The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.
What is a CircIe?A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.
The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and Area οf the TriangIe.
Area οf an Arc =(θ /360) × π r²
Area = (90/360) × π × (8)²
Area οf the arc = 16 π in²
Area οf the triangIe = (1/2) × base × height
Area οf the triangIe = (1/2) × 8 × 8 = 32 in²
Area οf the shaded pοrtiοn = (16 π -32) inch²
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(Scale Factor HC)
A rectangular oil painting is 14 inches wide and 24 inches long. A museum wants to create a larger print of the painting using a scale factor of 3.
Part A: What are the dimensions of the print, in feet? Show every step of your work. (2 points)
Part B: What is the area of the print, in square feet? Show every step of your work. (2 points)
Part A:
First, we need to find the dimensions of the print by multiplying the dimensions of the original painting by the scale factor of 3.
The width of the print is 14 inches x 3 = 42 inches
The length of the print is 24 inches x 3 = 72 inches
To convert these dimensions into feet, we need to divide by 12 (since there are 12 inches in a foot):
Width of print = 42 inches / 12 = 3.5 feet
Length of print = 72 inches / 12 = 6 feet
Therefore, the dimensions of the print are 3.5 feet by 6 feet.
Part B:
To find the area of the print, we need to multiply the width by the length:
Area of print = (3.5 feet) x (6 feet) = 21 square feet
Therefore, the area of the print is 21 square feet
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Pyramid ABCD is similar to pyramid WXYZ. The perimeter of triangle BCD is 16, and the perimeter of triangle XYZ is 32. What is the scale factor
to dilate ABCD to WXYZ?
The scale factor is
N
Answer:
The scale factor to dilate ABCD to WXYZ is 1/sqrt(2) or (sqrt(2))/2.
The scale factor to dilate ABCD to WXYZ is k = 2.
Given data:
To find the scale factor between two similar figures, compare the corresponding side lengths.
The perimeter of triangle BCD is 16 and the perimeter of triangle XYZ is 32. Since corresponding sides of similar triangles are proportional, the ratio of their perimeters to determine the scale factor.
The scale factor is calculated by dividing the perimeter of triangle XYZ by the perimeter of triangle BCD:
Scale factor = Perimeter of XYZ / Perimeter of BCD
Scale factor = 32 / 16 = 2
Hence, the scale factor to dilate pyramid ABCD to WXYZ is 2.
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42 E This histogram shows battery life (in hours) of 40 batteries of the same brand. When reading a histogram, it is important to look at the shape, center and spread of the data. Relative Frequency 0.30 100 110 120 130 Battery Life (hours) 140 150 Complete the following statements about the shape of the data shown.
A. The distribution of the data is approximately
B. The mean battery life is
The answer of the given question based on the histogram that shows battery life is, (A). The distribution of the data is approximately symmetric. (B). The mean battery life is around 125 hours.
What is Data distribution?Data distribution refers to pattern or shape of how data is spread out or distributed over range of values. It is important to understand distribution of data because it can provide insights into nature of the data and inform statistical analysis.
There are several ways to describe distribution of data, including measures of center (like mean, median, and mode) and measures of spread (like range, variance, and standard deviation)
A. The distribution of the data is approximately symmetric.
B. The mean battery life can be estimated by finding the center of the histogram, which appears to be around 125 hours. However, without knowing the exact bin widths or the midpoint of each bin, it is difficult to estimate the mean precisely.
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Based on the histogram that displays energy life, the following is the response to the question:
a). The data are distributed in a roughly symmetrical manner.
b). An average charge lasts for about 125 hours.
What is Data distribution?Data distribution describes the way that data is dispersed or distributed across a variety of values. Understanding data distribution is crucial because it can shed light on the character of the data and help with statistical analysis.
Measures of the center (like mean, median, and mode) and measures of spread are two methods to describe data distribution. (like range, variance, and standard deviation).
A). The facts are distributed in a roughly symmetrical manner.
B). You can determine the average battery life by locating the histogram's center, which looks to be 125 hours.
It is challenging to calculate the mean exactly without knowing the precise bin widths or the midpoint of each bin, though.
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The image of the question attached below,
What’s the answer to this question?
If anyone can help
Me ur a life saver
Answer:
(-6,-3), (3,6), and (3,-3)
Step-by-step explanation:
the triangle has 3 points: (-2,-1), (1,2), and (1,-1)
for (x,y) => (3x,3y)
then
(-2,-1) => (-6,-3)
(1,2) => (3,6)
(1,-1) => (3,-3)
so you should draw the triangle with 3 points: (-6,-3), (3,6), and (3,-3)
a backpack that normally sells for $40 is on sale for $30. find the percentage of a change.
Answer:It would be 40•.25=10
Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off
Zendaya randomly selected marbles from a bag during a probability experiment. She completed 50 rounds and recorded the results in the table shown. Based on the information from her experiment, in how many of the next 200 rounds would she pick a blue marble?
We can expect her to pick about 70 blue marbles in the next 200 rounds.
How many of the next 200 rounds would she pick a blue marble?We must divide the number of blue marbles by the total number of marbles to determine the likelihood of selecting a blue marble in a single round:
P(blue) = 14/40 = 7/20
Since the experiment has been conducted 50 times, we may anticipate that the proportion of blue marbles will eventually be around 7/20. This suggests that in the subsequent 200 rounds, Zendaya will likely choose to focus on:
70 blue marbles result from P(blue) 200 = (7/20) 200.
So, in the following 200 rounds, we can anticipate her choosing roughly 70 blue marbles.
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A motorboat travels 205 kilometers in 5 hours going upstream. It travels 275 kilometers going downstream in the same amount of time. What is the rate of the
boat in still water and what is the rate of the current?
Answer:
205:275
300:
Find the answer
The length of one of the legs of a right triangle is 13. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the the larger of the two missing sides (the hypotenuse).
Answer:
Leg 1 = 13
Leg 2 = 84
Hypotenuse = 85
Step-by-step explanation:
Hello!
The larger of the other two legs would be the hypotenuse, as the hypotenuse is the largest side in a right triangle (as stated in the problem.
The Pythagorean theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.
Let the smallest of the other legs be x, and the hypotenuse be x + 1.
The equation is: [tex]13^2 + x^2 = (x+1)^2[/tex]
Solve for x:[tex]13^2 + x^2 = (x+1)^2[/tex][tex]169 + x^2 = x^2 + 2x + 1[/tex] => Expand[tex]169 = 2x + 1[/tex] => Subtract x² from both sides[tex]168 = 2x[/tex] => Subtract 1 from both sides[tex]x = 84[/tex] => Divide both sides by 2We found the value for x, so we can find the hypotenuse by adding 1, which gives us 85.
Given that co-factor matrix M=16-12-4-5-33 - 12-3 find the adjoint M
The answer of the given question based on the finding the adjoint of M is 16 -4 -33
-12 -5 -12.
What is Co-factor?In linear algebra, a cofactor is a scalar value that can be computed for each element of a square matrix. To find the cofactor of a specific element of a matrix, we first remove the row and column containing that element, and then compute the determinant of the remaining matrix. The sign of the cofactor depends on the position of the element within the matrix: it is positive if the sum of the row and column indices is even, and negative if the sum is odd.
The cofactor matrix of a given matrix is obtained by replacing each element of the matrix with its corresponding cofactor. Cofactor matrices are useful in computing the inverse of a matrix and in solving systems of linear equations.
The adjoint of matrix is transpose of its co-factor matrix.
First, we need to find the transpose of the co-factor matrix:
16 -12
-4 -5
-33 -12
Therefore, the adjoint of M is:
16 -4 -33
-12 -5 -12
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Need help will give brainliest and 5 stars for the fastest answers with work.
The point (2, 2) would end up at the point (1, 1) after the transformations.
Describe Function?Functions can be represented in different ways, including graphs, tables, and equations. A graph of a function is a visual representation of the relation between the inputs and outputs, usually plotted on a coordinate plane. A table of values lists the inputs and corresponding outputs of a function. An equation of a function expresses the rule for calculating the output in terms of the input variable.
To sketch the graph of the new function h(x), we can start by considering the effect of each transformation on the original function f(x).
First, we have a horizontal shift of 1 unit to the left, since we are subtracting 1 from the argument of f(x). This means that the graph of f(x+1) will be shifted 1 unit to the left compared to the graph of f(x).
Next, we have a vertical stretch by a factor of 2, since we are multiplying the output of f(x+1) by 2. This means that the graph of 2f(x+1) will be twice as tall as the graph of f(x+1).
Finally, we have a vertical shift downwards by 3 units, since we are subtracting 3 from the output of 2f(x+1). This means that the graph of h(x) will be shifted 3 units downwards compared to the graph of 2f(x+1).
To find where the point (2, 2) ends up after these transformations, we can first apply the horizontal shift of 1 unit to the left, which gives us the point (1, 2). Next, we apply the vertical stretch by a factor of 2, which gives us the point (1, 4). Finally, we apply the vertical shift downwards by 3 units, which gives us the point (1, 1).
Therefore, the point (2, 2) would end up at the point (1, 1) after the transformations.
To sketch the graph of h(x), we can start with the graph of f(x) and shift it 1 unit to the left, stretch it vertically by a factor of 2, and shift it 3 units downwards. The resulting graph will have the same shape as the graph of f(x), but will be shifted and scaled as described above. The point (1, 1) will be on this graph as well.
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A. Regardless of the values of b and c, the point (-2,2) is included in the curve of g(x).
B. On the graph of h(x), the point (2,2) would be changed into the point (2,1).
What is graph?A graph is a graphical representation of data, functions, or variable connections. It is a method of displaying information that is simple to analyse and comprehend.
Graphs are widely used in a variety of disciplines, including science, economics, business, engineering, and others. They make it simpler for researchers and analysts to visualise data and identify trends or patterns, allowing them to draw conclusions and make educated choices based on the data.
A. To include the spot (-2,2), we must shift the f(x) graph two units to the right and two units up. So far, we have:
g(x) = a f(x - (-2)) + 2
g(x) = a f(x + 2) + 2
We must now determine the worth of "a." Because the point (3,4) on the f(x) graph is transferred to the point (2,2) on the g(x) graph, we have:
g(3) = a f(3 + 2) + 2 = 2
4a + 2 = 2
4a = 0
a = 0
Therefore, the function g(x) is:
g(x) = 0 f(x + 2) + 2
g(x) = 2
As a result, independent of the values of b and c, the point (-2,2) is included in the graph of g(x).
B. The function h(x) has a slope of 2 and a y-intercept of -1. We plug x=2 into h(x) to determine where the point (2,2) would end up after the transformations and get:
h(2) = 2(2+1)-3 = 1
As a result, the point (2,2) on the graph of h(x) would be changed to the point (2,1).
The transformations applied to f(x) to produce h(x) are a one-unit horizontal shift to the left (x+1), a two-unit vertical stretch (2(x+1)), and a three-unit vertical shift downwards (-3).
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Complete question and graph attached below,
7. Lin is making blueberry muffins. She has a total of 4 cups of
blueberries. Each batch of muffins uses 3/2 cups of blueberries. How
many batches of blueberry muffins can Lin make using ALL of the
blueberries?
A.) Draw a diagram to represent this situation.
B) How many batches can Lin make?
X
13
C) What fraction of a batch will Lin need to make in order to use all of
the blueberries?
30
B. Lin can make 2 batches of blueberry muffins.
C. Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.
What is mixed fraction?
A mixed number is one that contains both a whole number and a fraction. The fraction is written after the whole number, with a space or plus sign placed between them. The mixed number 2 1/4 serves as an explanation for how the numbers 2 and 1/4 were added. Objects that aren't whole numbers but are close to them, such length or time measurements, are typically represented by mixed numbers.
a) Diagram
4 cups of blueberries
__ __ __ __
| | | | |
|__|__|__|__|
Each batch uses 3/2 cups of blueberries
B) To find the number of batches Lin can make, we need to divide the total amount of blueberries by the amount of blueberries per batch:
4 cups of blueberries ÷ (3/2 cups of blueberries per batch)
= (4 cups of blueberries) × (2/3 batches per cup of blueberries)
= 8/3 batches
Therefore, Lin can make 8/3 or approximately 2.67 batches of blueberry muffins using all of the blueberries.
C) To find the fraction of a batch Lin will need to make in order to use all of the blueberries, we need to subtract the number of whole batches from the total number of batches:
8/3 batches - 2 batches = 2/3 of a batch
Therefore, Lin will need to make 2/3 of a batch in order to use all of the blueberries.
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Select the correct answer. Camille is saving for a laptop that costs about $850. To model her savings plan and determine how many more months it will take her to reach her goal, she recently created this equation, where y represents the total amount saved and x represents the number of months. Which statement about her work is true?' Step Calculation Step 1: y = 80 + 70x Step 2: y − 80 = 80 + 70x − 80 Step 3: y − 80 = 70x Step 4: = Step 5: = x Step 6: = x Step 7: 11 = x A. Camille used the associative property in step 3. B. Camille used the multiplication property of equality in step 4. C. Camille used the subtraction property of equality in step 5. D. Camille used the substitution property in step 6.
Answer:
C. Camille used the subtraction property of equality in step 5.
Step-by-step explanation:
In step 2, Camille subtracted 80 from both sides of the equation. In step 3, she simplified the equation by combining like terms. In step 4, Camille divided both sides of the equation by 70 to isolate the variable x. In step 5, she subtracted y-80 from both sides of the equation to isolate x. In step 6, Camille simplified the equation by dividing both sides by -1/70. Finally, in step 7, she calculated the value of x.
Therefore, option C is the correct answer.
The first three terms of an arithmetic sequence are 2k – 7; k + 8 and 2k −1. The sum of the first 30 even terms of the sequence is
Question 11 (5 points)
(Experimental Probability MC)
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows
the frequency of each card drawn.
Card A23
Frequency 47567
Based on the table, what is the experimental probability that the card selected was a K or 6?
a
Ob
Od
100 11-
4
10JQK
Question 12(5 points)
The experimental probability that the card selected was a K or 6 is option B.
What is Probability?
PrοbabiIity is the study οf the chances οf οccurrence οf a resuIt, which are οbtained by the ratiο between favοrabIe cases and pοssibIe cases.
Frοm the tabIe, we can see that the frequency οf drawing a K οr 6 is:
Frequency(K οr 6) = Frequency(K) + Frequency(6) = 4 + 10 = 14
The tοtaI number οf draws is 100.
The experimentaI prοbabiIity οf drawing a K οr 6 can be caIcuIated as:
ExperimentaI PrοbabiIity(K οr 6) = Frequency(K οr 6) / TοtaI number οf draws
ExperimentaI PrοbabiIity(K οr 6) = 14 / 100
ExperimentaI PrοbabiIity(K οr 6) = 0.14
Therefοre, the experimental prοbabiIity that the card seIected was a K οr 6 is 0.14 οr 14%. Optiοn b is the cοrrect answer.
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The widths of 94 randomly selected doors were found to have a standard deviation of 4.11. Construct the 80% confidence interval for the population standard deviation of the widths of all doors in this factory. Round your answers to two decimal places.
To create a confidence range for the population standard deviation, we can use the chi-square distribution. Finding the chi-square values that correlate to 10% and 90% in the right tail of the distribution is necessary given that we have 94 samples and want an 80% confidence range.
The chi-square value for the 10th percentile is 71.47, and the chi-square value for the 90th percentile is 112.31, according to a chi-square distribution chart with 93 degrees of freedom (n-1).
The confidence interval's calculation is:
((n-1)*s2)/sqrt(X), (n-1)*s2)/sqrt(Y))
Where:
The group number is n.
The sample's standard variation is s.
X represents the bottom limit of the confidence interval's chi-square value.
Y is the chi-square value for the upper bound of the confidence interval
Substituting the values we have:
(sqrt((94-1)*4.11^2)/sqrt(112.31)) = 5.63
(sqrt((94-1)*4.11^2)/sqrt(71.47)) = 4.81
Therefore, the 80% confidence interval for the population standard deviation of the widths of all doors in this factory is (4.81, 5.63).
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For questions 3 and 4, you will be answering by filling in the blanks. Please be aware that your answer must include any commas or decimals in their proper places in order to be correct. The dollar signs have been provided. For example, if the answer is $1,860.78, then you will enter into the blank 1,860.78. Do not place any extra spaces between numbers, commas, or decimal places. Round any decimals to the nearest penny when the answer involves money, so that $986.526 would be typed into the blank as 986.53 and $5,698.903 would be typed into the blank as 5,698.90.
What is your weekly median income if you are a female with an advanced degree?
The weekly median income of a female with an advanced degree is 1,323.
What is a median?
The median, which is the centre value in a sorted, ascending or descending list of numbers, can better describe a data set than the average.
We are given three tables representing different data. The table 1 represents the total data, table 2 represents the data relating to men and the last table represents the data relating to female.
We are asked weekly median income of a female with an advanced degree.
So, from table 3 we get this data wherein the weekly median income of a female with an advanced degree is given as $1,323.
Hence, the weekly median income of a female with an advanced degree is 1,323.
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The diameter of a cone's circular base is 18 inches. The height of the cone is 3 inches.
What is the exact volume of the cone?
Enter your answer in the box.
(I need the answer in √ form
Answer:
The volume of a cone is given by the formula V = 1/3πr²h, where r is the radius of the circular base and h is the height of the cone.
Since the diameter of the circular base is 18 inches, the radius is 9 inches. The height of the cone is 3 inches.
Substituting the values in the formula, we get:
V = 1/3π(9²)(3) V = 81π/3 V = 27π
Therefore, the exact volume of the cone is 27π cubic inches.
Answer:
Step-by-step explanation:
really need help with this question don’t get it at all
Answer:
v = 40 cm
w = 126
x = 30
y = 63 cm
Step-by-step explanation:
So are given that ΔBIG is similar to ΔMOP. This means that their respective angles are the same measurements, but different side lengths. By definition of similar triangles, their respective side lengths are equal in proportion.
∠I corresponds to ∠O, so their measurements are equal. w = 126°.
∠B corresponds to ∠M, so their measurements are also equal. We don't know the angle measurement for x, but we have all the angles for two similar triangles, so we can find the measure of the third angle. The total angle measure for any triangle is 180°.
x = 180 - 24 - 126
x = 30°
Now that we have all the angle measurements, we can proportions to calculate the lengths of the unknown sides. The proportion of ΔBIG to ΔMOP can be calculated using the corresponding side length for each triangle.
Segment BG corresponds to segment MP. The proportion of BG to MP is:
48/72. Proportions are fractions, so this ratio can be simplified to 2/3 (divide by 24 on top and bottom).
Now we know that the ratio of ΔBIG to ΔMOP is 2/3.
Segment BI (aka v) = (2/3) * 60 cm
v = 40 cm
Segment PO (aka y) * (2/3) = 42 cm
y = 42 * 1.5
y = 63 cm
The fire logs in a backyard are arranged so that each row has 5 fewer logs than the row below it. If the first row has 58 logs, how many logs are in the 6th row?
a
28
b
33
c
38
d
53
Using arithmetic progression, number of logs in 6th row are 33.
How to find no. of logs are in the 6th row?We can use the information that each row has 5 fewer logs than the row below it to create a sequence of the number of logs in each row. Let's call the number of logs in the first row "a" (which we know is 58 logs). Then, the number of logs in the second row will be "a - 5", the number of logs in the third row will be "(a - 5) - 5" or "a - 10", and so on.
So, we have the sequence of the number of logs in each row as:
a, a - 5, a - 10, a - 15, a - 20, ...
To find the number of logs in the 6th row, we need to find the 6th term in this sequence. We can use the formula for the nth term of an arithmetic sequence:
an = a₁ + (n - 1)d
where an is the nth term, a1 is the first term, n is the number of the term we want to find, and d is the common difference between terms (which is -5 in this case, since each row has 5 fewer logs than the row below it).
Substituting the given values, we get:
a₆ = a₁ + (6 - 1)(-5)
= a - 25
So, the number of logs in the 6th row is a - 25. Since we know that a is 58 logs, we can substitute and simplify:
a - 25 = 58 - 25 = 33
Therefore, the answer is (b) 33.
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a jar contains 30 coins, all dimes and quarters. the value of the coins is $4.80. how many of each coin is in the jar
Answer:
Step-by-step explanation:
1 quarter = 25 cents
1 dime = 10 cents
Let
q = the number of quarters, q>=0, q is integer
d = the number of dimes, d>=0, d is integ
30 coins totaling $4.80 = 480 cents:
q + d = 30
25q + 10d = 480
q = 12 quarters
d = 18 dimes
12 quarters and 18 dimes.
Answer:
Let x be the number of dimes in the jar.
Then the number of quarters in the jar would be 30 - x.
The total value of the dimes in the jar would be 0.10x, and the total value of the quarters would be 0.25(30 - x) = 7.50 - 0.25x.
We know that the total value of the coins is $4.80, so we can set up the equation:
0.10x + 7.50 - 0.25x = 4.80
Simplifying and solving for x, we get:
0.15x = 2.70
x = 18
Therefore, there are 18 dimes and 30 - 18 = 12 quarters in the jar.
Step-by-step explanation:
If Gretchen randomly chooses one of the boxed lunches, what is the probability that she will get a roast beef sandwich on wheat bread and popcorn in her box?
To calculate the probability of Gretchen getting a roast beef sandwich on wheat bread and popcorn in her boxed lunch, we need to know the total number of possible boxed lunch combinations and the number of boxed lunches that contain roast beef on wheat bread and popcorn.
Let's assume there are 4 different types of sandwiches available: roast beef on wheat bread, turkey on white bread, ham on rye bread, and vegetarian on whole wheat bread. Also, let's assume there are 3 different snack options available: popcorn, chips, and fruit.
If each boxed lunch contains one sandwich and one snack, then there are 4 x 3 = 12 possible boxed lunch combinations.
Out of these 12 combinations, we need to determine how many contain roast beef on wheat bread and popcorn. Let's say there are 2 boxed lunches that contain roast beef on wheat bread and popcorn.
Therefore, the probability of Gretchen randomly choosing a boxed lunch with roast beef on wheat bread and popcorn is 2/12, which simplifies to 1/6, or approximately 0.1667.
So, there is a 16.67% chance that Gretchen will get a roast beef sandwich on wheat bread and popcorn in her box.
I need to know the answer in the photo
The solution of the composite function (f. g)(x) in standard form is x⁵ - 2x³ + 2x² - 8x + 4.
How to solve function?The function (f . g)(x) is a composite function. Composite function is a function that depends on another function. In other words, composite function is a function that is within another function
Therefore, let's solve the composite function as follows:
f(x) = x³ - 4x + 2
g(x) = x² + 2
Hence,
(f. g)(x) = f(x) × g(x)
f(x) × g(x) = (x³ - 4x + 2)(x² + 2)
f(x) × g(x) = x⁵ + 2x³ - 4x³ - 8x + 2x² + 4
f(x) × g(x) = x⁵ - 2x³ + 2x² - 8x + 4
Therefore,
(f. g)(x) = x⁵ - 2x³ + 2x² - 8x + 4
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100 points!! brainliest.
The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:
Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.
Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.
Answer:
If the scale factor is -5, it means that the new image will be a reflection across the origin (negative scale factor means reflection) and enlarged by a factor of 5.If the scale factor is 1/2, it means that the new image will be half the size of the original image.If the scale factor is 0.4, it means that the new image will be 40% of the size of the original image.If the scale factor is 3/2, it means that the new image will be enlarged by a factor of 3/2 or 1.5 times the size of the original image.If the scale factor is 1, it means that the new image will be the same size as the original image.II. The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.
Step-by-step explanation:
ohn spent 20% of his money on food. He spent 2/5 of the remainder on a toy. The toy cost $12.
(a) What percentage of his money did he spend on the toy?
(b) How much money did he have at first?
Answer: (a) John spent 2/5 of the remainder of his money on a toy. Let's first find the remainder of his money after he spent 20% on food. If he spent 20% on food, then he has 80% of his money remaining. So, if he had $x initially, he has $0.8x remaining.
John spent 2/5 of the remainder on a toy, so we can set up the equation:
(2/5)(0.8x) = 12
Simplifying, we get:
0.32x = 12
Dividing both sides by 0.32, we get:
x = 37.5
So, John initially had $37.5.
To find the percentage of his money he spent on the toy, we can use the following formula:
Percentage = (amount spent on toy / initial amount) * 100%
The amount John spent on the toy is $12, and his initial amount is $37.5, so we get:
Percentage = (12 / 37.5) * 100% = 32%
Therefore, John spent 32% of his money on the toy.
(b) John initially had $37.5.
Step-by-step explanation:
Please answer question below.
Answer:
y=y^2
Step-by-step explanation:
because you have to change X into y
WITH SOLUTION PLEASEE
subtitution
y= 6;
x= 4.
Step-by-step explanation:1. Write the 2 equations.[tex](1)y=6\\ \\(2)-x+y=2[/tex]
2. Substitute "y" in equation 2 using the value of "y" in equation 1 (which is 6).[tex](2)-x+(6)=2\\ \\-x+6=2\\ \\[/tex]
3. Subtract 6 from both sides of the equation.[tex]-x+6-6=2-6\\\\-x=-4[/tex]
4. Multiply both sides of the equation by "-1".[tex](-1)-x=-4(-1)\\ \\x=4[/tex]
5. Express the final result.y= 6;
x= 4.
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I hope it's helpful for you
You are a salesman for XYZ Limited. Total sales for company Z last year were R900 000,00. You were responsible for obtaining R300 000,00 worth of these sales. As a fraction, what was your share of the total sales? Simplified
Answer: 1/3 or 33.33%
Step-by-step explanation:
30000000/90000000=1/3 or 33.33%
what is 9+10? and please dont say 19
Answer:
the answer is most certainly 21
Step-by-step explanation:
Alexa is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Alexa has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf, x, and how much shelf space the books take up (in inches), y.
The equation that models this relationship is y=2x.
How many books will take up 16 inches of shelf space? Write your answer as a whole number or decimal.
Answer: 8 books
Step-by-step explanation:
y= how much shelf space take up (inches)
x= # of books
y=2x
in this situation 16=y
16=2x
divide both sides by 2
8=x