On solving the provided question, we can say that - here in the slope intercept [tex]2y / 2 = -4x /2 + 24 / 2 = > y = -2x + 12\\[/tex]
what is slope intercept?The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.
y = mx + c
m = slope, c = y-intercept
[tex]4x + 2y = 24\\2y = -4x + 24\\2y / 2 = -4x /2 + 24 / 2\\y = -2x + 12\\[/tex]
To know more about slope intercept visit:
https://brainly.com/question/19824331
#SPJ1
Imagine a box with an ant at one corner. The ant wants to travel to the opposite corner by the most direct path. It must travel across the top of box at some stage. The top of the box is the light area. It cannot travel along the ground or under the box. (Hint : it does not have to travel along an edge)
The solution is Option A.
The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the shortest distance be represented as X
Let the first triangle be the first face of the rectangular box ΔABC
The length of the triangle AB = 3 cm
The height of the triangle BC = 2 cm
Now ,
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
The measure of AC = √ ( 3² + 2² )
The measure of AC = √13 cm
And , the second triangle is the second face of the rectangular box ΔDEF
The length of the triangle DE = 4 cm
The height of the triangle EF = 2 cm
The measure of DF = √ ( 4² + 2² )
The measure of DF = √18 cm
Now , the shortest distance X = The measure of AC + measure of DF
Substituting the values in the equation , we get
The shortest distance X = √13 cm + √18 cm
The shortest distance X = 3.60 + 4.24
The shortest distance X = 7.8 cm
Therefore , the value of A is 7.8 cm
Hence , the shortest distance for the ant is 7.8 cm
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ1
Can someone answers this
Answer: ( see image )
Step-by-step explanation:
A 3-gallon container of disinfectant costs $36.24. What is the price per quart?
Answer:
10.74666666666667 per quart
Step-by-step explanation3 divided 36.24
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
The three statements that are always true regarding this diagram are:
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Here's why:
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.
The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.
Step-by-step explanation:
Suppose that R, S and T are digits and that N is the four-digit positive integer
8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones
(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the
following conditions are all true:
• The two-digit integer 8R is divisible by 3.
• The three-digit integer 8RS is divisible by 4.
The four-digit integer 8RST is divisible by 5.
The digits of N are not necessarily all different.
The number of possible values for the integer N is
(A) 8
(B) 16
(C) 12
(D) 10
87
(E) 14
Answer:
8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones
(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the
following conditions are all true:
• The two-digit integer 8R is divisible by 3.
• The three-digit integer 8RS is divisible by 4.
The four-digit integer 8RST is divisible by 5.
The digits of N are not necessarily all different.
The number of possible values for the integer N is
(A) 8
(B) 16
(C) 12
(D) 10
87
(E) 14
Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.
Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.
Since 8RST is divisible by 5, T must be 0 or 5.
The possible values for N are therefore:
8000 + 300 + 00 + 0 = 8300
8000 + 600 + 00 + 0 = 8600
8000 + 900 + 00 + 0 = 8900
8000 + 300 + 20 + 0 = 8320
8000 + 600 + 20 + 0 = 8620
8000 + 900 + 20 + 0 = 8920
8000 + 300 + 40 + 0 = 8340
8000 + 600 + 40 + 0 = 8640
8000 + 900 + 40 + 0 = 8940
8000 + 300 + 60 + 0 = 8360
8000 + 600 + 60 + 0 = 8660
8000 + 900 + 60 + 0 = 8960
8000 + 300 + 80 + 0 = 8380
8000 + 600 + 80 + 0 = 8680
8000 + 900 + 80 + 0 = 8980
8000 + 300 + 00 + 5 = 8305
8000 + 600 + 00 + 5 = 8605
8000 + 900 + 00 + 5 = 8905
8000 + 300 + 20 + 5 = 8325
8000 + 600 + 20 + 5 = 8625
8000 + 900 + 20 + 5 = 8925
8000 + 300 + 40 + 5 = 8345
8000 + 600 + 40 + 5 = 8645
8000 + 900 + 40 + 5 = 8945
8000 + 300 + 60 + 5 = 8365
8000 + 600 + 60 + 5 = 8665
8000 + 900 + 60 + 5 = 8965
8000 + 300 + 80 + 5 = 8385
8000 + 600 + 80 + 5 = 8685
8000 + 900 + 80 + 5 = 8985
There are a total of 30 possible values for N. The answer is therefore (E) 14.
Step-by-step explanation:
The minute hand of a clock is 7 minutes. How far does the tip of the minute hand move in 50 minutes?
The distance that the minute hand moves in 50 minutes, given that it started at 7 minutes, is 258 degrees.
How to find the distance moved ?A rotatation around the clock by the minute hand, is a full 360 degrees as it begins at 12 and ends at 12 .
If a minute hand is at 7 minutes, then it means that the degrees moved is:
= 7 / 60 x 360
= 42 degrees
At 50 minutes, the degrees moved is :
= 50 / 60 x 360
= 300 degrees
Seeing as the minute hand started at 7 minutes, the distance moved is :
= 300 - 42
= 258 degrees
Find out more on minute hand at https://brainly.com/question/17106527
#SPJ1
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 9 14
Not in Physics 24 2 26
Total 29 11 40
it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both using principle of inclusion-exclusion we can say 38 students are enrolled in either algebra or physics.
How to find the number of students enrolled in either algebra or physics?To find how many students are enrolled in either algebra or physics, you can use the principle of inclusion-exclusion, which states that the total number of elements in two sets can be found by adding the number of elements in each set and then subtracting the number of elements that are in both sets.
So, the number of students enrolled in either algebra or physics is:
29 (students enrolled in algebra) + 14 (students enrolled in physics) - 5 (students enrolled in both) = 38
So, 38 students are enrolled in either algebra or physics.
It is important to notice that in the table you provided is a two-way frequency table also known as a contingency table, it shows the relationship between two variables, in this case, Algebra and Physics and the frequencies of each combination.
To learn more about principle of inclusion-exclusion visit:
https://brainly.com/question/27975057
#SPJ1
Which is not a factor pair of 300
Answer:
Step-by-step explanation:
So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. [Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300.
I need help with this!
To prevent deer from running across highways, researchers are investigating sound-emitting devices that would frighten deer before they reach the highway. As part of the investigation, the researchers set up 20 devices along a two-mile stretch of road. When a deer approached a device, the device would activate and emit a sound. The researchers recorded whether the deer moved toward the highway (positive response), away from the highway (negative response), or did not move (neutral response).
The researchers kept the loudness of the sound constant at 60 decibels. However, they varied the pitch of the sound. There were 6 treatment levels, all measured in kilohertz (kHz): 0, 0.28, 1, 8, 15, and 28. The order of the treatments was randomly assigned.
(a) The control in the experiment was 0 kHz, or no sound. What information is gained by using the control with no sound that could not be obtained if no control were used?
(b)(i) What is one advantage to keeping the loudness at a constant 60 decibels for all treatments?
(b)(ii) What is one disadvantage to keeping the loudness at a constant 60 decibels for all treatments?
(c) The results of the experiment are shown in the following bar chart.
Based on the results, would you recommend using a sound-emitting device to keep deer from running across highways? Explain your answer.
Answer: a) The control in the experiment, 0 kHz, or no sound, serves as a baseline against which to compare the other treatments. By using the control with no sound, researchers can determine whether the deer's response to the sound-emitting devices is due to the sound itself or some other factor. Without the control, it would be unclear what caused any differences in the deer's responses to the different sound treatments.
(b)(i) One advantage to keeping the loudness at a constant 60 decibels for all treatments is that it allows researchers to directly compare the deer's responses to the different sound pitches without the added variable of loudness.
(b)(ii) One disadvantage to keeping the loudness at a constant 60 decibels for all treatments is that loudness may also play a role in deer's response. So, it would be unclear if the different in deer's responses are due to sound frequency only or also caused by sound loudness
(c) Based on the results shown in the bar chart, it can be seen that the deer's response to the sound-emitting devices varies depending on the pitch of the sound. At lower pitches, around 0.28 kHz, the deer's response is more likely to be negative or neutral, indicating that they move away from or don't move towards the highway. At higher pitches, around 15 kHz, the deer's response is more likely to be positive, indicating that they move towards the highway. It suggests that the frequency of sound has an impact on the deer's response. So, based on this data, we cannot recommend using a sound-emitting device to keep deer from running across highways without further research on the optimal frequency and loudness that should be used to make sure that it is effective and safe for the deer.
Step-by-step explanation:
The sound-emitting device may have both advantages and disadvantages depending on the pitch. More research is necessary to find the optimal frequency and volume for the device to be effective and safe.
Explanation:Based on the results of the experiment, it would not be advisable to use a sound-emitting device to prevent deer from running across highways without further research. The experiment showed that the deer's response varied depending on the pitch of the sound. Although the device showed some advantages, such as moving deer away from the highway at lower pitches, it also presented potential disadvantages. At higher pitches, the deer had a tendency to move towards the highway, which could increase the risk of accidents. More research would be needed to determine the optimal frequency and volume to use for the device to be both effective and safe for the deer.
Learn more about Sound-emitting devices here:https://brainly.com/question/3788707
#SPJ2
5. Mariel volunteers at the
animal shelter 3 times a month.
After 6 months, how many
times has she volunteered at
the animal shelter?
Find the common difference of the arithmetic sequence − 19 , − 11 , − 3
Answer:
+ 8
Step-by-step explanation:
This is an arithmetic progression (AP) as there is a common difference between successive terms.
For example, looking at the first two terms,
Difference = 2nd term - 1st term
= -11 -(-19)
= -11 + 19
= +8
To check,
Looking at the second and third terms,
Difference = 3rd term - 2nd term
= -3 -(-11)
= -3 + 11
= +8
Hence, there is a common difference of +8 between consecutive terms, making it an AP.
PLEASEEEE HELP MEE WITH THIS EQUATION
Answer:
Basically, LON would be 8z + 112 + 6z - 17
So, our equation will look like this
8z + 112 + 6z - 17 = -1z + 65
Subtract the 6z from the 8z
2z + 112 - 17 = -1z + 65
112 - 17 = 95
2z + 95 = -1z + 65
add the 1z
3z + 95 = 65
subtract the 95
-30
3z = -30
The answer is -10 :)
Step-by-step explanation:
Answer:
LON=75
Step-by-step explanation:
LON= LOM=NOM
-1z+65=8z+112-6z-17
-1z+65=2z+95
3z=-30
z=-10
LON= -1z+65
= -1(-10)+65
= 10+65
LON= 75
Josh and Diego are comparing how much candy they have. Josh has five boxes and fifteen loose candies. Diego has six
boxes and three loose candies. However, they each have the same total amount of candy. If there are the same number of
candies in each box, how many pieces are in a box?
3. Equation:
4. Number of pieces in each box:
The solution of given algebra question is-The number of candies in each box is 12.
What are the Algebra Basics?In algebra, the fundamental concepts are numbers, parameters, constants, expressions, coefficients, linear equations, and quadratic equations. Additionally, it requires adding, subtracting, multiplying, and dividing basic arithmetic operations within the algebraic formulas.
What is the algebraic first rule?Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.
According to given information:Let the number of candies in the box be x
Total candies with Josh=5x+15
Total candies with Diego=6x+3
Since, they have same number of candies,
Hence,
5x+15=6x+3
6x-5x=15-3
x=12
To know more about algebra visit:-
brainly.com/question/24875240
#SPJ1
Round 0.265625 to the nearest hundredth
Answer:
0.27 is the answer
I wish you luck in your assignments.
Answer:
Step-by-step explanation:
0.27
LMNP is a rectangle. Find the value of x and the length of each diagonal. LN=x and MP=4x-6
Answer: x = 2.
LN = MP = 2.
Solution in the photo, below.
Which graphs show continuous data?
Select each correct answer.
HELP ME PLEASE!!!
Answer: the bottom two graphs show continuous data
Step-by-step explanation:
A netball court measures 31 metres long and 15 metres wide.
What is the perimeter of a netball court?
The perimeter of the netball court is equal to 92 meters.
What does perimeter mean?
The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline.
A netball court is a rectangle,
it is given that length of the net ball court is equal to 31 meters.
The width of the netball court is equal to 15 meters.
Therefore the perimeter of the netball court is equal to the length of all sides of the rectangle.
Perimeter of netball court = 2(31+15)=92 meters.
Therefore perimeter of the netball court is equal to 92 meters.
To learn more about perimeter, refer to the link below:
https://brainly.com/question/397857
#SPJ1
Between 2020 and 2021, the population of a town decreased by 35%
In 2021, the population of the town was 94 900. What was the population of the town in 2020?
Answer:
Step-by-step explanation:
if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.
so, we do the rule of three:
x = (94900 * 100)/ 65
x = 146000
and that is the population in 2020.
Answer:
Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?
PLEASE HELP ME ASAP
Select all the key features of the graph of the equation.
The key features of the graph of the given equation -8x + 20y = 240 include the following:
D. As x → -∞, y → ∞.
E. The y-intercept is (0, 12).
H. The x-intercept is (-30, 0).
How to determine the key features of this equation?Making y the subject of formula in order to determine the slope, we have:
20y = 8x + 240
Dividing both sides of the equation, we have:
y = 8x/20 + 240/20
y = 8x/20 + 12
Therefore, the slope is equal to 8/20.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
When x = 0, the y-intercept is given by;
20y = 8(0) + 240
y = 240/20
y = 12.
Therefore, the y-intercept is equal to (0, 12).
When y = 0, the x-intercept is given by;
-8x + 20(0) = 240
x = -240/8
x = -30
A condominium owner pays property taxes of $2,000 per year. If taxes are figured
at a rate of $1.25 for every $100 in value, what is the value of his condominium?
Step-by-step explanation:
the tax rate gives us a ratio of tax amount to value.
this ratio (in our case 1.25/100) is constant for any value.
therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.
in other words, we multiply
1.25/100 × f/f
so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.
f = 2000 / 1.25 = 1600
so, we get
1.25/100 × 1600/1600 = 2000 / 160000
so, the value of the condominium is
value = $160,000
evaluate the expression when m=8 and n = 37
Answer:
31Step-by-step explanation:
[tex]\sf 37-\cfrac{48}{8}[/tex]
Divide numbers ( 48/8 = 6)
[tex]\sf 37-6[/tex]Subtract numbers:-
[tex]\sf 31[/tex]31 is your answer!
___________________
Hope this helps!
Have a great day!
Sketch the Asymptotes and graph the function.
the quadratic equation have been solved and the required graph is attached below.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation:
[tex]\frac{x^{2}-7x+12 }{x^{2} -1}[/tex]
Its a quadratic equation in both numerator and denominator, by dividing the x² will be get a graph as given in the attached file.
Hence, the quadratic equation will be solved and the required graph is attached below.
Learn more about quadratic equations, by the following link.
brainly.com/question/1214333
#SPJ1
Which statement is true based on a graph of the line that passes through the given coordinates? (2, 1), (3,3), (5,7), (6,9) Please help
A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
D. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
The correct statement regarding the linear function passing through the coordinates (2, 1), (3,3), (5,7), (6,9) is given as follows:
A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
When does a linear function represents a proportional relationship?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the change in y divided by the change in x.b is the y-intercept, representing the value of y when x = 0.A linear function represents a proportional relationship if it has an intercept of zero.
For the points in this problem, when x increases by one, y increases by two, hence the slope is given as follows:
m = 2/1 = 2.
Hence:
y = 2x + b.
When x = 2, y = 1, hence the intercept b is given as follows:
1 = 2 + b
b = -1.
As the intercept is different of zero, this is not a proportional relationship, and option A is correct.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Given that the polynomial x² - 10x + 14 leaves the same remainder when divided by x + 2b orx + 2c where 3b - 2c = 0 and b # c . Find the values of b and c.
Step-by-step explanation:
please refer to the 3 pages of sketch for details
The average number of customers at the cafe fell by 10% in the month of May. If 140 fewer customers visited the cafe in May, how many customers visited in April?
Answer:
1400
Step-by-step explanation:
You want to know the number of customers in April if the number in May was 10% lower. That number was 140 fewer.
PercentThe problem statement is telling us ...
April - (10% × April) = April - 140
10% × April = 140 . . . . . . . . subtract April, multiply by -1
April = 140/10% = 1400 . . . . divide by 10%
The number of customer visits in April was 1400.
__
Additional comment
The 1400 customers in April fell by 140 to 1260 in may. That's 10% fewer than in April.
<95141404393>
the fraction 3/5 fits into 2 1/5 less than more than 1 time
Answer:
Q = 3.667
Step-by-step explanation:
10. What is a composition of rigid motions and a dilation that maps APZY onto ARST
I’m confused on this subject please explain to me how you got an answer thank you
Answer:
dilation by a factor of 1/2reflection over the line y = -xStep-by-step explanation:
You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.
DilationFirst of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.
The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...
k = RS/PZ
Counting grid squares in the figure, we see this ratio is ...
k = 2/4 = 1/2
Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.
Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.
ReflectionWhen we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.
The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.
We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.
Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.
This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.
__
RotationIf we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.
So, another sequence of transformation that will make the required mapping is ...
dilation by a factor of 1/2reflection across the y-axisrotation 90° CCWThe order of reflection and rotation is important. The dilation can occur anywhere in the sequence.
Alternate solutionPerhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...
dilation by a factor of 1/2reflection across the x-axisrotation 90° CWIf you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.
__
Additional comment
Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.
Tracing paper and/or transparencies can be helpful for these exercises.
Helen draws a random circle, she then measures the circumference and diameter.
She gets a circumference C of 405mm correct to 2 significant figures
She gets a diameter D of 130mm correct to 2 significant figures
Helen wants to find the value of [tex]\pi[/tex] using the formula [tex]\pi[/tex] = C÷D
Calculate the lower and upper bound for Helens value of [tex]\pi[/tex]
Give your answer correct to 3 decimal places
The value of π can be written with upper and lower limits as -
3.12 ± 0.062.
What are significant figures?Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.
We can write -
Circumference {C} = (405 ± 2) mm
Diameter {D} = (130 ± 2) mm
The value of π can be calculated as -
π = {C}/{D}
π = (405 ± 2)/(130 ± 2)
Now, divide the numbers without errors first -
405/130
3.12
Now, we will calculate the relative errors in each number -
2/405 = 0.004
2/130 = 0.016
Adding the relative errors -
0.004 + 0.016
0.02
Absolute error = 0.02 x 3.12 = 0.062
The value of π can be written with upper and lower limits as -
3.12 ± 0.062
Therefore, the value of π can be written with upper and lower limits as -
3.12 ± 0.062.
To solve more questions on significant figures, visit the link below -
https://brainly.com/question/13263124
#SPJ1
Simplify: -20z^8+ (-2z^8)
Enter the original expression if it cannot be
simplified.
Therefore , the solution of the given problem of expression comes out to be 22[tex]z^{8}[/tex].
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : -20[tex]z^{8}[/tex]+ (-2[tex]z^{8}[/tex])
=> -22[tex]z^{8}[/tex]
So ,
In order to find the solution we add them
Thus ,
simplification of given expression is:
=> - 22[tex]z^{8}[/tex]
Therefore , the solution of the given problem of expression comes out to be 22[tex]z^{8}[/tex].
To know more about expression , visit
https://brainly.com/question/14083225
#SPJ1