How to find the gradient of the straight lines? I don’t want direct answer, I want explanation please. I’m confused how can I find the x and y axis
Answer:
Question 27
[tex]\textsf{(a)} \quad -\dfrac{6}{5}[/tex]
[tex]\textsf{(b)} \quad \dfrac{1}{10}[/tex]
[tex]\textsf{(c)} \quad \dfrac{4}{5}[/tex]
Question 28
[tex]\textsf{(a)} \quad \dfrac{6}{0}=\textsf{und\:\!efined}=\textsf{no gradient}[/tex]
[tex]\textsf{(b)} \quad -\dfrac{3}{10}[/tex]
[tex]\textsf{(c)} \quad \dfrac{3}{10}[/tex]
Step-by-step explanation:
The gradient of a straight line can be found by dividing the difference in the y-coordinates by the difference in the x-coordinates between two points on the line.
A positive gradient slopes up from left to right.
A negative gradient slopes down from left to right.
[tex]\boxed{\begin{minipage}{4.3cm}\underline{Gradient Formula}\\\\$m=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}[/tex]
We can use the formula to find the gradients, or we can simply calculate the change in y and change in x by looking at the graph.
Example:
If we take line (a) from question 27 as an example.
The change in y from the beginning to the end of the line is 6 units.The change in x from the beginning to the end of the line is 5 units.The line slopes down, so the gradient is negative.Therefore, the gradient is -6/5.
Using the gradient formula, define two points on the line:
Let (x₁, y₁) = (0, 6)Let (x₂, y₂) = (5, 0)Input the points into the formula:
[tex]\textsf{Gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-6}{5-0}=-\dfrac{6}{5}[/tex]
Solutions
Question 27
(a) The gradient is -6/5, as calculated above.
(b) The change in y is 1 unit and the change in x is 10 units. The line slopes up so the gradient is positive. Therefore, the gradient is 1/10.
(c) The change in y is 4 units and the change in x is 5 units. The line slopes up so the gradient is positive. Therefore, the gradient is 4/5.
Question 28
(a) The change in y is 6 units and the change in x is 0 units. Therefore, the gradient is undefined since anything divided by 0 is undefined. Therefore, this line has no gradient.
(b) The change in y is 3 units and the change in x is 10 units. The line slopes down so the gradient is negative. Therefore, the gradient is -3/10.
(c) The change in y is 3 units and the change in x is 10 units. The line slopes up so the gradient is positive. Therefore, the gradient is 3/10.
Attachment
I have marked the change in y (green) and the change in x (blue) for line (c) on both graphs.
Your friend and your cousin discuss measuring with a ruler. Your friend says that you must always line up objects at the zero on a ruler. Your cousin says it does not matter. Who is correct, and why?
friend; A measurement always starts with a value of zero.
friend; A ruler does not match numbers one to one unless the measurement starts at zero.
cousin; you can choose any number for the start of the object and any number for the end.
cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object.
The correct option is the last one:
"Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object."
Who is correct, your friend or your cousin?
Now, remember that a rule is equivalent to a number line.
Now, suppose that you are measuring an element with a length of 16 centimeters.
If you measure it by lining up one of the ends of the element with the zero, then the other end will be at the line number 16.
And if you line it up from a different number, let's say 3cm, then the other end of the object (which still measures 16cm) will be at 19cm.
In both cases, to find the measure of the object that you are measuring with the ruler, you need to find the difference between the two numbers on the ruler that line up with the object ends.
If you line up with the zero, you need to subtract zero, so the measure is easier:
16cm - 0cm = 16cm
If you line up with other number, like the 3 in this case, you need to perform the subtraction:
19cm - 3cm = 16cm
In both cases, we will get the same measure. So your cousin is correct, and the correct option is the last one:
Cousin; The distance is the absolute value of the difference of the numbers lined up with the beginning and the end of the object.
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16-2x=4(1/4 x-2)
i need it in 4 steps and what you are doing in each step.
Answer:
x = 8
Step-by-step explanation:
Solve for x:
-2 x + 16 = 4 (x/4 - 2)
Put each term in x/4 - 2 over the common denominator 4: x/4 - 2 = x/4 - 8/4:
-2 x + 16 = 4 (x/4 - 8/4)
x/4 - 8/4 = (x - 8)/4:
-2 x + 16 = 4 ((x - 8)/4)
(4 (x - 8))/4 = 4/4×(x - 8) = x - 8:
-2 x + 16 = x - 8
Subtract x from both sides:
(-2 x - x) + 16 = (x - x) - 8
-2 x - x = -3 x:
-3 x + 16 = (x - x) - 8
x - x = 0:
-3 x + 16 = -8
Subtract 16 from both sides:
(16 - 16) - 3 x = -16 - 8
16 - 16 = 0:
-3 x = -16 - 8
-16 - 8 = -24:
-3 x = -24
Divide both sides of -3 x = -24 by -3:
(-3 x)/(-3) = (-24)/(-3)
(-3)/(-3) = 1:
x = (-24)/(-3)
The gcd of -24 and -3 is -3, so (-24)/(-3) = (-3×8)/(-3×1) = (-3)/(-3)×8 = 8:
Answer: x = 8
Follow the steps of this magic number puzzle for two
starting numbers of your choice. One of your
numbers should be negative. Then write the steps for
any number, n, in column 3.
Directions
Write down a number.
Add 10.
Multiply by 2.
Subtract 2.
Divide by 2.
Results
How is the ending number related to the starting
number?
The ending number is nine more than the starting number.
The steps of the magic number puzzle are given.Let us consider the general number "n".The starting number is "n".The first step is to add 10 to the number.The number becomes "n+10".The next step is to multiply it by 2.The number becomes "2n+20".The next step is to subtract 2 from it.The number becomes "2n+18".The final step is to divide it by 2.The number finally becomes "n+9".The ending number is "n+9".Thus, the ending number is 9 more than the starting number.To learn more about numbers, visit :
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Keith has a credit card balance of $732. he cannot pay the whole amount due, so he pays the minimum of $75. after the minimum amount has been deducted from the $732 balance, he is charged 1.2% (or .012) fee. what will his balance be next month if he doesn't make any additional charges? if necessary, round your answer to 2 decimal places.
Keith credit card balance by next month is $664.88 if he doesn't make any additional charges
Information about the problem:
Total balance = $732Minimum paid = $75Charge fee = 1.2%Final balance =?Calculating the amount he could not pay, we have:
Amount to pay= Total balance - minimum paid
Amount to pay= $732 - $75
Amount to pay= $657
Calculating the final balance he will pay:
Final balance = Amount to pay + (amount to pay * Charge fee/100)
Final balance = $657 + ($657 * 1.2/100)
Final balance = $657 + ($657 * 0.012)
Final balance = $657 + ($7.884)
Final balance = $664.88
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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in a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution. how many liters of the 10% acid solution are needed?
There are 4 liters of solution are needed for the 10% acid solution.
Unitary method:
Unitary method is the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Given,
In a chemistry class, 8 liters of a 4% acid solution must be mixed with a 10% acid solution to get a 6% acid solution.
Here we need to find how many liters of the 10% acid solution are needed.
First, we have to convert the percentage into decimal,
4% = 4/100 = 0.04
10% = 10/100 = 0.10
6% = 6/100 = 0.06
Let x be the required liter of solution.
So, based in the given details,
We have to write the equation as,
=> 0.04*8 + 0.10x = 0.06(8+x)
=> 0.32 + 0.10x = 0.48 + 0.06x
=> 0.10x - 0.06x = 0.48 - 0.32
=> 0.04x = 0.16
=> x = 0.16/0.04
=> x = 4
x = 4 liters of 10% solution is used.
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pleas help quick as possible,
" Lara's drink coaster has a diameter of 6 centimeters. What is the coaster's circumference?
Use 3.14 for ." Thank you
Answer: 18.84 cm
circumference = 2πr, where r is the radius.
radius is half of the diameter.
6/2 = 3 so radius is 3
2x3.14x3= 18.84 cm
hope it helps.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Write an equation for a line parallel to y=4x+5 and passing through the point (4,13)
for this question choose as many answers as are correct. if the earth reversed its direction of spin
For the given condition- If the earth reversed its direction of spin. Then,
The Sun will indeed rise in the west & set in the east, The stars would revolve clockwise around Polaris.The Moon will indeed rise westward and set eastward.What is spinning of Earth?The Earth is constantly in motion. Every day, the Earth completes one full rotation around its axis. The axis is an imaginary line that runs through the earth from the North Pole to the South Pole.
Some key features regarding the Earth's rotation are-
The sun appears to move across the sky as the Earth rotates, but it is actually the Earth that's also spinning. One rotation takes 24 hours hours to complete, which explains why there are 24 hours in a day.In the other words, if a sun is visible in the morning beginning around 6:00 AM, the Earth will have rotated completely approximately by the next morning at 6:00 AM, and you will see the sun in roughly the same location.To know more about rotation of earth, here
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The complete question is -
If you are standing at the Earth's North Pole.
For this question choose as many answers as are correct. if the earth reversed its direction of spin
What method can be used to write the equation of a line in slope-intercept form given two points? Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the slope using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept. Find the y-intercept using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slope. Find the y-intercept using the formula m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction, and then substitute one point and the y-intercept into the equation y = m x + b to find the slop
The method that can be used to write the equation of a line in slope-intercept form given two points is A. Find the slope using the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, and then substitute one point and the slope into the equation y = m x + b to find the y-intercept.
How to illustrate the information?It should be noted that the equation of line passing through two point = y = mx + b.
Also, b can find out via putting values of x, y, and m in the equation of the line to get y-intercept.
In this case, the slope of the line will be y2 - y1/x2 - x1.
In conclusion, the correct option is A.
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M is the midpoint of segment JK. The coordinate of J are (-4, 7) and the coordinates of M are (2, 5). Find the coordinates of K.
The coordinates of K are (8,3).
There is a line segment JK with M as its midpoint. This means the length of JM = length of MK.
Also the coordinates of J is (-4,7) and the coordinates for M are (2,5).
As M is the midpoint, the x-distance and y-distance between (-4,7) and (2,5) are same as that between (2,5) and K.
x- distance between (-4,7) and (2,5) = 2- (-4) = 6
So x- coordinate of K = 2+6 = 8
y-distance between (-4,7) and (2,5) = 5-7 = -2
So y-coordinate of K = 5+(-2) = 3
Hence the coordinates of K are (8,3).
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4 to the 7th power times 8 to the 7th power?
Answer:
3.435973837*10^10
Step-by-step explanation:
4 to the 7th power is 16384
and 8 to the 7th power is 2097152
multiplied by each other is 3.435973837*10 to the 10th power
if you have to round to the nearest 10th the answer is 3.44
The profit Mrs. Kelly makes from making and selling x pairs of earrings is represented by
10−(2+23)
10x − (2x + 23). Which expression is equivalent?
Group of answer choices
8 - 23
8x− 23
−15 − 15
x 31 31
8+23
Answer:
8x-23
Step-by-step explanation:
10x-2x=8x, and since the 23 was in the parenthesis that was being subtracted, then the 23 gets subtracted.
Fill in the table using this function rule.
y=2x-2
X
3
5
6
10
y
0
0
10
0
Using the function rule y=2x -2 the values in the given table are as follow:
x y
0 -2
1 0
2 2
3 4
4 6
As given,
Given function:
y=2x - 2
Substitute the value of x in the given function y=2x - 2
x=0
⇒y=2(0) -2
=-2
x=1
⇒y=2(1) -2
=0
x=2
⇒y=2(2) -2
=2
x=3
⇒y=2(3) -2
=4
x=4
⇒y=2(4)-2
=6
Therefore, using the function rule y=2x -2 the values in the given table are as follow:
x y
0 -2
1 0
2 2
3 4
4 6
The complete question is :
Fill in the table using this function rule.
y=2x-2
x y
0
1
2
3
4
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what’s the answer? i need it asaappapapapapapa
By reading the given graph, we conclude that:
-8*f(1) - 4*g(4) = -8
How to get the wanted value?
Here we have two graphed functions, f(x) which is the blue one, and g(x) which is the purple one.
We want to find the value of:
-8*f(1) - 4*g(4)
So first we need to find the values of f(1) and g(4), and to do that, we need to use the given graphs.
On the graph we can see that:
f(1) = -2
g(4) = 6
Replacing that in the expression we get:
-8*f(1) - 4*g(4) = -8*-2 - 4*6 = 16 - 24 = -8
Then, by reading the given graph, we conclude that:
-8*f(1) - 4*g(4) = -8
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3. Check for Reasonableness Two students are
asked to write an equivalent algebraic expression
for (5v-3)2. Chen writes the equivalent algebraic
expression as 25v-6. Mia writes the equivalent
25 Who is correct?
algebraic expression as
V6
None of Chen and Mia have got the solution right for the given expression.
It is given that two students are asked to write an equivalent expression for (5v - 3 ) × 2.
We have to find out that which of the both students have got it correct ?
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.
As per the question ;
The expression is (5v - 3 ) × 2.
Let's solve this equation to find out who of Chen and Mia is correct.
So ;
(5v - 3) × 2
= (5v × 2) - (3 × 2)
= 10v - 6
So ; None of Chen and Mia is correct.
Thus , none of Chen and Mia have got the solution right for the given expression.
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Answer: Both Chen, and Mia are correct.
Step-by-step explanation:
The expression they gave us:
(5v^-3)^2.
Mia: 25/v^e
Chen: 25v^1
Now,
5v^-3)^2
Step 1: (5v^-3).= (5^2)v^3x2
Step 2: (5x5)v^3x2=25v^3x2
Step 3: 25v^-6. As you see Chen is correct. But..
Step 4: 25/1 x 1/v^6= 25/v^6
That also makes Mia to be correct.
So, in this problem there are two answers.
= 25v^-6, and 25/v^6.
Please help with work/explanation thank you
Answer: y = xw/v
Step-by-step explanation:
v = ( 1/y )*xw
⇒ y = xw/v
Sara is 5 years younger than Geoff. What is an equation that relates the age of Sara S and the age of Geoff G?
The equation that relates the ages is as follows:
G = S + 5
How to find equation to relate ages?Sara is 5 years younger than Geoff.
The equation that can be used to relates the age of Sara S and the age of Geoff G is as follows:
where
G = age of GeoffS = age of SarahTherefore, Sarah is 5 years younger than Geoff.
The equation that relates the ages is as follows:
G = S + 5
Therefore, Geoff is 5 years older than Sarah. In other words, Sarah is 5 years younger than Geoff.
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Elisa withdrew $20 at a time from her bank account and withdrew a total of $140. Francis withdrew $45 at a time from his bank account and withdrew a total of $270. Who made the greater number of withdrawals? ( This is Dividing Integers 2.2 so the numbers might go in the negatives)
Answer: Elisa made the greater number of withdrawals
Step-by-step explanation:
140/20=7
270/45=6
Find the mean and the median of the distribution of corrected long jump distance have?
The corrected mean and median, respectively, are 557.3 and 557.
The total number of athletes is 40.The already calculated mean is 577.3.The sum of the distances of all the athletes is the product of the number of the athletes and the mean distance.The sum of distances is 40*577.3.The sum of distances is 23,092.The correction in each jump is a reduction of 20.The total correction is the product of the number of athletes and the correction.The total correction is 40*20.The total correction is 800.The corrected mean is the ratio of the corrected sum of the distances and the number of athletes.The corrected mean is (23,092-800)/40.The corrected mean is 557.3.The already calculated median is 577.The median will shift by the same amount as the correction.The corrected median is 577–20.The corrected median is 557.To learn more about median, visit :
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ruben made a scale drawing of a petting zoo. the scale of the drawing was 1 millimeter : 10 meters. if the actual length of the goat pen is 20 meters, how long is the pen in the drawing?
The length of the pen in the drawing will be 2 millimeters.
As we can't create a real-life dimension in a small sheet of paper, we opted for a small scale that covers up the large length.As we are given, the scale of the drawing is 1 millimeter: 10 meters, which is 1 millimeter for every 10 meters
As we have been given that the actual size of the goat pen is 20 meters, so the length of the pen in the drawing is = 20*(1/10)
= 2 millimeters
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'
write the expression that can be used to find the slope find the slope of the line, if it is defined
We can the slope of the line using:
m = (y 2 - y 1)/ (x 2 - x 1) where, m is the slope of the line.
What is a Slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.
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If someone leave a 20% tip and the meal is 35$how much was the tip
Answer:
$7
Step-by-step explanation:
Since 100/20 = 5, 20% is 1/5, so 20% of 35 is 35/5, or 7
Answer:
If someone leave a 20% tip and the meal is 35$how much was the tip :
$35.00 ÷ 20% = $7.00
Which pattern below shows an arithmetic sequence with a third term of 8 and a constant difference of 5?
Answer:
Step-by-step explanation:
Soua read 8 pages in 3 minutes. if she keeps reading at this pace, how many pages will she read in 10 minutes? round Ur answer to the nearest tenth.
Answer:
Step-by-step explanation:
e
The number of pages read by Soua in 10 minutes are 26.7 pages.
It is given in the question that Soua can read 8 pages in 3 minutes.
We have to find the number of pages that she will she read in 10 minutes.
We will use the unitary method for this question.
The method by which we find out the value of one unit and further use it to find the value of multiple units is known as the unitary method.
Pages read by Soua in 1 minute = 8/3 pages
Hence, we can write,
Pages read by Soua in 10 minutes = 10*(8/3) = 80/3 pages = 26 and(2/3) pages = 26.667 pages ≈ 26.7 pages.
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a test worth 100 points has 14 questions. short-answer questions are worth 5 points and essay questions are worth 15 points. how many short-answer questions are on the test? how many essay questioons are on the test?
There are 11 questions worth 5 points and 3 questions worth 15 points.
What is the equation?An equation is a mathematical statement composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the correct number of questions:
Let, 5-point questions are x and 15 marks questions are y.
So, x + y = 14. ...(1)The total points are 100 so the other equation will be:
5x + 15y = 100 ...(2)Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:
Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.
5 (x + y = 14) ⇒ 5x + 5y = 70Now,
5x + 5y - 70 - 5x - 15y + 10010y = 30y = 3So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.
Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.
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A car valued at $20,000 depreciates at a rateof 2% during the first 5 years, then at a rateof 2.5% every year after that. What will thecar’s value be after 10 years?)
Answer:
$15928.81
Step-by-step explanation:
hope this works
2000 x (0.98)^5 = ans
ans x (0.975)^5 = 15928.81442 which rounds to $15928.81
Solve x in terms of y
Y=6x
Answer:
Y/6 = x
Step-by-step explanation:
Y = 6x
Y/6 = x
Sophia borrowed $11,020 at 4% simple interest for 10 months. How much will the interest amount
to? What is the total amount that she will have to pay back at the end of 10 months? Round
answers to the nearest cent if necessary.
The total amount that she will have to pay back at the end of 10 months is $11,385.864.
We have Sophia .who borrowed $11,020.
We have to determine the total amount that she will have to pay back at the end of 10 months.
What is the formula to calculate the Simple Interest ?The Simple interest can be calculated using the formula -
S.I. = (P x R x T)
where -
P = Principle amount
R = Rate of interest
T = time in years
According to the question -
P = $11020
R = 4%
T = 10 months = 0.83 years
Therefore -
Interest = (P x R x T) = (11020 x 0.04 x 0.83) = $365.864
Now -
Interest = Total amount - Principle
Total Amount = Interest + Principle = 11020 + 365.864 = $11,385.864
Hence, the total amount that she will have to pay back at the end of 10 months is $11,385.864.
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