Answer:
y = 3 x - 9
Step-by-step explanation:
Find the equation of the line in slope-intercept form with the properties:
point: p_1 = (5, 6)
point: p_2 = (6, 9)
The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):
m = (9 - 6)/(6 - 5) = 3
Substitute the slope m = 3 and point (x_1, y_1) = (5, 6) into the point-slope equation y - y_1 = m (x - x_1):
y - 6 = 3 (x - 5)
Add 6 to both sides:
y = 6 + 3 (x - 5)
Distribute: 3 (x - 5) = 3 x - 15:
Answer: y = 3 x - 9
Members of a softball team raised $2045.50 to go to a tournament. They rented a bus
for $1041.50 and budgeted $62.75 per player for meals. Which equation or tape
diagram could be used to represent the context if p represents the number of players
the team can bring to the tournament?
The equation used to represent the context is 1041.50 + 62.75p = 2045.50.
How to compute the equation?From the information, they rented a bus for $1041.50 and budgeted $62.75 per player for meals.
Therefore, the equation will be:
1041.50 + (62.75 × p) = 2045.50
1041.50 + 62.75p = 2045.50
Therefore, the equation will be 1041.50 + 62.75p = 2045.50.
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find the value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1?
The value of 5x - 2y + 3z when x = 7 , y = 11 , z = -1 is 10.
Expression
An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.
Given that:-
Expression : 5x -2y + 3z
x = 7, y = 11 , z = -1
We have to find the value of 5x - 2y + 3z
According to the data given in the question, we can write,
The value of the expression 5x - 2y + 3z is:-
5*(7) -2*(11) + 3*(-1) = 35 -22 - 3 = 35 - 25 = 10.
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|2b – 3y| + 5z if b = −3, y = −4, and z = −1
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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Theoretically, If the spinner is spun 400 times, how many times would you expect to get blue?
Based on the experiment, if the spinner is spun 400 time, how many times would you expect to get blue.
The number of times that blue will be expected will be 100 times.
What will be the probability of getting a blue?It should be noted that from the information given, the spinner is divided into four equal sections labeled yellow, green, red, and blue.
It simply means that each color has a 1/4 chance for each scenario.
Therefore, the number of times that blue will be expected will be:
= 1/4 × 400
= 100 times
Therefore, the number of times that blue will be expected will be 100 times.
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A spinner is divided into four equal sections labeled yellow, green, red, and blue. If the spinner is spun 400 times, how many times would you expect to get blue?
3 2/5 + -7 1/5.
Please hurry I am desperate!
Answer:
-3.4 or -17/5
Step-by-step explanation:
3 and 2/5= 17/5 or 3.4
-7 and 1/5 = -34/5 or -6.8
24 ÷ (−6) =
−15 ÷ 0.3 =
−4 ÷ (−20) =
pls hlp :< i feel rly nauseous
Answer:
1st Question 24 ÷ (-6) = -4
2nd Question -15 ÷ 0.3 = -50
3rd Question -4 ÷ (-20) = 0.2
This should be correct. I used a calculator Lol. :3.
Which pattern below shows an arithmetic sequence with a third term of 8 and a constant difference of 5?
Answer:
Step-by-step explanation:
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:
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
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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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.
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.
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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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
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.
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
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.
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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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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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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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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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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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
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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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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ian and his brother are driving from city a to city b. the two cities are 294 miles apart. ian drives 49 miles per hour. how long does it take them to make the trip?
Answer: 6 hours
Step-by-step explanation: The distance is 294 miles. The speed is 49 miles per hour. In that case, we divide 294 by 49, which gives us 6.
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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'
Jack purchased 3 yards of material to make a coat. He used
5
-
8 yard. How many yards of material does Jack have left?
Jack has left with the 19/8 yards fraction part of material.
What is Yards?In mathematics, yard is the unit of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:
In inches :1 yard = 36 inches
In feet :1 yard = 3 feets
In meters :1 yard = 0.914 meters
For the question given,
If we have to find the remaining material that has been left we must find the difference between the two i.e. used and purchased material by simply subtracting them.
So, Material purchased = 3 yards
Material used = 5/8 yards
now, material left = Material purchased - material used
= 3 - 5/8
= 19/8 yards
Thus, Jack has left with the 19/8 yards material.
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