On the following number line, two rational numbers are graphed. Represent the two numbers as fractions (or mixed numbers) in lowest terms, and write two different expressions to represent the difference between them. Then, find the difference, showing all of your work.
Answers
Answer:
The answer is below
Step-by-step explanation:
A rational number is a number in the form p/q where p and q are both integer numbers.
From the number line, each one unit is divided into six, therefore each one point is 1/6 unit. For the first number, it is between 0 and 1 and is on the fifth point, therefore the expression of the first number = 0 + 5(1/6) = 0 + 5/6 = 5/6
For the second number, it is between -1 and -2 and is on the third point, therefore the expression of the second number = -1 - 3(1/6) = -1 - 3/6 = -9/6
The difference between the two numbers is:
5/6 - (-9/6) = 5/6 + 9/6 = 14/6
Related Questions
Can someone please tell me how to solve this problem??!! I literally have to go back in math if I don’t pass this HELP!!
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Answer:
D. 270° < φ < 360°Step-by-step explanation:
Imagine coordinate system
I quarter is where x>0 and y>0 {right top} and it is (0°,90°)
II quarter is where x<0 and y>0 {left top} and it is (90°,180°)
III quarter is where x<0 and y<0 {left bottom} and it is (180°,270°)
IV quarter is where x>0 and y<0 {right bottom} and it is (270°,360°)
Now, we have an angle wich vertex is point (0,0) and one of its sides is X-axis and the second lay at one of the quarters.
For the trig functons of an angle created by this second side always are true:
In first quarter all functions are >0
in second one only sine
in third one: tangent and cotangent
and in fourth one: cosine
{You can check this by selecting any point on the second side of angle and put it's coordinates to formulas of these functions:
[tex]\sin \phi=\dfrac y{\sqrt{x^2+y^2}}\,,\quad \cos \phi=\dfrac x{\sqrt{x^2+y^2}}\,,\quad \tan\phi=\dfrac yx\,,\quad \cot\phi=\dfrac xy[/tex] }
So:
sinφ<0 ⇒ III or IV quarter
tanφ<0 ⇒ I or IV quarter
IV quarter ⇒ φ ∈ (270°, 360°)
convert -1.2i - 1.6j to polar cordinates
Answers
Answer:
Step-by-step explanation:
z=xi+yj
x=-1.2=r cosθ (say)
y=-1.6=r sinθ(say)
square and add
r²cos²θ+r² sin ² θ=(-1.2)²+(-1.6)²=1.44+2.56=4
r²=4
r=2
divide
tanθ=y/x=-1.6/(-1.2)=16/12=4/3
θ=tan ^{-1}(4/3)≈53.13°
so polar coordinates are (2,53.13°)
Is 3+(-4) the same as -4+3 ? Explain
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Solve the equation
(If possible please show work)
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1. Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? 2. What is the vertex of the parabola with the equation y=(x−2)2+10?
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Answer:
Step-by-step explanation: u hv 2 make a table for x and y and put in #'s like 1,2,3,4 so u get 1 side of the parabola. x-1, y-11/x-2,y-11/x-3,y-11/x-4,y-14; here u c that u have 2 y's=11 so the points between are the Vertex Points of (2,10)
X has a coefficient, the vertext is (2,10)
70000000000x50000000000000
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Answer:
Step-by-step explanation: Multiply
70000000000*50000000000000=3.5e+24
Find the area of the green sector if m2 A-T
and the circle has a radius of 10 inches.
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The area is:
A = πR² ------- 2π
A = x --------- π/6
x = πR²/12
x = π.(10)²/12
x = 26.18 in²
Hope it helps x
need help...!!ASAP..!! plz....
Answers
the answer for this is A
Answer:
Correct option is A
Step-by-step explanation:
3x - 7
Three times a number x minus 7
Or
The difference of there times a number and 7
85,58,72,85,46,93 mean,mode,range,median
Answers
Answer:
mean: 73.2
mode : 85
range:47
median: 78.5
Step-by-step explanation:
85,58,72,85,46,93
first put the numbers in order from least to highest
46,58,72,85,85,93
mean: is the sum of the terms divided by the number of terms
(85+85+72+58+46+93)/6=73.2 ( rounded to the nearest tenth)
mode : is the element that occurs the most: in this case it is 85 occurs twice
range : subtract the minimum data from max. data: 93-46=47
median : is the middle number, in this case it is even so take the middle two numbers and divide by 2: 85+72/2= 157/2=78.5
median = 78.5
The mean value is 73.
The mode value is 85.
The range value is 47.
The median value is 78.5.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
85,58,72,85,46,93
Mean = (85 + 58 + 72 + 85 + 46 + 93) / 6
Mean = 73
Mode is the number that occurs the most times in the set.
Mode = 85.
Range = Highest value - Lowest value.
Range = 93 - 46 = 47.
The Median is the middle value after arranging the set in order.
46, 58,72,85, 85, 93
Median = (72 + 85) / 2
Median = 78.5
Thus,
The means is 73.
The mode is 85.
The range is 47.
The median is 78.5.
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Consider the function f(x)=|-x-3/2|-1
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Answer:
x1(1 is on the bottom)= -5/2 (fraction), x2(2 on the bottom)=-1/2 (fraction)
Step-by-step explanation:
Bismah is building 5 raised garden beds in a community garden. Each raised garden bed will need 1 7 8 bags of soil. How many bags of soil will Bismah need for all 5 raised garden beds?
Answers
Answer:
890 if it’s 178 bags per garden bed
Step-by-step explanation:
since 1 raised garden bed is supposedly 178 bags, 5 would be 890 since it’s just 5x178. if it’s not 178 bags (which would make sense since 178 is a big number), just multiply 5 by that number and if it’s a decimal round up to the next whole number if it’s about how many bags Bismah needs to buy, since you can’t by 1/2 of a bag
Bismah will need a total of 890 bags of soil for all the 5 raised garden. beds.
What is Multiplication?.Multiplication is one of the basic operations in mathematics where a number is added repeatedly to itself up to the times as the value of the other number.
That is, if a number p is multiplied to another number q, p × q, implies that p is added repeatedly to itself q times or q is added repeatedly to itself up to p times.
Number of garden beds Bismah has raised = 5
Number of bags of soil needed for a garden bed = 178 bags
Number of bags of soil needed for 5 garden bed = 178 × 5 bags
= 890 bags
Hence Bismah would need 890 bags of soil for the 5 raised garden beds in the community garden.
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What number increased by 15% equal 161
Answers
Answer:
100%+15% = 115%
proportionally:
x - 100%
161 - 115%
x = (161 * 100%) / 115% = 140
Answer:
[tex]\Large\boxed{140}[/tex]
Step-by-step explanation:
[tex]\sf Let \ x \ be \ the \ number.[/tex]
[tex]\sf x \ increased \ by \ 15\% \ is \ 161.[/tex]
[tex]x \times (1+15\%)=161[/tex]
[tex]x \times (1+0.15)=161[/tex]
[tex]x \times (1.15)=161[/tex]
[tex]\displaystyle \frac{x \times (1.15)}{1.15}=\frac{161}{1.15}[/tex]
[tex]x=140[/tex]
A clerk at Agency Y has determined that at speeds of 25 pages per minute it is typical for 3 out of every 100 pages she photocopies to contain some type of printing error. How many pages with printing errors would she expect to find during a 4-hour photocopying session at 25 pages per minute
Answers
Answer:
180 pages
Step-by-step explanation:
Since her photocopy session is 25 pages per minute, the total number of pages photocopied in 4 hour session can be calculated as;
number of pages = time × speed
= (4 × 60) × 25
= 240 ×25
= 6000 pages
Thus, number of pages photocopied in 4 hours is 6000.
For every 100 pages, 3 would contain some type of printing error. The number of pages she expect with printing error during 4 hour session can be determined as;
= [tex]\frac{6000}{100}[/tex] × 3
= 60 × 3
= 180 pages
The expected number of pages with printing error during 4 hour photocopying session is 180 pages.
Which statement compares the two numbers correctly? (2 points) Fifty-seven thousand, eight hundred and twenty-two hundredths ________ fifty-seven thousand eight hundred and three tenths Select one: a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths b. Fifty-seven thousand eight hundred and twenty-two hundredths > fifty-seven thousand eight hundred and three tenths c. Fifty-seven thousand nine hundred and three tenths > fifty-seven thousand eight hundred and twenty-two hundredths d. Fifty-seven thousand eight hundred and three tenths = fifty-seven thousand eight hundred and twenty-two hundredths
Answers
Answer:
a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths
Step-by-step explanation:
In numbers it is written in the order
Th H Tens Units Decimal Tenths Hundredths Thousandths
57 8 0 0 . 0 22
57 8 0 0 . 3
This could be simply explained that the if we make compare the numbers before the decimal they are same but after the decimal we can analyze
3/10 and 22/100
Converting them into decimals we get
0.3 and 0.22
therefore 0.3 is greater than 0.22
so Choice a is only correct .
a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths
Answer: The person above me is correct
explanation:
I said that because i don't want no one saying that i copied them
. Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north. a. The train station is the origin. What is the coordinate of each train? b. Using the train station and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form. c. The city wants to build a second train station 2 miles directly north of the first train station. They are going to build a train track from the second train station that is parallel to the path the first train would've traveled if it had taken a direct route to its stopping point. What would be the equation of the line in slope intercept form of the new track?
Answers
Answer:
a. The coordinates of the first train are (-12,6). The coordinates of the second train are (20,35).
b. The slope of the line for the first train is [tex]-\frac{1}{2}[/tex]. The slope is neither horizontal or vertical. It slopes diagonally downward from left to write since the slope is negative. In slope-interdept form, it is written as [tex]y=-\frac{1}{2} x[/tex]. In standard form, it is written as [tex]x+2y=0[/tex]. The slope of the line for the second train is [tex]\frac{7}{4}[/tex]. The slope is neither vertical or horizontal. It slopes diagonally upward from left to right since the slope is positive. In slope-intercept form, it is written as [tex]y=\frac{7}{4}x[/tex]. In standard form, it is written as [tex]-7x+4y=0[/tex].
c. The equarion of a line in slope-intercept form of the new track would be [tex]y=-\frac{1}{2} x+2[/tex].
Step-by-step explanation:
a. The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual. The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6). On a coordinate plane, that would be marked as (-12,6). The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35). On a coordinate plane that would be marked as (20,35). This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).
b. The way to find slope is to find [tex]\frac{delta "x"}{delta "y"}[/tex]. "Delta" means "the change in". The equation would be [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. So, let's find the slope of the first train's travel path. We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope. [tex]\frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}[/tex]. That makes the slope of the first train's travel path to be (-1/2). Now, let's find the slope of the second train's travel path. We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope. [tex]\frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}[/tex]. That makes the slope of the second train's travel path to be (7/4). They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like. To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path. A horizontal line would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either. The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative. The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing). The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left. Finally, the equations for this part of the question. For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation. The slope-intercept form of an equation of a line is [tex]y=mx+b[/tex] where "m" is the slope and "b" is the y-intercept. The "b" value is 0, so that will not be written. The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x. The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x. As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0. And for the second train, standard form would be -7x+4y=0.
c. Parallel means having the same slope but a different y-intercept. The second train station would be placed two miles north, or two units up, from the first train station. The first train station is at (0,0), so the second train station would be placed at (0,2). That makes 2 the y-intercept for if the first train had taken the second train station's travel route. The slope for the intitial route was (-1/2), so that will stay the same. Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.
New York City is a popular feild trip destination. This year the senior
class at High School A and the senior class at High School B both
planned trips there. The senior class at High School A rented and filled
8 vans and 4 buses with 220 students. High School B rented and filled 12 vans and 4 buses with 228 students. Every van had the same
number of students in it as did the buses. How many students can a
van carry? How many students can a bus carry?
Answers
Step-by-step explanation: look so if you have
shcool A its 8v+4b=12
and
School B: 12v+4b= 16
since both classes used 4 busses we can use elimination by subtracting the A class Equation from the b class equation to solve from v for its value Then, use either equation and the now found value for v to solve for b.
You should find part of the process to be
12v+4b-(8v+4b)=12-16 which shows the van holds only a few people even before continuing the solution.
Answer -4
Is the relation a function?
Answers
Answer:
Yes it's a function
Step-by-step explanation:
Yes it is a function.
Please answer quickly i will give you brainliest if its correct- it has to be a simplified fraction please
Answers
Answer:
[tex]\large \boxed{{r=\frac{1}{9}}}[/tex]
Step-by-step explanation:
x and y are proportional.
[tex]y=rx[/tex]
Let x = 45 and y = 5.
[tex]5=r(45)[/tex]
Solve for r (constant of proportionality).
Divide both sides by 45.
[tex]\displaystyle \frac{5}{45} =r[/tex]
Simplify and switch sides.
[tex]\displaystyle r=\frac{1}{9}[/tex]
WILL MARK BRAINLIEST HELP ASAP The student's in Roberto's school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. What are the length and width of the scale drawing in feet?
Answers
Answer:
4ft and 3ft
Step-by-step explanation:
Real mural: 8ft by 15ft
Scale: 2ft by 5ft
Length and width of scale drawing> 8t / 2ft= 4ft (length
>15ft/ 5ft= 3ft(width)
ANSWER 4FT BY 3FT
Axel has spent 25% of his money on a video game. If the price of the video game was $ 45, how much money did Axel have before the purchase?
Answers
Answer:
$180
Step-by-step explanation:
25% = 1/4
x/4 = 45
45*4 = 180
find the positive square root upto 3 decimal points of 3
Answers
Answer:
1.732050808
Step-by-step explanation:
Evaluate the expression for the given value of the variable. −3x3, when x = 4
Answers
Answer:
The answer is - 192Step-by-step explanation:
The expression
- 3x³
To find the value of the expression when
x = 4 substitute the value of x that's 4 into the expression
We have
- 3(4)³
= - 3( 64)
The final answer is
- 192Hope this helps you
Two similar figures have sides in the ratio of 2:3. Ita side of the smaller triangle has a length of 7, what is
the length of the corresponding side of the other triangle?
Answers
Answer:
10.5
Step-by-step explanation:
2/3=7/x
2x=21
x=21/2=10.5
Ava's car used 6 gallons of gas to drive 132 miles. At what rate does her car use gas in gallons per mile? Express your answer in simplest form.
Answers
Answer:
Rate of gas in gallons per mile
= 0.045454545 gallon/mile
Or
Rate of gas in gallons per mile
= 1/22 gallon/mile
Step-by-step explanation:
Ava's car uses 6 gallons of gas to drive through a distance of 132 miles.
Thanks rate of gallon to distance will be given by the formula below
Rate of gas in gallons per mile
=Number of gallons/ distance covered in miles
Rate of gas in gallons per mile= 6/132
Rate of gas in gallons per mile= 1/22
Rate of gas in gallons per mile
= 0.045454545 gallon/mile
solve the equation
x/3+y/4=4
Answers
Answer: [tex]y=-\dfrac{4}{3}x+16[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{3}+\dfrac{y}{4}=4\\\\\\\text{Multiply everything by 12 to eliminate the denominator:}\\\dfrac{x}{3}(12)+\dfrac{y}{4}(12)=4(12)\\\\4x+3y=48\\\\\\\text{Subtract both sides by 4x:}\\3y=-4x+48\\\\\\\text{Divide everything by 3:}\\y=-\dfrac{4}{3}x+16[/tex]
The distance between two points on a number line can be found by taking the blank of the blank of the coordinates.
absolute
value
sum
quotient
difference
product
Answers
Answer:
The correct options are;
Absolute value
Difference
Step-by-step explanation:
The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates such that the result will always have a positive value
The distance between two, points a and b on the number line is defined as [tex]\left | a - b \right |[/tex] that is the distance is found by taking finding the absolute value of the difference of the two numbers.
A. 19
B. 20
C. 15
D. 25
Help please !!
Answers
Answer:
A
Step-by-step explanation:
What is the equation for the line of symmetry in this figure?
Answers
Hey there! I'm happy to help!
A line of symmetry is a line that cuts a figure in half so that it is the same on both sides. We cannot do a vertical line because one side is different than another. We could do a horizontal line where y=3 the whole time. This would cut the shape in half so it is the same on both sides.
Therefore, the equation for the line of symmetry in this figure is y=3.
Have a wonderful day! :D
The horizontal line y = 3 is the required equation of line that makes the symmetric figure.
What is a line of symmetry?A line of symmetry is a line that splits a figure in two and makes the two halves identical.
In the given figure,
One side is different from the other, we are unable to draw a vertical line.
A horizontal line with y = 3 throughout could be drawn. This would split the form in half, making both sides identical.
Therefore, line y = 3 is the equation of line that will make figure symmetric.
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I'm stuck, please help
Answers
Step-by-step explanation:
A).[tex] \frac{2}{ \sqrt{x} } [/tex]Using the rules of indices
[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]So we have
[tex] \frac{2}{ {x}^{ \frac{1}{2} } } [/tex]And also by the rules of indices
[tex] \frac{1}{ {a}^{b} } = {a}^{ - b} [/tex]Applying the rules to the above expression we have the final answer as
[tex]2 {x}^{ - \frac{1}{2} } [/tex]B).[tex] \frac{3}{ {x}^{2} } [/tex]By using the rules of indices
[tex] \frac{1}{ {a}^{b} } = {a}^{ - b} [/tex]Applying the rules to the above expression
We have the final answer as
[tex]3 {x}^{ - 2} [/tex]Hope this helps you
Find the equation of a line given the point and slope below. (6, 6) no slope
Answers
Answer:
x = 6
Step-by-step explanation:
no slope means vertical line x = ?
