The equation of teh second line is y = -1/3x + 5/3
How to determine the equation?The first equation is given as
y = -1/3x + 14
The slope of the above equation is
m = -1/3
Parallel lines have equal slope
So, the slope of the other line is
m = -1/3
The equation is then calculated as
y = m(x - x1) + y1
So, we have
y = -1/3(x + 7) + 4
Expand
y = -1/3x - 7/3 + 4
Evaluate
y = -1/3x + 5/3
Hence, the equation of teh second line is y = -1/3x + 5/3
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A canoe and a paddler have a combined mass of 100.0 kg. The canoe is dropped into a river flowing from east to west. The flowing water exerts a force of 18.0 N on the canoe. The paddler exerts a force of 36.0 N [E 37.0° N]. Determine the net force on the canoe at this instant.
At this point, the canoe will be under a net force of 51.52 N.
What is the force?The total mass of a canoe and a paddler is 100.0 kg. A river that runs from east to west is where the canoe is thrown in. The power of the water current on the canoe is 18.0 N. The paddler exerts a force of 36.0 N [E 37.0° N].
The Free Body Diagram is then displayed below.
The canoe's net force would then be indicated as follows:
F = (18 + 36 cos 37°) i + (36 sin 37°) j
F = 46.75 i + 21.67 j
Therefore the force's strength will be
|F| = √(46.75² + 21.67²)
|F| = √2655.15
|F| = 51.52 N
Thus, at this point, the canoe will be under a net force of 51.52 N.
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You save $15 each month to buy a tablet that
Cost $84.99. Describe the number of months
gou need to save to buy the tablet.
Answer:
5 2/3 months
Step-by-step explanation:
Divide 84.99 by 15.
84.99/15 = 5 2/3
Solve for x.
4x-7=3x+21
Answer: x=28
Step-by-step explanation:
4x-7=3x+21
4x-3x-7=3x-3x+21
x-7=21
x=28
use the distributive property to remove the parentheses
-2(4w-2v-1)
Answer: -8w+2v+2
Step-by-step explanation:
3/4 - 5/8 step by step
Answer:
1/8
3/4 - 5/8
*2/2
6/8 - 5/8 = 1/8
Step-by-step explanation:
Which of the following is a valid claim based on the graph?
Time Spent Studying for
Math Mid-Term Exam
il..
Sandra Evan
Marie Ted Jose
Students
OA. Marie finds math easier than the other students.
Time (in hours)
O B. Marie had another test to study for the same night.
4
OC. Evan received the highest score on the exam.
O D. Evan studied twice as long as Ted.
A valid claim based on the graph is that: D. Evan studied twice as long as Ted.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
By critically observing the graph (see attachment), we can logically deduce the following data points:
Sandra's study time, S = 4 hours.Evan's study time, E = 6 hoursMarie's study time, M = 1 hour.Ted's study time, T = 3 hours.Jose's study time, J = 4 hours.From the information provided, we have the following true statements:
S = T
E = 2T
In conclusion, we can reasonably infer and logically deduce that a valid claim based on the graph is that Evan studied twice as long as Ted.
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A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towards music. How much can he spend in December, taking into consideration that in the other 4 months he spent $30, $80, $45, and $35, respectively?
The amount he can spend in December given that he spent $30, $80, $45, and $35, respectively in the other 4 months is; x = $60.
How much can he spend in December given his spending in the last four months?It follows from the task content the intention is to spend a mean of $50 a month towards music.
On this note, it follows that the since the mean is given by the ratio of the sum of all data values and the number of data values, it follows that;
Mean = 50 = (30+80+45+35 + x)/5
where x = spending in December.
multiply both sides by 5;
(30+80+45+35 + x) = 250
x = 250 -30 -80-45-35
x = $60.
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please refer to the image, thank you!
The values of the piecewise function is g(1) = 3, g(2) = 1 / 2, g(3) = 1 / 4.
How to evaluate a piecewise function
Piecewise functions are functions consisting in two or more expression constrained by intervals. In this case, we find a piecewise function formed by three equations. In this exercise we need to evaluate the function, whose expression depends on the x-value to be used. There are three values to be evaluated:
x = 1
g(1) = (1 + 1)² - 1
g(1) = 2² - 1
g(1) = 4 - 1
g(1) = 3
x = 2
g(2) = - (1 / 4) · 2 + 1
g(2) = - (1 / 2) + 1
g(2) = 1 / 2
x = 3
g(3) = - (1 / 4) · (3) + 1
g(3) = - (3 / 4) + 1
g(3) = 1 / 4
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The length of a rectangle is 3m less than double the witch, and the area of the rectangle is 27m^2. Find the dimensions of the rectangle.
Answer:
the area of the rectangle is A=L•W
The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m
A=L-W
27m²=(2W-3m)-W
27m2=2w2-3m-W
2w2-3wm-27m2=0
....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)
W=
2-2
w=(3m± √9m²+216m²)
w=(3m+ √225m²)
W=(3m± 15m...you need only positive root because width cannot be negative
W= 3m+15m
4
W=. 4
18m
W=4.5m ......now find the L
L=2.4.5m-3m
L=9m-3m
L=6m
Answer:
W = 4.5cm
L = 6cm
Step-by-step explanation:
A company with offices in Anchorage, Alaska wants to lease 10 small planes to fly a group of clients to Nome for a summer fishing trip. They can choose from 6, 8 and 10-passenger planes. The trip will include 84 passengers, total. Find the 5 solutions for how many of each type of plane could be leased? (please show your work)
The solutions of the equations of the situation can be:
z = 1 , y = 5, x = 4
z= 2 , y = 3, x = 5
z=3 , y = 1, x = 6
z = 0 , y = 7, x =3
The question can be expressed as a equation
6 x + 8 y + 10 z = 84
also, x + y + z = 10
⇒ x = 10- y - z
Putting it in first equation,
6(10 - y - z ) +8y + 10z = 84
⇒ 60 +2y + 4z = 84
⇒2(y + 2z ) = 14
⇒ y + 2z = 7
Now putting
z = 1 , we get y = 5,
z= 2 , y = 3
z=3 , y = 1
z = 0 , y = 7
So, only 4 possible solutions.
Therefore, there can only be 4 possible solutions for the equations.
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Use an integer to describe the
situations.
6 meters
above sea level
sea level
An integer to describe 6 meters above the sea level would be [tex]+6[/tex] meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as [tex]=6meters[/tex].
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In the formula l=p.r.t what does P stand for
In a study conducted by a human resource management organization, human resource professionals were surveyed. Of those surveyed, % said that their companies conduct criminal background checks on all job applicants. Complete parts (a) through (d).
What is the exact value that is 41% of 379 survey subjects?
(Type an integer or a decimal. Do not round.)
The exact value is ____
Using proportions, it is found that the exact value of 41% of 379 is of 155.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The proportion of 41% of 379 is given as follows:
0.41 x 379 = 155.39.
Since 0.39 < 0.5, the exact value is rounded to 155.
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A taxi ride for the airport to your hotel costs a flat fee of $10 the moment you sit in the back seat plus $0.75 each mile plus a tip of $5 to the driver at the end of the ride. Your hotel is 24 miles from the airport and you have $30 in your pocket. Do you have enough money to make it to your hotel in the taxi, including the tip? Declare what your variable represents, write the equation or inequality that models the situation, solve for the variable showing your steps, and answer the question.
Greetings from Brasil...
We have 2 fixed fees:
→ $10 when you sit on the bench
→ $5 tip
So, fixed fees = $10 + $5 = $15
The rate that varies would be the distance traveled. The fee will be $0.75 per mile moved. In this case we can write that:
C = 0.75M + fees
C = 0.75M + 15let
C = cost
M = mile(s)
for 24 miles, M = 24, then
C = 0.75M + 15
C = 0.75 · 24 + 15
C = 18 + 15
C = $33
With $30 it will not be possible to make this trip, as the total cost would be $33
One solution or alternative would be to reduce the tip amount. Instead of $5, pay only $2 of tip.
We can rewrite the cost expression involving a variable for the tip:
C = 0.75M + T + 10
let T = tip
For the exercise example.... The distance (M) its 24 miles and the value of C has to be what I have in my pocket: 30.... then M=24 and C=30
C = 0.75M + T + 10
30 = 0.75 · 24 + T + 10
30 = 18 + T + 10
30 - 18 - 10 = T
T = 2
Is it possible to do this ride if you pay only $2 tip
X-5>10;x=2 tell where the value is a solution of the inequality help please
Answer:
No, 2 is not a solution
Step-by-step explanation:
x - 5>10 Add 5 to both sides of the equations
x > 10 The solutions are all numbers greater than 10. Two is not greater than 10.
can someone help me with this
The cube of the product of 4 and a number
hi
if you call the number "n" you have : ( 4n)³
The cube formed by the product of 4 and a number is (4 * n)^3.
What are cubes?A number's third power, or the outcome of multiplying three occurrences of the number n together, is known as the cube In mathematics and algebra. A superscript 3 represents the cube of a number or any other mathematical expression.The name comes from the fact that the volume of a geometric cube is equal to the cube of its side length.According to our question ,
Let n be any number on any integer.The cube of the product of and any number will be = (4 * n)^3.Hence we can say that the cube formed by the product of 4 and a number is (4 * n)^3.
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The terminal side of angle θ intersects the unit circle in the first quadrant at x=2/5. What are the exact values of sinθ and cosθ?
Answer:
sin(θ) = (√21)/5cos(θ) = 2/5Step-by-step explanation:
You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.
Pythagorean identityThe coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...
cos(θ) = 2/5
The Pythagorean identity in trigonometric terms is ...
sin²(θ) +cos²(θ) = 1
Then the sine of the angle is ...
sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)
sin(θ) = (√21)/5
The exact values of sine and cosine are ...
sin(θ) = (√21)/5cos(θ) = 2/52. Last week, Abe's carpet store sold 160 square feet of a particular carpet for $878.40. Bob's carpet store sold 85 square feet of the same carpet for $466.65
a. Is Cost proportional to area for this carpet? Show all relevant calculations and then explain your conclusion in a full sentence.
b. Answer ONE of the questions below depending on whether or not cost is proportional to area for this carpet
if cost is proportional to area, what is the cost of 118 square feet of carpet? Show your work. Use dimensional analysis
if cost is not proportional to area, which store has the better unit price for carpet explain your choice.
Consequently, the carpet's price is diversely correlated with its size. Then the cost of the carpet will be $647.82.
What are ratio and proportion?160 square feet of a certain carpet were purchased for $878.40 last week at Abe's carpet shop. The identical carpet, measuring 85 square feet, cost $466.65 at Bob's Carpet.
The cost of carpet per square foot in both cases will be
In the First case, we have
⇒ 878.40 / 160
⇒ $5.49 per square foot
In the second case, we have
⇒ 466.65 / 85
⇒ $5.49 per square foot
Consequently, the carpet's price is directly correlated with its size. Then the equation will be
Cost = 5.49 x Area
Then the cost of the carpet when the area is 118 square feet will be
Cost = 5.49 x 118
Cost = $647.82
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Graph the linear equation.
x = 6
Use the graphing tool to graph the linear equation.
The graph of the linear equation, x = 6, is shown in the image attached below.
How to Graph the Equation of a Vertical Line?The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.
Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.
Thus, the graph of the linear equation, x = 6, is shown in the image attached below.
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Rewrite -4/15 as an equivalent fraction
[tex](\frac{-4}{5} )[/tex] in the form of Equivalent Fraction can be written as [tex]\frac{-4x}{15x}[/tex], where "x" is any integer.
As per the question statement, we are provided with a fraction, [tex](\frac{-4}{5} )[/tex].
We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.
To solve this question, we need to know what an equivalent fraction is.
Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.
For example, [tex](\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})[/tex] all equate to [tex]\frac{1}{2}[/tex] when simplified.
Now, for this case, equivalent fractions of [tex](\frac{-4}{5} )[/tex] are [tex](\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)[/tex], where
[tex]\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}[/tex]
i.e., the equivalent fractions of [tex](\frac{-4}{5} )[/tex] are in the form of [tex]\frac{-4x}{15x}[/tex], where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)
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A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 14 feet less than 3 times the height. Find the width and the height if the carpenter expects
to use 28 feet of lumber to make it.
Width:
feet
Height:
feet
Question Help: Video
Answer:
w= 3 feet
h= 5 feet
Step-by-step explanation:
H=height; W=width=2H-7ft
W=2H-7ft
2H+4W=22ft Substitute for W
2H+4(2H-7ft)=22ft
2H+8H-28ft=22ft Add 28 ft to each side.
10H=50ft
H=5 ft ANSWER 1: The bookshelf is 5 feet high.
W=2H-7ft=2(5ft)-7ft=10ft-7ft=3ft
ANSWER 2: the bookshelf is 3 feet wide.
CHECK:
2H+4W=22ft
2(5ft)+4(3ft)=22ft
10ft+12ft=22ft
22ft=22ft
Hope this helps!
Use left-endpoint approximation to estimate the area under the curve of f(x)=x^3 on [1,3]. Use n = 4. Using the same function use midpoint approximation to estimate the area.
Split up the interval [1, 3] into 4 intervals of equal length,
[tex]\Delta x = \dfrac{3 - 1}4 = \dfrac12[/tex]
The left endpoint of the [tex]i[/tex]-th interval is
[tex]\ell_i = 1 + \dfrac i2[/tex]
The area under the curve is then approximately
[tex]\displaystyle \int_1^3 f(x) \, dx \approx \sum_{i=1}^4 f(\ell_i)\Delta x \\\\ ~~~~~~~~ = \frac12 \sum_{i=1}^4 \left(1 + \frac i2\right)^3 \\\\ ~~~~~~~~ = \frac12 \sum_{i=1}^4 \left(1 + \frac{3i}2 + \frac{3i^2}4 + \frac{i^3}8\right) = \boxed{27}[/tex]
4 divided by 527 step by step
What’s 14/20 - 81/90
Answer: -1/5
Step-by-step explanation:
14/20 - 81/90=
7/10-9/10= ==> 10 is the GCF of 20 and 90
(7-9)/10=
-2/10=-1/5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{14}{20} - \dfrac{81}{90}}[/tex]
[tex]\mathsf{= \dfrac{14\div2}{20\div2} - \dfrac{81\div 9}{90\div9}}[/tex]
[tex]\mathsf{= \dfrac{7}{10} - \dfrac{9}{10}}[/tex]
[tex]\mathsf{= \dfrac{7 - 9}{10 - 0}}[/tex]
[tex]\mathsf{= \dfrac{-2}{10}}[/tex]
[tex]\mathsf{= \dfrac{-2\div 2}{10\div2}}[/tex]
[tex]\mathsf{= \dfrac{-1}{5}}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{-\dfrac{1}{5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Question
The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 60 feet. If w is the width of the rectangle, which expression represents the length?
w+6w plus 6
w−6w minus 6
6w6 w
16w1 sixth w
The length expression is 6 + w
How to determine the length expression?The given parameters are:
Length =6 more than the width
Width = w
Perimeter = 60
Subsitute Width = w in Length =6 more than the width
This gives
Length =6 more than the w
More than mean +
So, we have
Length = 6 + w
Hence, the length expression is 6 + w
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A 12- by 16-foot rectangular floor will be
covered by square tiles that measure 2 feet
on each side. If the tiles are not cut, how many
of them will be needed to cover the floor?
Translate the sentence into an equation.
The sum of 8 times a number and 9 is 7.
Use the variable b for the unknown number.
Answer:
8 x b + 9 = 7
Step-by-step explanation:
sum is to add and 8 times means to multiply it by 8
Find the domain and range for the absolute value function f(x)
graphed below. Then determine where the function is increasing and/or decreasing
Step-by-step explanation:
the domain is the interval or set of all valid x values.
as we can see, the function goes continuously from all the way to the left (until all eternity to -infinity) all the way to the right (until all eternity to +infinity).
the domain is
-infinity < x < +infinity
the range is the interval or set of all valid y (function result) values.
we see, the lowest y value is -1. and then the function goes on both sides up, up, up in all eternity to +infinity.
the range is
-1 <= y < +infinity
f(x) is decreasing for
-infinity < x < -1
f(x) is increasing for
-1 < x < +infinity
which of the following statements is true about the function f in the equation f(10)=5
The cordinates of the turning point of the graph of y=f(x) occurs at (1.1) and (5/3, 23/27)
2
(x−2)+1
Now, differentiating w.r.t. x, we get
f
′
(x)=2(x−1)(x−2)+(x−1)
2
=(x−1)[2(x−2)+x−1]
=(x−1)[3x−5]
Hence,
f
′
(x)=0 implies x=1 and x=
3
5
Corresponding values of y are y=1 and y=
27
23
respectively.
∴ Co-ordinates of turning point of the graph of f(x) occurs at (1,1) and (
3
5
,
27
23
)
Now,
f(x)=(x−1)
2
(x−2)+1
=(x
2
−2x+1)(x−2)+1
=x
3
−2x
2
−2x
2
+4x+x−2+1
=x
3
−4x
2
+5x−1
The value of p for which the equation f(x)=p has 3 distinct solutions lies in interval (
27
23
,1)
Area enclosed by f(x),x=0,y=1 and x=1 is
A=∫
0
1
(1−f(x))dx
⇒∫
0
1
(4x
2
−x
3
−5x+2) dx
⇒A=
12
7\
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