Which is an equation of the given line in standard form?
A. -6x+5y=13
B. -6x+7y=-11
C. -6x+7y=11
D. -7x+6y=-11
Answers
The coordinates of the points:
[tex](-3;\ -1)\to x_1=-3;\ y_1=-1;\ \left(\dfrac{1}{2};\ 2\right)\to x_2=\dfrac{1}{2};\ y_2=2[/tex]
Substitute: [tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}[/tex]
We have: [tex]y=\dfrac{6}{7}x+b[/tex]
Substitute the coordinates of the point (-3; -1) to the equation of the line:
[tex]-1=\dfrac{6}{7}\cdot(-3)+b\\\\-1=-\dfrac{18}{7}+b\ \ \ |+\dfrac{18}{7}\\\\b=\dfrac{11}{7}[/tex]
Therefore we have:
[tex]y=\dfrac{6}{7}x+\dfrac{11}{7}\ \ \ |\cdot7\\\\7y=6x+11\ \ \ |-6x\\\\\boxed{-6x+7y=11}[/tex]
Answer: C. -6x + 7y = 11
Related Questions
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f x( ) = 20x + 4. What is the range of the function for this situation? Please explain.
Answers
The range of the function is the possible output values for the function. In this case, it is from zero to the highest possible weight. Since there are 6 pairs of weight plates, we can input 12 for x to get the maximum.
20(12) + 4 = 244
what does the expression 0.30y represent ?
Answers
harry buys a sofa set that costs$2,000.he pays for it with 12 month installments. how much will he pay each month? if he has to pay5%in interest how much will he pay in all for the sofa set?
Answers
Harry's monthly payment for the sofa set is approximately $175, which includes principal and simple interest. The estimated total payment amount after 12 months is $2100.
Harry buys a sofa set that costs $2000 and chooses to pay for it in 12 monthly installments. First, to find out the monthly payment without interest, we divide the total cost by the number of installments. So, $2000 divided by 12 months equals to $166.67.
However, there is an interest of 5% on the outstanding amount. To calculate the total interest on an installment plan, we typically would need to calculate the interest on the reducing balance each month; however, for simplicity, let's assume it's 5% of 2000 for the year, which is $100 (5/100 * $2000). Divided by 12 months, that's about $8.33 in interest per month, giving a total monthly payment of $175 ($166.67 + $8.33).
This simplistic approach gives us a rough estimate, and the actual amount could be slightly different due to the reducing balance method used by most financing options. Assuming the simple interest calculation, Harry will pay $175 per month, and in all, he will pay an estimated total of $2100 ($175 * 12) for the sofa set.
A company says that the probability of finding an all-star card in a game pack is 12.5%. A student wants to determine the probability that, if he buys 6 game packs, 2 or more will have an all-star card.
To do this, he uses a random number table to pick 6 numbers from 1 to 8. He lets 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card. He repeats this for a total of 15 trials. The results are shown in the table.
561673 366468 314255 361362 838443 126285 257231 768551 652585 468113 123711 322764 487626 783134 384664
Select from the drop-down menus to correctly complete each statement.
To estimate the probability that 2 or more out of 6 packs will have an all-star card, the student must count the number of trials with BOX RIGHT HERE and divide by the number of trials.
This gives an estimated probability of about . BOX RIGHT HERE
PLEASE I NEED THIS ANSWERED I HOPE ITS CLEAR ENOUGH.
Answers
Answer:
the first box is "two or more 1s"
the second box is "0.13"
Step-by-step explanation: Im a K12 Student
The probability that 2 or more out of 6 packs will have an all-star card is given by the equation P = 0.1333
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that 2 or more out of 6 packs will have an all-star card be P
The probability of finding an all-star card in a game pack is 12.5 %
The student has pointed that 1 represent a pack with an all-star card and 2 through 8 represent a pack without an all-star card
The test results are given in set A = { 561673, 366468, 314255, 361362, 838443, 126285, 257231, 768551, 652585, 468113, 123711, 322764, 487626, 783134, 384664 }
The number of trials that represent that 2 or more out of 6 packs have an all-star are = { 468113 , 123711 }
Therefore , the probability is given as
Probability that 2 or more out of 6 packs will have an all-star card P = 2/15
On simplifying the equation , we get
Probability that 2 or more out of 6 packs will have an all-star card P = 0.133
Hence , the probability is 13.33 %
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Teo has 4 2/3 pitchers of juice. One glass holds 1/6 of a pitcher. How many glasses can Teo fill?
Answers
Change 4 2/3 to 14/3
14/3 / 1/6 = 14/3 x 6/1
84 glasses
Simplify 5 √180 (show work)
Answers
= 5 \/4 x \/45
= 5 x 2 \/9 x \/5
= 10 x 3 x \/5
= 30 \/5
I did this a couple of years ago in AS maths and I think this is how it’s done. Hope it’s helpful!
To simplify 5√180, break down 180 into its prime factors, take out the square of the prime factors, and simplify.
Explanation:To simplify 5√180, we can break down 180 into its prime factors which are 2^2 * 3^2 * 5. Then, we can take out the square of the prime factors since we have a square root. This leaves us with 2 * 3 * 5√5. Simplifying further, we get 30√5.
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Is how many countries are in North America a statistical question
Answers
The question, "How many countries are in North America" is not a statistical question.
What are statistical Questions?Statistical questions are defined as the questions which are answered by collecting data from many which will probably vary.
The given question is,
How many countries are in North America"How many countries are in North America.
Although the answers to this from the students may vary because they don't know, the answer to this question is a constant.
This is not something which varies.
Hence this is not a statistical question.
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write the function for the graph below
Answers
y=√(x-2)
plz make ,....................
Answers
the length of rectangle is 5*(x+6) cm
the breadth of rectangle is (2x+6) cm
perimeter=192 cm
perimeter of a rectangle=2*[length+breadth]
so
192=2*[5*(x+6)+(2x+6)]----> 192/2=[5x+30+2x+6]---> 96=7x+36
7x=96-36-----> 7x=60--------> x=60/7 cm
the answer is
x=60/7 cm or 8.57 cm
Your last five customer interactions lasted 2,3,6,8 and 4minutes how many minutes did i average across the 5
Answers
2 to 3 is 1
3 to 6 is 3
6 to 8 is 2
8 to 4 is 4
adding 1+2+3+4= 10 minutes; the average
You average across 4.6 minutes per customer.
What is average?The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.
Given:
Your last five customer interactions lasted 2,3,6,8 and 4 minutes.
The total number of observation is 5.
The average = the sum of the observations / the number of observations.
The average = (2 + 3 + 4 + 6 + 8)/5
The average = 23/5
The average = 4.6 minutes.
Therefore, 4.6 minutes per customer is the average.
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Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 5 more days than the other?
Answers
If the second constructor works alone for one day he will do (1/(x+5)) part of work.
If they work together, they will do for one day
[tex] \frac{1}{x} + \frac{1}{x+5} part of work. Also, if they work together, for one day they will do 1/6 part of work. So, [/tex]
[tex] \frac{1}{x} + \frac{1}{x+5} = \frac{1}{6} , \frac{x+5+x}{x(x+5)} = \frac{1}{6} , \frac{2x+5}{ x^{2} +5x} = \frac{1}{6} , 6(2x+5)=x^{2} + 5x 12x+30 =x^{2}+5x x^{2} -7x-30=0 (x-10)(x+3)=0 x_{1}= 10, x_{2}=-3 For our problem we can use only positive value, x=10 days will work the first worker. The second worker will work x+5=10+5= 15 days. First worker alone will work 10 days, second worker alone will work 15 days. Check, (1/10)+(1/15)=(1/6) (3+2)/30=(1/6) 1/6=1/6 True [/tex]
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's call the faster constructor "A" and the slower constructor "B".
We know that B takes 5 more days than A to complete the job.
Let's call the number of days it takes A to build the room "x".
Then the number of days it takes B to build the room is "x+5".
Now,
We also know that if they work together, they can finish the room in 6 days.
Let's call the fraction of the job that A can do in one day "a"
(which means that B can do "a - 1/6" of the job in one day).
We can use the following equation to solve for "a":
1 = (a + a - 1/6) x 6
Simplifying this equation, we get:
1 = (2a - 1/6) x 6
1 = 12a - 1
12a = 2
a = 1/6
So A can do 1/6 of the job in one day.
We can use this information to solve for "x" and "x+5":
1/x + (1/(x+5)) = 1/6
Multiplying both sides by the least common multiple of the denominators (6x (x+5) ), we get:
6 (x+5) + 6x = x (x+5)
Expanding and simplifying, we get:
x² - 7x - 30 = 0
Solving for x using the quadratic formula, we get:
x = 10 or x = -3
Since x has to be a positive number (because it represents the number of days it takes A to build the room), we can ignore the negative solution.
Now,
It takes A 10 days to build the room, and it takes B 15 days to build the room (since B takes 5 more days than A).
Therefore,
A can build the room by himself in 10 days, and B can build the room by himself in 15 days.
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Which group of numbers is ordered from least to greatest
Answers
Sarah wants to hang a mirror in her room. The mirror and frame must have an area of 15 square feet. The mirror is 3 feet wide and 4 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? Square with an inner frame with height of 3ft on the left frame and width of 4ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. 3x2 + 14x − 2 = 0 4x2 + 14x − 3 = 0 x2 + 12x − 14 = 0 2x2 + 7x − 14 = 0
Answers
Width of the outer frame:3+2x
Area of the outer out frame"(4+2x)(3+2x)=15
Expand the equation:12+8x+6x+12x^2=15
Combine like terms :4x^2+14x-3=0
m∠HGF = 16 x + 4, m∠EGF = 110°, and m∠HGE = 3 x + 11. Find x .
Answers
The length of a rectangle is 3 m longer then it’s width the area of the rectangle is 154 m^2 what is the width of the rectangle
Answers
You can get this by setting up an equation that says:
x (x - 3) = 154
Then distribute and use the quadratic equation to solve.
solve the equation 30t - 4 = 1 for t
Answers
[tex]30t - 4 = 1 \\ 30t = 5 \\ t = \frac{5}{30} \\ t = \frac{1}{6} [/tex]
Answer : t = 1/6, or in decimal form, 0.17
Hope this helps. - M
Answer:
A) 1/6
Step-by-step explanation:
Is 35 over Pi (35 divided by pi):
Slightly less than 9
Slightly more than 9
Slightly less than 12
OR
Slightly more than 12
Please help and no wrong answers!
Answers
Our calculators record pi as 3.141592654
35/pi = 11.14084602 which is just under 12. <<<<< answer
35/pi is a calculator question. A standard calculator has pi to about 10 digits stored in it's memory. As an educated guess before doing it (according to the bible is just under 12 since pi is recorded as 3 in Kings I think).
Our calculators record pi as 3.141592654
35/pi = 11.14084602 which is just under 12. <<<<< answer
1
Angle P measures 112 degrees, what are the measures of angle N and O?
Answers
in this triangle the lines NP and OP are identical so the 2 unknown angles would be equal
so the 2 unknown angles would be 180 - 112 = 68 / 2 = 34 each
angle N & O are 34 degrees
The measures of angle N and O are: 34°
How to find the angle of the Isosceles triangle?We know that Isosceles triangle has two equal sides and we also know that the sum of angles in a triangle is equal to 180 degrees.
Since an Isosceles triangle has two equal sides, we know that the base angles are equal.
We are given the apex angle as 112 degrees. Thus:
2x + 112 = 180
2x = 180 - 112
2x = 68
x = 34
Thus:
The measures of angle N and O are 34°
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Richard and samantha are charting their monthly cash flow. They have some expenses like car repairs and vacations that are not paid each month. How can they account for these non-monthly expenses ?
Answers
This way they can take vacations or if they have car troubles
It would make their life so much easier
Final answer:
Richard and Samantha should estimate yearly costs for non-monthly expenses, divide by 12, and save this amount each month, incorporating it as a fixed expense in their budget.
Explanation:
Richard and Samantha can account for non-monthly expenses in their monthly cash flow by setting aside money each month for these irregular expenses. To do this, they should estimate the total cost of these expenses for the year and divide that amount by 12. This will provide the monthly amount they need to save in order to cover costs such as car repairs and vacations without disrupting their budget. Each month, this amount should be treated like a fixed expense and set aside in a savings or separate account, ensuring that funds are available when these expenses occur.
Example:
Car Repairs: Estimated at $600 per year (divide by 12 = $50 per month)
Vacations: Estimated at $1200 per year (divide by 12 = $100 per month)
By including these estimated expenses in their monthly budget, they can create a more accurate and effective budget that accommodates all their financial activities throughout the year.
The area of a circular pool is 314 square feet. Write and solve an equation to find the diameter of the pool cover.
Answers
Use the area of a circle formula to first calculate the radius.
A= πr^2
plug in known numbers
314= (3.14)r^2
divide both sides by 3.14
100= r^2
take square root of both sides
10 feet= r
STEP 2:
find the diameter
Diameter= 2 * radius
D= 2 * 10
D= 20 feet
CHECK:
A= (3.14)(10)^2
A= (3.14)(100)
A= 314 feet squared
ANSWER: The diameter is 20 feet.
Hope this helps! :)
Write an algebraic expression for the word expression
The sum of 15 and the product of 5 and v
use parentheses
Answers
Hope this helps!
On a spinner: P(3) = ⅜ and p(4) = ⅓ What is the probability of getting 3 or 4?
Answers
Answer:
3/8. + 1/3
9/24 +8/24
17/24
i need alot of help in math
Answers
1. The diameter of the bottom of the cone is 4 so the radius (half that) is 2. Volume = 1/3 * pi * (2)² * 6
= 1/3 * pi * 4 * 6
= 1/3 * pi * 24
= 8 * pi
≈ 25.1327 cm³
2. They give you all you need, the radius.
Volume = 4/3 * pi * (6)³
= 4/3 * pi * 216
= 288 * pi
≈ 904.7787 in³
Frank wants to know how many people live in each household in his town. He conducts a random survey of 10 people and asks how many people live in their household. His results are shown in the table.
Number of People per Household
1 6 2 4 4 3 5 5 2 8
Calculate the mean absolute deviation of the number of people per household
Answers
The mean absolute deviation is 1.6.
Given that the number of People per Household
1 6 2 4 4 3 5 5 2 8
We have to determine the mean absolute deviation
What is the mean deviation?The mean absolute deviation is found by finding the mean, then finding how far each number is to the mean, then finding the mean of that.
The mean is: (1 + 6 + 2 + 4 + 4 + 3 + 5 + 5 + 2 + 8)/10 = 40/10 = 4
The distances of all of the numbers are
(absolute value of the difference between 3.5 and the number)
3,2, 2, 0, 0, 1, 1, 1, 2, 4
The mean of those is: 3+2+2+ 0+ 0+1+1+ 1+ 2+ 4 /10 = 16/10 = 1.6
Therefore the mean absolute deviation is 1.6.
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the fifth grade classes at sunshine School you six identical buses to go on the field trip there were a total of 30 seats on each bus all the seats on 5 buses were filled the 6 bus had 4/6 of the seats filled 1/5 of all the passengers were adults how many adults went on the field trip with the fifth grade class
Answers
50 PIONTS AND BRANLIEST PWEASE HELP
The product of two rational numbers is positive. What can you conclude about the factors? Express your answer in two or more complete sentences.
Answers
The google family built a rectangular swimming pool in their backyard.The floor of the pool has an area of 485 5/8 square feet.If the width of the pool is 18 1/2 feet,what is the length of the pool?
Answers
W= Width= 18 1/2 ft
L= Length= ?
Area= LW
plug in known numbers
485 5/8= (L)(18 1/2)
convert to improper fractions
3885/8= (L)(37/2)
divide both sides by 37/2
3885/8 ÷ 37/2= L
to divide fractions, multiply by the reciprocal/inverse of 37/2
3885/8 * 2/37= L
multiply numerators; multiply denominators
(3885*2)/(8*37)= L
multiply inside parentheses
7770/296= L
simplify
105/4 feet= L
change to mixed number
26 1/4 feet= L
ANSWER: The length is 26 1/4 feet (or 26.25 feet).
Hope this helps! :)
[tex]485 \dfrac{5}{8} = 18 \dfrac{1}{2} \times \text{ Width}[/tex]
Divide both side by 18 1/2:
[tex]\text{ Width} = 485 \dfrac{5}{8} \div 18 \dfrac{1}{2} [/tex]
Convert to improper:
[tex]\text{ Width} = \dfrac{3885}{8} \div \dfrac{37}{2} [/tex]
Change divide fraction to multiplicationf fraction:
[tex]\text{ Width} = \dfrac{3885}{8} \times \dfrac{2}{37} [/tex]
Mutliply and simplify:
[tex]\text{ Width} = \dfrac{104}{4} = 26 \dfrac{1}{4} \text{ feet}[/tex]
Answer: Length = 26 1/4 feet
Help please! Don’t understand!
Answers
[tex]6 + 2 - ( - 1) + ( - 8) = [/tex]
Keep in mind that the sum of a plus and a minus ends up in a minus. So
+ - = -
Keep in mind that the sum of a minus and a minus ends up in a plus.
- - = +
[tex]6 + 2 + 1 - 8 = [/tex]
Now add from left to right.
[tex]8 + 1 - 8 = [/tex]
Add once more
[tex]9 - 8 = [/tex]
Subtract
[tex]1[/tex]
Hence, the answer is 1.
~ Hope this helps you!
What is the sum of 74.835 and 2.67
Answers
I provided you a picture to help you out a little. ^.^
74.835 + 2.67 = 77.505.
Hope this helps!! :)
use the integer values of x from -3 to 13 to graph the equation y= -x
Answers
This is an equation of the straight line, therefore we need only two points to the graph.
for x = -3 we have y = -(-3) = 3 → (-3; 3)
for x = 0 we h→ve y = -0 = 0 → (0; 0)
The graph in the attachment