Answer:Range
Step-by-step explanation:the set of all images of the elements in the domain of a function is called the Range .
The set of all images of the elements in the domain of a function is called the range. The range is the set of all possible outputs or y-values that a function can produce for its corresponding inputs or x-values in the domain.
The range can be determined by either analyzing the function algebraically or by graphing it. It is important to note that not all functions have a defined range, as some may produce infinite or undefined outputs. The range plays a crucial role in understanding the behavior and characteristics of a function, as it helps identify its domain and any possible restrictions or limitations.
The set of all images of the elements in the domain of a function is called the range of the function. The range represents the output values of a function that result from applying the function to every element within its domain. In other words, the range consists of all possible values that the function can produce when it is applied to the elements in its domain.
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the issubset() method can be used to determine whether set1 is a subset of set2. True or false?
True. The is subset() method is used to check if all elements of set1 are present in set2, which means set1 is a subset of set2 if the is subset() method returns true.
True. The "is subset()" method can be used to determine whether set1 is a subset of set2. If all elements of set 1 are present in set 2, then set 1 is considered a subset of set 2. The method returns `True` if set1 is a subset of set2 and `False` otherwise.
In mathematics, if all the elements of A are also elements of B, then the set A is one of the set B; then B is a superset of A. A and B may be equal; if they are not, A is a necessary condition of B. A relationship in which one group is one of the other is called existence (or sometimes existence). A is part of B, it can also indicate that B contains (or contains) A, or that A contains (or contains) B. A k-subset is a subset with k elements.
A linked subset defines the partial order of a set. In fact, intersection and union give intersection and intersection, with subsets of the given set being Boolean algebra in the relationship, and the link itself is a Boolean coverage relationship.
Example usage:
```python
set1 = {1, 2, 3}
set2 = {1, 2, 3, 4, 5}
result = set1.issubset(set2)
print(result) # Output: True
```
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In three hours, James read 18 pages of his history book. In four hours, he read 21 pages. Write the equation of the line that passes through the two points that represent the data in the problem. Use the equation to predict how many pages James will read in six hours.
Answer:
27
Step-by-step explanation:
(3,18), (4,21)
M = (21-18)/(4-3) = 3
Y = mx + c
18 = 3(3) + c
C = 18 - 9 = 9
Y = 3x + 9
6 hours implies x=6
Y = 3(6) + 9 = 18 + 9 = 27
Num of pages = 27
14 let z be a standard normal variable. find p(-1.63 < z < 0.25).
the probability of having a standard normal variable z between -1.63 and 0.25 is approximately 0.5471.
Using a standard normal table or a calculator, we can find the area under the standard normal curve between -1.63 and 0.25.
The standard normal distribution is a continuous probability distribution with mean 0 and standard deviation 1.
Therefore,
P(-1.63 < z < 0.25) = P(z < 0.25) - P(z < -1.63)
Using a standard normal table or a calculator, we can find that:
P(z < 0.25) = 0.5987
P(z < -1.63) = 0.0516
Therefore,
P(-1.63 < z < 0.25) = P(z < 0.25) - P(z < -1.63)
= 0.5987 - 0.0516
= 0.5471
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value that ranges from 0 (indicating the event is impossible) to 1 (indicating the event is certain).
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Which of the following expressions represents "five more than half of x"?
The expression that represents "five more than half of x" is
We have,
"five more than half of x"
To understand , let's break down the phrase
"five more than half of x". "Half of x" can be represented as 0.5x,
and "five more than" means we add 5 to that result.
Therefore, the expression is 0.5x + 5.
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Adam has been walking to the post office each day. He walks 3.6 miles in 32 minutes. He decided to walk to the store which is 5.2 miles away. About how long should Adam expect the walk to take?
Adam should expect the walk to the store to take approximately 46 minutes and 13 seconds.
To calculate how long it will take Adam to go to the storeWe can set up the following proportion:
32 minutes x 3.6 miles equals 5.2 miles.
When we solve for x, we obtain the following:
x = (5.2 miles x 32 minutes) / 3.6 miles
x = 46.22 minutes.
So, Adam should expect the walk to the store to take approximately 46 minutes and 13 seconds.
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LarCalcET6 10 2.038
Eliminate the parameter and obtain the standard form of the rectangular equation Circle: x = h + r cos (θ), y = k + r sin(θ) Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a cos(θ), y = k + b sin(θ)
The standard form of the rectangular equation for the given circle is (x - h)² + (y - k)² = r². The standard form of the rectangular equation for the given ellipse is b²(x - h)² + a²(y - k)² = a² b².
To eliminate the parameter and obtain the standard form of the rectangular equation for a given parametric equation, we need to express one of the variables (either x or y) in terms of the other variable, and then substitute this expression into the other equation to eliminate the parameter.
For the circle given by x = h + r cos(θ), y = k + r sin(θ), we can eliminate the parameter θ by expressing sin(θ) and cos(θ) in terms of x, y, h, and k using the Pythagorean identity:
sin²(θ) + cos²(θ) = 1.
Solving for sin(θ) and cos(θ), we get:
cos(θ) = (x - h) / r
sin(θ) = (y - k) / r
Substituting these expressions into the original equations, we get:
(x - h)² / r² + (y - k)² / r² = 1
Multiplying both sides by r², we get the standard form of the equation of a circle centered at (h, k) with radius r:
(x - h)² + (y - k)² = r²
For the ellipse given by x = h + a cos(θ), y = k + b sin(θ), we can eliminate the parameter θ in a similar way.
Using the Pythagorean identity and some algebraic manipulation, we can obtain the following expressions for sin(θ) and cos(θ):
cos(θ) = (x - h) / a
sin(θ) = (y - k) / b
Substituting these expressions into the original equations, we get:
(x - h)² / a² + (y - k)² / b² = 1
Multiplying both sides by a² b², we get the standard form of the equation of an ellipse centered at (h, k) with semi-axes a and b:
b²(x - h)² + a²(y - k)² = a² b².
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the mean annual tuition and fees for a sample of 14 private colleges was 35,400 with a standard deviation of 4700. a dotplot shows that it is reasonable to assume that the population is approximately normal. you wish to test whether the mean tuition and fees for private colleges is different from 31,400. compute the p-value of the test statistic
The p-value of the test statistic is given as follows:
0.0072.
How to obtain the p-value of the test statistic?The test statistic is calculated as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters for this problem are givne as ofllows:
[tex]\overline{x} = 35400, \mu = 31400, s = 4700, n = 14[/tex]
Hence the test statistic is given as follows:
[tex]t = \frac{35400 - 31400}{\frac{4700}{\sqrt{14}}}[/tex]
t = 3.18.
We have a two-tailed test, as we are testing if the mean is different of a value, with t = 3.18 and 14 - 1 = 13 df, hence the p-value is given as follows:
0.0072.
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Look at the system of equations below.
Which coordinate plane shows the solution to this system of equations?
a recent study of 3,000 of a college's recent alumni found that 1,725 of them were homeowners. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The mean of the sampling distribution is equal to the population proportion, and the standard deviation can be calculated using the formula sqrt(p*(1-p)/n), where p is the population proportion and n is the sample size.
Explanation: The sample proportion of homeowners can be calculated as the ratio of the number of homeowners to the sample size:
p^- = 1725 / 3000 = 0.575
This sample proportion provides an estimate of the population proportion of homeowners among recent alumni of the college. Therefore, we can conclude that the population proportion is estimated to be 0.575.
The mean of the sampling distribution is equal to the population proportion, which is 0.575. This means that if we were to take an infinite number of random samples of size n from the population, the average of the sample proportions would be equal to the population proportion.
The standard deviation of the sampling distribution can be calculated using the formula:
σ = sqrt(p*(1-p)/n)
Where p is the population proportion and n is the sample size. Substituting the values, we get:
σ = sqrt(0.575*(1-0.575)/3000) = 0.015 (rounded to three decimal places)
This means that if we were to take an infinite number of random samples of size n from the population, the sample proportions would be distributed around the population proportion with a standard deviation of 0.015.
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A tent with sides of 3 ft has a rope of 5 ft going from the tent to the tent post. How far away are the posts placed in the ground?
The posts are placed 4 feet away from the tent in the ground by using pythagoras theorem
The sides of the tent form a right triangle, with one side of length 3 ft and the other side of length x ft (the distance between the post and the tent). The rope forms the hypotenuse of the triangle, with a length of 5 ft.
Using the Pythagorean theorem, we can write:
5² = 3² + x²
Simplifying and solving for x, we get:
25 = 9 + x²
x² = 16
x = ±4
Since we're looking for a distance, we take the positive root, x = 4.
Therefore, the posts are placed 4 feet away from the tent in the ground.
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Find the segment length indicated. Assume that lines which appear to be tangent are tangent.
Neil had some olive oil. He used 1/5 liter to make a salad dressing. There was 1/2 liter of olive oil remaining in the bottle. Which of these shows the amount of olive oil Neil had in the bottle before using some for the salad dressing?
Neil had 7/10 liter of olive oil in the bottle before using some for the salad dressing.
To find the amount of olive oil that Neil had in the bottle before using some for the salad dressing, we can use subtraction.
Neil had 1/2 liter of olive oil remaining in the bottle after using 1/5 liter to make the salad dressing.
So, the amount of olive oil that Neil had before using some for the salad dressing is:
1/2 liter + 1/5 liter
To add these fractions, we need to find a common denominator:
1/2 liter + 1/5 liter = 5/10 liter + 2/10 liter = 7/10 liter
Therefore, Neil had 7/10 liter of olive oil in the bottle before using some for the salad dressing.
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A girl is making bracelets and necklaces to sell at a yard sale. Each bracelet uses 2 red beads, 6 blue beads, and 10 white beads. Each necklace uses 3 red beads, 6 blue beads, and 9 white beads. What
simplest fraction form of the number of red beads to the total number of beads for the bracelets? For the necklaces? Are these ratios proportional? Use pencil and paper to explain your reasoning.
The ratio of the number of red beads to the total number of beads for the bracelets is,
= 1 / 9
And, The ratio of the number of red beads to the total number of beads for the necklace is,
= 1 / 6
Given that;
A girl is making bracelets and necklaces to sell at a yard sale. Each bracelet uses 2 red beads, 6 blue beads, and 10 white beads. Each necklace uses 3 red beads, 6 blue beads, and 9 white beads.
Hence, We can formulate;
In bracelets,
Total number of beads = 2 + 6 + 10 = 18
In necklace,
Total number of beads = 3 + 6 + 9 = 18
Thus, The ratio of the number of red beads to the total number of beads for the bracelets is,
= 2 / 18
= 1 / 9
And, The ratio of the number of red beads to the total number of beads for the necklace is,
= 3 / 18
= 1 / 6
Hence, They are not in proportion.
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Select the real world situation that can be represented by 2m+3
A. A music download website has a membership fee of $2 and charges $3 for each download.
B. An online company charges a $3 shipping fee and $2 per item for a purchase.
C. Grace bikes 2 more than 3 times the miles Jamie bikes.
D. Bentley swims 3 less than 2 times the lap Dan swims.
Option C is the real-world situation that can be represented by 2m + 3. The equation 2m + 3 represents the number 3 more than twice a certain number (m).
In option A, the equation that represents the situation would be 3d + 2, where d is the number of downloads. In option B, the equation that represents the situation would be 2i + 3, where i is the number of items purchased.
In option D, the equation that represents the situation would be 2l - 3, where l is the number of laps Dan swims.
Therefore, option C is the correct answer as it is the only option that represents the situation where one person bikes 2 more than 3 times the miles another person bikes.
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When a storm moved into Park City, the temperature dropped
5 degrees.
What integer represents the change in Park City's temperature?
The integer that represents this change is -5.
We have,
The change in temperature is represented by the difference between the temperature before and after the storm.
In this case,
The temperature dropped, which means it decreased.
The integer that represents the change in temperature is negative because it indicates a decrease or a loss.
In particular,
The integer that represents a decrease of 5 degrees is -5.
Therefore, if the temperature before the storm was, for example, 20 degrees, the temperature after the storm would be 20 - 5 = 15 degrees, which is 5 degrees lower.
Thus,
The integer that represents this change is -5.
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determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
To determine a point estimate for the conditional mean of the response variable corresponding to a specified value of the predictor variable, we can use regression analysis.
Regression analysis helps us establish a relationship between the predictor variable and the response variable based on the given data. By fitting a regression model, we can estimate the conditional mean of the response variable at a specific value of the predictor variable.
Once the regression model is established, we can substitute the specified value of the predictor variable into the model equation to obtain the corresponding estimated value of the response variable. This estimated value serves as the point estimate for the conditional mean.
It's important to note that the accuracy of the point estimate depends on the quality and representativeness of the data, as well as the assumptions and limitations of the regression model used.
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For the following quadratic function, find the axis of symmetry, the vertex and the y-intercept. y= x^2 + 16x+ 24
A. axis of symmetry: x = -16; vertex (-16,24); y-intercept: -16
B. axis of symmetry: x = 8; vertex: (8,194); y-intercept: 24
C. axis of symmetry: x = 16; vertex: (16,536); y-intercept: 16
D. axis of symmetry: x = -8; vertex: (-8,-40); y-intercept: 24
Explain how u got the answer
For the given quadratic equation y = x² + 16x + 24 the axis of symmetry x = -8, and the vertex is (-8, -40) and the y-intercept is 24. So, the correct option is D.
Given quadratic equation y = x² + 16x + 24
From the above equation a = 1; b = 16; c = 24. [co-efficients]
The formula for axis of symmetry x = -b/2a = -16/2(1) = -16/2 = -8.
The formula for vertex is ((-b/2a), f(-b/2a)) = (-8, ((-8)² + 16(-8) + 24))
= (-8, (64-128+24))
= (-8, -40)
The formula for y-intercept = f(0) = (0)² + 16(0) + 24 = 24
From the above analysis,
axis of symmetry = -8vertex = (-8, -40)y-intercept = 24So the option D is the correct answer.
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three people are selected from a group of 8 freshmen and 6 sophomores. the probability 2 freshmen and 1 sophomore are selected is
Answer: The probability that 2 freshmen and 1 sophomore are selected is 42/91.
Step-by-step explanation:
To obtain the probability that 2 freshmen and 1 sophomore are selected from a group of 8 freshmen and 6 sophomores, we can use the combinations formula:
The total number of ways to select 3 people from a group of 8 + 6 = 14 people is:
C(14, 3) = 14! / (3! * 11!) = 364
The number of ways to select 2 freshmen from a group of 8 freshmen is: C(8, 2) = 8! / (2! * 6!) = 28
The number of ways to select 1 sophomore from a group of 6 sophomores is: C(6, 1) = 6! / (1! * 5!) = 6
Therefore, the number of ways to select 2 freshmen and 1 sophomore from the group of 14 people is: 28 * 6 = 168
The probability of selecting 2 freshmen and 1 sophomore is:P(2F, 1S) = 168 / 364 = 42 / 91
Therefore, the probability that 2 freshmen and 1 sophomore are selected is 42/91.
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A beam of light in air is incident upon a stack of four flat transparent materials with indices of refration 1.20,1.40, 1.32, 1.28. If the angle of incidence for the beam on the first of the four materials is 60 degrees, what angle does the beam make with the normal when it emerges into the air after passing through the entire stack?
When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.
We need to apply Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction for two different media.
Step 1: Calculate the angle of refraction in the first material using Snell's Law.
n1 * sin(i1) = n2 * sin(r1)
1 * sin(60°) = 1.20 * sin(r1)
sin(r1) = 0.5/1.20
r1 ≈ 25.4°
Step 2: Repeat the process for the remaining materials, using the previous angle of refraction as the new angle of incidence. Calculate the final angle of refraction in the last material.
For the second material:
1.20 * sin(25.4°) = 1.40 * sin(r2)
r2 ≈ 21.4°
For the third material:
1.40 * sin(21.4°) = 1.32 * sin(r3)
r3 ≈ 22.9°
For the fourth material:
1.32 * sin(22.9°) = 1.28 * sin(r4)
r4 ≈ 23.3°
Step 3: Calculate the angle of emergence in air.
1.28 * sin(23.3°) = 1 * sin(e)
e ≈ 29.4°
When the beam of light emerges into the air after passing through the entire stack, it makes an angle of approximately 29.4° with the normal.
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Eric has 54 yards of fencing to use for a flowerbed. Some possible measurements are
shown below. For which flowerbeds does Eric have enough fencing? Color in all the
possible answers.
A.
length = 30 yards
area = 300 square yards
B.
length = 20 yards
width = 5 yards
C.
width = 12 yards
perimeter = 48 yards
D.
length = 26 yards
width = 22 yards
E.
length = 16 yards
width = 14 yards
F.
width = 9 yards
area = 162 square yards
what does the taylor polynomial error bound guarantee regarding the errors in using the above approximations?
The Taylor polynomial error bound provides an upper bound on the error between a Taylor polynomial approximation and the actual function value within a given interval.
Specifically, it guarantees that the absolute value of the difference between the actual function value and the Taylor polynomial approximation is no more than the maximum value of the absolute value of the (n+1)th derivative of the function within that interval, multiplied by the maximum distance between the point of approximation and the center of the Taylor series expansion. In other words, the error bound guarantees that the error in using the Taylor polynomial approximation is no larger than a certain value, which can be computed using the given formula.
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what is the sample size needed to create a 90% confidence interval estimate for a population mean with a width of no more than 1 unit given that the population standard deviation is 10? a. 17 b. 33 c. 1083 d. 27
The answer is d. 27 is not a correct answer as it is much smaller than the required sample size of 271.
To create a 90% confidence interval estimate for a population mean with a width of no more than 1 unit, we need to find the sample size required to achieve this level of precision.
Using the formula for the margin of error of a confidence interval, we have
Margin of Error = z* (σ / sqrt(n))
where z* is the critical value from the standard normal distribution corresponding to a 90% confidence level, σ is the population standard deviation (given as 10), and n is the sample size.
We want the margin of error to be no more than 1 unit, so we can write
1 = z* (σ / sqrt(n))
Solving for n, we get
n = (z* σ / 1)^2
Using a standard normal distribution table or calculator, we can find that the critical value z* corresponding to a 90% confidence level is approximately 1.645. Substituting this value and the given population standard deviation into the formula for n, we get
n = (1.645 * 10 / 1)^2 = 270.25
Rounding up to the nearest integer, we get n = 271. Therefore, the answer is d. 27 is not a correct answer as it is much smaller than the required sample size of 271.
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Find the P-value for the test value.
t = 1.619, n = 23, right-tailed
0.0299
0.1196
0.0598
0.0704
The P-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
In this case, the null hypothesis is not provided, so we cannot determine the exact P-value.
However, we can use the t-distribution table or a calculator to estimate the P-value for a one-sample t-test with a sample size of 23 and a right-tailed alternative hypothesis.
Using a t-distribution table with 22 degrees of freedom (n-1), we find that the t-critical value for a 0.05 level of significance (alpha) is 1.717. Since the observed t-value of 1.619 is less than the critical value, we can conclude that the P-value is greater than 0.05.
Using a calculator or software, we can obtain a more accurate estimate of the P-value. For a one-sample t-test with the given parameters, the P-value is approximately 0.1196. This means that if the null hypothesis is true, we would expect to obtain a t-value as extreme or more extreme than 1.619 in about 11.96% of all possible samples of size 23.
Therefore, the answer is 0.1196.
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Determine all generators of Z18 with addition as the group operation. This is called the set of congruence classes modulo 18 (sometimes denoted by Z/18Z). Enter your answer as a comma-separated list.
The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder. It is commonly used to simplify fractions and to find the lowest common denominator of two or more fractions.
An integer is a whole number, either positive, negative, or zero, that does not include fractions or decimal points. Integers can be used in a variety of mathematical operations.
The generators of Z18 with addition as the group operation are 1, 5, 7, 11, 13, and 17.
The generators of Z18 with addition as the group operation are the congruence classes that have a greatest common divisor (GCD) of 1 with 18. In other words, the generators are those elements that are relatively prime to 18. The elements satisfying this condition are 1, 5, 7, 11, 13, and 17. Therefore, the generators of Z18 are {1, 5, 7, 11, 13, 17}.
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Given: KLMN is a trapezoid, KL = MN,
angle 1 = angle 2, LM/KN = 8/9,
Perimeter of KLMN = 132
Find: The length of the legs
The length of each leg of trapezoid KLMN is 6.
The length of the legs of trapezoid KLMN can be found using the given information and the formula for the perimeter of a trapezoid, which is P = a + b1 + b2 + c, where a and c are the lengths of the legs and b1 and b2 are the lengths of the bases.
Since KL = MN and angle 1 = angle 2, trapezoid KLMN is an isosceles trapezoid. Let x be the length of each leg and y be the length of each base. Then we have:
a = c = x
b1 = KN = 9x
b2 = LM = 8x
Using the given perimeter of 132, we can substitute these values into the perimeter formula and solve for x:
132 = x + 9x + 8x + x
132 = 19x + 2x
132 = 21x
x = 6
Therefore, the length of each leg of trapezoid KLMN is 6.
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G
X
Jen has two ropes. The blue rope is 13 feet long and the green rope is 21 feet long.
Calculate how much longer the green rope is than the blue rope.
O A. 21 - 13
= 8²/ feet longer
OB. 21-13 = 21 - 13 = 8 feet longer
c. 21+13= 21 + 13 = 33 feet longer
D. 21 - 13 = 21 - 13 = 8 feet longer
The green rope is 8 ft longer than the blue rope.
Given that Jen has two ropes. The blue rope is 13 feet long and the green rope is 21 feet long.
We need to calculate how much longer the green rope is than the blue rope.
So,
To find the same we will just subtract the shorter blue rope from the longer green rope,
21-13 = 8
Hence the green rope is 8 ft longer than the blue rope.
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The height and base of a triangle are in the ratio 1 : 3 respectively. if the area of the triangle is 216cm², find the length of the base.
The solution is, the length of the base is 36 cm.
Here, we have,
given that,
The height and base of a triangle are in the ratio 1 : 3 respectively.
if the area of the triangle is 216cm²,
let, the length of the base is 3x
so, we get, The height = x
now, we know that,
area = 1/2 * base * height
so, we have,
216 = 1/2 * x* 3x
or, 432 = 3x^2
or, x^2 = 144
or, x = 12
Hence, The solution is, the length of the base is 36 cm.
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An angle measures 32.2° more than the measure of its complementary angle. What is the measure of each angle?
The angle measures 61.1 degrees, and its complementary angle measures 28.9 degrees.
Let x be the measure of the angle.
Then the measure of its complementary angle is 90 - x.
We know that x = (90 - x) + 32.2°, because the angle measures 32.2° more than its complementary angle.
Simplifying this equation, we get:
2x = 90 + 32.2
2x = 122.2
x = 61.1
Therefore, the angle measures 61.1 degrees, and its complementary angle measures 90 - 61.1 = 28.9 degrees.
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factorise 6x+9xcubed
The factored form of expression 6x + 9x³ is 3x(2 + 3x²).
The given expression is 6x + 9x³
Six times of x plus nine times of x cube
x is the variable in the expression
To factorize 6x + 9x³, we can take out the greatest common factor, which is 3x:
6x + 9x³
= 3x(2 + 3x²)
Hence, the factored form of 6x + 9x³ is 3x(2 + 3x²).
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1+1=
2+2=
3+3=
4+4=
4163123 x 418247 =
please help
Answer:
2
4
6
8
1.7412137e+12
Step-by-step explanation:
the first 4 are basic addition and the last one I put into calculator and it came up with that