Derek walks to his best friends house at a rate of 1 block per minute, then turns around and walks home. The graph shows the distance Derek walks in the given amount of time. Write an equation for the graph.
Answers
In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
Equation of a line:
The equation of a line is given by:
[tex]y = mt + b[/tex]
In which m is the slope and b is the y-intercept(value of y when x = 0).
This situation:
One line for x between 0 and 10;Another for x between 10 and 20;x between 0 and 10:
From here, we can take two points (t,y). I will take (0,0) and (10,10).
From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:
[tex]y_1 = mt[/tex]
To find the slope, when we have two points, it is given by change in y divided by change in t, so:
Change in t: 10 - 0 = 10
Change in y: 10 - 0 = 10
Slope: [tex]m = \frac{10}{10} = 1[/tex]
Thus, the first definition is:
[tex]y_1 = t, 0 \leq t < 10[/tex]
x between 10 and 20:
I will take the points (10,10) and (20,0).
First, we find the slope:
Change in t: 20 - 10 = 10
Change in y: 0 - 10 = -10
Slope: [tex]m = \frac{-10}{10} = -1[/tex]
Thus:
[tex]y_2 = -t + b[/tex]
For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So
[tex]0 = -20 + b[/tex]
[tex]b = 20[/tex]
Thus, the second definition is:
[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]
Write an equation for the graph.
We use the two definitions, that is:
[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]
So
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
A similar question can be found at https://brainly.com/question/16024991
Related Questions
convierte los decimales a fracción:
a) 3, 1233333 =
b) 4, 3855555 =
c) 37, 22222 =
d) 16, 2929292929 =
e) 2, 33333333 =
Answers
(a) Let x = 3.12333…. Then 100x = 312.333… and 1000x = 3123.333…, so that
1000x - 100x = 3123.333… - 312.333…
==> 900x = 2811
==> x = 2811/900 = 937/300
(b) x = 4.38555… ==> 100x = 438.555… and 1000x = 4385.555…
==> 900x = 3947
==> x = 3947/900
(c) x = 37.222… ==> 10x = 372.222…
==> 9x = 335
==> x = 335/9
(d) x = 16.292929… ==> 100x = 1629.292929…
==> 99x = 1613
==> x = 1613/99
(e) x = 2.333… ==> 10x = 23.333…
==> 9x = 21
==> x = 21/9 = 7/3
Which of the following is a correct sine ratio for the figure? Question 20 options: A) C = 5∕12 B) C = 5∕13 C) C = 12∕13 D) C = 13∕12
Answers
Answer:
B
Step-by-step explanation:
Sine is opposite/hypotenuse. Sine C would be 5/13 so option B is correct.
Answer ASAP please!
….
Answers
Answer:
A
Step-by-step explanation:
Cos=A/H
Cos35=x/28.7
28.7×cos 35
Answer:
the answer is A
I hope this helps out
the sum of 5 times a number and 8 is equal to 9
Answers
Answer:
The unknown number is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Let's make the unknown number x.
The sum of 5 TIMES a number (x) & 8 is 9.
Let's write it mathematically.
5x + 8 =9
We are trying to find the unknown number, so let's remove all the numbers from the left side to find x. Minus 8.
5x=1
5x is basically 5 times x, so to find x, we need to divide and from there we can remove 5.
x= [tex]\frac{1}{5}[/tex]
Find the value of x in the diagrams below
Answers
Answer:
1. x = 24
2. x = 31
Step-by-step explanation:
For number 1, 3x - 1 = 71 because opposite angles are congruent. Solving that gives us x = 24.
For number 2, 2x + 4x - 6 = 180, because they lie on the same line and a straight line is 180 degrees. Solving that gives you 6x - 6 = 180, x = 31 degrees.
Answer:
1. 24
2. 31
Step-by-step explanation:
1. opposite angles are equal
( 3x-1)°=71°
3x=72
x=24
2. remember opposite angles are equal,
180°= (2x)°+(4x-6)°
186=6x
x=31
Help me plz thank you
Answers
Answer:
1) Distance=Speed*time
90=(x+1)*(x)+(2x+5)(x-1)
90=x^2+x+2x^2-2x+5x-5
3x^2+4x-95=0
2) 3x^2+4x-95=0. Using quadratic formula, we get
x=(-4±sqrt(16-4*3*(-95)))/6, x=5 or - 19/5 but since x also represents time, it can't be negative.
3) Total time take she took for the journey is x+x-1=2x-1=2*5-1=9 hours
The sum of two numbers is 71648.one of the number is 7 times the other.find the numbers
Answers
Answer
8956
explanation step by step
Answer: numbers are 8956 and 62692
Step-by-step explanation:
Let the numbers be x and 7x
ATQ
x + 7x = 71648
8x = 71648
x = 71648/8
x = 8956
Therefore the numbers are 8956 and 62692 respectively
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Which of the following is a radical equation?
x^3=13
x+√3=13
5x + 3 = 13
X+3= 13
Answers
Answer:
none
Step-by-step explanation:
Radical equation is an equation un which variable involve under the radical sign.
but in all given equation not a single variable is under radical sign.
Note: if you need to ask any question please let me know.
The path from the subway station to the art museum is three blocks to the north then four blocks to the west.
What is the straight-line distance in blocks from the subway station to the art museum?
Answers
Answer:
7 block s
Step-by-step explanation:
3 from North plus
4 from West
4+3=7
A. Find x
B. Find the measure of angle b
C. Find the measure of angle c
Answers
Answer:
3, 50 and 70
Step-by-step explanation:
Using exterior angle property, we have 15x+5+22x+4=120, 37x+9=120. x=3
B=15x+5=50
C=22x+4=70
Are the numbers 10 and 10% the same? By what percent is the number smaller than the greater one?
Answers
Answer:
The way to consider this problem is to realize that the
% symbol actually is equal to a number just like [tex]\pi[/tex] is
whereas [tex]\pi[/tex] is equal to 3.1415... , % is equal to .1 (as a decimal ) or 1/100 as
a fraction... thus
10% is actually 10 * 1/100 or 10/100 which is not 10...
as for the size the 1/100 essentially a DIVISION thus it ends up being SMALLER
Step-by-step explanation:
We can not compare a number and a percentage. 10% of something means 1/10th of something and it can be anything for instance.
What is the percentage?The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period. Later, the period was eliminated, and the two portions were combined to create the current one-word form of a percent.
The best way to approach this issue is to understand the percentage. The % sign actually corresponds to a number. While equals 3.1415, % is equivalent to.1 (as a decimal) or 1/100 as a portion, hence, 10% is actually 10 * 1/100, which is not the same as 10. Regarding size, since 1/100 is essentially a division, it becomes smaller.
Therefore, A number and a percentage cannot be compared. 10% of something is equal to one-tenth of it, and it can be anything, for example.
Learn more about percentages here:
https://brainly.com/question/29116686
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can anyone solve it plzzzz
Answers
Answer:
1.A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
2.
Solution given:
We have
Sin²[tex]\theta[/tex]-Cos ²[tex]\theta[/tex]=1
Sin²[tex]\theta[/tex]=1+Cos²[tex]\theta[/tex]
Sin[tex]\theta[/tex]=[tex]\sqrt{1-Cos²\theta}[/tex]
3.
4Tan²[tex]\theta[/tex]+4Cot²[tex]\theta[/tex]-3Tan²[tex]\theta[/tex]-3Cot²[tex]\theta[/tex]
4Tan²[tex]\theta[/tex]-3Tan²[tex]\theta[/tex]+4Cot²[tex]\theta[/tex]-3Cot²[tex]\theta[/tex]
Tan²[tex]\theta[/tex]-Cot²[tex]\theta[/tex]
Determine the period.
Answers
Answer:
4
Step-by-step explanation:
The period is the length of one cycle.
By cycle, I mean the smallest piece that can be traced and copied over and over to form the whole graph. If you notice the graph starts at x=0 and the curve makes a complete cycle by x=4. The cycle starts over again at x=4 and ends at x=8. I hope you are seeing the graph looks exactly the same from x=0 to x=4 as x=4 to x=8.
The length of one cycle of this graph is 4.
The period of function is,
P = 4
Since, In order to find the period of a graph in general, first, find the period of the parent function, and divide that by the absolute value of the coefficient of the independent variable.
Here, Graph of function is shown.
Hence, The period of function is,
P = 4
Therefore, The period of function is,
P = 4
Learn more about the function visit:
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#SPJ7
1) Let f be the function defined by the
graph shown at right, with y = f(x).
a) What is the value of f(-9)?
-14-13-12-)1-10-9
10 11 12
b) How many solutions are there to
the equation f(x) = -2? (Just
state how many there are.)
c) State any and all intervals on which fis decreasing
d State any and all values of x for which fax>0. Ilse intervals to do this
Answers
find the next three sequence of 1,3, 9, 27,
Answers
Answer: 81, 243, 729
Step-by-step explanation:
STEP ONE: Find a pattern in the sequence
3 ÷ 1 = 3
9 ÷ 3 = 3
27 ÷ 9 = 3
As we can see from the given sequence, each number multiplies 3 to get the next term.
STEP TWO: Find the next three terms
27 × 3 = 81
81 × 3 = 243
243 × 3 = 729
Hope this helps!! :)
Please let me know if you have any questions
Somebody help me please!!!!!!!!!
Answers
Answer:
[tex](x-5)^2+(y+3)^2=10[/tex]
Step-by-step explanation:
equation of a circle: (x – h)^2 + (y – k)^2 = r^2 where (h,k) is the center
The center of the circle is at (5, -3)
(x-5)^2+(y+3)^2
To find the radius, use distance formula: [tex]\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]
[tex]\sqrt{(6-5)^2 + (3)^2}[/tex]
[tex]\sqrt{1^2 + 3^2} = \sqrt{1+9} = \sqrt{10}[/tex]
[tex](x-5)^2+(y+3)^2=10[/tex]
Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
Answers
Answer:
Does the answer help you?
Round 96.1825899389 to 4 decimal places.
Answers
Because the 5th number is over 5 you round up the 4th number to 6 :)
2x+3y=19 // 6x+2y=22
Answers
Answer:
(2, 5 )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 19 → (1)
6x + 2y = 22 → (2)
Multiplying (1) by - 3 and adding to (2) will eliminate the x- term
- 6x - 9y = - 57 → (3)
Add (2) and (3) term by term to eliminate x
0 - 7y = - 35
- 7y = - 35 ( divide both sides by - 7 )
y = 5
Substitute y = 5 into either of the 2 equations and solve for x
Substituting into (1)
2x + 3(5) = 19
2x + 15 = 19 ( subtract 15 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
solution is (2, 5 )
Geometry, please answer question ASAP
Answers
Answer:
length = 11 ft
breathe = 5 ft
perimeter of rectangle = lxb
= 11ft x 5ft
= 55 ft
the answer is 55 ft
Answer:
Perimeter of rectangle = 2(l+b)
=2(11+5)
=2x16=32ft
Three different sizes of sports-drinks mix are shown with their prices. Can the relationship between price and volume (in grams) be described by a constant rate? Explain
Answers
Answer:
Step-by-step explanation:
No, because unit prices are different.
[tex]\frac{9.00}{150}[/tex] = $0.06 per gram
[tex]\frac{12.50}{250}[/tex] = $0.05 per gram
[tex]\frac{22.75}{325}[/tex] = $0.07 per gram
Explain how the concepts of perimeter and circumference are related
A window
A door
A carpet
A fence
Answers
Answer:
A fence
Step-by-step explanation:
On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from
Saugerties to Catskill be on this map?
Answers
Answer:
10miles
Step-by-step explanation:
Answer:
I have no clue what is going on wit dis g
Write the equation of the line that passes through the points (−4,1) and (−9,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Help plz
Answers
Step-by-step explanation:
gradient(m)=change in y/change in x
=5-1/-9-(-4)
=4/-9+4
=4/-5
equation now
y-y1=m(x-x1)
y-1=4/-5[x-(-4)]
y=4/-5(x+4)+1
y=-4/5x-16/5+1
y=-4/5x-21/5
Answer:
y = -4/5x - 11/5
Step-by-step explanation:
First, find the slope using the slope formula.
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{1-5}{-4-(-9)}\\\\m=-\frac{4}{5}[/tex]
Then, use the point-slope formula and substitute the values for the variables. I'll use (-4, 1) in this instance.
[tex]y-y_1=m(x-x_1)\\\\y-1=-\frac{4}{5}(x+4)\\\\y-1=-\frac{4}{5}x-\frac{16}{5}\\\\y=-\frac{4}{5}x-\frac{11}{5}[/tex]
This polygon is a Quadrilateral (4 sided
2
figure). Based on the interior angle sum,
find the value of x.
80 degrees
to
60 degrees
xº
to
O 100 degrees
O 110 degrees
Answers
Answer:
Step-by-step explanation:
3x° + 60° = 360°
3x = 360 - 60
3x = 300
x° = 100°
Point M is the midpoint of AB. The coordinates of point A are (-7, 1) and the coordinates of M are (-2,2).
What are the coordinates of point B?
Answers
Answer:
B = (3.3)
Step-by-step explanation:
D= -2
E = [1 2]
17. Multiply matrix D by matrix E.
A. 2
B. [
48]
5 101
C.-2-4
1 2
D.
5-2 1
4 2
Answers
Answer:
here's the answer to your question
Determine the value of k if 12x2 + kx/ 4x= 3x – 5.
Answers
Answer:
k = -20.
Step-by-step explanation:
Do the division:
4x ) 12x^2 + kx ( 3x
12x^2 + k/4
So k/4 = - 5
k = -20.
A shipping container is in the shape of a right rectangular prism with a length of 13 feet, a width of 9 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.61 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answers
Answer:
285pound
Step-by-step explanation:
Volume of the container = length * width * height
= 13 * 9 * 4
= 468 cubic feet
Weight of the contents in the container = 468 * 0.61 = 285.48 = 285pound
simplify: 2y + 16 + 2y + 30 + 4y - 13 + 3y - 21
Answers
Answer:
2y + 16 +2y +30 +4y –13 +3y - 21
11y + 12
I hope I helped you^_^
