Based on the mathematical statement, the unit rate is 3/4 books per hour
How to rewrite the expression as a unit rate?The mathematical statement is given as
"rewrite 1/4 book 1/3hour as a unit rate"
The above means that
Book = 1/4
Time = 1/3 hour
The unit rate is then calculated as
Unit rate = Book/Time
Substitute the known values in the above equation
So, we have the following equation
Unit rate = (1/4)/(1/3)
Evaluate
Unit rate = 3/4
Hence, the solution is 3/4 books per hour
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Prove the identity.
(csc²x - 1) secx = cosx csc x
Question content area top Part 1 The temperature in a town is 31.6 during the day and -17.2 at night. Find the difference in the temperatures.
Answer: The difference in temperature is 45.9F.
HELPHELPHELPHELP plssssssssssssssssssssssss
What is equivalent to 0.325 in as a fraction
Answer:
0.325 as a fraction is expressed as 13/40
Step-by-step explanation:
What is a fraction ?
A fraction is a portion of any quantity out of a whole. It consists of a numerator and a denominator.
To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.
In this case, 0.325 has three numbers after the decimal, so, we place 1000 in the denominator and remove the decimal point.
⇒ 325/1000
After reducing this fraction we get,
⇒ (325 ÷ 25) / (1000 ÷ 25) = 13/40
So, 0.325 as a fraction is 13/40.
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The slope of MN¯¯¯¯¯¯¯ is −6. what segments are parallel to MN¯¯¯¯¯¯¯?
The slope of the parallel line to line MN -6
How to determine the slope of the line?From the question, the line is given as
Line MN
Also, we have the slope of line MN to be
Slope of MN = -6
As a general rule in linear functions and parallel lines
The slopes of parallel lines are equal
This means that any line that is parallel to the line MN and the line MN would have the same slope of -6
Hence, the slope of the line segments that are parallel to line MN is -6
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What is the slope of the line that passes through the points (10, 8) and
(7, 14)? Write your answer in simplest form.
Answer:
Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Slope of line = (14-8)÷(7-10)
= 6÷(-3)
= -2
helpppp meeee pleaseee
What is the value of -3/15-s+ 25³ when s=-3?
Answer:
=[tex]\frac{78139}{5}[/tex]
Step-by-step explanation:
[tex]-\frac{3}{15}-(-3)+25^{3} \\=\frac{78139}{5}[/tex]
Which postulate could we use to prove that the angles
The postulate that could be used is the: linear pair postulate.
What is the Linear pair Postulate?If two angles share a common side and also a common vertex lie on a straight line, they both form a special angle relationship that is called the linear pair.
Based on the linear pair postulate, it is proven that angles that form a linear pair add up to 180 degrees and are therefore regarded as supplementary.
Angle CAD and angle CAB have a common side, side CA, and a common vertex, angle A. They are also on the straight line, line AB.
Thus, it can be proved that the angles CAB and CAD are supplementary based on the linear pair postulate.
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Write an algebraic expression that matches Six less than a number
ANSWER
x - 6
EXPLANATION
We want to write an algebraic expression that matches the statement:
Six less than a number.
First, let that unknown number be x.
So, 6 less than x.
Since it means that we are taking 6 from x, we subtract 6 from x.
That will be:
x - 6
Is a triangle with vertices G(3, 2), H(8, 5), and K(0, 10) a right triangle? Justify your answer.
First you need to ubicate those vertices in a plane as follow:
Then you link the vertices with lines to form the triangle:
Knowing that a right triangle must have one angle of 90º
The answer is that yes, it is a right triangle because it has an angle of 90º in the vertice H(8,5)
Janell is standing on a set of bleacher and throws a ball in the air at an initial velocity of 35 ft/s. The height of the ball, h, at t seconds is modeled by the equation h=-16t^2+35t+6. How many seconds will it take the ball to reach the ground?
The time taken by the ball to reach the ground is 0.067 seconds
Given,
The initial velocity of the ball (speed) = 35 feet/second
The height of the ball (distance), h = -16t² + 35t + 6
We have to find the time, (t in seconds) taken by the ball to reach the ground.
Speed = distance/time
So, Time = distance/speed
Here,
Time = (-16t² + 35t + 6) / 35
We have to solve the equation first.
-16t² + 35t + 6 = 0 is in quadratic form. So, we can solve this by using quadratic formula.
Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = -16, b = 35, c = 6
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-35(+-)\sqrt{35^{2}-4(-16)(6) } }{2(-16)}[/tex]
= [tex]\frac{-35(+-)\sqrt{1225 +384} }{-32}[/tex]
= (-35±√1609) / -32
= (-35±40.11) / -32
Now,
Solve for:
(-35 + 40.11) / -32 = 5.11/-32 = -0.15
Solve for
(-35 - 40.11) / -32 = -75.11 / -32 = 2.35
Lets take the height as 2.35 feet.
Now,
Time = distance/speed
Time = 2.35/35 = 0.067
Therefore, the time taken by the ball to reach the ground is 0.067 seconds.
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What is the slope of the line that passes through the points (7,-6) and (6, -6)
Write your answer in simplest form
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, - 6 ) and (x₂, y₂ ) = (6, - 6 )
m = [tex]\frac{-6-(-6)}{6-7}[/tex] = [tex]\frac{-6+6}{-1}[/tex] = [tex]\frac{0}{-1}[/tex] = 0
What is the equation of the line?
Answer:
Thr equation is y=x-1
Step-by-step explanation:
The y intercept is negative 1 so that eliminates options 1 and 3 and the slope goes up which leaves only option 2 left
-3x+14-11+11x I tried getting help with this question and it didn’t give me enough information to fully understand.
Answer:
0.375
Step-by-step explanation:
-3x+14-11+11x
-3x+11x = 8x
14-11 = 3
8x=3
÷8 on both sides
Andrew would like to put six different Rubik's cubes onto 3 shelves. The order of the cubes does not matter.
In how many ways can Andrew do this if a shelf can have zero cubes?
What if each shelf must have at least one cube?
Answer:
540
Step-by-step explanation:
we know that on average the time it takes to complete a homework assignment is 2.3 hours with a standard deviation of .5 hours. with 13 students in the class, the average to complete the homework was 1.5 hours. what is the percentile of this class
In standard deviation, 120 is the percentile of this class.
Why is there a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.Test statistic (z) = (weekly study time - average study time)/standard deviation
weekly study time = 2.3 hours
average study time = .5 hours
standard deviation = 1.5 hours
z = (2.3 - 0.5)/1.5
= 1.8/1.5 = 1.2 (to 2 decimal places)
Cumulative area of the test statistic is 1.2
Percentile = 1.2×100 = 120
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Hi can anyone help with this question? I have been stuck on this for hours
Answer:
ab = - 1
Step-by-step explanation:
GivenEquations:
1 - a tan θ = sec θ,b - cot θ = cosec θ.To find The value of abSolutionRecall the identities:
tan θ = sin θ / cos θsec θ = 1 / cos θ cot θ = cos θ/ sin θcosec θ = 1 / sin θsin² θ + cos² θ = 1(a + b)(a - b) = a² - b²Now find a and b, then find their product.
1 - a tan θ = sec θ1 - a sin θ / cos θ = 1 / cos θ cos θ - a sin θ = 1a sin θ = cos θ - 1a = (cos θ - 1) / sin θb - cot θ = cosec θb - cos θ/ sin θ = 1 / sin θb = cos θ/ sin θ + 1 / sin θb = (cos θ + 1) / sin θab = (cos θ - 1) / sin θ × (cos θ + 1) / sin θ = (cos² θ - 1) / sin² θ = - sin² θ / sin² θ = - 1The relationship between the number of $4 lunches you buy with a $105 school lunch card and the money remaining on the card
The relationship will be a solid line.
How many $4 meals you may purchase with a $100 school lunch card and how much money is still on the card.
Given that the slope is common and linear, the connection will be a solid line. The balance on the card will drop by $5 each time you purchase lunch.
Let x be the amount of lunches you purchase.
Let the balance on the card be = y.
Equation then becomes:
y= 105-4x
when x=1
y = 105 - 4(1) = 101
when x= 2
y= 105 - 4(2) = 97
when x=3
y= 105 - 4(3) = 93
We can see that the decline is gradual and same.
On the graph that is provided, you can also observe that a straight line is created.
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if 2 x 2 whats the divided by -3 to 4
Answer:its 2
Step-by-step explanation:
For Items 12–14, use the figure shown.
Two vertical parallel lines are intersected by two diagonal transversals, one slanting up and one slanting down. They intersect the left line at the same point, creating 6 angles, starting at the bottom left of the right line and moving clockwise, they are: 3, 2, 1, left parenthesis 4 y times 3 right parenthesis, left parenthesis 3 x times 9 right parenthesis, and left parenthesis 5 x right parenthesis. The line slanting up intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 6, 4, 5, and left parenthesis 9 x times 3 right parenthesis. The line slanting down intersects the right vertical line creating 4 angles, starting at the bottom left and moving clockwise, they are: 8, 7, left parenthesis 7 y times 6 right parenthesis, and 9.
What is m∠2?
A. 12
B. 18
C. 45
D. 120
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Solve {2c+8}={10c} . Answer in simplest fraction form.
Answer: c=1
Step-by-step explanation:
Move the variable to the left side
2c+8−10c=0
Subtract the terms
−8c+8=0
Move the constant to the right side
−8c=0−8
Subtract the terms
−8c=−8
Divide both sides
−8c = −8
−8 -8
Simplify
what set of numbers dose -17 belong to?
A. integers, rational numbers, real numbers
B. rational numbers, real numbers
C. whole numbers, integers, real numbers
D. whole numbers, integers, rational numbers, real numbers
A
-------------------------------------------------------
bc it is an integer but not whole numbers
line has an x-intercept of -5 and a y-intercept of 3. Use this information for questions
8 through 10.
8.
Find the slope of the line.
9. Write the equation of the line in slope-intercept form.
10. Write the equation of the line in standard form.
Answer:
[tex](1)\;\;\;\text{Slope }= \dfrac{3}{5}\\[/tex]
(2) Equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation of line in standard form is:
[tex]5y - 3x = 15[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept
Slope = [tex]\dfrac{y2 - y1}{x2-x1}[/tex]
where (x1, y1) and (x2, y2) are two points on the line.
y2 - y1 is known as the rise
x2 - x1 is known as the run
Slope is also defined as rise/run
We are given x-intercept = -5.
The ex-intercept is the point at which the line crosses the x-axis. At this point the y-value = 0.
So we get one of the points (-5, 0)
We are given y-intercept = 3
The y-intercept is the point at which the line crosses the y-axis. At this point the x-value is 0
So another point on the line is (0, 3)
Knowing this we can compute rise and run
rise = y2 - y1 = 3 - 0 = 3
run = x2 - x1 = 0 - (-5) = 0+5 = 5
[tex](1)\;\;\;\text{Slope = $\dfrac{3}{5}$}[/tex]
(2) Equation is
y = mx + b where m = slope and b = y-intercept
Slope = 3/5 from (1) and y-intercept = 3
So equation of line in slope-intercept form is
[tex]y = \dfrac{3}{5}x + 3[/tex]
(3) Equation in standard form
In (2) subtract (3/5)x from both sides.
[tex]y - \dfrac{3}{5}x = 3[/tex]
We can multiply both sides by 5 to get
[tex]5(y - \dfrac{3}{5}x )= 5 \times 3\\\\= 5y - 3x = 15[/tex]
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
Enter your answer in the box.
Answer:
1 7/8 inches is 1.875 in decimal form.
For each ordered pair, determine whether it is a solution to 5x + 2y = -1. (x, y) (1, − 3) (2,8) (-4, -6) (-3,7) what is the soulsion
The following ordered pairs are the solutions to 5x+2y=-1 :
(1,-3) and (-3,7)
Given we have the ordered pairs and the equation.
To find out whether the ordered pair is a solution or not, we just need to replace the x and y values from the ordered pair (x,y) and check if both the sides equate.
a. (1,-3)
5x+2y=-1
5(1)+2(-3) = -1
consider L.H.S
5-6
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (1,-3) is a solution to 5x+2y=-1.
b. (2,8)
5x+2y=-1
5(2)+2(8) = -1
consider L.H.S
10+16
= 16
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (2,8) is not a solution to 5x+2y=-1.
c. (-4,-6)
5x+2y=-1
5(-4)+2(-6) = -1
consider L.H.S
-20-12
= -32
Therefore, L.H.S ≠ R.H.S
hence the ordered pair (-4,-6) is not a solution to 5x+2y=-1.
d. (-3,7)
5x+2y=-1
5(-3)+2(7) = -1
consider L.H.S
-15+14
= -1
Therefore, L.H.S = R.H.S
hence the ordered pair (2,8) is a solution to 5x+2y=-1.
Therefore the ordered pairs which are solutions to 5x+2y=-1 are:
(1,-3) and (-3,7)
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help please
What is the correct way to break 12 into parts and multiply each part by 6?
Answer:
2nd one
Step-by-step explanation:
Hope I helped!
HI NEED THIS ASAPP GRAOHS OF INVERSE FUNCTIONS
Answer: D (last bubble)
Step-by-step explanation:
slope of f is 2/3
inverse of 2/3 is 3/2
that is graph h
these graphs are symmetrical around the line y = x
soyala went to the college traveling 25 mph and returned home traveling 15 mph. if the total trip took 8 hours, how long did soyala travel at each speed?
Soyala travelled for 3 hours with a speed of 25 mph and 5 hours with a speed of 15 mph
We know that Distance = Rate x Time. The distance traveled to the library is assumed to be same as the distance traveled on the way to home from the library. Let t be the time it took to travel to the library after which (8 - t) = the time it took to travel back home. We can write following two equations using the formula for distance:
d = 25t ---------> (1)
d = 15(8 - t) = 120 - 15t -----------> (2)
Since the distance d is equal for both trips, let's set the two expressions of time t equal to each other.
25t = 120 - 15t
40t = 120
t = 3 hours
Therefore, Soyala travelled for 3 hours at 25 mph and for 8 - 3 = 5 hours at 15 mph. Each rate will yield a distance traveled of 125 miles.
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Sandra Keegan worked 38 hours at $12.95 per hour and 6 hours of overtime at time and a half what was her pay for the week?
Answer:
$569.80
Step-by-step explanation:
She worked $12.95 per hour for 6 hours of overtime, meaning we would multiply $12.95 by 6 which is equal to $77.70, since she worked for 38 hours that week, we would multiply $12.95 by 38 which is $492.10, so now we add how much she earned for the total. Her overtime pay was $77.70 + her regular pay was $492.10 which adds up to $569.80