The equation of the line that passes through these coordinates is 3x-4y= 36
How to calculate slope?
If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. m=(y2-y1)/(x2-x1), or the ratio of the change in the y values to the change in the x values, is the slope formula.
To find the equation of the line we first have to find the slope which is represented by m.
The slope or m is given by : y₂ - y₁ / x₂ - x₁
thus, m= 3-(-12)/ 16-(-4)
m= 3+12/ 16+4 = 15/20
m= 3/4
The equation of a slope is y-y₁=m (x-x₁)
y- (-12) = 3/4 (x- (-4))
y+12 = 3/4 (x+4)
On solving it further we get:
4y+48= 3x+12
3x-4y= 36
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Any buyer of a new sports car has to pick between 2 of 5 options for seat colors and 3 of 4 options for dashboard accessories. how many different combinations of colors and dashboard options are available to this buyer?
There are 40 different combinations of colors and dashboard options available to this buyer.
Combination is a counting technique where the order of the selected items from a collection does not matter. The formula in finding the number of combinations when ‘r’ items are chosen out of a total of ‘n’ objects.
nCr = n! / [r! (n - r)!]
If there are 2 of 5 options for seat colors, then using the formula, the number of combinations for the seat color is:
5C2 = 5! / [2! (5 - 2)!]
5C2 = 120 / 12
5C2 = 10
If there are 3 of 4 options for dashboard accessories, then using the formula, the number of combinations for the dashboard accessories is:
4C3 = 4! / [3! (4 - 3)!]
4C3 = 24 / 6
4C3 = 4
Multiplying the two results will give the total number of different combinations of colors and dashboard options available.
combination = 10 x 4
combination = 40
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Jesse and amir were assigned the same book to read. jesse started reading on saturday, and he is reading 30 pages a day. amir didn't start until sunday, but he is reading 35 pages a day.
He will read 210 pages of the book and it will take Amir 6 days to catch up with Jesse
Day Jesse started reading: Saturday
Number of pages read by Jesse each day: 30 pages
Day Amir started reading: Sunday
Number of pages read by Amir each day: 35 pages
Let x represent the number of days Amir has been reading and y represent the number of pages he has read
Formulating the equation for Amir we get:
y = 35*x
y = 35x
The equation for Jesse will be:
y = 30*(x+1)
y = 30(x+1)
Equating both equations we get:
35x = 30(x+1)
35x = 30x +30
5x = 30
x=6
So, the number of pages read will be 210 and it will take 6 days for Amir to catch up with Jesse
Although a part of your question is missing, you might refer to this full question: Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day. How many days will it take Amir to catch up to Jesse, and how many pages will they each have read? Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read
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can someone help me find the vertex of y=1/2x^2+2?
Answer:
(0,2)
Step-by-step explanation:
a gigabyte of computer storage space is 2^30 bytes.A computer has a total storage space of 128 gigabytes.How many bytes of total storage space does the computer have?Write your answer as a power.
There are 2 ³⁷ bytes in 128 gigabytes.
Bytes, which typically contain eight bits, are the basic building blocks of digital information.
Because previously a single character of∀⊅ text required only a certain number of bits to be encoded in a computer, the byte is the lowest addressable unit of memory in all computer systems. To distinguish them from the standard 8-bit definition, network protocol documents like The Internet Protocol (RFC 791) refer to an 8-bit byte as an octet. An octet's bits are commonly counted from 0 to 7 or 7 to 0, depending on the bit endianness. The eighth bit is a seven since the first bit is a zero.We know that 128 = 2⁷
Now each gigabyte = 2³⁰ bytes
So the total number of bytes in 128 gb is
2⁷ × 2³⁰ = 2³⁰⁺⁷ = 2 ³⁷
Therefore there are 2³⁷ bytes in 128 gigabytes.
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Juan's company spent $2,350 on an event, They spent
about $1,500 on food and about $900 on entertainment,
What could the actual cost of the food and entertainment be?
work.
Show your work!!
The actual cost of the food and entertainment be $2,400.
What is defined as the actual cost?The sum of money paid to obtain a product or asset is referred to as the actual cost in accounting. The actual cost is exactly as it sounds like. This cost may be a historical, previous, or current day product cost. You may be wondering what other costs exist aside from the actual cost of a product. Keep in mind that in managerial accounting, costs are budgeted and forecasted.For the given question;
The amount spent by Juan's company = $2,350.
The amount spent of the food = $1,500.
The amount spent on entertainment = $900.
Thus, the actual amount will be;
Actual amount = food + entertainment
Actual amount = $1,500 + $900
Actual amount = $2,400.
Thus, the actual cost of the food and entertainment be $2,400.
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Find the differential dy in each of the followings:
y = 2t² +t+1
Answer:
4t + 1.
Step-by-step explanation:
Use the General form of the differential:
If y = ax^n,
dy/dx = anx^(n-1)
So:-
y = 2t^2 + t + 1
dy.dt = 2*2t^(2-1) + t^(1-1) + 0
= 4t + 1.
There are 12 bags of apples on a market store. The main number of apples in each bag is eight. The table shows the number of apples in 11 of the bags. Calculate the number of apples in the bag.
The main number of apples in each bag is eight therefore 12 bags contain 96 apples.
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.
Given that :There are 12 bags of apples on a market store. The main number of apples in each bag is eight
Eight apples on average fit into each bag.
We need to figure out how many apples are in the 12 bag.
The total number of apples is 8×12 = 96.
Therefore, 12 bags contain 96 apples.
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How many times greater is 72,980,001 than 54,908?
A. 1.4 x 10^3
B. 7.14 x 10^-4
C. 1.4 x 10^4
D. 7.14 x 10^3
The correct option is A. 1.4 x 10^3
Exponents: The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
The first number = 72,980,001
The second number = 54908
Dividing the first number by the second number we get:
=72980001/54908 = 1329.13
Which is equivalent to 1.4 x 10^3
So, 72,980,001 is 1.4 x 10^3 times greater than 54,908
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14.549 - (8.131 + 3.7024)
Answer: 2.7156
Step-by-step explanation:
Using Bidmas: we do the brackets first so 8.131 + 3.7024 = 11.8334
Then 14.549 - 11.8334 = 2.7156
Hope this helps :)
Answer:
Step-by-step explanation:
Graph the line with slope of 5/3 and goes through the point (2,1). please help
Answer:
y = 5/3x -7/3
Step-by-step explanation:
y = mx + c
sub in values:
1 = 5/3(2) + c
1=10/3 + c
-7/3 = c
equation of line:
y = 5/3x -7/3
pls help ill give brainly
The slope of this straight line is equal to: A. 2
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
By critically observing the given graph, we can logically deduce the following points:
Point (x, y) = (1, 1) Point (x, y) = (-1, -3)Note: Each interval on this graph represents 1 unit.
Substituting the given points into the formula, we have;
Slope = Δy/Δx
Slope = (-3 - 1)/(-1 - 1)
Slope = -4/-2
Slope = 2
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At Silver Gym, membership is $20 per month, and personal training sessions are $45 each. At Fit Factor, membership is $90 per month, and personal training sessions are $35 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy _____ personal training sessions to make the total cost at the two gyms equal.
Answer: 7
Step-by-step explanation:
Let the number of sessions be x. Then,
[tex]20+45x=90+35x\\\\10x=70\\\\x=7[/tex]
A bag of sweets weighs 120g and costs
£0.89. It contains 14 gummy bears, 6 jelly
beans and 4 chocolate buttons.
What is the ratio of bears:beans:buttons in
it's simplest form?
The ratio of bears:beans: buttons in the simplest form is 7:3:2
Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.
Weight of sweet bag = 120g
Cost of a sweet bag = 0.89 euros
Number of gummy bears = 14
Number of jelly beans = 6
Number of chocolate buttons = 4
The ratio of bears:beans:buttons = 14:6:4
Dividing the ratio by 2 throughout we get:
Ratio of bears:beans:buttons = 7:3:2
So, In its simplest form, the ratio of bears to beans to buttons is 7:3:2.
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help please i don't understand this
Sounds at 85 dBA can cause hearing loss if listened to for more than 8 hours. Sounds above 85 dBA can damage your hearing more quickly. For every 3-dB increase in noise levels above 85 dBA, the safe listening time is cut in half. You can, for example, listen to sounds at 85 dBA for up to 8 hours.
What is meant by decibel?The decibel (dB) is 10 times the decimal logarithm of the ratio of two variables' values. Decibels are calculated using a logarithm, which allows very large or very small relationships to be represented with a conveniently small number. The decibel, abbreviated dB, is the scale's unit. Sound intensity as a reference ( = 10 ^{ -12 } Watts per square meter.) The decibel (dB) is a logarithmic unit of measurement for sound level. It is also widely used in electronics, communications, and signals. The dB is a logarithmic measure of a ratio. Power, sound pressure, voltage, or intensity are all examples of ratios.A noise or sound level of 85 decibels is equivalent to that of a food blender, heavy traffic while driving, a noisy restaurant, or a movie theater. As you can see, we are exposed to high noise levels in a variety of situations in our daily lives.To learn more about decibel, refer to:
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Phyllis invested $9,500 a portion earning a simple interest rate of 7 1/5% per year and the rest earning a rate of 7% per year. After 1 year the total interest earned on these investments was $677. How much money did she invest at each rate?
Using simple interest, it is found that the amounts invested are given as follows:
$2,350 at a rate of 7.2%.$6,650 at a rate of 7%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount of the investment.r is the interest rate of the investment, as a decimal.The interest accrued over t years is:
I(t) = Prt.
For this problem, we have that:
She had two investments totaling $9500, hence P and 9500 - P.The rates are of [tex]r_1 = 0.072, r_2 = 0.07[/tex].From the interest earned, we have that:
[tex]I_1 + I_2 = 677[/tex]
In which:
[tex]I_1 = 0.072P[/tex][tex]I_2 = 0.07(9000 - P)[/tex]Replacing both these relations in the sum of interests, we have that:
0.072P + 0.07(9000 - P) = 677
0.002P = 677 - 0.07(9000)
P = (677 - 0.07(9000))/0.02
P = 2350.
Hence she invested $2,350 at a rate of 7.2% and $6,650 at a rate of 7%, as 9000 - 2350 = 6650.
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Which measure of spread is the most appropriate for the data set represented by the graph?
Number of Chocolates
11-
10-
9
8-
7 9
S
ST
3
2-
1 2
3
4 5 678
Number of Children
9 10 11
your answer is B
your welcome
After being exposed to an electromagnetic shrinking machine, joe's height decreased by 120cm over 1.5 seconds. his height decreased by the same amount each second.
Main Answer:
Height decreased in 1 second is 80 cm
Explanation:
The total amount of height decreased is 120.
Total amount of time taken is 1.5 s.
Height decreased in 1 second = [tex]\frac{120}{1.5}[/tex]
⇒ [tex]\frac{1200}{15}[/tex]
⇒ 80 cm
Therefore, height decreased in 1 second is 80 cm.
help with geometry please.
Answer:
Surface area: 432 Area: 576
Step-by-step explanation:
Surface area fomula: 2lh+2wl+2wh
Area formula:lh
Please help me. I will give brainly to anyone who helps.
a
so the first one is 817(the amount at the beginning) +19x
817+19x
the second pool is 38x, cause there's no water at the start.
38x
b
it would be 817+19x=38x
What is the difference?
− 3 − 6
Answer:
-9
Step-by-step explanation:
If you find the -6 point on the number line and move to the left three spaces, you stop at -9. You are taking away three spaces from an already negative number. So, you move to the left to show you subtracting something.
Hope this helps! :)
Answer:
-9
Step-by-step explanation:
Using absolute value (6+3) you can add -6 to -3.
I don’t know 6-8 I need help. Please do not write random I fr need help
In functions, value of x = 45 and y = 45
What is function in math?
A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.6) x = 15
y = 49
3x = 3 * 15 = 45
y - 4 = 49 - 4 = 45
7) 3x + 23 = 4x
4x - 3x = 23
x = 23
y = 4 * 23 = 92°
8) y + 12 = 5x °
3x + 50 =
According to the question
y + 12 = 3x + 50
5x = 3x + 50
2x = 50
x = 25
y + 12 = 5x °
y = 5 * 25 - 12
y = 125 - 12 = 113
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How do I answer this question?
The surface area of the regular pyramid is 151.9 m².
How to find the surface area of a pyramid?The surface area of the regular pyramid can be found as follows:
surface area of the pyramid = A + 1 / 2 ps
where,
A = base areap = perimeter of the bases = slant heightTherefore,
A = 61.9 m²
p = 6 × 5 = 30 m
s = 6m
Hence,
surface area of the pyramid = 61.9 + 1 / 2 × 30 × 6
surface area of the pyramid = 61.9 + 180 / 2
surface area of the pyramid = 61.9 + 90
surface area of the pyramid = 151.9 m²
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EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
-2, 8, 18, 28
Answer:
The sequence is arithmetic.
-2 , 8 , 18 , 28 , 38 , 48 , 58 , 68 , 78 , . . .
21st term value is 198.
Step-by-step explanation:
Select all the digital construction tools that do the same job as a straightedge.
-Line
-Segment
-Point plotted on an object
-Point of intersection
-Circle with center through point
The correct answers are line and segment.
Drag a number to each box to complete the product. Numbers may be used more than once.
0.476
4.76
47.6
476
4,760
Equation Product
476 × 0.001
0.476 × 10¹
4.76 × 10³
47.6 x 0.1
476 x 0.001 = 0.476
0.476 x 10¹ = 4.76
4.76 x 10³ = 4,760
47.6 x 0.1 = 4.76
We have to find the following products of the equations.
The basic rule for multiplication between numbers with decimal points can be described through some examples first.
Decimal point is shifted leftwards up to the power of 10 which is divided with it. Also decimal point is shifted rightwards when multiplied with powers of 10.
Now we will find the product for each equation:
For 476 × 0.001, 0.001 = 1/1000
Therefore, 476 × 0.001 = 476 × 1/1000 = 0.476 [decimal point shifted left]
For 0.476 × 10¹ = 0.476 × 10 = 4.76 [decimal point shifted right]
For 4.76 × 10³ = 4.76 x 1000 = 4760 [decimal point shifted right]
For 47.6 x 0.1 = 47.6 x 1/10 = 4.76 [decimal point shifted left]
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solve this equation
[tex] \frac{33}{3} = c + 2[/tex]
Answer:
c=9
Step-by-step explanation:
[tex]11=c+2 \\ \\ c=9[/tex]
For each event, write the sample space and tell how many outcomes there are. Roll a standard number cube. Then flip a quarter. How many outcomes are there?
The total number of outcomes is 12.
An outcome is a potential outcome of an experiment or trial in probability theory.
Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment). The components of a sample space are all the potential results of an experiment. There is a chance that outcomes will occur with probabilities between 0 and 1. (inclusively). In a discrete probability distribution whose sample space is finite, each result is assigned a certain probability. A continuous distribution, on the other hand, only allows non-zero probabilities to be assigned to ranges of events, with all individual outcomes having zero probability.When a number cube is rolled there are 6 distinct outcomes {1,2,3,4,5,6} = 6
Again when a quarter is flipped then there are two possible outcomes {heads , tails } = 2
The total number of outcomes = 6 × 2 = 12
Hence there are 12 distinct outcomes.
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María Fernanda buys a bag of cookies that contains 7 chocolate chip cookies, 5 peanut butter cookies, 6 sugar cookies and 8 oatmeal cookies.
What is the probability that María Fernanda reaches in the bag and randomly selects 2 chocolate chip cookies from the bag?
Based on the number of cookies in the bag of cookies, if María Fernanda is to reach in and select 2 chocolate chip cookies, the probability of that happening is 6.46%
How to find the probability?The events that María Fernanda picks one chocolate chip cookie and then another, are both independent events.
To find the probability of independent events, the formula is:
= Independent event probability 1 x Independent probability 2
Find the total number of cookies:
= 7 chocolate chip cookies + 5 peanut butter cookies + 6 sugar cookies + 8 oatmeal cookies
= 26 cookies
The probability of two chocolate cookies being picked by María Fernanda is:
= Number of chocolate cookies / Number of total chips x Number of chocolate cookies left / Number of cookies left
= 7 / 26 x 6 / 25
= 42 / 650
= 21 / 325
= 6.46%
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Question 6 (Yes/No Worth 1 points) (02.01 LC) Is the following relation a function? x y 1 −2 1 −3 2 1 3 −2 Yes No
This is not a function, we know this because the input x = 1 is mapped into two different outputs.
Is the following relation a function?A relation maps elements from one set, the domain, into elements from another set, the range. A relation is only a function if each element of the domain is mapped into only one element of the range.
In this case, we have the relation:
x: 1, -2, 1, -3
y: 2, 1, 3, -2
The input x = 1 is mapped into two different values, y =2 and y = 3.
Thus, the relation is not a function.
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see the picture instead:
Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities.
see the picture instead :(
The maximum value of the function is at (8, 7).
The inequalities are :4x + 4y ≥ 28-2x + 6y ≤ 26-6x + 2y ≥ -34The objective function is f(x, y) = 7x + 6y.Convert the above inequalities into equations and plot them on the graph, and find the coordinates of their intersection as shown in the graph attached below.Shade the side of the area which satisfies the inequality. Do this for every inequality.Now we check the corner points which fall within the first quadrant as well as in the shaded region of the inequalities.We obtain three points (2, 5), (8, 7), and (6, 1).We will now check which point gives us the maximum value of our objective function.f(2, 5) = 7(2) + 6(5) = 44f(8, 7) = 7(8) + 6(7) = 98f(6, 1) = 7(6) + 6(1) = 48The function achieves its maximum value at (8, 7).To learn more about inequalities, visit :
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