The equation in slope-intercept form of the line that passes through (6, −1) and (3, −7) is:y = 2x − 13.
To write an equation in slope-intercept form of the line that passes through (6, −1) and (3, −7), you will use the point-slope form, as follows:
y − y1 = m(x − x1),
where:
m = slope (or gradient) of the line, and
(x1, y1) = the coordinates of a point on the line.
Let us calculate the slope (gradient) of the line using the given points:
(6, −1) and (3, −7).
m = (y2 − y1)/(x2 − x1)
m = (−7 − (−1))/(3 − 6)
= −6/−3
= 2
Thus, the slope of the line is 2.
Using the coordinates of one of the points, say (6, −1), in the point-slope form, we obtain:
y − y1 = m(x − x1)y − (−1)
= 2(x − 6)y + 1
= 2x − 12
Subtracting 1 from both sides, we get:
y = 2x − 13
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What is the equation of a line that contains point (4, –3) and is PARALLEL to –4x + y = 7?
Answer:
Step-by-step explanation:
First, put -4x+y=7 into y=mx+b format
move -4x to the other side (or add 4x on both sides)
y=4x+7
now, parallel lines have the same slopes, but not the same y intercepts.
So, you already know the slope of your new line
y=4x+b
now we need to find b (y intercept)
take the point (4,-3) and put it into the equation above
-3=4(4)+b
-3=16+b
move 16 to the other side (or subtract 16)
-19=b
therefore the new line will be y=4x-19
Hope this helps!
A square has a side length of 16.5 in. If the area is multiplied by 9, what happens to the side length?
The side length is multiplied by 4.5.
The side length is multiplied by 9.
The side length is tripled.
The side length is doubled.
Answer: The side length is tripled.
Step-by-step explanation: Area is length times width, or in the case of a square, s²
If the area is multiplied by 9, (that is 3²) it means the sides are 3 times as long.
16.5² = 272.25
(3)(16.5) = 49.5
49.5² = 2450.25
the same as 272.25 × 9
Triple the side length results in 9 times the area.
A gardener has 140 feet of fencing to put around a rectangular vegetable garden. The function A(w)=70w-w^(2) gives the garden's area A (in square feet ) for any width w (in feet ). Does the gardener have enough fencing for the area of the garden to be 1300ft^(2) ?
No, the gardener does not have enough fencing for the area of the garden to be 1300 square feet. The maximum possible area that can be achieved with 140 feet of fencing is given by the function A(w) = 70w - w^2. We need to find the width value (w) that corresponds to an area of 1300 square feet.
To determine if the gardener has enough fencing, we can set up an equation using the given function: 1300 = 70w - w^2. Rearranging this equation, we get w^2 - 70w + 1300 = 0.
By solving this quadratic equation, we find that the roots are w = 25 and w = 45. Since the width value (w) must be positive, we can conclude that the width of the garden cannot be 45 feet. Therefore, the gardener does not have enough fencing to create a garden with an area of 1300 square feet.
In summary, based on the given quadratic equation, the gardener cannot achieve an area of 1300 square feet with the available 140 feet of fencing. The maximum achievable area corresponds to a width of 25 feet.
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Light travels 186,282 miles per second. How many miles will light travel in one year? (Use 365 days in a year) This unit ofdistance is called a light-year.
Answer:
5,874,589,152,000 mi.
Step-by-step explanation:
What is the slope of the line in the graph?
Tyler had $150 in his bank account. He deposited $300 into his bank account. The next day, he withdrew $50. How much money does he have in his account now? ASAP!!!!
Answer:
$400
Step-by-step explanation:
150 + 300 = 450
450 - 50 = 400
Answer:
150+300=450 then 450-50=400
Step-by-step explanation:
I hope this is the right answer ^-^
29.3 is what percent of 32? Round to the nearest tenth.
.Billy-Joe and Bob purchased a pool with capacity of 60 gallons for the farm. One day, at 13.00, Billy-Joe placed a horse into the pool, filling it with water at a rate of 3 gal per hour. After ten hours (23.00), horses and cow started drinking the water at a combined rate of 1 gal/hr. Five hours later (4.00), Bob noticed the animals drinking and placed a second hose in the pool which filled it at a rate of 2 gal/hr. At what time could Bob declare the pool was full of water?
Bob could declare the pool was full of water at 6.00.Bob could declare the pool was full of water at 6.00 after Billy-Joe initially filled it and animals drank from it for a certain period.
From 13.00 to 23.00, Billy-Joe filled the pool with water at a rate of 3 gallons per hour for 10 hours, resulting in 3 gallons/hour * 10 hours = 30 gallons of water in the pool.
From 23.00 to 4.00, the combined drinking rate of the horses and the cow was 1 gallon per hour. Therefore, during this period, the water level decreased by 1 gallon/hour * 5 hours = 5 gallons.
At 4.00, Bob placed a second hose in the pool, which filled it at a rate of 2 gallons per hour.
Now let's calculate the remaining capacity of the pool after 4.00:
The initial capacity of the pool was 60 gallons.
From 13.00 to 23.00, 30 gallons were filled.
From 23.00 to 4.00, 5 gallons were consumed.
So, the remaining capacity is 60 gallons - 30 gallons - 5 gallons = 25 gallons.
With the second hose filling the pool at a rate of 2 gallons per hour, it would take 25 gallons / 2 gallons/hour = 12.5 hours to fill the remaining capacity.
Adding the time it took to reach 4.00, the total time needed to fill the pool would be 12.5 hours + 5 hours = 17.5 hours.
Therefore, Bob could declare the pool was full of water at 4.00 + 17.5 hours = 21.5 hours after 13.00, which is equal to 6.00.
Bob could declare the pool was full of water at 6.00 after Billy-Joe initially filled it and animals drank from it for a certain period.
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Will give Brainliest! The Math Club at North High School decided to have a car wash to raise money for expenses related to math competitions. The graph below shows the relationship between cars washed and earnings (in dollars). What is the domain of the graph?
-20 ≤ y ≤ 40, where x ≥ 0
-20 ≤ y ≤ 40, where y is all integers
0 ≤ x ≤ 12, where x ≥ 0
0 ≤ x ≤ 12, where x is all non-negative integers
Answer:
the second one Step-by-step explanation:
what is the final cost of a $42 meal with a 15% tip?
Answer: $48.03
Step-by-step explanation: I think
Answer:
$48.00 + $7.20 = $55.20.
Step-by-step explanation:
First, convert the 15% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.
Second, you need to find out what 15% of your $48 meal cost is.This is always done by multiplying 0.15 by $48.00, or
0.15 x $48.00=$7.20.
So, the amount of tip you are going to leave is $7.20.
This makes the total cost of your meal (to write on your charge slip or other payment)
hope this helped UwU
Write the equation of the line, given the y and x-intercepts.
y-intercept = –2, x-intercept = –3
(need help asap so please hurry thank you!!)
Answer:
y = -(2/3)m - 2
Step-by-step explanation:
recall that the general equation of a straight line in slope-intercept form is
y = mx + b
where, m is the slope and b is the y - intercept
here we are given that the y - intercept is -2, hence the equation becomes:
y = mx + (-2)
or
y = mx -2
we are also given that the x-intercept is -3, which means that when y = 0, x = -3 (simply substitute this into our new equation to solve for m)
0 = m(-3) -2
0 = -3m - 2 (add 3m to both sides)
3m = -2 (divide both sides by 3)
m = -(2/3)
hence our equation is now
y = -(2/3)m - 2
A school volleyball team consists of 7 male and 8 female players. Only 12 of the players are to be selected to attend the tournament in Vancouver next weekend. Determine the probability to the nearest hundredth that equal numbers of males and females are selected to go to Vancouver.
The probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.
To determine the probability that equal numbers of males and females are selected to go to Vancouver, we need to calculate the number of ways to select 6 males and 6 females from the total pool of 7 males and 8 females.
The number of ways to select 6 males out of 7 is given by the combination formula:
C(7, 6) = 7! / (6!(7-6)!) = 7
Similarly, the number of ways to select 6 females out of 8 is:
C(8, 6) = 8! / (6!(8-6)!) = 28
Since we need to select equal numbers of males and females, we multiply the number of ways to select males and females together:
Total number of favorable outcomes = C(7, 6) * C(8, 6) = 7 * 28 = 196
Now, we need to calculate the total number of ways to select any 12 players from the total pool of 15 (7 males + 8 females):
Total number of possible outcomes = C(15, 12) = 15! / (12!(15-12)!) = 455
Finally, we can calculate the probability of selecting equal numbers of males and females by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 196 / 455 ≈ 0.431
Therefore, the probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.
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g=c-x solve for x please
Answer:
x=c-g or x=-g+c
Step-by-step explanation:
Simplify 9 ^ 3/2 - 25 ^ 1/2
9514 1404 393
Answer:
as written: 352as perhaps intended: 22Step-by-step explanation:
When you ask for evaluation of a math expression, you need to write what you mean.
Here, the order of operations requires you compute the exponentials before you do the division or addition:
9 ^ 3/2 - 25 ^ 1/2 = (9^3)/2 -(25^1)/2
= 729/2 -25/2 = 364.5 -12.5 = 352
__
It seems quite likely that you intend the exponents to be 3/2 and 1/2. In that case, parentheses are required.
9 ^ (3/2) - 25 ^ (1/2) = 27 -5 = 22
_____
Your calculator can evaluate arithmetic expressions for you.
Mrs. Peele's family went out to dinner. They spent $42.50 on dinner, 7% tax, and on top of both costs they left an 18% tip. How much total did her family pay for dinner?
Answer: $53.13
Step-by-step explanation:
First find how much they spent on tax by multiplying 42.50 by 7%.
7% * 42.50 = 2.98 This means the tax amount was $2.98.
Next find the how much the tip was by multiplying 18% by 42.50.
18% * 42.50 = 7.65 This also means the tip was $7.65.
Now combine the cost of the dinner plus the cost of tax plus the cost of tip to find how much in total they spent.
42.50 + 7.65 + 2.98 = 53.13
z/6 + 6 = 7 - z/6
z=
PLEASE HELP PLEASE I AM DESPERATE
9514 1404 393
Answer:
z = 3
Step-by-step explanation:
Add z/6 to both sides.
z/6 +z/6 +6 = 7
z/3 + 6 = 7
Subtract 6 from both sides.
z/3 = 1
Multiply both sides by 3.
z = 3
HELP QUICK!!WILL FIVE BRAINLIEST
Convert 94 yards to inches
Answer:
3,384 inches.
Step-by-step explanation:
1 yard = 36 in
36 times 94 = 3,384
64 unit cubes are glued together to makea big cube. The exterior of the big cube is
painted red in colour. Find how many of the
64 unit cubes would have been
(a) painted red on only one of their faces?
(b) painted red on two of their faces?
(c) painted red on three of their faces?
(d) without red paint on their faces?
The number of unit cubes in each category is as follows:(a) Cubes painted red on only one face: 24 (b) Cubes painted red on two faces: 20 (c) Cubes painted red on three faces: 8 (d) Cubes without red paint on their faces: 12.
To solve this problem, let's analyze the different types of cubes based on the number of faces painted red.
(a) Cubes painted red on only one face:
On the big cube, there are 6 faces exposed to the outside. Each face consists of a 2x2 grid of unit cubes. Thus, each face has 4 unit cubes painted red.
Since there are 6 faces, the total number of unit cubes painted red on only one face is 6 * 4 = 24.
(b) Cubes painted red on two faces:
On the big cube, the corner unit cubes have two faces exposed to the outside, and each edge unit cube has three faces exposed. There are 8 corner unit cubes and 12 edge unit cubes in total. Therefore, the number of unit cubes painted red on two faces is 8 + 12 = 20.
(c) Cubes painted red on three faces:
On the big cube, there are 8 corner unit cubes, and each of these cubes has three faces exposed to the outside. Therefore, the number of unit cubes painted red on three faces is 8.
(d) Cubes without red paint on their faces:
To determine the number of unit cubes without red paint on their faces, we subtract the sum of the previous three categories from the total number of unit cubes, which is 64.
Number of cubes without red paint = 64 - (24 + 20 + 8) = 12.
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Given the following relations on the set of all people. Check ALL correct answers from the following lists:
(a) a is (strictly) older than b
A. irreflexive
B. symmetric
C. antisymmetric
D. reflexive
E. transitive
(b) a and b have a common grandparent
A. irreflexive
B. antisymmetric
C. symmetric
D. reflexive
E. transitive
(c) a has the same first name as b
A. transitive
B. irreflexive
C. antisymmetric
D. symmetric
E. reflexive
(d) a and b were born on the same day
A. transitive
B. reflexive
C. irreflexive
D. antisymmetric
E. symmetric
The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.
irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.
The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.
This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:
This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.
(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.
The correct answers for each given relation are listed above.
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What is the solution to the inequality? 3(x−2)+x≤2
Answer:
x ≤ 2
Step-by-step explanation:
Expand
3x - 6 + x ≤ 2
Rearrange
4x ≤ 8
x ≤ 2
Answer:
x ≤ 2
Step-by-step explanation:
Step 1: Write inequality
3(x - 2) + x ≤ 2
Step 2: Solve for x
Distribute 3: 3x - 6 + x ≤ 2Combine like terms: 4x - 6 ≤ 2Add 6 to both sides: 4x ≤ 8Divide both sides by 4: x ≤ 2Here we see that any number less than or equal to 2 will work.
a coin is tossed 7 times. what is the probability of getting all heads? express your answer as a simplified fraction or a decimal rounded to four decimal places.
the probability of getting all heads after 7 tosses of a coin is 1/128, expressed as a simplified fraction or a decimal rounded to four decimal places is 0.0078.
When a coin is tossed, the probability of getting either heads or tails is 1/2. This probability remains constant regardless of the number of tosses.
In order to determine the probability of getting all heads after 7 tosses of a coin, we must calculate the probability of getting a head on each toss and multiply the individual probabilities together:
Probability of getting a head on the first toss = 1/2
Probability of getting a head on the second toss = 1/2
Probability of getting a head on the third toss = 1/2
Probability of getting a head on the fourth toss = 1/2
Probability of getting a head on the fifth toss = 1/2
Probability of getting a head on the sixth toss = 1/2
Probability of getting a head on the seventh toss = 1/2
The probability of getting all heads = (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) = 1/128
Therefore, the probability of getting all heads after 7 tosses of a coin is 1/128, expressed as a simplified fraction or a decimal rounded to four decimal places is 0.0078.
Answer: 0.0078
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Find all numbers such that 85 minus three times the number is at least 250.
Answer:
x < -55
Step-by-step explanation:
Step 1: Convert word to math
85 - 3x > 250
Step 2: Solve for x
Subtract 85 on both sides: -3x > 165Divide both sides by -3: x < -55Here we see that any value smaller than -55 will work.
a bucket contains 512 gallons of water. water spills from the bucket so that only 5 pints remain. how many pints of water spill from the bucket?
The given problem states that a bucket contains 512 gallons of water. Water spills from the bucket so that only 5 pints remain. We need to find out how many pints of water spill from the bucket. The first step towards the solution of the problem is to convert 512 gallons to pints, which is given below;
1 gallon = 8 pints512 gallons = 8 × 512 pints = 4096 pints. Now, we know that 5 pints of water are remaining after the spill. Hence, the total water that has spilled from the bucket would be;4096 - 5 = 4091 pints. Therefore, 4091 pints of water would have spilled from the bucket.
To solve the given problem, we need to convert gallons to pints, which is given below;1 gallon = 8 pints512 gallons = 8 × 512 pints = 4096 pints. Now, we know that only 5 pints of water remain in the bucket. Hence, we need to find out the total amount of water that has spilled from the bucket. To find out the total amount of water spilled, we need to subtract the remaining water from the initial water, which is given below;4096 - 5 = 4091 pints. Therefore, 4091 pints of water would have spilled from the bucket. Hence, t 4091 pints of water.
It can be concluded that if a bucket contains 512 gallons of water, and water spills from the bucket so that only 5 pints remain, then 4091 pints of water would have spilled from the bucket.
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Describe how to find the mean of the following set of data.
12, 12, 18, 20
An icecream shop has 10 flavors. One can choose 4 different
flavors. What is the total number of possible flavor
combinations?
a.
252
b.
462
c.
120
d.
330
e.
210
2.
An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.
In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.
Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors
.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).
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3. Fun Zone charges an entrance fee of $6.00 and $0.45 per token to play
games. Crazy World charges an entrance
fee of $12.00 and $0.30 per token to play
games. How many tokens must be purchased in order for the total at Fun
Zone and Crazy World to be the same?
A. 120 tokens
B. 8 tokens
C. 40 tokens
D. 24 tokens
Answer:
C. 40
Step-by-step explanation:
.45x +6 = .3x + 12
.15x =6
.15x/.15=1 6/.15=40
Express ✓-18 in terms of i.
✓-18 =
Enter your next step h
Answer:
3✓2 i (3 times the square root of two times i; the i is not under the square root sign)
Step-by-step explanation:
✓-18
✓18*✓-1
✓(2*9)*✓-1
3✓2 i
Shoreline Park In Mountain View, California, Has Kept Close Tables On The Number Of Patrons Using The Park Since Its Opening I
Shoreline Park in Mountain View, California, has diligently maintained records of the number of visitors to the park ever since its establishment.
Shoreline Park, located in Mountain View, California, has implemented a comprehensive system to monitor and track the number of patrons visiting the park since it first opened. This proactive approach allows park management to gather data on the park's popularity and usage patterns, enabling them to make informed decisions regarding park maintenance, amenities, and future development plans. By closely monitoring the number of visitors, Shoreline Park can ensure that it meets the needs of the community and maintains a pleasant environment for everyone to enjoy.
Maintaining records of the number of patrons using the park serves multiple purposes. Firstly, it helps in understanding the park's peak times and off-peak periods, enabling park officials to allocate resources effectively and plan events or activities accordingly. It also aids in assessing the park's capacity and evaluating any potential overcrowding issues that may arise during busy periods. Additionally, tracking visitor numbers can assist in evaluating the success of marketing and promotional efforts aimed at attracting more people to the park. Overall, by keeping close tabs on the number of patrons using Shoreline Park, the park management can ensure that it remains a popular and well-utilized recreational space for the community while addressing any concerns or challenges that may arise.
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Barry rode his scooter for 24 minutes at a speed of 0.5 miles per minute. How far did he go?
Answer:
12 miles
Step-by-step explanation:
24 divided by 0.5 = 12
12 miles
Answer:
12 miles
The step-by-step explanation he went .5 a minute so every minute he went.5 he rode for 25 minutes so we multiply the two
