Answer:
The pair of equations which has (2,12) as its solution is,
equation B and equation C.
Step-by-step explanation:
According to the question,
equation of line A is [tex]\frac {y - 16}{x + 6} = \frac {16 + 4}{-6 - 9}[/tex]
or, [tex]\frac {y - 16}{x + 6} = \frac {-4}{3}[/tex]
or, [tex] 3y - 48 = -4x - 24[/tex]
or, 3y + 4x = 24 ------------------(1)
Now, the point (2, 12) doesn't satisfy (1). Hence, (2,12) is not a solution for the line A.
Equation of line B is, [tex]\frac {y - 20}{x + 2} = \frac {20 - 0}{-2 - 8}[/tex]
or, [tex]\frac {y - 20}{x + 2} = -2[/tex]
or, [tex] y - 20 = -2x - 4[/tex]
or, y + 2x = 16 -----------------------------(2)
The point (2,12) is satisfied by (2). Hence, (2, 12) is a solution for line B.
Equation of line C is, [tex]\frac {y + 6}{x + 7} = \frac {20 + 6}{6 + 7}[/tex]
or, [tex]\frac {y + 6}{x + 7} = 2[/tex]
or, y + 6 = 2x + 14
or. y - 2x = 8 -----------------------------------(3)
The point (2, 12) is satisfied by (3). Hence, (2 , 12) is a solution for the line C.
Equation of line D is, [tex]\frac {y - 20}{x - 7} =\frac {20 + 7}{7 - 0}[/tex]
or, [tex]\frac {y - 20}{x - 7} = \frac {27}{7}[/tex]
or, 7y - 140 = 27x - 189
or, 7y - 27x = -49----------------------------------------(4)
The point (2, 12) is not satisfied by (4). hence, (2, 12) is not a solution of the line D
Hence, the pair of equations which has (2,12) as its solution is,
equation B and equation C.
Y=-3/4x+4 find it in slope intercept form
Answ
this is slope intercept form
Step-by-step explanation:
Find 7/9 of 1 and 2/7
Answer:
1
Step-by-step explanation:
bc theyre even
What is the value of x?
Enter your answer in the box.
°
Answer:
x = 84
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 5, thus
sum = 180° × 3 = 540°
Sum the interior angles and equate to 540 for x
131 + 108 + 107 + 110 + x = 540, that is
456 + x = 540 ( subtract 456 from both sides )
x = 84
On his bicycle, Trevor rode 15 miles in 30 minutes. What was his average rate of speed?
Answer:
0.5 miles/min
Step-by-step explanation:
average speed = total distance / total time
= 15 miles / 30 min
= 0.5 miles/min
A sprinkler can spray 7 feet out and rotates in a circle to cover all directions. What is the total area covered by the sprinkler?
The sprinkler covers an area that is shaped like a circle, with its range as the radius. Using the formula for the area of a circle, πr², and substituting 7 feet for the radius, we find that the sprinkler covers approximately 154 square feet.
Explanation:The total area that the sprinkler covers can be found by considering the sprinkler's range as the radius of a circle. The formula to find the area of a circle is πr² where π (Pi) is a constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius of the area the sprinkler covers is 7 feet. So, we plug this value into the formula:
Area = π(7ft)²
Thus, the total area the sprinkler covers is approximately 154 square feet.
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Kong took 15\%15%15, percent fewer seconds than Nolan took to complete his multiplication timed test. Kong took 858585 seconds.
How many seconds did Nolan take?
Answer:
Nolan took 100 seconds.
Step-by-step explanation:
Given:
Kong took 15%, percent fewer seconds than Nolan took to complete his multiplication timed test.
Kong took 85 seconds.
Now, to find the number of seconds Nolan take to complete the test.
Let the number of seconds Nolan take be [tex]x.[/tex]
Kong took = 85 seconds.
As, given Kong took 15%, percent fewer seconds than Nolan took.
Now, to get the number of seconds Nolan took:
[tex]x-15\%\ of\ x=85[/tex]
[tex]x-\frac{15}{100} \times x=85[/tex]
[tex]x-0.15x=85[/tex]
[tex]0.85x=85[/tex]
Dividing both sides by 0.85 we get:
[tex]x=100.[/tex]
Therefore, Nolan took 100 seconds.
Answer:
100 seconds
Step-by-step explanation:
easy math
Crayons come in a carton a carton holds 6 packages each package holds 10 small boxes each small box holds 12 crayons how many crayons come in a carton
Answer:720
Step-by-step explanation: think about it, 6 packages, 10 per box hold 12 crayons, 10•12=120. 120•6 boxes equals 720. I may be wrong idk but try that. Im fully confident in that answer
Final answer:
To calculate the total number of crayons in a carton, multiply the number of crayons in a small box by the number of boxes in a package, and then by the number of packages in a carton. This results in 720 crayons per carton.
Explanation:
To find out how many crayons come in a carton, we need to do a series of multiplications. We start at the smallest unit, which is the crayon, and work our way up to the carton.
Each small box holds 12 crayons.Each package holds 10 small boxes, so 10 boxes × 12 crayons each = 120 crayons per package.A carton holds 6 packages, so 6 packages × 120 crayons each = 720 crayons in a carton.Therefore, there are 720 crayons in a carton.
(03.04 LC) Write the equation of the graph shown below in factored form.
the graph starts at the bottom left and continues up through the x axis at negative four to a maximum around y equals three and goes back down through the x axis at negative three to a minimum around y equals negative eleven and back up through the x axis at negative one
A. f(x) = (x + 4)(x − 3)(x − 4)
B. f(x) = (x − 1)(x + 3)(x + 4)
C. f(x) = (x + 1)(x + 3)(x + 4)
D. f(x) = (x − 1)(x − 3)(x − 4)
Answer:
The equation of the graph in factored is [tex]C) f(x)=(x+1)(x+3)(x+4)[/tex]Step-by-step explanation:
From the graph given,
In order to find the equation, we need to consider the points where the curve cuts x- axis
From the graph, we have
[tex]x=-4, x= -3 \, and \, x= -1[/tex]
In factor form
[tex]x+4=0, \, x+3=0, \, and \, x+1=0[/tex]
Now, combine the factors above by multiplying together to form the equation, we have
[tex]f(x)=(x+1)(x+3)(x+4)[/tex]
Therefore, the equation of the graph in factored form is [tex]f(x)=(x+1)(x+3)(x+4)[/tex]
The question requires the equation of a graph in factored form, with the graph cutting the x-axis at -4, -3 and -1. These roots correspond to the factored form of the equation as f(x) = (x + 4)(x + 3)(x + 1). However, this equation is not listed among the choices provided. The correct option is C.
The question is asking for the equation of a graph in factored form. The graph cuts the x-axis at -4, -3, and -1.
This implies these are the roots of the equation. When a graph crosses the x-axis at a particular point, it implies the x-value of that point is a root (or zero) of the polynomial.
Therefore, the roots of the function are -4, -3, and -1. We can then convert these roots into factors by changing their signs and setting them as (x - root).
Therefore, the factored form of the equation would then be: f(x) = (x + 4)(x + 3)(x + 1). However, this equation is not listed among the choices. There might be a mistake the options provided.
It's always vital to carefully check the roots and ensure they correspond to the x values where the graph intersects the x-axis.
Therefor the correct option is C.
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Person A can paint the neighbor's house 6 times as fast as Person B. The year A and B worked together it
took them 2 days. How long would it take each to paint the house?
Person A takes 2.3 days to paint the house working alone
Person B takes 13.8 days to paint the house working alone
Solution:
Let "x" be the number of days it takes person A to paint the house
Person A can paint the neighbor's house 6 times as fast as Person B
Therefore.
Number of days it takes person B to paint the house = 6x
Their rates of painting are added to get the rate working together
[tex]\frac{\text{1 house}}{\text{x days}} + \frac{\text{1 house}}{\text{6x days}} = \frac{\text{1 house}}{\text{2 days}}[/tex]
[tex]\frac{1}{x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{1 \times 6}{6x} + \frac{1}{6x} = \frac{1}{2}\\\\\frac{7}{6x} = \frac{1}{2}\\\\\ x = \frac{7}{3}= 2.3[/tex]
Thus person A takes 2.3 days to paint the house working alone
Person B = 2x = 6(2.3) = 13.8
Thus person B takes 13.8 days to paint the house working alone
I need an answer ASAP I will thank you and give you a like!
The table below represents the function f(x).
x 0 2 4 6 8 10 12
f(x) 4.1 5.3 6.5 7.7 8.9 10.1 11.3
If g(x) is a linear function that contains the points (6, -2) and (3, 7), which statement is true?
A.
As x approaches positive infinity, f(x) and g(x) both approach negative infinity.
B.
As x approaches positive infinity, f(x) and g(x) both approach positive infinity.
C.
As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.
D.
As x approaches positive infinity, f(x) approaches negative infinity, and g(x) approaches positive infinity.
Answer:
Option C. As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.
Step-by-step explanation:
we know that
Observing the table
The function f(x) is a increasing function
As the value of x increases, the value of f(x) increases
so
As x approaches positive infinity, f(x) approach positive infinity
Find the slope of the linear equation g(x)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points (6, -2) and (3, 7)
substitute
[tex]m=\frac{7+2}{3-6}[/tex]
[tex]m=\frac{9}{-3}=-3[/tex]
The slope of the linear equation g(x) is negative
That means ----> Is a decreasing function
As the value of x increases, the value of g(x) decreases
so
As x approaches positive infinity, g(x) approach negative infinity
therefore
As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.
60th term of the arithmetic sequence 4, -1 -6
Answer:
Step-by-step explanation:
d=-1-4=-5
[tex]t_{60}=4+(60-1)(-5)=4-295=-291[/tex]
Car A is going 72km per Hour and Car B is going 90km per hour but started 140m behind Car A. How long will it take for Car B to reach Car A
Answer:
going into new york using the george washington bridge, consumers must pay a toll (there is not toll to return to New jersey). they can pay $6 cash or they can pay $5 (during peak hour) using the E Z pass system. The E Z pass system is a prepaid plan that also requires a one-time $12 account activation fee. How many trips to new york would a person need to make (during peak hours) so that the total amount spent with the E Z pass is equal to the amount spent for tolls without the E Z pass?
Step-by-step explanation:
The sum of four consecutive multiples of 7 is 378. Find the numbers
Answer:i have no idea but go back to your math book and lesson and check :p
Step-by-step explanation:
Answer:
84, 91, 98, 105
Step-by-step explanation:
7x + 7 (x+1) + 7(x+2) + 7(x+3) = 378
28x + 42 = 378
28x = 336
x = 12
7x12, 7x13, 7x14, 7x15 i.e. 84, 91, 98, 105
check: 84 + 91 + 98 + 105 = 378
Mr. Elliot's class created a
mural about Martin Luther
King in their school. The
mural was 4 12 feet long by
3 14 feet wide. If it took the
class 30 minutes to paint 1
square foot of the mural,
| about how long did it take
them to complete the
whole thing?
Answer:
it would take 3881040 minutes to complete the entire mural
PLEASE HELP/ANSWER! From 1980 to 1990, Lior’s weight increased by 25%. If his weight was k kilograms in 1990, what was it in 1980?
The weight in 1980 is [tex]\frac{4k}{5}[/tex] kilograms
Solution:
From 1980 to 1990, Lior’s weight increased by 25%
His weight is "k" kilograms in 1990
To find: weight in 1980
This is a percentage increase problem
Let "x" be the weight in kilograms in 1980
The percentage increase is given by formula:
[tex]\text{Percentage increase } = \frac{\text{Final value - initial value}}{\text{initial value}} \times 100[/tex]
Here,
Initial value in 1980 = x
Final value in 1990 = k
Percentage increase = 25 %
Substituting the values in formula,
[tex]25 = \frac{k-x}{x} \times 100\\\\25x = 100(k-x)\\\\x = 4(k-x)\\\\x = 4k - 4x\\\\5x = 4k\\\\x = \frac{4k}{5}[/tex]
Thus the weight in kilograms in 1980 is [tex]\frac{4k}{5}[/tex]
============================================================== Don't delete please
Answer:
The First one To the right is The Correct Shape
Solve proportion to x:
12/15=36/x
And then 160/10.
Don’t use a calculator show the work. PLEASE
Answer:
45
Step-by-step explanation:
12/15=4/5
4/5=36/x
cross product
5*36=4*x
180=4x
x=180/4
x=45
51%, 0.57, 0.61, 6/10 least to greatest
Answer:
least is 51%
Step-by-step explanation:
so 51%, .57,6/10 and .61
A total of 631 tickets were sold for the school play. They were either adult tickets or student tickets. There were 69 fewer students tickets sold then adult tickets. How many adult tickets were sold?
Final answer:
To solve the problem, two equations were set up and solved for the number of adult tickets (A). The equations A + S = 631 and S = A - 69 led to finding that 350 adult tickets were sold for the school play.
Explanation:
The school play ticket problem is a basic algebraic question involving setting up and solving equations. We need to determine the number of adult tickets and student tickets sold, given the total tickets and the difference between them.
Let's denote the number of adult tickets as A and the number of student tickets as S. According to the information provided:
A + S = 631 (The total number of tickets sold)
S = A - 69 (There were 69 fewer student tickets sold than adult tickets)
By substituting the second equation into the first, we get:
A + (A - 69) = 631
2A - 69 = 631
2A = 631 + 69
2A = 700
A = 350
So, 350 adult tickets were sold.
need help with ixl please give right answer
A car company charges a $45 fee to use their vehicle. They also charge an additional $0.35 per mile 9 (m). write a function that models the total cost (c) of taking a passenger to the airport. What does C represents What does M represents what is the equation
The total cost function for taking a passenger to the airport is C = 45 + 0.35M, where C is the total cost and M is the number of miles driven. The $45 is a fixed fee, and $0.35 is the charge per mile.
The student is interested in creating a function that models the total cost of taking a passenger to the airport. This function includes a fixed fee and a variable fee that depends on the number of miles driven. To model this, let C represent the total cost and M represent the miles driven.
The total cost C can be represented by the equation C = 45 + 0.35M. Here, the $45 is a fixed fee for using the vehicle, and $0.35 is the additional charge per mile driven.
C represents the total cost of the trip to the airport and M represents the number of miles driven to the airport.
What is the equation of a line that is parallel to the line with the equation y=2/3x+2 and passes threw the point 1,-1
The equation of line parallel to given line is: [tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y = \frac{2}{3}x+2[/tex]
As the line is in slope-intercept form, the co-efficient of x is the slope of the line
So,
[tex]m_1 =\frac{2}{3}[/tex]
Let m2 be the slope of required line
As both the lines are parallel,
[tex]m_1 = m_2[/tex]
So,
[tex]m_2 = \frac{2}{3}[/tex]
The slope intercept form of line is:
[tex]y = mx+b[/tex]
Putting the value of the slope
[tex]y = \frac{2}{3}x+b[/tex]
To find the value of b, putting (1,-1) in the equation
[tex]-1 = \frac{2}{3}(1) +b\\-1 = \frac{2}{3} +b\\b = -1-\frac{2}{3}\\b = \frac{-3-2}{3}\\b = \frac{-5}{3}[/tex]
Putting b=-5/3 in the equation
[tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]
Hence,
The equation of line parallel to given line is: [tex]y = \frac{2}{3}x-\frac{5}{3}[/tex]
Keywords: Equation of line, slope
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Amazon was valued at 430 billion dollars. Write this number in scientific notation
Answer:
430 billion (430,000,000,000) is 4.3 x 10^11 in scientific notation
To convert 430 billion into scientific notation, express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion becomes 10^11. Therefore, the scientific notation of 430 billion is 4.3 x 10^11.
Explanation:The process of writing large numbers or small numbers in scientific notation involves expressing the number as a product of a number between 1 and 10 (inclusive) and a power of 10. To write 430 billion dollars in scientific notation, firstly express it as 4.3 multiplied by 100 billion. In scientific notation, 100 billion is 10^11. So, Amazon's worth in scientific notation is 4.3 x 10^11.
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Which of the following represents the graph of f(x) = 2x?
Answer:
I believe it is the fourth graph
Step-by-step explanation:
The only graph that correctly represents the exponential function f(x) = 2ˣ is the fourth graph
How to Identify the exponential function graph?The exponential function is given as:
f(x) = 2ˣ
Thus:
When x = -2, we have:
f(-2) = 2⁻²
f(-2) = 1/2² = 1/4
When x = -1, we have:
f(-1) = 2⁻¹
f(-1) = 1/2¹ = 1/2
When x = 0, we have:
f(0) = 2⁰
f(0) = 1
When x = 1, we have:
f(1) = 2¹
f(1) = 2
When x = 2, we have:
f(1) = 2²
f(1) = 4
Thus, the only graph that correctly represents these values is the fourth graph
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You entered Kente invested a total of $8000. He invested part of the money for 2yr in a stock fund that earned the equivalent of 6.5% simple interest. He put the remaining money in an 18 month certificate of deposit that earned 2.5% simple interest. If the total interest from both investments was $855 , determine the amount invested in each account?
Step-by-step explanation:
Given,
Kente invested part of money for 2 yr in stock fund that earned the equivalent of 6.5 % simple interest.He put remaining money in a 18 month certificate of deposit that earn of 6.5%simple interest.
Let he invested in stock fund be$ x. Remaining money =$(8000-x)
∴He got interest from stock fund was = [tex]\frac{PRt}{100}[/tex]
=$[tex]\frac{x\times6.5\times2}{100}[/tex] [here P =x , R = 6.5% and t = 2 yr]
=$ [tex]\frac{{13 x}}{{100} }[/tex]
Again he got interest from deposit was = [tex]\frac{PRt}{100}[/tex]
=$ [tex]\frac{(8000-x)\times 2.5\times\frac{18}{12} }{100}[/tex] [here P = (8000-x), R=2.5% and t =[tex]\frac{18}{12} yr[/tex]]
=$ [tex]\frac{(8000-x) \times 7.5}{200}[/tex]
According to problem
[tex]\frac{{13 x}}{{100} }+\frac{(8000-x) \times 7.5}{200}= 855[/tex]
⇔[tex]\frac{26x + 60000 - 7.5}{200} =855[/tex]
⇔18.5 x =171000 - 60000
⇔x = [tex]\frac{11100}{18.5}[/tex]
⇔x = 6000
So he invested in stock fund was = $6000
and in certificate of deposit was =$(8000- 6000)= $ 2000
if steve throws a football 60meters in 3seconds what is the football speed ?
The football thrown by Steve has a speed of 20 meters per second, as it covers a distance of 60 meters in 3 seconds.
Explanation:To calculate the speed of the football that Steve throws, we can use the basic physics concept of speed which is the distance traveled divided by the time taken. Since Steve throws the football a distance of 60 meters in 3 seconds, the calculation for the speed v is:
v = distance / time = 60 meters / 3 seconds = 20 meters per second.
Therefore, the football is traveling at a speed of 20 meters per second.
Final answer:
The speed of the football thrown by Steve is 20 meters per second, calculated by dividing the distance thrown, 60 meters, by the time taken, 3 seconds.
Explanation:
If Steve throws a football 60 meters in 3 seconds, we can calculate the speed of the football by using the formula for speed: speed = distance/time. To find the speed of the football, we simply divide the distance Steve's throw covered by the time it took for the football to cover that distance.
The calculation is as follows:
Speed = Distance / Time
Speed = 60 meters / 3 seconds
Speed = 20 meters/second
Therefore, the speed of the football is 20 meters/second
Nike is having a sale $100 shoes is 30% off an additional 20% off what is the amount?
Answer:
50% off would be $50
Step-by-step explanation:
20% + 30% = 50% original price was $100 but now with 50% off it is $50
Nike is having a sale $100 shoes is 30% off an additional discount 20% off. The amount to be paid for shoes now is $56.
Discount is the amount of off offered by the seller to the customer on a certain product. It is always offered as a percentage of the marked price of the product to lure the customer to buy the product.
Selling price is the price at which the product is finally sold. It is the marked price of the product minus the discount given.
Marked price = $100
initial discount = 30%
price of shoes becomes = $100 - 30% of $100 = [tex]100 - \frac{30}{100} *100 = 100- 30 = 70[/tex]
Additional discount offered = 20%
selling price of shoes = $70 - 20% of $70 = [tex]70 - \frac{20}{100} *70 = 56[/tex]
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5. Write the number 81 as a power with a base of 3 and a base of 9.
Answer:
3^4 and 9^2
Step-by-step explanation:
The sum of two numbers is 31. Twice the larger number is 7 more than three times the smaller number. What is the number
Answer: x=6
Step-by-step explanation:
3x+7+x=31
4x+7=31
-7 -7
4x=24
24/4= 6
Simplify a^15/ a^5
Pleaaaaseeeeee
When you divide the same value raised to different powers keep the value and subtract the powers.
A^15 / a^5 = a ^(15-5) = a^10
Answer:
a^10
Step-by-step explanation: