The equation for the shifted graph is y = x + 6.This equation represents the same line as the original equation, y = x + 1, but shifted up by 5 units.
Define shifting of graph?Shifting a graph involves moving it horizontally or vertically while maintaining the same shape and orientation.
To shift the graph of y = x + 1 up by 5 units, you need to add 5 to the y-coordinate of every point on the graph.
The original graph of y = x + 1 is a straight line with slope 1 and y-intercept 1.
To create the shifted graph, you can start by plotting a few points on the original graph and then adding 5 to their y-coordinates to get the corresponding points on the shifted graph.
Alternatively, you can use the general equation for a straight line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation for the shifted graph.
The slope of the original graph is 1, so the slope of the shifted graph is also 1.
To find the y-intercept of the shifted graph, you can plug in x = 0 and y = 6 (since you want the graph to pass through the point (0, 6)) and solve for b:
6 = 1(0) + b
b = 6
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On Sunday, 8 friends earned $44 by washing people's
Cars. They want to share the money equally. How much
money does each friend get?
There is 1/4 gallon of water in a 2 gallon container. What fraction of the container is filled?
1. Write a multiplication equation and a division equation to represent the situation.
Answer:
2/(1/4) = 8 1/4th gallons to fill the container and 1/8 * x = 8/8 (x=8) times you can fill the tank with 1/4th gallon
Step-by-step explanation:
First let's answer the first part of the question: what fraction of the container is filled?
If there is 1/4 a gallon of water in the container which holds 2 gallons, we can show this by adding 0/4 to 1/4 to get 1/8 as the fraction of the container filled. (Or just double the denominator for both gallons instead of 1)
To represent this with a multiplication equation, we will take the holding of the container which is 2 gallons
1/8 times x = how many times you can fill the container with 1/4 gallon of water (which is 8 total)
and then our division which is
2 divided by 1/4 = how many shares of water can fit in the container
I hope this helps :)
Find the general solution for dy/dx cosx=ysinx+sin113x
Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.
What does a differential equation in calculus mean?A differential equation explains the unknown derivative or derivatives of a function. Example: Think about the equation. The equation d y d x = x sin represents the derivative of an unknown function.
We can solve this differential equation by using separation of variables.
First, we'll rearrange the equation to isolate the y term on one side:
cos x = y sin x + sin 113x
cos x - sin 113x = y sin x
y = (cos x - sin 113x) / sin x
Now we can integrate both sides with respect to x:
∫dy = ∫(cos x - sin 113x) / sin x dx
Using integration by parts, we can integrate the second term on the right side:
∫dy = ∫cos x / sin x dx - ∫sin 113x / sin x dx
The first term on the right side can be integrated using substitution:
u = sin x, du/dx = cos x dx
∫cos x / sin x dx = ∫du/u = log |u| + C1 = log |sin x| + C1
The second term on the right side can be rewritten as:
∫sin 113x / sin x dx = - ∫sin 113x / sin 113x cos x dx
= - ∫csc x cos 113x dx
Using substitution again:
u = sin 113x, du/dx = 113 cos 113x dx
∫csc x cos 113x dx = - ∫du/u = - log |sin 113x| + C2
y = log |sin x| - log |sin 113x| + C
Simplifying:
y = log |sin(x) / sin(113x)| + C
Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.
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PLEASE THIS IS URGENT SOMEONE GAVE THE ANSWER
Answer: what's so urgent?
Step-by-step explanation:
Use an algebraic equation to find the measure of each angle that is represented in terms of x.
Answer:
5x+10° = 20°10x +50° = 70°Step-by-step explanation:
You want the measures of the angles (5x+10°) and (10x+50°) that are divisions of an angle marked as a right angle.
Angle additionThe angle addition theorem tells you the whole is the sum of its parts. Here, the right angle in the diagram is divided into two parts, marked 5x+10° and 10x+50°. The measure of the right angle is the sum of these parts:
90° = (5x +10°) +(10x +50°)
30° = 15x . . . . . . . subtract 60°
2° = x . . . . . . . . . divide by 15
Using this value for x, we find the angle measures to be ...
5x+10° = 5(2°) +10° = 10° +10° = 20°
10x+50° = 10(2°) +50° = 20° +50° = 70°
In summary, ...
5x+10° = 20°10x +50° = 70°The volume of a storage unit needs to be 400 cubic ft with a width of 10ft and a lengths of 8 ft. What does the height of the unit need to be?
Answer:
to find the height of the storage unit, we can use the formula for volume:
Volume = length x width x height
We know that the volume needs to be 400 cubic ft, the width is 10ft and the length is 8ft. So, we can plug in these values and solve for the height:
400 = 8 x 10 x height
400 = 80 x height
height = 400/80
height = 5 ft
Therefore, the height of the storage unit needs to be 5 ft.
1a)Due to the fuel scarcity in Japan the cost of a phone rises from 4500Naira to 5500 find the increment in price = (1b)Use the information above to find the percentage increase in price = (2) The discount of 10% was given to a customer and she paid 3,000Naira for an article, find the marked price = (3) 30 crates of eggs was bought by a distributor at 30 Naira each, she was given a commission of 4% on a crate. How much commission did she get ? = (4) A dealer sells articles worth 49000 Naira and get a commission of 7% calculate his commission = (5) A dealer wanted to buy an article for Naira39.28kobo,but the marketed price for the article is Naira44.48kobo. How much discount did the customer request for? = (6) A trader appealed to buy an article for 225.00Naira but the marketed price for the article is 245.00 Naira what percent of discount did the trader request for ? = (7) Am agent was given a commission of 3% on a house he sold for 33.00Naira . How much commission did the agent get ? = (8) A company increases the salary of all employees by 5% of their salaries. If an employee earns 250Naira a month what is his new salary ? = (9) A man gives a discount of 5% on the fridge he bought for 55.00Naira. Find the marketed price of the fridge.= (10) A trader demanded a discount of 55.00Naira ok the goods she bought for 845.00Naira . What is the marketed price and the percentage discount ? =.
Answer:
1a) Increment in price = 5500 - 4500 = 1000 Naira
1b) Percentage increase in price = (increment in price / old price) x 100%
= (1000 / 4500) x 100%
= 22.22%
2) Marked price = selling price / (1 - discount percentage)
= 3000 / (1 - 0.1)
= 3333.33 Naira
3) Total cost of 30 crates of eggs = 30 x 30 = 900 Naira
Commission = (4/100) x 900
= 36 Naira
4) Commission = (7/100) x 49000
= 3430 Naira
5) Discount = marked price - selling price
= 44.48 - 39.28
= 5.20 Naira
6) Discount = (245 - 225) / 245 x 100%
= 8.16%
7) Commission = (3/100) x 33
= 0.99 Naira
8) New salary = old salary + 5% of old salary
= 250 + (5/100) x 250
= 262.50 Naira
9) Marketed price = selling price / (1 - discount percentage)
= 55 / (1 - 0.05)
= 57.89 Naira
10) Marketed price = selling price + discount
= 845 + 55
= 900 Naira
Percentage discount = (discount / marked price) x 100%
= (55 / 900) x 100%
= 6.11%
Step-by-step explanation:
(-3x²+6x³- 4-x) ÷ (2x+1) Show work
The terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1)
What is numerator?A numerator is the part of a fraction that is above the line and indicates how many parts of a whole are being considered. It is the number that is being divided.
The first step in solving this problem is to factor out the numerator. Using the distributive property, we can rewrite the numerator as:
(-3x² + 6x³ - 4 - x) = (-3x² + 6x³ - 4) - x
Now, we can factor out -3x² from the first two terms, giving us:
(-3x² + 6x³ - 4) - x = -3x²(1 + 2x - 4/3x²) - x
We can now divide the numerator and denominator by the common factor of -3x², giving us:
(-1 - 2x + 4/3x²) - (x/(-3x²)) ÷ (2x + 1)
By dividing the numerator and denominator by -3x², we can now cancel out the -3x² terms, leaving us with:
(-1 - 2x + 4/3x²) - (1/3) ÷ (2x + 1)
The next step is to simplify the fraction. To do this, we must multiply the numerator and denominator by the reciprocal of the denominator. In this case, the reciprocal is -1/(2x + 1) giving us:
[(-1 - 2x + 4/3x²) - (1/3)] × (-1/(2x + 1))
Simplifying the numerator yields:
(2x + 1 - 4/3x² + 1/3) × (-1/(2x + 1))
Finally, we can combine the terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1).
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Question
Which of the following statements is MOST LIKELY TRUE?
A-The lower half of Sample A's data is closer to the value 5 than the lower half of Sample B's data.
B-Both of the data sets range from 1 to 10 on the number line.
CThe upper half of Sample A's data is closer to the value 10 than the upper half of Sample B's data.
D-The data in Sample B is clustered around the center where Sample A is more spread out
Explain
(Real answers no bots)
Answer:
D-The data in Sample B is clustered around the center where Sample A is more spread out
Step-by-step explanation:
maybe sorry if wrong
classifying parallelagram
a. Slope of RS = [tex]-\frac{7}{5}[/tex] and slope of adjacent to RS = [tex]-\frac{5}{7}[/tex]
b. Length of RS = [tex]\sqrt{74}[/tex] and Length of adjacent to RS = [tex]\sqrt{74}[/tex]
c. The parallelogram PQRS is Rhombus.
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
[tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]
a. for the points R (-6, 6) and S (-1, -1)
Slope of RS = [tex]\frac{-1 - (+6)}{-1 - (-6)}[/tex] = [tex]-\frac{7}{5}[/tex]
Slope of RS = [tex]-\frac{7}{5}[/tex]
Slope of adjacent side (RQ, SP) to RS = [tex]\frac{6-1}{-6-1}[/tex] = [tex]\frac{5}{-7}[/tex]
Slope of adjacent to RS = [tex]-\frac{5}{7}[/tex]
b. Length of a line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]
points R (-6, 6) and S (-1, -1)
Length of RS = [tex]\sqrt{({-1- (-6))^{2} } + ({-1-6})^{2}}[/tex] = [tex]\sqrt{74}[/tex]
Length of RS = [tex]\sqrt{74}[/tex]
Length of adjacent to RS = [tex]\sqrt{({-6- 1))^{2} } + ({6-1})^{2}}[/tex] = [tex]\sqrt{74}[/tex]
Length of adjacent to RS = [tex]\sqrt{74}[/tex]
c. All sides are equal
PQ=QR=RS=SP=√74
So, diagonal PR = [tex]\sqrt{({-6- 6))^{2} } + ({-6-6})^{2}}[/tex] = [tex]12\sqrt{2}[/tex]
and diagonal QS = = [tex]\sqrt{({-1- 1))^{2} } + ({-1-1})^{2}}[/tex] = [tex]2\sqrt{2}[/tex]
Diagonals are unequal then parallelogram PQRS is Rhombus.
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Combine like terms to create an equivalent expression. 9/8 m + 9/10 - 2m - 3/5
Combine like terms to create an equivalent expression.[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5}[/tex] then we formed the equation is [tex]= \frac{1}{8} m - \frac{3}{50}[/tex]
How can you locate comparable expressions?When two expressions can be reduced to a single third expression or when one of the statements can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variables and both expressions yield the same result, you may also tell if expressions are equal.
What phrase has the same meaning as x2 2x 2?The final response is 2 x - 2; alternatively, you might write 2 x - 3. The ultimate response is -2 point to the right. You could see that choice d is right in this case.
In this expression, we have two terms with the variable m: [tex]9/8 m[/tex] and [tex]-2m[/tex]. We can combine these by subtracting [tex]2m[/tex] from [tex]9/8 m[/tex], which gives us [tex]1/8 m[/tex].
We also have two constant terms: [tex]9/10[/tex] and [tex]-3/5[/tex]. We can combine these by adding them, which gives us [tex]-3/50[/tex].
Putting it all together, we get:
[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5} = \frac{1}{8} m - \frac{3}{50}[/tex]
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Answer:-7/8m+3/10
Step-by-step explanation:
Problem 3
A bottle filling machine fills an average of 20,000 bottles
a day with a standard deviation of 2000. Assuming that
production is normally distributed and the year
comprises 260 working days, calculate the approximate
number of working days on which:
a) Under 18,000 bottles are filled
b) Over 16,000 bottles are filled
c) Between 18,000 and 24,000 bottles are filled.
Answer: a) To find the number of working days on which under 18,000 bottles are filled, we need to calculate the z-score for this value:
z = (18,000 - 20,000) / 2000 = -1
Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587. Therefore, the approximate number of working days on which under 18,000 bottles are filled is:
0.1587 x 260 ≈ 41
b) To find the number of working days on which over 16,000 bottles are filled, we need to calculate the z-score for this value:
z = (16,000 - 20,000) / 2000 = -2
Using a standard normal distribution table or calculator, we find that the probability of a value being less than -2 standard deviations is approximately 0.0228. Therefore, the approximate number of working days on which over 16,000 bottles are filled is:
0.0228 x 260 ≈ 6
c) To find the number of working days on which between 18,000 and 24,000 bottles are filled, we need to calculate the z-scores for these values:
z1 = (18,000 - 20,000) / 2000 = -1
z2 = (24,000 - 20,000) / 2000 = 2
Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587, and the probability of a value being less than 2 standard deviations is approximately 0.9772. Therefore, the approximate number of working days on which between 18,000 and 24,000 bottles are filled is:
(0.9772 - 0.1587) x 260 ≈ 236
Step-by-step explanation:
Explain how to find Wich one is greater: 1/4 of 12 or 1/3 of 12
What is the equation to vertically dilate a quadratic function by 2 units?
(use f(x)=x^2 as a base to dilate it)
Answer:
g(x) = 2x²
Step-by-step explanation:
You want the vertical dilation of function f(x) = x² by a factor of 2.
Vertical dilationAny function is dilated vertically by a factor of k by multiplying the function value by k:
g(x) = k·f(x) . . . . . . dilates f(x) vertically by a factor of k
g(x) = 2x² . . . . . . dilates f(x) = x² vertically by a factor of 2
John takes out a loan of $10600 that charges 12% interest compounded monthly. If John makes $170 monthly payments, determine how long it will take him to pay off the loan. Round your answer up.
Answer:
it would be 70months when rounded up.
Step-by-step explanation:
if not then 69months 7days
eric wanted to run 8 miles around track . how many times does he need to run around track
Answer: 32 times
Step-by-step explanation:
there are 4 laps on a track to reach a mile
4x8=32
On a coordinate plane, trapezoid J K L M is shown. Point J is at (negative 7, 4), point K is at (negative 4, 4), point L is at (negative 2, 3), and point M is at (negative 8, 3). What is the perimeter of trapezoid JKLM? StartRoot 2 EndRoot + StartRoot 5 EndRoot units 2 + StartRoot 2 EndRoot + StartRoot 5 EndRoot units 9 + 2 StartRoot 2 EndRoot units 9 + StartRoot 2 EndRoot + StartRoot 5 EndRoot units
Correct option is D, The perimeter of the trapezoid J K L M is units 9 + StartRoot 2 EndRoot + StartRoot 5 EndRoot units (= 9 + √5 + √2 units. )
What is meant by perimeter?The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. Such shape's perimeter is equal to the side lengths added together algebraically. We have formulas for the various geometric shapes.
The vertices of KLMN an isosceles trapezoid are (-7,4), (-4,4), (-2,3), (-8,3).
perimeter of trapezoid JKLM = sum of sides
Using distance formula [tex]\sqrt{(x2-x2)^2 + (y2 - y1)^2}[/tex],
Distance between the sides of trapezoid is,
(-7,4), (-4,4) =
[tex]\sqrt{(-7 + 4)^2 + (4 - 4)^2}\\= \sqrt{9}\\= 3 units[/tex]
(-4,4), (-2,3) =
[tex]\sqrt{(-2 + 4)^2 + (3 - 4)^2}\\= \sqrt{5} units[/tex]
(-2,3), (-8,3) =
[tex]\sqrt{(-8 + 2)^2 + (3-3)^2}\\= \sqrt{6}^2\\= 6 units[/tex]
(-7,4), (-8,3)
[tex]\sqrt{(-8 +7)^2 + (3-4)^2}\\= \sqrt{-1^2 + -1^2}\\= \sqrt 2 $ units $[/tex]
So, the sum of sides will be -
= 3 + √5 + 6 + √2
= 9 + √5 + √2 units.
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Answer:
its D
Step-by-step explanation:
i took the test on edg
the bottom 8 problems please help
Answer:
Here'd how to do problems like these. For example with #1 in your image (below)
Step-by-step explanation:
The sum of the series with the general terms k + 2 from k= 1 to k= 5
All you have to do is plug in all the numbers WITHIN the interval so in this case it would be 1,2,3,4, &5. After you plug in each of those numbers into the equation, you add them up.
Like so:
(1) + 2= 3
(2) + 3= 5
(3) + 3 = 6
(4) + 3 = 7
(5) + 3 = 8
3+5+6+7+8= 30
Please help me with this math
Answer: 1. 8.94
2. 13
3. True
Step-by-step explanation:
A family drank 4 gallons of juice over 5 weeks. During this time period,
at what rate did the family drink juice.
Therefore, the family drank juice at a rate of 0.8 gallons per week.
What is percent?Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.
Here,
To find the rate at which the family drank juice, we need to divide the total amount of juice consumed by the time it took to consume it.
The total amount of juice consumed is 4 gallons. The time period is 5 weeks.
So, the rate at which the family drank juice is:
4 gallons ÷ 5 weeks = 0.8 gallons per week
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Grade 10 QUESTION 1 1.1 Kayla is having a class party. She plans on buying cupcakes for everyone. If there will be 34 people attending the party and the cupcakes are sold in packs of 6. How many packs Kayla ought to buy? 1 1.2 A Seamstress (someone doing sewing) has 4,5m of material and plans to cut out a pattern that uses 0, 8m of material for each pattern. How many times can she cut out the pattern? (2) (2)
Kayla has to purchase [tex]6[/tex] packs of cupcakes, and the dressmaker can make [tex]5[/tex] copies of the pattern.
What does "with purchase" mean?Provide a discount on a third element in exchange for the first item's purchase, also known as purchase with purchase. Although it may also encourage sales of the side product, its primary goal is to increase sales of the main products.
Which account was bought?The purchase accounts is a nominal account, and as per nominal account rules, business costs are debited. All purchases made on credit are noted in the purchase diary, whilst purchases made with cash are noted in the cash book.
number of packs [tex]=[/tex] (total number of cupcakes) / (number of cupcakes in each pack)
We know that there are [tex]34[/tex] people attending the party
total number of cupcakes [tex]= 34[/tex]
Plugging this into the formula above, we get:
number of packs [tex]= 34 / 6 = 5.67[/tex]
Therefore, Kayla should buy [tex]6[/tex] packs of cupcakes.
number of pattern cuts [tex]=[/tex] (total amount of material) / (amount of material used for each pattern)
We know that the seamstress has [tex]4.5m[/tex] of material and each pattern uses [tex]0.8m[/tex] of material, so we can plug these values into the formula above:
number of pattern cuts [tex]= 4.5 / 0.8 = 5.625[/tex]
Therefore, the seamstress can cut out the pattern [tex]5[/tex] times.
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The chicken coup at the petting farm is 10 feet by 14 feet. The farm would like to double the current area by adding the same amount, x, to the length and width. What are the dimensions of the new enclosure? Round to the nearest hundredth of a foot.
From the quadratic equation, we found the new dimensions:
Length = 14.85 feet
Width = 18.85 feet.
What is a quadratic equation?
The polynomial equations of degree two in one variable of type
f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of
f (x).
The current dimensions of the farm are 10 feet by 14 feet.
Length l = 10 feet
Width w = 14 feet
Area a = l * w = 10 * 14 = 140 sq. feet.
Now the new area is doubled.
A = 2a = 2 * 140 = 280 sq.feet
The new dimensions are:
L = l + x = 10 + x
W = w + x = 14 +x
A = (10+x)(14+x)
280 = 140 + 10x + 14x + x²
x² + 24x - 140 = 0
This is a quadratic equation.
Solving the equation, we get
x = 4.85, -28.85
Neglecting the negative value, we get the value of x as 4.85.
Therefore from the quadratic equation, we found the new dimensions:
L = 10 + 4.85 = 14.85 feet
W = 14 + x = 14 + 4.85 = 18.85 feet.
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Write the prime factorization of 27. Use exponents when appropriate and order the factors from least to greatest (for example, 2235)
Answer:
Step-by-step explanation:
[tex]27=3\times 3 \times 3=3^3[/tex]
ordered: [tex]3^3[/tex]
Can anyone help me solve for x
Based on the congruent angles theorem, the value of the variable x in the circle is 40 degrees
How to determine the solution to the variableAn angle is a figure formed by two rays that share a common endpoint, called the vertex of the angle
From the question, we have the following parameters that can be used in our computation:
The circle with center O
In the figure, angles with the same marks are congruent angles
Using the above as a guide, we have the following:
x =40
Hence, the value of x is 40 degrees
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Find the measure of the angle
Answer:
? ≈ 58°
Step-by-step explanation:
since all 3 sides of the triangle are given, we can use any of the 3 trigonometric ratios.
using the sine ratio
sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{45}{53}[/tex] , then
? = [tex]sin^{-1}[/tex] ( [tex]\frac{45}{53}[/tex] ) ≈ 58° ( to the nearest degree )
Answer:
58°
Step-by-step explanation:
[tex]sin(?)=\frac{45}{53}[/tex]
[tex]?=sin^{-1} (\frac{45}{53})[/tex]
[tex]?=sin^{-1} (0.8491)[/tex]
[tex]?=58.1^{0}[/tex]
Hope this helps.
Please someone give me the answer to this or how to do this? I will mark brainly
Answer:
Step-by-step explanation:
Cody has a bag of 30 pencils each pencil is 16 centimeters long what is the combined length in meters?
Answer:
The total length of the 30 pencils in centimeters is:
30 x 16 = 480 cm
To convert centimeters to meters, we divide by 100:
480 cm / 100 = 4.8 m
Therefore, the combined length of the 30 pencils is 4.8 meters.
Step-by-step explanation:
This image has rotational symmetry. What is the smallest number of degrees you need to rotate the image for it to look the same?
the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.
What is rotational symmetry?
Rotational symmetry is a type of symmetry where a shape or object can be rotated by a certain angle and still appear exactly the same as it did before the rotation. The smallest angle of rotation for which the shape or object appears the same is called the angle of rotational symmetry or the order of the rotational symmetry.
In light of the posed query
There is rotational symmetry in the image.
This picture can be seen as a circle. A whole circle has 360 degrees.
Six wings cover the figure.
360/6
=60°
Hence, the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.
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Katie had 12 gallons of gas in her car when she left her house. She used 2 1/2 gallons of gas each hour that she drove. How many gallons did she have after driving for 2 hours?
She has 7 gallons of gas after driving for 2 hours.
What is Subtraction?
Subtraction is a mathematical operation that involves finding the difference between two numbers or quantities. It is the inverse of addition, which means that it is the opposite process of adding numbers.
In subtraction, a number or quantity (called the subtrahend) is subtracted from another number or quantity (called the minuend), resulting in the difference. The symbol used for subtraction is "-" and the resulting value is called the remainder or difference.
Katie had 12 gallons of gas.
She used 2 1/2 gallons of gas each hour.
Now, She drove 2 hours.
So, gallon of gas use for 2 hours = 2 × 2 1/2
= 2 × 5/2
= 5 gallons of gas.
Now, Gallons of gas left after 2 hours
= total gallons of gas - Gallons used for 2 hours
= 12 - 5
= 7.
Hence, She is left with 7 (12-5) gallons of gas.
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Write a polynomial function of the least degree with integral coefficients that have the given zeros. 1,-5,-1/2
Answer:
If 1, -5, and -1/2 are zeros of a polynomial function, then the factors of the polynomial are:
(x - 1), (x + 5), and (2x + 1)
To find the polynomial function, we multiply these factors together and simplify:
(x - 1)(x + 5)(2x + 1)
= (x^2 + 4x - 5)(2x + 1)
= 2x^3 + 9x^2 - 6x - 5
Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 1, -5, and -1/2 is:
f(x) = 2x^3 + 9x^2 - 6x - 5