4.
Write the equation of the line, in slope-intercept form, that goes through the point ( 10, 6 ) and is perpendicular to the line: y = ( - 5 / 4 ) x + 1.
Answers
Answer: \(\boxed{y=\frac{4}{5}x-2}\)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.
Substituting into point-slope form,
\(y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}\)
Related Questions
What is the solution of 2 + 2 =
Answers
The graph of an arithmetic sequence is shown.What is the value of the 7 th term?Round your answer to the nearest tenth. Add a decimal point and a zero if youranswer is a whole number (for example, 10 would be entered as 10.0)
Answers
10.0
Explanation
an arithmetic sequence is given by the expression
\(\begin{gathered} a_n=a_1+(n-1)d \\ \text{where} \\ a_{_1}\text{ is the first term} \\ \text{and d is the common diference} \end{gathered}\)in the graph , to know the value of the 7 th terms, we need to take the value that y takes, when x= 7
so
therefore, the answer is
10.0
I hope this helps you
Do two negatives make a positive? (E.x --3)
Straight forward and simple answers please!
Answers
Answer: yes
Step-by-step explanation:
if you multiply or divide 2 negatives together they make a positive if you add no
Answer:
Yes
Step-by-step explanation:
\(-(-3)=+3\), so yes
4) Amy traveled to the recycling plan
back. It took one hour less time to get
there than it did to get back. The average
speed on the trip there was 50 km/h. The
average speed on the way back was 40
km/h. How many hours did the trip there
take?
Answers
The time taken by Amy to travel to the place was t = 4 hours.
What is average speed?A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.
In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.
Let the time taken to get back = t + 1.
Now, it took one hour less time to get there thus time = t.
Now, average speed is given as:
average speed = total distance / total time
Substituting the values:
50 km/h = d / t
d = 50t .........(1)
40 km/h = d / (t + 1)
d = 40(t + 1)......(2)
Setting the value of d as equal we have:
50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4
Hence, the time taken by Amy to travel to the place was t = 4 hours.
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What kind of line can be drawn through the points (2, 3) and (-2, 3)?
Answers
Answer:
a zero line
Step-by-step explanation:
i dont have a diagram to show
How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?
Answers
Using the principle of inclusion-exclusion, we can see that the total number of numbers with the given restrictions is:
586,071
How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?o find the number of 7-digit numbers where the digits 1, 2, and 3 each appear at least once, we can use the principle of inclusion-exclusion.
Step 1: Find the total number of 7-digit numbers without any restrictions.
Since each digit can be chosen independently from 0 to 9 (excluding leading zeros), there are 9 options for the first digit (1-9) and 10 options for each subsequent digit (0-9). Therefore, the total number of 7-digit numbers without any restrictions is 9 * 10⁶.
Step 2: Subtract the number of 7-digit numbers that do not contain 1, 2, or 3.
The number of 7-digit numbers that do not contain 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding 1, 2, and 3). So for each digit position, there are 7 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without 1, 2, or 3 is 7⁷.
Step 3: Add back the number of 7-digit numbers that do not contain two of the digits 1, 2, or 3.
The number of 7-digit numbers that do not contain two of the digits 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding two of 1, 2, and 3). For each digit position, there are 6 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without two of 1, 2, or 3 is 6⁷.
Step 4: Subtract the number of 7-digit numbers that do not contain all three digits 1, 2, and 3.
The number of 7-digit numbers that do not contain all three digits 1, 2, and 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding all three of 1, 2, and 3). For each digit position, there are 4 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without all three of 1, 2, and 3 is 4⁷.
Now we can apply the principle of inclusion-exclusion to find the desired count:
Total number of 7-digit numbers = 9 * 10⁶ - 7⁷ + 6⁷ - 4⁷
Calculating this expression, we find:
Total number of 7-digit numbers = 586,071
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The sum of the areas of all the faces of a 3D object is called:
(a) Area
(b) Surface Area
(c) Volume
(d) Perimeter
( i dont know why its hard for me but welp-)
Answers
Answer:
Surface area
Step-by-step explanation:
The sum of the areas of all the faces of a 3D object is called Surface Area
Answer:
Step-by-step explanation:
C=Volume
Ms. April likes for the twenty students in her
class to have a carton of milk each day at break
time. She sends three of her students down to
the cafeteria to ask for the cartons of milk, but
she likes to mix things up a bit and wants to
send a different group of students down every
day. Will she have enough different groups of
three students in her class of twenty students to
send a different group every day of the school year? (There are 180 days in the school year)
Answers
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.
Write the equation of the line that passes through the points (-3, 2 ) and - (- 1 , 6)
Answers
Given:
The two points given are,
\((-3,2),(-1,6)\)Required:
The equation of the line passing through given two points.
Explanation:
Let the given two points be
\(\begin{gathered} (x_1,y_1)=(-3,2) \\ (x_2,y_2)=(-1,6) \end{gathered}\)Therefore, by two-point form, the equation of the line passing through two points is given by,
\(\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \Rightarrow y-2=\frac{6-2}{-1-(-3)}(x-(-3)) \\ \Rightarrow y-2=\frac{4}{2}(x+3) \\ \Rightarrow y-2=2(x+3) \\ \Rightarrow y-2=2x+6 \\ \Rightarrow y=2x+6+2 \\ \Rightarrow y=2x+8 \end{gathered}\)Final Answer:
The equation of the line passing through given two points is,
\(y=2x+8\)First option is correct.
Three ballet dancers are positioned on stage. Kendall is straight behind Bridget and directly left of Lena. If Bridget and Kendall are 5 feet apart, and Lena and Bridget are 7 feet apart, what is the distance between Kendall and Lena? If necessary, round to the nearest tenth.
Answers
Answer:
Travis and Shawn form the vertical leg of a right angle triangle of length = 8 ft. Andy and Travis form the hypotenuse of the right angle triangle of length = 9 ft.
Step-by-step explanation:
Using the Pythagorean theorem to find the distance between Shawn and Andy which is the length of the horizontal leg of the right angle triangle; let that length be x. Then:
92 = 82 + x2 , x2 = 92 - 82 = 81 - 64 = 17 , and x = √ 17 = 4.13 ft
Answer:
The distance between Kendall and Lena is approximately 8.6 feet, rounded to the nearest tenth.
Work:
Start by drawing a diagram to visualize the positions of the three ballet dancers. Let's represent Kendall, Bridget, and Lena with the letters K, B, and L, respectively. Based on the given information, we can write:
Kendall is straight behind Bridget and directly left of Lena, so the positions of the dancers are arranged in a straight line as follows:
L --- B --- K
Bridget and Kendall are 5 feet apart, so we can write:
KB = 5 feet
Lena and Bridget are 7 feet apart, so we can write:
BL = 7 feet
To find the distance between Kendall and Lena, we can use the Pythagorean theorem. Let's call the distance between Kendall and Lena "KL". Then we have:
KL^2 = KB^2 + BL^2
KL^2 = 5^2 + 7^2
KL^2 = 74
Taking the square root of both sides, we get:
KL ≈ 8.6 feet
A bag with 8 marbles has 4 red marbles, 3 blue marbles, and 1 yellow marble.A marble is chosen at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
SOMEONE PLEASE HELP ME IM SO STUCK
Answers
Answer:
1/4
Step-by-step explanation:
First you add all of the marbles in the bag which is 16 marbles. The fraction of red marbles to the total would be 4/16. In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.
Write an equation for the table below.
Answers
The equation that represents the table, in slope-intercept form, is expressed as: y = 5x.
How to Write the Equation for the Table?To write the equation of the table, find the slope (m) and the y-intercept (b), and express the equation as y = mx + b.
Let x represent time (min) and y represent water used (gal).
Slope (m) = change in y / change in x = 10 - 5 / 2 - 1 = 5/1
Slope (m) = 5
Find the y-intercept (b) by substituting m = 5 and (x, y) = (1, 5) into y = mx + b:
5 = 5(1) + b
5 - 5 = b
b = 0
Substitute m = 5 and b = 0 into y = mx + b:
y = 5x + 0
y = 5x
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Nicole had a collection of 60 stuffed animals. She gave away 5 stuffed animals per month until all her stuffed animals were gone. Which graph best represents this situation?
Answers
The graph will have a slope of 15 and is attached with the answer below.
What is a constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
When y and x are two quantities that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
Given that Nicole had a collection of 60 stuffed animals. She gave away 5 stuffed animals per month until all her stuffed animals were gone.
The equation can be written as:-
y = kx
The value of k will be calculated as :-
60 = k x 5
k = 60 / 5
k = 12
The equation will be:-
y = 12x
The graph of the linear relation is attached with the answer below.
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Can u help me on the mystery sequence hidden in the dominoes
Answers
Answer: 80
Step-by-step explanation:
A) The first domino is 3, the second is 4. Hence 34.
B) The first domino is 5, the second is 1. Hence 51.
C) The first domino is 6, the second is 11. Hence 71.
D) The first domino is 7, the second is 10. Hence 80.
The .............. from the regular selling price to the discounted sale price is 20%
Answers
Answer:
80%
Step-by-step explanation:
regular price is 100%
so, after the discounted price is 20%
the discount is 80%
A moving truck states that it holds 300 cubic feet of boxes. The truck is 25feet in length and 8 ft in height. What is the width of the moving truck
Answers
Answer:
77
Step-by-step explanation:
Answer:
25x8xW=300
We=300/25x8
W=1.5 feet
2 (UHS)
Comparing Exponential Functions
How do the graphs of the functions f(x) = (3) and g(x)
= (ş) compare?
Answers
Answer:
Both sides are equal.
Step-by-step explanation:
whats -4+1 is it -3?
Answers
Answer: YES
Step-by-step explanation:
Answer:
the corrects answer is -3
Step-by-step explanation:
joey goes to the carnival. he spends $26. he buys himself a supersize shake for $5.00. He also buys six regular-size sundaes. Write an equation that you could solve to find out how much each sundae costs.
HELP PLS, IT'S A TEST-
Answers
($3.5 x 6 (amount of shakes) = $21 which is the amount he had after buying the $5 supersize shake)
Explain your answer to the question in the picture with steps please, thank you.
Answers
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
The Flash runs 100 km in 25 seconds. What is the Flash's velocity
Answers
Answer:
yo moma smell like stank
Step-by-step explanation:take showers
A direct variation includes the points (2,18) and (n,9). Find n?
Answers
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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Over which part of the domain does the graph represent a cubic function?
Answers
The graph attached represents a cubic function at
x < -2
What are cubic functions?Cubic functions are a type of polynomial function that has a degree of 3, meaning the highest power of the variable is 3.
The general form of a cubic function is:
f(x) = ax³ + bx² + cx + d
where a, b, c, and d are coefficients and x is the variable
At point x = -2 the graph has an open circle hence -2 would not be part of the equation, this makes x ≤ -2 an incorrect option.
From x < -2 in the graph, represents the graph of a cubic function
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what is a golden rectangle where can I find it
Answers
The golden rectangle is a rectangle whose length divided by its width is equal to 1.618. You can find it on great masterpieces of artwork, like the Monalisa and it is derived from the observation of ratios in nature.
1) Golden rectangle refers to the golden proportion, the one we can find by dividing the lengths in a ratio where:
In the Renaissance, this was rediscovered and said to be the perfect proportion found in many other proportions. This irrational number φ =1.618... is found when we divide the length by the width of the golden rectangle.
This golden ratio can be found in artwork, and in nature like the spirals that an Italian mathematician called Fibonacci found
If we divide the length by the width of any of these rectangles, we'll find the same ratio: φ =1.618.. or
\(\varphi=\frac{1+\sqrt[]{5}}{2}=1.618\ldots\)
Change 8 a.m. to 24 hour clock time.
Use a colon : to separate hours and minutes
Answers
Answer:
08:00
Step-by-step explanation:
Answer:
8:00
Step-by-step explanation:
12/midnight would be 00:00 so 8am would be 8:00. if it were 8pm it would be 20:00
What is the slope of a line that is perpendicular to 5 x – 2 y = 1 ?
Answers
Answer:
The slope is 5/2
Suppose MarketOne is a marketing company that has small businesses for clients. MarketOne charges an upfront cost of $350 for new clients and an additional $195 per month to run and maintain the client's website. A linear equation could be used to relate the total cost, in dollars, of MarketOne's services and the number of months that the client's website is running. Which solution is viable for this situation? For full points, write the equation and show your work.
Answers
C = 195m + 350
where the constant term of 350 represents the upfront cost and the coefficient of 195 represents the monthly cost.
To check if this equation is viable for the situation, we can use some reasonable values for the number of months and see if the resulting costs make sense.
For example, if the client's website is running for 6 months, the total cost would be:
C = 195(6) + 350
C = 1,170 + 350
C = 1,520
This means that the client would pay $1,520 in total for 6 months of service from MarketOne.
Similarly, if the client's website is running for 12 months, the total cost would be:
C = 195(12) + 350
C = 2,340 + 350
C = 2,690
This means that the client would pay $2,690 in total for 12 months of service from MarketOne.
Based on these calculations, we can see that the linear equation is viable for the situation. The equation allows us to calculate the total cost of MarketOne's services based on the number of months the client's website is running, which is a useful tool for budgeting and planning.
Four students have interviews for summer internships. One is a first-year student, two are second-year students, and one is a third-year student. They are interviewed in the following order: third-year student, second-year student, first-year student, and second-year student. The following conditions apply:
Ashley interviewed after Carlos but before Brianna.
David interviewed before Carlos.
Brianna interviewed last.
Who is the first-year student?
Answers
Answer:
Ashley
Step-by-step explanation:
Lets understand the conditions.
Carlos < Ashley < Brianna
David < Carlos
Clearly, this tells us that David < Carlos < Ashley < Brianna, meaning the order is
David, Carlos, Ashley, Brianna
Since Ashley was interviewed third, she is the first year student
Cheers
If the following data were transformed and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
X
1
2
3
y
12
83
580
Answers
If the data were transformed and points with the coordinates
(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.
To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.
Let's calculate the logarithms for the given data:
x y log(y)
1 12 log(12) = 1.079
2 83 log(83) = 1.919
3 580 log(580) = 2.763
Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)
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Jeff said that 0.8/ 40 = 0.2 Is he correct?
Answers
Answer:
no
Step-by-step explanation:
0.8 / 40 = 0.02
Answer:
0.02
Step-by-step explanation:
Jeff is wrong since 0.8 / 40 = 0.02 and not 0.2