Use the given conditions to write and equation for the line in the indicates form:
1. Passing through (2,5) and perpendicular to the line whose equation is -3x+y-6=0; slope-intercept form
2. Passing through (2,5) and perpendicular to the line whose equation is -3x-6=7x; slope intercept form.
Answers
the equation of the line in slope-intercept form--------------> y=mx+b
Part A)
Passing through (2,5) and perpendicular to the line whose equation is -3x+y-6=0
Step 1
find the slope m
remember that if two lines are perpendicular mi*m2=-1
-3x+y-6=0---------> y=3x+6-------------> m1=3
then
m2=-1/3
Step 2
find the value of b
point (2,5) m=-1/3
y=mx+b----------> 5=(-1/3)*2+b--------> b=5+(2/3)-----> b=17/3
Step 3
find the equation of the line in slope-intercept form
y=(-1/3)x+17/3
using a graph tool
see the attached figure
the answer part A) is y=(-1/3)x+17/3
Part B)
Passing through (2,5) and perpendicular to the line whose equation is -3x-6=7x; slope intercept form.
Step 1
-3x-6=7x---------> 10x=-6 -----> x=-6/10-----> x=-3/5 (parallel to the axis y)
equation of the line is a constant so its perpendicular will be another constant defined by the coordinate y of the point through which it passes parallel to the axis x
point (2,5) ----------> the coordinate y=5
therefore
the perpendicular line is y=5 (parallel to the axis x)
using a graph tool
see the attached figure
the answer part B) is y=5
Related Questions
A rectangle of length 10 units and width 5 units is shown. Inside this rectangle is another rectangle of length 9 units and width 3 units placed symmetrically inside the larger rectangle. The smaller rectangle is shaded gray. If you choose a point inside the large rectangle, what is the probability that it is not inside the shaded rectangle?
24%
27%
46%
54%
Answers
First, we need to find the area of the rectangles.
10 × 5 = 50
9 × 3 = 27
Now, we find the percent of increase.
27 ÷ 50 = 0.54
Convert into a percentage:
0.54 = 54%
And subtract from 100%.
100% - 54% = 46%
The answer is 46%.
Hope this helps!
Answer
46% is the answer. :)
John has 8/9 of a gallon of apple cider vinegar. If it takes 1/7 of a gallon of vinegar to make a batch of collard greens, how many batches can john make?
Answers
[multiply by 7 through]
1 gallon = 7 batches
[multiply by 8/9 through]
8/9 gallon = 7 x 8/9
8/9 gallon = 6 2/9
[Good enough to make 6 batches, not enough to make 7 batches]
So he can make 6 batches of collard green
John can make 6 whole batches of collard greens with 8/9 of a gallon of apple cider vinegar, accounting for each batch requiring 1/7 of a gallon of vinegar.
The question asks how many batches of collard greens John can make with 8/9 of a gallon of apple cider vinegar, considering that each batch takes 1/7 of a gallon.
To find the answer, divide the total amount of vinegar John has by the amount of vinegar required for one batch:
Total amount of vinegar John has: 8/9 gallon
Amount of vinegar required for one batch: 1/7 gallon
Now, we use division to find out how many batches can be made:
(8/9), (1/7)
Multiply the first fraction by the reciprocal of the second fraction: (8/9) * (7/1)
Simplify the multiplication: (8 * 7) / (9 * 1)
Calculate the result: 56/9
Finally, we determine how many whole batches John can make, since partial batches are generally not considered. As 56/9 is equal to 6 with a remainder, John can make 6 whole batches of collard greens.
Where does A and B go HURRY ASAP
Answers
C is (-4, -4) so A is (-4, 4)
D is (4, -4) so B is (4, 4)
Find the value of x in the solution to the system of equations shown.
A. x = 2.33
B. x = 3
C. x = 4.2
D. x = 5.4
Answers
y = 14x - 6
y = -4x + 48
14x - 6 = -4x + 48
add 6 to both sides
14x = -4x + 54
add 4x to both sides
18x = 54
divide both sides by 18
x = 3
The option is B.) x = 3
Hope this helps!
The value of x in the solution to the system of equations will be 3. Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The system of linear equations is given below.
y = 14x - 6 ...1
y = -4x + 48 ...2
From equations 1 and 2, then the value of the variable 'x' will be given as,
14x - 6 = -4x + 48
14x + 4x = 48 + 6
18x = 54
x = 3
The value of x in the solution to the system of equations will be 3. Then the correct option is B.
More about the solution of the equation link is given below.
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Joelle plans to sell two types of balloons at her charity event: 171717‑inch latex balloons that require 222 cubic feet (\text{ft}^3)(ft 3 )left parenthesis, f, t, start superscript, 3, end superscript, right parenthesis of helium and 181818‑inch mylar balloons that require only 0.5 \,\text{ft}^30.5ft 3 0, point, 5, space, f, t, start superscript, 3, end superscript. She only has access to 1{,}000 \,\text{ft}^31,000ft 3 1, comma, 000, space, f, t, start superscript, 3, end superscript of helium, 15\%15%15, percent of which will be unused due to pressure loss in the tanks. She wants to have at least 500500500 balloons for sale in total. For the number of latex balloons, LLL, and number of mylar balloons, MMM, which of the following systems of inequalities best represents this situation? Choose 1 answer:
Answers
L+M >= 500 (greater than or equal to)
2L + 0.5M <= 850 (less than or equal to)
The first inequality deals with the total number of balloons. She wants the total to be at least 500, so add the variables and set it greater than or equal to 500.
The second inequality deals with the helium. 2L comes from each latex balloon using 2 ft^3 of helium. 0.5M comes from each Mylar balloon using 0.5 ft^3. Together they can use no more than 85% of the 1000 ft^3 tank; 85% = 0.85; 0.85×1000=850. "No more than" tells us it must be less than or equal to.
In a square of a side length s, what is the length of a diagonal?
Answers
d - length of a diagonal
d = s√2
why?
Use the Pythagorean theorem:
d² = s² + s²
d² = 2s²
d = √(2s²)
d = √2 · √s²
d = s√2
Final answer:
The length of the diagonal in a square with side length s is s√2, calculated by using the Pythagorean theorem which relates the side lengths of a right triangle.
Explanation:
To find the length of a diagonal in a square with side length s, we can use the Pythagorean theorem. In a square, the diagonal splits the square into two right triangles. Therefore, the length of the diagonal can be seen as the hypotenuse of a right triangle where the other two sides are both of length s. The Pythagorean theorem tells us that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Here is the step-by-step solution using the Pythagorean theorem:
Let the side length of the square be s.
Since the sides of the square are equal, the lengths of the two sides of the right triangle (formed by the diagonal) are also s.
According to the Pythagorean theorem, the square of the diagonal length d is d² = s² + s².
This simplifies to d² = 2s².
Take the square root of both sides to find the length of the diagonal d = √(2s²).
Therefore, the length of the diagonal is d = s√2.
Use the distributive property to simplify the expression (12 + 10x) 1/2
Answers
Answer:
2(5x + 6)
Step-by-step explanation:
i think you need to rearrange 12 + 10x which that is also 2(5x + 6) ?
sorry if i didn't explain well
Answer:
i Don’t understand
Step-by-step explanation:
pls give me brainliest for the love of god
PLEASE HELP!
Drag and drop an answer into each box to correctly complete the statement
Answers
PC = P'C . . . and . . . m∠ACP = 90°
Answer:
A reflection is a transformation that maps point P in a figure, over a line AB, such that for point C at the intersection of AB and PP', PC = PC' and m∠ACP = 90°
Step-by-step explanation:
After the reflection of P across the line AB, P' is created, where PP' and AB are perpendicular. Given that point C is at the intersection of the lines, then m∠ACP = 90° and PC = PC'.
How do you find the area of a rectangular prism?
Answers
Let's first define what area means. Area is for two-dimensional shapes, and expressions how big something is and to what extent. There are formulas that can measure area because these shapes are totally flat, and there's nothing more to measure.
However, when we have three-dimensional figures such as rectangular prisms, we use surface area. Surface area measures the total area that the object takes up, and is a sum of the areas of all the faces. The formula for surface area of a rectangular prism is:
2(lw + wh + lh)
So if we had:
L = 5
W = 6
H = 3
We would have:
A = 2(5×6 + 6 × 3 + 5×3) =
2(30 + 18 + 15) =
2(48 + 15) =
2(63) =
A = 126 units cubed
Notice how it's units cubed because there's 3 dimensions.
Hope this helps!
on the left bottom, im not sure what to do there
Answers
Two sides of a right triangle measure 7 units and 3 units. What is the area of the square that shares a side with the third side of the triangle?
Answers
We can use the Pythagorean theorem to find the length of the third sides.
c²=a²+b²
Where c is the longest (unkwon ) side, a and b are the remaining sides. So,
c²=7²+3²
= 49+9
= 58
So, c=√58
So, the length of the third side or the side length of square is √58.
So, the area of the shaded region (square)= c²
=(√58)²
=58
So, the area of the square is 58 units².
Answer: 58 units squared
Step-by-step explanation:
HELP QUICK PLEASE!!!!
explain in a short paragraph how the figure below shows this is a right angle, by the converse of the phythagorean theorem
Answers
As you see the biggest square is 5x5 = 25 squares unit
Two others
3x3= 9
4x4 = 16
9+16 = 25
How can I find the Slope intercept
Answers
An online store randomly samples three groups of 100 customers on which delivery method they use. The data shows the results of the three samples.
Overnight 2-Day Standard Total
Group 1 27 20 53 100
Group 2 32 17 51 100
Group 3 34 19 47 100
The online store has 2755 customers one day.
Based on the samples, what is a reasonable estimate of the number of people who will use overnight delivery?
Enter your answer rounded to the nearest whole number in the box.
Answers
The answer is 854 for sure. I did the test and got it all right.
Answer:
854 customers.
Step-by-step explanation:
An online store randomly samples three groups of 100 customers on which delivery method they use. The data shows the results of the three samples.
Overnight 2-day Standard Total
Group (1) 27 20 53 100
Group (2) 32 17 51 100
Group (3) 34 19 47 100
Total customers 93 56 151 300
We have to calculate the number of people who will use overnight delivery.
Out of 300 customer there are 93 people who would use overnight delivery, so the percentage = [tex]\frac{93}{300}[/tex] × 100 = 31%
The online store has 2755 customers one day.
Therefore, 31% of the 2755 customers = [tex]\frac{31}{2755}[/tex] × 100 = 854.05 ≈ 854 customers.
854 customers would use overnight delivery.
Use equal intervals to make a frequency table for the average number of movies per person. You do not need to show tally marks.
Country Average Number of Movies
Turkey 0.5
Japan 1.2
UK 1.3
Finland 1.3
Austria 1.5
Germany 1.8
Spain 2.2
Sweden 2.2
Denmark 2.2
Switzerland 2.5
France 2.5
Norway 3.0
Canada 3.0
US 4.5
Answers
When you create a frequency table, you have set intervals. In this case, our small number is close to 0 and our largest number is 4.5. We could create an interval for each number. Then, count the number of countries in each.
It would look like:
Interval Frequency
0-0.99 1
1-1.99 5
2-2.99 5
3-3.99 2
4-4.99 1
0-0.7 | 1
0.8-1.5 | 4
1.6-2.3 | 4
2.4-3.1 | 4
3.2-3.9 | 0
4-4.7 | 1
Which is C= 100w/l solved for w?
A.)W=100CL
B.)W= LC/100
C.)W= 100C/L
D.)W= 100/LC
Answers
w is on the right side multiplied by 100/L.
[tex] C = \dfrac{100}{L} \times w [/tex]
Now multiply both sides by the reciprocal of 100/L,
which is L/100, to isolate w.
[tex] C \times \dfrac{L}{100} = \dfrac{L}{100} \times \dfrac{100}{L} \times w [/tex]
[tex] \dfrac{CL}{100} = w [/tex]
[tex] w = \dfrac{CL}{100} [/tex]
[tex] w = \dfrac{LC}{100} [/tex]
Answer: choice B.
Final answer:
To solve for 'w' in the equation C = 100w/l, multiply both sides by 'l' and then divide by 100, resulting in 'w = Cl/100', which is option B.
Explanation:
To solve the equation C = 100w/l for w, we need to isolate w on one side of the equation:
Multiply both sides by l to get Cl = 100w.
Divide both sides by 100 to isolate w, which gives us w = Cl/100.
Therefore, the equation solved for w is w = Cl/100, which corresponds to option B.) W = LC/100.
A can of juice has a diameter of 6.6 centimeters and a height of 12.1 centimeters. What is the total volume of a six pack of juice cans
Answers
Volume of one can : (3.14)(3.3)^2(12.1)
: 413.75
Volume of 6 cans = 413.75 * 6 = 2482.53
To find the total volume of a six-pack of juice cans, calculate the volume of one can using the cylinder volume formula, [tex]V = \pi r^2h[/tex], and multiply by six. One can's volume, with a diameter of 6.6 cm and a height of 12.1 cm, is approximately 414.18 [tex]cm^3[/tex]. Multiplying by six gives a total volume of approximately 2485.08 [tex]cm^3[/tex] for the six-pack.
To calculate the total volume of a six-pack of juice cans, we first need to find the volume of a single can and then multiply that by six, since a six-pack contains six identical cans.
First, let's find the volume of one can using the formula for the volume of a cylinder [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.
Given the diameter of a juice can is 6.6 centimeters, the radius r is half of that, which is 3.3 centimeters. The height h is 12.1 centimeters. Therefore, the volume of one can is:
[tex]V = \pi (3.3 cm)^2(12.1 cm) = \pi (10.89 cm^2)(12.1 cm) = \pi (131.769 cm^3) = 414.18 cm^3[/tex]
Now, to find the total volume for a six-pack, we multiply the volume of one can by six:
Total volume = 6 × 414.18 [tex]cm^3[/tex] ≈ 2485.08 [tex]cm^3[/tex]
Thus, the total volume of a six-pack of juice cans is approximately 2485.08 cubic centimeters.
Khafre was a son of Khufu. He also had a pyramid built, but it was not as big as his father’s. The volume of the Pyramid of Khafre is about 2,115,072 cubic meters, and its height is about 136 meters. Approximate the length of each side of the base.
Could you work it out also!
Answers
the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to return to earth? round your answer to the nearest tenth of a second. show all your work.
Answers
The equation is:
[tex]0=-9.8t^2+v_0t+h_0[/tex]
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height. We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42. This gives us:
[tex]0=-9.8t^2+42t[/tex]
We will use the quadratic formula to solve this. The quadratic formula is:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Plugging in our information we have:
[tex]t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)} \\ \\=\frac{-42\pm \sqrt{1764-0}}{-19.6} \\ \\=\frac{-42\pm \sqrt{1764}}{-19.6} \\ \\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6} \\ \\=\frac{-84}{-19.6}\text{ or }\frac{0}{-19.6} \\ \\=4.3\text{ or }0[/tex]
x=0 is when the rocket is launched; x=4.3 is when the rocket lands.
The rocket takes approximately 8.6 seconds to return to earth.
Explanation:To calculate the time it takes for the rocket to return to earth, we need to consider the projectile motion in the vertical direction. The initial vertical velocity of the rocket is 42 m/s. We can use the equation for vertical displacement to find the time:
Δy = v0yt + (1/2)gt²
Since the rocket returns to the same altitude, the displacement is 0. Therefore, we have:
0 = (42)t + (1/2)(-9.8)t²
Simplifying this equation and solving for t, we find that it takes approximately 8.6 seconds for the rocket to return to earth.
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if the measure of AB is 8 find the length of the radius of C
Answers
8/2 = 4
the radius is 4
55% decrease followed by a 25% increase
Answers
Can someone help me and also try to explain how they got their answer
Answers
Your answer should be 2 over 3 ,
2 thirds,
2/3
I wish you the best of luck Buddy!
Please help ‼️ I’m doing functions
Answers
8v-2v=-3u-4u
6v=-7u
V= (-7u)/6
H(u)= (-7u)/6
If five people share three cartons of Chow mein, what is each person sharing
Answers
Which of the following is true about the age of rock layers and the age of the Earth? A. All rock layers are older than the Earth. B. The Earth is older than any rock layer. C. The bottom layer in a sequence of rock layers is older than the Earth. D. The top layer in a sequence of rock layers is older than the Earth.
Answers
The Earth is older than any rock layer. This fact is determined through the use of principles like the law of superposition and radioactive dating methods, such as uranium-lead dating. The oldest rocks on Earth have been dated to be almost 4.4 billion years old, whereas the Earth itself is estimated to be around 4.5 billion years.
Explanation:This is based on geological principles and radioactive dating methodologies. One of the foundational principles in geology is the law of superposition, which states that in an undisturbed sequence of rock layers, each layer is younger than the one below it.
The age of Earth is estimated to be around 4.5 billion years. We can deduce this from radioactive dating methods, such as uranium-lead dating. In this method, the oldest rocks on Earth, known as the Jack Hills zircons from Australia, have been dated at almost 4.4 billion years old.
Given these findings, it is understood that no existing rock layer can be older than the Earth itself.
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B. The Earth is older than any rock layer.
The Law of Superposition states that in an undeformed sequence of sedimentary rocks, the bottom layer is the oldest and the top layer is the youngest. Applying this principle to the Earth's rock layers, we can conclude that the Earth is older than any rock layer as the layers closer to the surface are younger compared to those at the bottom.
Express 23,495 in scientific notation.
Answers
You are working as an office apprentice for the bksb Newcastle Arena. The arena is deciding what events to book for next year. Examine the market research below and answer the questions that follow. Look at the bar chart below.
*What music genre is the 26 to 36 age group’s favorite?
*How many people from the 37 to 47 age group like ‘other’ music?
*Which three genres has the most fans?
Answers
2- 20
3- Pop, Rock, Dance
Comment if you have any questions!
Answer:
What music genre is the 26 to 36 age group’s favorite? It's pop
How many people from the 37 to 47 age group like ‘other’ music? 20 people
Which three genres has the most fans? "Pop", "Rock" and "Dance"
Step-by-step explanation:
What music genre is the 26 to 36 age group’s favorite?
The colors indicate the different age ranges. So first you must locate the color belonging to the range of 26 to 36 years, which is gray.
Now, you place that color in the graph and to determine which genre of music is the favorite in that age, you must place the genre with more people aged between 26 and 36. That reads on the “y” axis, which in the graph is seen as "the tallest gray rectangle". Once this is located, you read on the "x" axis the genre to which it belongs. This results in the music genre "pop"
How many people from the 37 to 47 age group like ‘other’ music?
For this case, as in the previous case, you first locate the color belonging to the age range of 37 to 47, which is the color yellow.
But now you must first place that color on the "x" axis, which is the one corresponding to the music genre. In this case you locate the genre "others". Then with the yellow color you read the number of people on the "y" axis.
Note that the numbers marked are every 100, but that between each number there are 5 divisions. This means that the scale is 20 people (obtained as 100 divided by 5)
The color belonging to the age range of 37 to 47 in the genus "others" reaches the first division. This means that the number of people who like this genre is 20.
Which three genres has the most fans?
In this case you should pay attention to which genders ("x" axis) have the greatest number of people ("y" axis), regardless of age. Observing "the longest colored rectangles", which indicate that more people like the genre, and reading the axis of music genres, you can see that the three genres that have more fans are "Pop", "Rock" and "Dance"
Help ASAP
Nina is participating in a swim-a-thon to raise money for a charity. For every lap that Nina swims, her grandmother has promised to donate $2.50. If Nina swims 18 laps, how much will her grandmother donate?
A.$45.00
B.$20.50
C.$18.00
D.$7.20
Answers
HELP ME!
The Pythagorean Theorem and Distance Formula are both used to find distances on the coordinate plane. Explain when it is appropriate to use each method.
Answers
Mike’s current restaurant measures 60 feet by 30 feet. Due to increase in the number of customers, he wants to rent a bigger restaurant. The dimensions of the bigger restaurant will be related by a scale factor of 2. What is the difference in area between Mike's new restaurant and his current restaurant, in square feet?
Answers
Next, we find the areas of the current restaurant and the new restaurant by multiplying the length times the width for each. Thus, the current restaurant is 1800 square feet (60 feet times 30 feet) and the new restaurant is 7200 square feet (120 feet times 60 feet). We find the difference by subtracting 7200 square feet minus 1800 square feet to get the answer of 5400 square feet.