean Theorem
diagonal squared = 21.7^2 + 9.3^2
diagonal^2 = 557.38
sqrt(diagonal^2) = sqrt(557.38)
diagonal = 23.61
To the nearest cm is 24
Part C
Area = L*W
Area = 21.7 * 9.3
Area = 201.8
Which best describes the product of these two radicals?
√2-√7
The product is rational because both V2 and V7 are rational numbers,
The product is irrational because both 2 and 7 are irrational numbers.
The product is rational because at least one factor is rational,
The product is irrational because one of the factors is an odd number.
Answer:
second option: product is irrational because both are irrational
Step-by-step explanation:
The second option which is the product is irrational because both are irrational numbers.
What is irrational number?
These are those numbers which are impossible to be written in the form of p/q.
How to determine the product?
We have been the given the following numbers.
[tex]\sqrt{2 } and \sqrt{7}[/tex] and we have been asked to find the description of the product of both. We know that these are irrational numbers because it cannot be written in the form of p/q. When we multiply this we can get root 14 which is also a irrational number.
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What is the value of x?
Answer:
98deg
Step-by-step explanation:
Angles in a triangular add to 180.
180-(53+45) is the top angle.
Angles on a line add a up to 180
180 - triangles top angle = x
Please answer max 10 min, I have a test.
Given a room is 12 feet by 10 feet and we have a circular rug with a radius of 3 feet, calculate the amount of floor left uncovered by the circular area rug in a rectangular living room
Step-by-step explanation:
floor = 12*10= 120 sq ft
rug = r² = 9 Пr2
120-9π = 91.74 sq ft
given parallelogram BCDE
what is the equation to find x?
what is x?
what is length of side CD?
please help
Answer:
x=3
CD = 13
Step-by-step explanation:
BE = CD in a parallelogram
1+4x = 5x -2
Subtract 4x from each side
1+4x-4x = 5x-2 -4x
1 = x-2
Add 2 to each side
1+2 = x-2+2
3 =x
The length of CD
CD = 5x-2 = 5*3 -2 = 15-2 = 13
Solve pleaseeeeeeeeeeeeee
Answer:
x > 3
Step-by-step explanation:
___________________
PLEASE HELP LOL
what type of angles are <4 and <8
Answer:
C. Corresponding angles
Step-by-step explanation:
Visualize the two points of intersection and the four angles around each of them being separated. If you put the on top of each other, you can see that angle 4 corresponds with angle 8.
Answer: corresponding :)
Step-by-step explanation:
corresponding angles are angles that are in the same position relative to lines intersected by a transversal
basically theyre equal and on the same side of the transversal
hope this helps :)
giving brainlist again:) please help
Answer:
midpoint x=5/2&y=-7/2 this might be helpful
Which decimal is equivalent to 4/3
Answer:
1.33333333333 repeating
Step-by-step explanation:
Hope this helps
Answer:
1.3333
Step-by-step explanation:
By visual inspection determine the best-fitting regression model for the data plot below
Answer:
Exponential
Step-by-step explanation:
By visual inspection the graph generated by the points plotted is an exponential graph as the graph curves upward. The graph is also continous and differs from either a decreasing or increasing Linear graph, which shows a straight best of fit pattern. Hence, the graph most closely represents an exponential graph from visual examination.
The best-fitting regression model for the considered data plot is given by:
Option A: Exponential.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).
Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.
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what time did he reach ???
Answer: 2050hrs
Step-by-step explanation:
If he is going 72 km/hr and he traveled 504 km we can calculate how long he took to go by dividing the distance he went by distance per hour. That will give us the amount of hours that he took to get there. That would be [tex]\frac{504}{72}[/tex]. [tex]\frac{504}{72}=7[/tex] so it took him 7 hours to get there. 7 hours after 1350 is 2050 assuming we are using the 24 hour clock notation.
The Marked price of a jacket at a dealer's shop is 2400. The dealer allows a discount of 15% to the retailer. As the company's policies the marked price of the retailer should be the same as the dealer's marked price. What SP should the retailer fix for the jacket? What would its final price be if 10% VAT is imposed? What would be the actual gain of retailer?
Ans
2280,2502,240
Answer:
2400
2640
360
Step-by-step explanation:
I am not sure the description is totally clear.
my assumptions are (based on my interpretations of the text) :
the retailer buys from the dealer with 15% discount.
but the retailer has to sell the jacket for the same price as the dealer.
so, both mark the sale price as 2400.
if the customer buys from the retailer, the retailer makes 15% profit (the discount he got from the dealer).
15% = 2400 × 15/100 = 24 × 15 = 360
the retailer makes this profit no matter what other fees or taxes are added.
if the customer buys from the dealer, the dealer makes these 15% and some more (we don't know how much) profit.
now, the final price is to include also 10% VAT
100% = 2400
1% = 2400 / 100 = 24
10% = 24 × 10 = 240
so,
final price = SP + VAT = 2400 + 240 = 2640
Write the equation of the line in fully simplified slope-intercept form.
12
11
10
-12-11-10-9-8
1 2 3
5 6
8 9 10 11 12
-3
-4
-9
-10
Answer:
y=1/2x+6
Step-by-step explanation:
Is the relationship between the variables in the table a direct or inverse variation or neither? If it is direct or inverse, write a function to model it.
x 4 8 16 32
y 32 16 8 4
Step-by-step explanation:
this is inverse variation
the function is
xy = 128
=> y = 128/x
Given any triangle ABC labeled as shown the law of sines states that:
Diane has $814 in her checking account. If she writes five checks for a total of $287, how much does she have left
in her account?
Answer:
$527
Step-by-step explanation:
Find how much she has left by subtracting 287 from 814:
814 - 287
= 527
So, she has $527 left in her account
78.4 divided by 0.56
Need help please anwer all its one page question i put in two bc it didnt fit
Answer:
sorry only doing the ones i know how to do
b) for the histogram, just write all the numbers on the table on the bottom, theres 13 lines but 2 repeats so it should be even. on the side write a range of minutes
c) mean = 7.8 ; standard deviation = 3.13
d)
min = 2
max = 13
range = 11
q1 = 5.5
q3 = 10.75
iqr = 5.25
median = 8
what does iqr represent? it represents the middle 50% of all the values
e) write the numbers from the table without repeats and mark them how many times theyre written
Find the solution to the equation 8n - 9 = 63.
Answer:
9
Step-by-step explanation:
63+9=72
72/8=9
hope this helped
Answer:
[tex]8n - 9 = 63 \\ 63 + 9 = 8n \\ 72 \div 8 = n \\ n = 9[/tex]
2. Si x representa la edad de Ana, ¿cómo se
escribe en simbolos "la mitad de la edad de
Ana"?
The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4 → 10x − 5y = −20 3x + 5y = 59 → 3x + 5y = 59 13x = 39 Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
Answer:
[tex]13x=39[/tex]
Step-by-step explanation:
Given
[tex]2x - y = -4 \to 10x - 5y =-20[/tex]
[tex]3x +5y =59 \to 3x +5y = 59[/tex]
Required
What can replace [tex]3x +5y = 59[/tex] ?
We have:
[tex]10x - 5y =-20[/tex]
and
[tex]3x +5y = 59[/tex]
Add up both equations:
[tex]10x +3x-5y+5y=-20+59[/tex]
[tex]10x +3x=39[/tex]
[tex]13x=39[/tex]
Since [tex]13x=39[/tex] is a result of [tex]10x - 5y =-20[/tex] and [tex]3x +5y = 59[/tex],
[tex]13x=39[/tex] can replace [tex]10x +3x=39[/tex]
What is the domain of the function y=%/x-1?
O-
o -1 < x < oo
0
O 1
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x - 1}[/tex]
Required
The domain
The given function is cubic root; there are no restrictions on cubic root functions
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer and Step-by-step explanation:
Mandy travels more miles.
We determine this by multiplying the distance from home by the number of trips.
For Mandy, she lives 10 miles away from school, and takes 9 trips. 9 times 10 is 90 miles.
For Matt, he lives 8 miles away from school, and takes 11 trips. 11 times 8 is 88 miles.
Many travels 2 more miles in total than Matt.
#teamtrees #PAW (Plant And Water)
Answer:
mandy
Step-by-step explanation:
so mandy has 10 miles and 9 trips to school matt has 8 miles and 11 trips to school so mandy is 10x9=90
and matt is 11x8=88
mandy=90
matt=88
Use the explicit formula an = a + (n-1). d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
Answer:
Step-by-step explanation:
The difference is a2 - a1 = 31 - 24 = 7
n = 500
a500 = a1 + (500 - 1) * 7
a500 = 24 + 499 * 7
a500 = 24 + 3493
a500 = 3517
Please help!?
Use △DEF, shown below, to answer the question that follows: What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below
Answer:
x=63.25
Step-by-step explanation:
Hi there!
We're given ΔDEF with m<E=90°, m<D=49°, DE=55, and EF=x
we need to find the value of x
Let's use trigonometry to do it
Since we are given the measures of the 2 legs (the sides that make up the 90° angle), let's use tangent, specifically tan(49), since we are given the measure of that angle
Recall that tangent is [tex]\frac{opposite}{adjacent}[/tex]
in reference to m<D (the angle that is 49°), the opposite side is EF (x) and the adjacent side is DE (55)
so tan(49)=[tex]\frac{x}{55}[/tex]
plug tan(49) into your calculator; remember to have the calculator on degree mode
tan(49)≈1.15 (rounded to the nearest hundredth)
so that means:
1.15=[tex]\frac{x}{55}[/tex]
multiply both sides by 55 to clear the fraction
63.25=x
Hope this helps!
Someone please help me It’s getting late and it’s due tomorrow
Explain why the equation
1- x= 5(x - 4) - 6x has no solution.
Answer:
After the distribution of the 5 and the addition of x to both sides, the x variable is cancelled out leaving 1 = - 20.
This statement is false. Hence, no solution
Step-by-step explanation:
1 - x = 5(x - 4) - 6x (Distribute 5)
1 - x = 5x - 20 - 6x (Combine like terms)
1 - x = -x - 20 add x to both sides
1 = - 20 False