Answer:
-2
Step-by-step explanation:
Slope = rise/run
[tex]\mathrm{Slope} = \frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-5}{4-2}\\1 - 5 = -4\\4 - 2 = 2\\=\frac{-4}{2}\\ =-2[/tex]
Simplify by combining like terms. 3 a+b+a
The simplification by combining like terms of 3a + b + a is 4a + b.
According to the given question.
We have an expression 3a + b + a.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 3a + b + a.
Here 3a and a both are the like terms.
So, we add coeffcients of a to simplify the given expression.
Therefore, the simplification of 3a + b + a is given by
3a + b + a
= 3a + a + b
= 4a + b
Hence, the simplification by combining like terms of 3a + b + a is 4a + b.
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Find the approximate circumference of a circle with a diameter of 6 inches. Use 3.14
as an estimate of 77 that is correct to two decimal places.
O A. C = 18.84 in
OB. C≈ 20.46 in
C. C 18.84 in
OD. C≈ 18.84954 in
The correct option is (C) 18.84 in. The circumference of the circle with a diameter 6 in is 18.84 in.
What is the circumference of a circle?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
Given, the diameter of the circle = 6 in.
The radius of a circle is calculated as
r = d / 2
r = 6 / 2
r = 3 in
The circumference of a circle is calculated as
C = 2πr
Substitute r = 3 in the circumference formula
=2 × 3.14 × 3
= 6 × 3.14
= 18.84 in
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The circumference of the given circle with a diameter of 6in is 18.84in.
What do we mean by the circumference of the circle?The circumference of a circle is known as its perimeter. It is the circumference of the entire circle. The circumference of a circle is calculated by multiplying its diameter by the constant. This diameter measurement is required for anyone crossing a circular park or enclosing a circle. Circumference, which is a linear variable, is measured in the same units as length.So, the diameter is 6in.
Then, the radius is:
r = d / 2r = 6 / 2r = 3 inThe formula for the circumference of the circle: 2πr
Now, substitute 'r = 3' in the formula of circumference as follows:
= 2 × 3.14 × 3= 6 × 3.14= 18.84 inTherefore, (C) 18.84 is the circumference of the given circle.
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Pls pls help whoever gets it right gets a crown
Answer:
Step-by-step explanation:
A. The common factor of the expression is 5[tex]x^{3}[/tex]y
B. In order to find a common factor, you find the prime factor. In this case, the biggest number that goes evenly into 40 and 25 is 5.
C. Divide the original problem by the common factor 5[tex]x^{3}[/tex]y
that gives you 5[tex]x^{3}[/tex]y(8x[tex]y^{2}[/tex]-5)
Hope this helps!
Using the diagram above, how many lines are located on plane A? Group of answer choices 8 6 12 4
The number of lines located on plane A using the given diagram are 4.
As given in the question,
Number of lines located on plane A are as follow:
Point outside the plane A are T, W, S
Points located on plane A are as follow:
V, M, N, P
Lines formed by located points V, M, N, P on plane A
VM, VN, VP and MP
Therefore, number of lines located on plane A using the given diagram are 4.
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If your tire says P235/65R17, what is the diameter of your wheel? (Note: this should include the tire and the rim).
If the tire says P235/65R17, the diameter of your wheel will be 17 inches.
How to illustrate the information?The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.
It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.
It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.
In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.
In conclusion, it is 17 inches.
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Add or subtract. Simplify where possible. 4 / x²-36 + x / x-6
Add or subtract.Simplify where possible.
[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6}[/tex] = [tex]\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]
How the given expression is simplified?
[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6} \\\\\text{On taking LCM of the denominator}\\\\\frac{4}{x^{2}-36} +\frac{x^{2}+6x }{x^{2}-36}\\\\\frac{4+x^{2}+6x}{x^{2}-36}\\\\\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]
What is simplification?
A mathematical expression is simplified when it is expressed in the simplest way possible.Generally, the simplest form is one that makes use of basic mathematical concepts like exponents, algebraic principles, and so forth.Its goal is to simplify the expression by getting rid of any repetition or redundancy.To learn more about simplification, refer:
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-4(x + 7) + 2(2 + x) = -20
Answer:
x = -2
Step-by-step explanation:
Step 1: Distribute
-4(x + 7) + 2(2 + x) = -20 ----> -4x-28 + 4+2x=-20
Step 2: Combine Like Terms
-4x-28+4+2x=-20 ----> -2x-24=-20 ----> -2x=4
Step 3: Divide both sides by -2, solving for x.
-2x=4 ----> -2/-2x = 4/-2 ----> x = -2
(Laws of Exponents with Whole Number Exponents MC)
Evaluate one third raised to the seventh power divided by one third raised to the sixth power comma all raised to the second power.
one eighteenth
one ninth
1
one and one ninth
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
The given expression is [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}[/tex].
We need to evaluate the given expression.
What are the laws of exponents?Laws of exponents:
When multiplying like bases, keep the base the same and add the exponents. When raising a base with power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.Now, [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}=((\frac{1}{3})^{7-6})^{2}[/tex] (Because [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex])
[tex]=(\frac{1}{3})^{2}[/tex]
=1/9
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
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You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per
minute. The second plan charges a monthly fee of $44.95 plus 8 cents per minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first and second
plans. Give an equation for each in terms of t, and then find the number of talk minutes that would
produce the same cost for both plans (Round your answer to one decimal place).
Answer:
257757
Step-by-step explanation:
Answer:
300 minutes 0.23c1=44.95+0.08c2
Step-by-step explanation:
The cost of Jake's cell phone bill is determined by how many megabytes of
data he uses each month, as shown in the graph below.
Jake's Cell Phone Bill
70
60
50
40
30
20
10
0
5
10
Data Usage (megabytes)
A. y = 0.5x + 40
B. y = 2x + 40
C. y 40x + 0.5
D. y = 40x + 2
15
X
Which equation represents the cost of Jake's cell phone bill, y, based on his
data usage in megabytes, x?
Step-by-step explanation:
Given that
The cost of Jake's cell phone bill is determined by how many megabytes of data he uses each monthas shown in the graphTo find
Which equation represents the cost of Jake's cell phone bill, y, based on his data usage in megabytes, x?So, according to the question
we have,
The co-ordinates of that line, from graph(0,40) and (15,70)
We have to find the equation of line
So, we know that
The equation of liney = mx + c, ---------------(1)
From graph,
c = 40 and
m = slope (we have to find it)
We kwon the slope of any two point
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where,
x₁ = 0 , and y₁ = 40
x₂ = 0 , and y₂ = 40
So,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{70-40}{15-0}[/tex]
m = [tex]\frac{30}{15}[/tex]
m = 2
Now putting the all values in equation (1)
We will get,
y = mx + c, ---------------(1)
y = 2x + 40
Answer:
The equation of line is y = 2x + 40. So option B is correct.To learn more about equation of line, please click on the link:
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help i have to do this in likee 7 days
Write a recursive definition for each sequence. 5,22,39,56, . . . . .
This sequence follows the rules of Arithmetic Progression
Arithmetic Progression is an example of mathematical sequences. In this sequence, the next term is generated by adding the previous term to a fixed number which is called 'Common Difference'. This is generally represented by 'd'. It is calculated by subtracting any two consecutive terms in the sequence.
We can generally find out any term of the given statement. The [tex]n^{th}[/tex] term of a sequence is calculated by adding the previous term to the common difference. The formula to calculate the [tex]n^{th}[/tex] term of an Arithmetic Progression is :
=> [tex]a_{n} = a_{n-1} + d[/tex]
Here, n = No. of term, [tex]a_{n-1}[/tex] = previous term, and d = common difference
In the given sequence, 5,22,39,56......
Each term is separated by a common difference 'd'
Calculating d = a2-a1 => d = 22-5 => d = 17
Every term has a common difference of 17 so this is an Arithmetic Sequence
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The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
2 seconds
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object falls during the time 2 seconds is 64 foot
Given,
The algebraic expression off the distance in feet that an object fall= [tex]16t^{2}[/tex]
Where t is time in seconds
Here,
Time t= 2 seconds
Substitute the values in the expression
[tex]16t^{2}=16(2)^{2}[/tex]
=64 foot
Hence, if the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object falls during the time 2 seconds is 64 foot.
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Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 3,-3,3,-3, . . . . . ..
In the given sequence, the next term is obtained by multiplying the next term by (-1), hence it is a geometric sequence with r = 1. The next two terms are 3, -3.
Arithmetic sequence.
In a arithmetic sequence, the next term = the previous term + common difference. Or mathematically:
a(n) = a(n-1) + d
or d = a(n) - a(n-1) for all n
Where d = common difference.
Geometric sequence.
In a geometric sequence, the next term = the previous term x common ratio. Or mathematically:
a(n) = a(n-1) . r
or r = a(n)/a(n-1) for all n
Where r = common ratio
The sequence given:
3,-3,3,-3, . . . . .
In this sequence:
a(1) = 3
a(2) = -3
a(3) = 3
a(4) = -3
Check whether it has a common differenceThe next two terms means a(5) and a(6). We already have a(4) = -3. Hence,
a(5) = a(4) . r = -3. (-1) = 3
a(6) = a(5) . r = 3. (-1) = -3
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If A-P-B and if AP=2x-9,AB=32 and PB=1.5x+6. Find Pb
Main Answer:
The required value of PB is 21.
An equation is a mathematical statement with an equal symbol between two expressions that have equal values.
Given: If A-P-B and if AP=2x-9, AB=32, and PB=1.5x+6.
To find: Find PB.
According to the question,
AP + PB = AB
On putting the given values, we get,
(2x-9)+(1.5x+6) = 32
2x - 9 +1.5x + 6 = 32
3.5x - 3 = 32
3.5x = 32+3
3.5x= 35
x=10
Now, we will substitute the value of x=10 in the equation, we get,
PB= 1.5x+6
PB= 1.5 × 10 + 6
PB=15 + 6
PB=21
Final Answer:
The simplified value of PB = 1.5x + 6 is 21.
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Darren teaches a class of 25 students. He assigns homework 3 times a week, and each assignment consists of 12 problems. How many problems must Darren correct each week?
The number of problems which Darren must correct each week according to the task content is; 900 corrections.
How many corrections must Darren provide?Since it follows from the task content that; the class contains 25 students, each who are each given 3 assignments per week consistent of 12 problems.
On this note, the number of problems he must correct since the homework is assigned distinctly to each student, the number of problems which he must correct is;
= 25 × 12 × 3
= 900 corrections.
However, if the assignment is same for all students; the number of corrections is;
= 12 × 3 = 36 corrections.
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Question down below, answer if you know :)
Answer:
Yes, they are similar as the difference between the smaller rectangle and the larger one is a scale factor of 2.
answer:
yes
explanation:
you can tell if figures are similar (proportional side lengths with points of the same orientation), if you can divide the respective side lengths of the image and preimage together.
how many positive integers are bigger than -3 and smaller than 5?
Answer:
4
Step-by-step explanation:
1,2,3,4
In which one of the following numbers are none of the zeros significant?
a) 298.010
b) 3100
c) 0.00001470
d) 2.70400
Significant digits are all non-zero numbers. The numbers are none of the zeros significant is 3100.
What are significant figures?Significant figures in positional notation are the digits in a number that may be trusted to accurately represent how much of something there is.
Only the digits allowed by the measurement resolution are reliable, and only these can be significant figures if a measurement result is reported as a number with more digits than those allowed by the measurement resolution.
What are the rules for significant zeroes?Significant digits are all non-zero numbers. Any pair of non-zero digits that is not divided by zero is significant. Every zero that is both right and left of a non-zero digit and the decimal point has no significance. Any zeros to the right of a decimal point are only important if a non-zero digit comes after them. All the zeros to the right of the last non-zero digit after the decimal point are significant. If a measurement includes the zeros to the right of the final non-zero digit, they are all meaningful.To learn more about significant zeroes, refer to:
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Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. -1,1,-1,1,-1,1, ......
The formula for finding any term of the given sequence is [tex]a_{n}[/tex] = [tex]n^3[/tex].
According to the given question.
We have a sequence
-1,1,-1,1,-1,1....
As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
The above of given sequence -1,1,-1,1,-1,1,..... is following a rule i.e. each term is the cube of its number of term.
Here,
The first term is -1, so the cube of -1 is -1.
The second term is 1, so the cube of 1 is 1.
So, the nth term of the given sequence is [tex]n^{3}[/tex].
Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = -1,1,-1,1,-1,1, .......
So, for n = -1
The first term will be -1.
for n =1
The second term will be 1
for n= 1
The fourth term will be 1 and so on .
Hence, the formula for finding any term of the given sequence is [tex]n^3[/tex].
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write an equation for the nth term of the arithmetic sequence
5,11,17,23
The equation for the nth term of the arithmetic sequence is (6n – 1)
The given arithmetic progression is 5,11,17,23
Here we have been given
a = 5
d = a2 – a1
= 11 – 5
d = 6
The formula for the nth term is given as follows:
an = a + (n-1)d (1)
where, a = first term
d = common difference
putting the required values of ‘a’ and ‘d’ in equation (1) we get
an = 5 + (n-1)6
an = 5 + 6n – 6
an = 6n – 1
which is the required equation for the nth term of the arithmetic sequence
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Find the value of x for the given values of a and b .
\a+2 / b+13=5 x , for a=18 and b=-1
The value of x so that the equation based on a and b has a solution is x = -7/5
What is an equation?An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.
Equations can be graphed, they are used to model many problems and theories.
As we can see, we have the following equation:
(a + 2)b + 13 = 5x
and we have the values of the coefficients a and b, and these are:
a = 18b = -1We substitute these values in the equation:
(a + 2)b + 13 = 5x
(18 + 2)-1 + 13 = 5x We solve the equation
(20)-1 +13 = 5x
-20 + 13 = 5x
5x = -7
x = -7/5
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Audrey has $500 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. She buys a new bicycle for $295.33. She buys 3 bicycle reflectors for $17.86 each and a pair of bike gloves for $33.62. She plans to spend some or all of the money she has left to buy new biking outfits for $55.17 each. Which inequality can be used to determine oo, the maximum number of outfits Audrey can purchase while staying within her budget?
The inequality that can be used to determine the maximum number of outfit she can purchase is 55.17oo ≤ 117.47.
What is the inequality?The first step is to determine which inequality sign would be used.
The following are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is the less than or equal to sign- ≤ . This is because Audrey cannot spend more than her budget.
The next step is to determine the total cost of items bought:
Total cost = $295.33 + (17.86 x 3) + 33.62 = $382.53
Now determine the amount of money she has left : $500 - $382.53 = $117.47
(Total amount spent on outfit) amount left
(oo x $55.17) ≤ 117.47
55.17oo ≤ 117.47
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These are the first four terms of a sequence, -2, 1, 8, 19. Write down the next term of this sequence.
Oabc is a square o is 0,0 a is -2,2 b is 0,4 c is 2,2 A single transformation of oabc is such that A is mapped to c. C is mapped to a O and b are invariant points Describe fully transformation
Using translation concepts, it is found that the transformation is a reflection over the y-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that A is mapped to C and vice-versa. Since they are equidistant to the y-axis, we have that the rule is given by:
(x,y) -> (-x,y).
Meaning that the transformation is a reflection over the y-axis.
For O and B, the rules are given as follows:
O: (0,0) -> (-0,0) = (0,0).B: (0,4) -> (-0, 4) = (0,4).Showing that points O and B are invariant, keeping the same coordinates and confirming that the transformation is a reflection over the y-axis.
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Please help I dont get this its due soon
the temperature in stratford starts at -5ºc, rises at -18ºc then falls at -8ºc what is the final temperature
Write the equation of the line that passes through the points (6,-4) and (6,-1) Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The line that passes through the points (6,-4) and (6,-1) is:
x = 6
How to find the equation of the line?We want to find the equation of the line that passes through the points (6, -4) and (6, -1)
Now, this is really trivial, as you can see that both points have the same x-value (the x-value is the first value of each coordinate pair), which means that our line is x = constant = 6
Then we have a vertical line:
x = 6
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Find the slope of the line that contains the points (7,2) and (3,4)
According to the given statement the slop of the given points are: -(1/2).
The line's slope is described as:The slope of the line is the mathematical ratio of overall rise to the run, or rise divided by the run. It expresses the slope of a line in the coordinate plane. Calculating the slope of a line is comparable to finding the slope between two separate places.
How do I calculate the slope of an equation?The procedure for calculating the slope from such an equation will vary based on the form of the equation presented to you. If the equation is written as y=mx+c, the slope (or gradient) is simply m. If the formula does not exist in this form, try rearrangement.
According to the given information:The slope of a line is easily calculated by hand using small, whole number coordinates.
so,
X1 = 7
X2 = 3
Y1 = 2
Y2 = 4
Applying the formula for slope:
slope = (y₂ - y₁) / (x₂ - x₁)
= (4 - 2) / (3 - 7)
= 2/(-4)
= - (1/2)
The slop of the given points are: -(1/2)
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Determine whether each sequence is geometric. If so, find the common ratio. 18,-6,2,-2/3, . . . . .
Th given sequence is geometric with the common ratio being [tex]\frac{-1}{3}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given: 18, -6, 2, -2/3, ....
Here, [tex]\frac{-6}{18}=\frac{2}{-6}=\frac{\frac{-2}{3}}{2}=\frac{-1}{3}[/tex]
Since, it follows the definition of a geometric progression, the sequence is geometric.
Thus, the given sequence is geometric, having common ratio = [tex]\frac{-1}{3}[/tex].
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At Central High School, there are 60 football players and 25 cheerleaders. What is the ratio of cheerleaders to football players?
Answer: 5:12
Step-by-step explanation:
25:60
But we can simplify this down too.
25:60
5:12
