The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].
As per the question statement, two points lie (-2, 1) & (-5,5) on a line.
We are supposed to find the slope of the line.
To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].
Using these values into above mentioned formula, we get,
Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].
Slope of a line: In mathematics, the slope or gradient of a line is a value that describes both, direction and the steepness of the line.To learn more about Slope of lines, click on the link below.
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Write an explicit formula for an, the nth term of the sequence 26, 24, 22
we get that the nth term of the arithmetic sequence is given by aₙ = 28 - 2 n.
We are given an arithmetic sequence:
26, 24 , 22 ....
We need to find the nth term of this sequence (aₙ)
We will first find the common difference between the terms:
Common difference = d = 24 - 26 = - 2
also, we know that initial term = a = 26.
We know the formula for aₙ is given by:
aₙ = a + ( n - 1 ) d
Substituting the values, we get that:
aₙ = 26 + ( n - 1 ) ( - 2 )
aₙ = 26 - 2 n + 2
aₙ = 28 - 2 n
Therefore, we get that the nth term of the arithmetic sequence is given by aₙ = 28 - 2 n.
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Suppose when you study 4 hours for an exan, your mark is 80 percent. and if you study for an extra hour, your mark is 85 percernt. the marginal benefir from studying one more hour is:_________
The marginal benefit from studying one extra hour is 5 percent.
What is marginal benefit?The maximum sum of money a consumer will spend on an additional commodity or service is known as the marginal benefit. As spending rises, customer contentment tends to decline.Now,
Given:
Marks scored on studying 4 hours = 80 percentMarks scored on studying 1 hour extra = 85 percentTo find: Marginal benefit on studying one hour extra.
Finding:
Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.
Thus, the extra percentage that is scored is because of the 1 hour of extra studying.
The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.
Hence, the marginal benefit from studying one extra hour is 5 percent.
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(3-x)² what is the standard form
Answer:
here is my answer........
Step-by-step explanation:
(3-x)^2 = 9 - 3x - 3x + X2
= X2 - 6x +9
Write a rule for the function:
1 6
2 11
3 16
4 21
Answer:
4 21
Step-by-step explanation:
Its probably the answer you are looking for
Determine the smallest integer that makes -3x + 7 -5x < 15 true.
Step-by-step explanation:
-3x+7-5x<15
-5x-3x+7<15
-8x+7<15
-8x<15-7
-8x<8
The smallest integer is -3x.
Find the area of the region that lies inside both curves. r = 9 sin(), r = 9 cos()
The area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The curves are:
r = 9 sin(θ) and
r = 9 cos(θ)
On graphing the above curves:
From the graph:
A = (1/2)∫(9sin(θ))2dθ + (1/2)∫(9cos(θ)2dθ
The region is symmetrical about π/4,:
A = 81∫sin2(θ)dθ from 0 to π/4
After solving:
= 11.56 square unit
Thus, the area of the region inside both curves r = 9 sin(θ) and r = 9 cos(θ) is 11.56 square units.
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f(x) = -x² - 8x - 16; Find ƒ(-3)
f(-3) = -1
Step-by-step explanation:We can find an unknown y-value by plugging an x-value into a given function.
Function Notation
Before we answer this question, we need to understand the notation of the equation. In function notation, the equation is given in terms of f(x).
"f(x)" represents the y-value of a function at the point "x".For example, f(-3) represents the value of y when x = -3.
Finding f(3)
As stated above, to find f(-3) we need to plug -3 in for x. *Remember to use PEMDAS when solving.* This creates the new equation:
f(-3) = -(-3)² - 8(-3) - 16Then, distribute the exponent.
f(-3) = -9 - 8(-3) - 16Next, multiply.
f(-3) = -9 - (-24) - 16Distribute the negative.
f(-3) = -9 + 24 - 16Finally, add the remaining terms.
f(-3) = -1This means that when x = -3, y or f(-3) = -1.
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. Joy walked 14 steps forward, and Shaunte walked 5 steps backwards. Which expression correctly represents the distance between the friends? 14 + |−5| = 19 steps 14 + 5 = 19 steps |−14| + |−5| = 19 steps |−14| + 5 = 19 steps
The number expression will be 14 + |-5| = 19 if Joy walked 14 steps forward, and Shaunte walked 5 steps backward option (A) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Two friends are playing with water balloons. They each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other.
Joy walked 14 steps forward, and Shaunte walked 5 steps backward.
Let forward direction be the positive
The backward direction is negative.
The number expression can be represented;
The distance between two friends:
14 + |-5| = 14 + 5 = 19
14 + |-5| = 19
Thus, the number expression will be 14 + |-5| = 19 if Joy walked 14 steps forward, and Shaunte walked 5 steps backward.
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A 9-foot roll of plastic wrap costs $4.41. What is the price per yard?
Answer:
$1.47 per yard
Step-by-step explanation:
3 feet = 1 yard
9 feet = 3 yards
set up a proportion
[tex]\frac{3}{4.41} = \frac{1}{x}[/tex]
cross multiply; 3x = 4.41 * 1
3x = 4.41
divide both sides by 3
x = 1.47
$1.47 per yard
PLEASE HELP THIS IS SO CONFUSING TO ME!!!
According to the American Sleep Disorders Association, the average teenager needs around 9.5 hours of sleep per night, possibly because of hormones that are critical. Yet studies show that teenagers generally get an average of only 7.4 hours a night or less. Calculate the number of seconds of sleep that an average teenager is lacking for the 180 days of school in one year.
Answer:
A
Step-by-step explanation:
The two sentences relate like They establish a contrast. As American Sleep Disorders Association is considering the teenager sleep and adult sleep.
What is sleeping disorder?
Sleep Disorders are mostly common nowadays as people are more busy in their scheduling, they don't get proper and sufficient time to sleep. This creates many problems in the human body.
The common type of sleeping disorder are insomnia, restless toughnesses' syndrome, narcolepsy and sleep apnea.
Thus, option A is correct.
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Jamal loves his dog, Rupert. On sunny days, Jamal keeps Rupert on a 12-foot leash
in the backyard. He secures the leash to a stake in the ground.
> Answer each question and use 3.14 for T.
1 Determine the diameter, circumference, and area of Rupert's play area.
Diameter = 24 foot, circumference = 75.36 foot, Area = 452.16 square foot
As the leash is 12 feet, and dog Rupert will form a circle in the backyard.
As the leash is of 12 feet, so it is the radius(r) of the circle.
Diameter = 2r
= 2×12
= 24 foot
Circumference = 2πr
=2×3.14×12
= 75.36 foot
Area of the circle = π[tex]r^{2}[/tex]
= 3.14×[tex]12^{2}[/tex]
=3.14 × 144
= 452.16 [tex]foot^{2}[/tex]
Therefore we get diameter = 24foot, circumference = 75.36 foot and area = 452.16 square foot.
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HELP ASAP!!!!!
Write a function g whose graph represents the indicated transformation of the graph of f.
f(x)=4x+1; translation 2 units left.
HELP PLEASE
Answer:
The translation of 2 units left in function f (x) = 4x + 1 is 4x + 3.
Here,
Function is given as, f(x)=4x+1
And, translation 2 units left.
We have to find the function after translation.
Now,
Function is given as, f(x)=4x+1
After translation 2 units left the function is;
f (x) = 4x + 1 + 2
f (x ) = 4x + 3
Hence, the function after translation 2 units is f (x) = 4x + 3
Please help with. Scale Factors
Answer:
5×8=40
x=7×8
=56
Step-by-step explanation:
5×8=40
x=7×8
=56
which of the following ordered pairs make this question true y=2x-4?
Answer:
There is not a single ordered pair which is a solution to y=2x−4 .
What's the GCF of 30,60 and 78
Answer:
6
Step-by-step explanation:
Answer: 6
Step-by-step explanation:
First, take the prime factorization of all 3 numbers.
30: 15*2 ==> 5*3*2
60: 30*2 ==> 15*2*2 ==> 5*3*2*2
78: 39*2 ==> 13*3*2
Notice any common factors? That's the GCF.
GCF: 3*2=6
GCF: 6
32-15x3-5(5-13+44)-33+3(576+13-375)
Answer:
416
Step-by-step explanation:
pemdas
simplify the equation 12-2/6+4
i need help asap !!!!
Answer:
47 / 3 ( Or 1 if you typed it wrong)
Step-by-step explanation:
When simplifying an equation like this, we always want to do our multiplication and division before addition and subtraction.
So for the first step, let's simplify the expression down to only addition and subtraction...
12 - 2 / 6 + 4 =
12 - (2 / 6) + 4 =
12 - 1/3 + 4
Now we can combine everything together from left to right...
(12 - 1/3) + 4 =
35/3 + 4 =
47 / 3
However...
If the original equation was:
[tex]\frac{12-2}{6+4}[/tex]
Then you would just simplify the top and bottom separately before dividing the two numbers, treating the fraction as parentheses.
So...
(12 - 2) = 10
(6 + 4) = 10
And since 10 / 10 = 1
The answer to the fraction simplification is 1.
The solution of the expression would be 47/3.
Given that,
The expression is,
[tex]12 - \dfrac{2}{6} + 4[/tex]
Now simplify the expression by applying the BODMAS rule,
[tex]12 - \dfrac{2}{6} + 4[/tex]
[tex]12 - \dfrac{1}{3} + 4[/tex]
[tex]16 - \dfrac{1}{3}[/tex]
[tex]\dfrac{(48 - 1)}{3}[/tex]
[tex]\dfrac{47}{3}[/tex]
Therefore, the solution of the expression is 47/3.
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a sporting event coordinator has 200 mini foam fingers she gives 2 foam fingers to each student in attendance. there are 26 left. how many students are in attendance?
thank u <3
The total number of students which are there in the sporting events are 87.
The total number of mini foam fingers which the sporting event coordinator has is 200. Since he gives 2 foam fingers to each student present in the event therefore each student has 1 pair of mini foam fingers.
So, in total there are 200/2 = 100 pairs of mini foam fingers.
The total number of mini foam fingers left after distribution is equal to 26.
So total pairs of mini foam fingers left = 26/2 = 13
Therefore, the number of students which are present in attendance is given by:
Total pairs of foam fingers - total pairs of foam fingers left
=> 100-13 = 87
Therefore, total number of students in attendance are 87.
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Find the volume of a cube with a side that measures 0.01 cm. (Hint: V = s ³).
Answer: V=[tex]\frac{1}{1000000}[/tex] cm^3
Step-by-step explanation:
V = s³
V = (0.01)³
V=(1/100)³
V=[tex]\frac{1}{1000000}[/tex] cm^3
the volume of cube with a side that measures 0.01 cm is answer v = a3
what's the answer? It's difficult to understand and my teacher doesn't really teach.
Step-by-step explanation:
So for questions 1 through 4, you're basically finding the number in the middle of the two letters. In question 1, D is above 7 on the number line and E is above 11. The mid-point would be 9.
For 5 and 6, we'll be using this formula: [tex](\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2})[/tex]
And now we just plug in the numbers from question 5 but it works the same way on 6 as well.
[tex](\frac{3 + 5}{2},\frac{1 + 3}{2})[/tex] => (8/2, 4/2)
Coordinate of the midpoint would be (4, 2).
Lastly, we follow this system in order to get the final answers:
(Answer below shown for question 7)
(x + 2)/2 = 5
x + 2 = 10
x = 8
(y + 0)/2 = 2
y + 0 = 4
y = 4
Missing endpoint is (8, 4)
4 plus 10 plus 12 plus 7
Answer:
33
Step-by-step explanation:
4+10+12+7
When applying PEMDAS, always work from left to right. True or False?
Answer:
False
Step-by-step explanation:
Sometimes, multiplication can occur after addition. For example, in 3+4*7, you don't add 3 and 4 first. You multiply 4 and 7 first since that's following the PEMDAS rule. After multiplying 4 and 7, then you add 3 to get a total of 31. ==> 3+4*7=3+28=31.
median and mode of 4.3,4.5,4.2,5
Check the picture below.
What is 0.29 as a fraction in simplest form ?
Answer:
Step-by-step explanation:
0.29 as a fraction is 29/100. Anytime you have a decimal, just turn it into a whole number and simplify it. However, 29/100 is already in its simplest form.
I need help with both of these
Answer:
i think the first one is C and second one is C
Step-by-step explanation:
the second one is a whole number because the square root of 49 is 7 and 7 is a whole.
Pls help I’m gonna fail
Answer:
3. w = 4
4 . g = 8
5. q = 1
6. m = -3
7. z = -32
8. a = 6
9. h = 4
10. d = -16
11. y = 4
12. n = 4
13. v = 3
14. c = -2
Step-by-step explanation:
3). 3w + 7 = 19
3w = 12
w = 4
4). 2g - 13 = 3
2g = 16
g = 8
5). 11 = 12 - q
q + 11 = 12
q = 1
6). 10 = 7 - m
m + 10 = 7
m = -3
7). -4 * (5) = (z/-4 - 3) * -4
-20 = z + 12
z = -32
8). 3 * (a/3 + 4) = (6) * 3
a + 12 = 18
a = 6
9). 5 * ((h + 6)/5) = (2) * 5
h + 6 = 10
h = 4
10). -2 * ((d - 8)/-2) = (12) * -2
d - 8 = -24
d = -16
11). 8y + 3y = 44
11y = 44
y = 4
12). 36 = 13n - 4n
36 = 9n
n = 4
13). 12v + 10v + 14 = 80
22v + 14 = 80
22v = 66
v = 3
14). 6c - 8 - 2c = -16
4c - 8 = -16
4c = -8
c = -2
You're welcomeA painting service charges $65 for a project in addition to $11 per hour. if they charge you a total of $263, how many hours did it take to complete the project?
Answer:
18 hours.
Step-by-step explanation:
Subtract $65 from the total.
263 - 65 = 198
Divide by 11.
198 ÷ 11 = 18
Answer:
18 hours
Step-by-step explanation:
$263-$65=$198
$198÷$11=18 hours
Find the mode(s) for the given sample data. (if there are more than one, enter the largest value for credit. if there is no mode, enter 0 for credit.) 42, 25, 86, 30, 25, 15, 42, 42
For the given sample data, 42, 25, 86, 30, 25, 15, 42, 42, the mode is 42.
In statistics, the mode, denoted by Mo, refers to the most frequent value or values in the data set. If all the numbers in the data set appears only once, then the data set has no mode.
For the given sample data,
42, 25, 86, 30, 25, 15, 42, 42
the number 42 appears thrice, 25 appears twice and the rest appears only once.
The number 42 appeared the most frequent among all the other data.
Hence, the mode of the data set that contains 42, 25, 86, 30, 25, 15, 42, 42 is 42.
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A. Find the GCMF of each pair of monomials 1. 4x and 10xy
Write two numbers so that the value of the digit 9 in the second number is 10 times the value of the digit 9 in the first number?
The two numbers with the value of 9 in the first digit being 10 times the value of 9 in the second digit are 98 and 9.
What are the two numbers?The first number will be 9 and the second number will be 98.
In the second number, the 9 is in the tens position which means that it has the value of 90.
In the first number, the value of 9 is simply 9.
90 is 10 times the value of 9 which means that 9 and 98 satisfy the requirements.
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