The distance between the pair of points X(-2,5) and Y(1,11) is [tex]\sqrt{45}[/tex] units.
We can find the distance between the points X and Y by using distance formula.
The distance formula is used to find the distance between two defined points on a graph (in the absence of a scale).
Here the two points are X(-2,5) and Y(1,11).
The distance formula for points (a,b) and (c,d) is given by :-[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]
Here,
(a,b) represents the point X(-2,5), and
(c,d) represents the point Y(1,11)
Putting the values of (a,b) and (c,d) in the distance formula, we get,
[tex]\sqrt{(11-5)^2+(1-(-2))^2}[/tex]
[tex]\sqrt{6^2+3^2} \\ \sqrt{36+9}\\ \sqrt{45}[/tex]
Hence, the distance is [tex]\sqrt{45}[/tex] units.
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The number 6 comma 107 comma 200 can be expressed using scientific notation as ________.
The number 6 comma 107 comma 200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex].
Scientific notation is used to represent a very large number or a very small number in Simple way.
Steps to find scientific Notation of a number
Step (i) Move the decimal point until a number between 1 and 10 is created.
Step (ii) Count the number of times the decimal is moved .
Step (iii) If the decimal is moved n times then multiply the term by n times of 10.
In the given question
the number 6107200.
Step (i) We will move the decimal 6 place towards left.
number becomes 6.107200
Step (ii) The decimal is moved 6 place towards left.
Step (iii) we will multiply by [tex]10^{6}[/tex].
[tex]=6.1072*1000000[/tex]
So , the number becomes [tex]6.1072*10^{6}[/tex]
Therefore , the number 6107200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex]
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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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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.
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
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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Find the geometric mean between pair of numbers. 4√3 and 10√3
The geometric mean between pair of numbers 4√3 and 10√3 is 10.95
We know that for a sequence of numbers x1, x2, . . . , xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers 4√3 and 10√3
We need to find the geometric mean between pair of numbers, 4√3 and 10√3.
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{4\sqrt{3}\times 10\sqrt{3} } \\\\\Pi=\sqrt{4\times 10 \times \sqrt{3}\times \sqrt{3} } \\\\\Pi=\sqrt{40 \times 3 } \\\\\Pi=\sqrt{120}\\\\ \Pi=2\sqrt{30}\\\\\Pi=10.95[/tex]
Therefore, the geometric mean between pair of numbers 4√3 and 10√3 is 10.95
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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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(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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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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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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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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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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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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help i have to do this in likee 7 days
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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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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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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Kara is standing about 50 feet from the base of her apartment building, looking up at it with an angle of elevation of 75^{\circ} . What is the approximate height of Kara's building?
When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. The height of Kara's building is 186.6 ft.
What is meant by height?In math, height can be defined as the vertical distance from the top to the base of the object. Height is the distance between an object's highest and lowest points.
The measurement of an object's height from the base to the top is known as the height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.
Mount Everest's summit serves as an illustration of height.
Ignoring the height of Kara,
h = 50 tan 75°
substituting the value of tan 75°, we get
= 50 × 3.7321
Height of building = 186.6 ft.
Therefore, the approximate height of Kara's building is 186.6 ft.
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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.
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 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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how many positive integers are bigger than -3 and smaller than 5?
Answer:
4
Step-by-step explanation:
1,2,3,4
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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solve this please and thank you
Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. When the frisbee is thrown, it follows a parabolic path that is modeled by the function h(t) = â€" 0. 145t2 0. 019t 5. 5. How many seconds will it take for the frisbee to hit the ground?
If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of seconds it will take for the frisbee to hit the ground is: 6.2 seconds.
Number of secondsGiven:
0.145t² + 0.019t + 5.5 = 0
Using almighty formula or quadratic formula
t=-b±√b²-4ac/2a
Where:
b²=19²
a=145
c=5500
Let plug in the formula
t=-19±√19²- 4(-145) (5500)/2(-145)
t=-19±√361+(3,190,000)/-290
t=-19±√3,190,361/-290
t=-19±1,786.158/-290
Hence,
-19-1,786.158/-290; -19+1,786.158/-290
t=6.2; 6.09
Therefore If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of seconds it will take for the frisbee to hit the ground is: 6.2 seconds.
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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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Which of the following expressions have the same value as the mixed number ( ), select ALL correct answers.
Answer:
C,D, and E
Step-by-step explanation:
-29/4 is an improper fraction version of -7 1/4
-7- 1/4 = -7 1/4
-(7 + 1/4) is -29/4
Just make -29/4 into a mixed number, which is -7 1/4
Answer:
Step-by-step explanation: the answer is the last 3 ones because if you add them together, you get -7 1/4. Remember that -(number) = -1(number). So, -(1) = -1(1).
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!
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:
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We have to simplify by factorizing
How to solve it
