Answers
The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2
We have,
∫√(2 + cos²x)/(sec x - cosec x)
We can start by simplifying the integrand by using trigonometric identities.
sec x = 1/cos x and cosec x = 1/sin x.
So,
√(2 + cos²x)/(sec x - cosec x)
= √(2 + cos²x) / [(1/cos x) - (1/sin x)]
= √(2 + cos²x) / [(sin x - cos x) / (sin x cos x)]
= √[(2 + cos²x) sin x cos x] / (sin x - cos x)
= √[2 sin x cos x + cos⁴ x] / (sin x - cos x)
= √[sin² x + cos² x + 2 sin x cos x + cos⁴ x] / (sin x - cos x)
= √[(sin x + cos² x)²] / (sin x - cos x)
= (sin x + cos² x) / |sin x - cos x|
The absolute value sign is needed because the denominator, sin x - cos x, can be negative for certain values of x.
Now we can integrate this expression:
∫√(2 + cos²x)/(sec x - cosec x) dx
= ∫(sin x + cos² x) / |sin x - cos x| dx
We can split this integral into two cases: when sin x - cos x > 0, and when sin x - cos x < 0.
Case 1:
sin x - cos x > 0 (when x is between -π/4 and π/4, or between 3π/4 and 5π/4)
In this case, we can drop the absolute value sign:
∫(sin x + cos² x) / (sin x - cos x) dx
= ∫(sin x / (sin x - cos x)) dx + ∫(cos² x / (sin x - cos x)) dx
= -ln|sin x - cos x| - ∫(1 + sin 2x) / (2sin x - 2cos x) dx
To integrate the second term, we can use the substitution u = sin x - cos x, so that du/dx = cos x + sin x and dx = du/(cos x + sin x):
∫(1 + sin 2x) / (2sin x - 2cos x) dx
= ∫(1 + 2u / √2) / (2u / √2) du
= -√2 ln|2sin x - 2cos x| - √2 ln|u| + √2 [tex]tan^{-1}[/tex] (u / √2) + C
= -√2 ln|2(sin x - cos x)| - √2 ln|sin x - cos x| + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C
= -√2 ln|sin x - cos x| - √2 ln 2 + √2 [tex]tan^{-1}[/tex] [(sin x - cos x) / √2] + C
= -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2
Note that we have used the logarithmic identity ln(ab) = ln a + ln b and the substitution u = sin x - cos x.
Thus,
The value of the integration is -ln|sin x - cos x| - √2 ln|sin x - cos x| - √2 ln 2
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Related Questions
Andrew is making fresh lemonade. If he needs 3 lemons to make one glass of lemonade, how many glasses can he make with 28 lemons?
Answers
Answer:
he can make 9 cups of lemonade and he will have 1/3 of a cup of lemonade left over
Step-by-step explanation:
28÷3=9.3333=28/3=9 1/3
Answer:
9.3 or just 9 glasses of lemonade in total.
Step-by-step explanation:
just divide 28 with 3. but just to round it up i would say 9 glasses of lemonade.
How do I solve the problem using substitutions?
Answers
By using the substitution method, the value for (x,y) = (-2, 2)
What is the substitution method in algebra?The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.
In essence, from the given system of equations; let's make x the subject of the formula in the first equation.
5x + 3y = -4
5x = -4 - 3y
Divide both sides by 5;
x = -4/5 - 3y/5
Now, we are going to substitute this value for x into the second equation. The second equation says:
y - 2x = 6
y - 2(-4/5 - (3y/5)) = 6
By solving for y;
y = 2
Now, let's replace the value of y with any of the given equation (2);
y - 2x = 6
2 - 2x = 6
-2x = 6 - 2
-2x = 4
Divide both sides by -2
-2x/-2 = 4/ -2
x = -2
Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)
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Lin is using technology to create a segmented bar graph from a spreadsheet and is following the steps listed. What is the missing step?
Step 1. Copy your relative frequency table into the spreadsheet.
Step 2: ?
Step 3: Highlight the data of the relative frequency table.
Step 4: Insert the proper type of graph using the “Insert” tab.
Step 5: Check the elements of the graph to ensure the appearance is correct.
ANSWER CHOICES
A.convert your data into percentages.
B. Total the columns.
C. Add a title to the graph.
D. Label each row and column.
Answers
Note the the missing step is: " Total the columns." (Option B) so the completed step with regard to the segmented bar graph is given below.
What is a segmented bar graph?A segmented bar chart uses vertical or horizontal bars to compare two or more categories. Typically, the stacked bars represent each group's percentage of the whole and are plotted by the proportion of each value inside each group.
This style of chart can be beneficial for comparing total amounts across each split bar or group. It may be an effective method of forecasting a company's profit over a period of months, with the earnings separated into distinct product lines.
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Explain whether the research topic is best investigated through an experiment or an observational study. Then describe the design of the experiment or observational study.
1. A cycling team wants to know whether incorporating yoga into a workout routine improves racing times.
2. A researcher wants to compare the effects of a new experimental cancer drug with a cancer drug that has been used for at least 10 years.
Answers
2. An experiment would also be the best method to compare the effects of a new experimental cancer drug with a cancer drug that has been used for at least 10 years. The researcher can randomly assign some patients to a group that receives the new drug and some patients to a group that receives the old drug. Then, they can compare the effectiveness of the two drugs in treating cancer.
In both cases, the experiment should be designed as a randomized controlled trial (RCT) to ensure that the results are unbiased. The participants should be randomly assigned to the groups to avoid any selection bias. The groups should be as similar as possible in terms of age, gender, and other relevant characteristics. The researchers should also use blinding procedures to ensure that the participants and the researchers are unaware of which group is receiving which treatment. This will help to reduce the risk of bias and increase the validity of the results.
What is the total of miles mark ran last week?
Answers
The total of miles mark ran last week is 10.75 miles.
We have the dot plot.
So, the total number of miles Mark ran
= 1 1/4 x 1 + 2 x 2 + 2 2/4 x 1 + 3 x 1
= 5/4 x 1 + 4 + 10/4 x 1 + 3
= 5/4 + 4 + 10/4 + 3
= 15/4 + 7
= 15/4 + 28/4
= 43/4
= 10 3/4
= 10.75
Thus, the total number of miles Mark ran is 10.75 miles.
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Penn volunteered a total of 96 hours
over the last 12 weeks. He
volunteered the same number of
hours each week.
How many hours did Penn volunteer
in one week? Write an equation
and solve the problem.
Equation:
Answer:
Answers
The number of hours Penn volunteer in one week is 8hours
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Representing the number of hours volunteered in a week by Penn by x
therefore for 12 weeks , the number of hour will be;
12×x = 12x
12x = 96
divide both sides by 12
x = 96/12 = 8 hours
therefore the number of hour volunteered by Penn in a week is 8 hours
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Mrs. Cowley purchases $32,000 worth of stock on her broker's advice and pays her broker a 0.75% broker fee. She is forced to sell it when it falls to $25,100 two years later, and uses a discount broker who charges $17 per trade. Compute her net loss after the broker fees are taken out.
Answers
Answer: $6,320.25
Step-by-step explanation:
Mrs. Cowley's broker fee is calculated by multiplying the purchase price by the broker fee percentage: $32,000 x 0.0075 = $240. Her total cost for the purchase is then $32,000 + $240 = $32,240. When she sells the stock for $25,100, she incurs another fee of $17 for using the discount broker. To calculate her net loss, we subtract her total cost from her selling price and subtract the two broker fees: $25,100 - $32,240 - $17 - $17 = -$6,320.25, which is rounded to $6,320.25 as a net loss.
Write a quadratic equation that has as solutions the given pair of numbers. (Use x as the independent variable.)
5i and −5i
Answers
The quadratic equation that has 5i and -5i as solutions is:
x²+ 25 = 0
The quadratic equation is the polynomial having the highest power of 2. If 5i and -5i are the solutions to the quadratic equation, then the quadratic equation can be written as:
(x - 5i)(x + 5i) = 0
Expanding this equation, we get:
x² - (5i)² = 0
x² - 25i² = 0
Since i² = -1, we can substitute -1 for i², giving us:
x² - 25(-1) = 0
x² + 25 = 0
Therefore, the quadratic equation that has 5i and -5i as solutions is:
x²+ 25 = 0
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Give me an example of a pictogram
Answers
Answer:
Step-by-step explanation:
help with this please. how many solutions and what are they
Answers
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
Here, we have,
A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.
given
We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
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For a standard normal distribution, given:
P(z < c) = 0.0234
Find c.
Answers
The value c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.
To find the value of c for which P(z < c) = 0.0234 for a standard normal distribution, we can use a standard normal distribution table or a calculator with a built-in normal distribution function.
Using a standard normal distribution table, we can look up the area to the left of c and find the corresponding z-score. This z-score will be the value of c for which P(z < c) = 0.0234.
Looking up the area 0.0234 in the table, we find that the corresponding z-score is approximately -2.07.
Therefore, c = -2.07 for a standard normal distribution with P(z < c) = 0.0234.
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Triangle ABC ~ triangle DEF. Use the image to answer the question.
a triangle ABC with side AB labeled 11, side CA labeled 7.6 and side CB labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Determine the measurement of DF.
DF = 1.58
DF = 1.52
DF = 1.1
DF = 5.5
Answers
The value of DF would be,
DF = 1.38
We are given that triangle ABC is similar to triangle DEF.
Therefore, we can set up the following proportion:
AB/DE = BC/EF = AC/DF
We are given the lengths of AB, AC, and BC, so we can substitute those values into the proportion:
11/2 = 7.9/EF = 7.6/DF
We are asked to find the length of DF, so we can isolate DF by cross-multiplying:
11/2 = 7.6/DF
DF = 7.6 x 2 / 11
DF = 1.38
Thus, The value of DF would be,
DF = 1.38
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Solve this quadratic equation using the quadratic formula. 2X^2 - 10x + 5 = 0
Answers
Answer:
If I am not mistaken, the answer is:
x1: 4.436
x2: 0.564
Step-by-step explanation:
Answer is
5 + √15 or 4.43649 decimal
2
and
5 - √15 or .56350 decimal
2
Step by step
Given 2x^2 -10x +5 = 0
Quadratic formula
-b +- √ b^2 - 4 a c
2a
- -10 +- √ -10^2 (-4)(2)(5)
2(2)
Simplify
10 +- √ 100 - 40
2(2)
10+- √ 60
2(2)
Factor out √60 = 2^2 * 3 * 5
Rewrite after moving 2 outside √
10 +- 2 √15
2(2)
Divide out one of the “2’s” with terms outside the √
5 +- √15
2
Solve
5 + √15
2
5 - √15
2
Help please, I don’t know how to solve this.
Answers
Answer: A
Step-by-step explanation:
Goes down to the integer 1. B is the only one that makes sense subtracting doesn't work 87654321 goes from the 2 half line.
The function,f(x), is plotted below, Evaluate each limit, if it exists.
Answers
The limit exists and is equal to 6.
The limit exists and is equal to 4.
Now, let's use this concept to evaluate the limits of the given function F(x). Looking at the graph of F(x), we see that it approaches different values as x approaches different points. We will evaluate each limit separately:
lim F(x) as x → 1
As x approaches 1 from the left side, the function appears to be approaching a value of 2. Similarly, as x approaches 1 from the right side, the function appears to be approaching a value of 4. However, the limit does not exist as the function is not approaching a single value as x approaches 1.
lim F(x) as x → 3
As x approaches 3, the function appears to be approaching a value of 4.
lim F(x) as x → ∞
As x approaches infinity, the function appears to be approaching a value of 6.
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is y=x-3 a function or an equation
Answers
Two cyclists leave towns 130 kilometers apart at the same time and travel toward each other. One cyclist travels 5 km/h faster than the other.If they meet in 2 hours, what is the rate of each cyclist?
Answers
Answer:
Faster cyclist = 37.5km/h
Slower cyclist = 32.5km/h
Step-by-step explanation:
Let's call the rate of the slower cyclist "r" (in km/h). Then the rate of the faster cyclist is "r+5" (in km/h), since they are traveling 5 km/h faster.
We know that the two cyclists are traveling towards each other and will meet in 2 hours. We can use the formula:
distance = rate × time
Let's call the distance each cyclist travels "d". Since they are traveling towards each other, their distances will add up to the total distance between the two towns, which is 130 km. So we can write:
d + d = 130
2d = 130
d = 65
Now we can use the formula again to find the rates of the two cyclists:
For the slower cyclist:
distance = rate × time
65 = r × 2
r = 32.5 km/h
For the faster cyclist:
distance = rate × time
65 = (r+5) × 2
r+5 = 32.5 + 5 = 37.5 km/h
So the rate of the slower cyclist is 32.5 km/h, and the rate of the faster cyclist is 37.5 km/h.
Number of hours at work
Graduates Non-graduates
9641 2138
6655432 3 13445559
93310 4 346889
92501
(a) What were the ranges for the two groups?
hours
Graduates
Non-graduates
hours
(b) Which group had more responses in the 40s?
O Graduates O Non-graduates O Each had the same
(c) Which group had the greater median number of hours?
O Graduates O Non-graduates O The medians were the same
Answers
(a) The range for the graduates is 86760 hours.
(c) The graduates had the greater median number of hours.
(a) The range is the difference between the maximum and minimum values in a set of data. We are given the following data:
Graduates: 9641 hours, 6655432 hours, 93310 hours, and 92501 hours
Non-graduates: 2138 hours, 3 hours, 4 hours, and 13445559 hours
The range for the graduates is 9641 - 92501 = 86760 hours.
The range for the non-graduates is 2138 - 13445559 = 13443421 hours.
(c) To find the median, we need to arrange the data in order from smallest to largest and find the middle value. If there are an even number of data points, we take the average of the two middle values.
Graduates: 9641 hours, 93310 hours, 92501 hours, 6655432 hours
The median is the average of 93310 hours and 92501 hours, which is (93310 + 92501)/2 = 92905.5 hours.
Non-graduates: 2138 hours, 3 hours, 4 hours, 13445559 hours
The median is the average of 3 hours and 4 hours, which is (3 + 4)/2 = 3.5 hours.
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For her end of year party Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit and Brand B contains 12% fruit juice. What percent of the mixture is fruit juice?
A. 30%
B. 28%
C. 20%
D. 32%
Answers
Answer:
B. 28%
Step-by-step explanation:
You want to know the percent of the mixture that is fruit juice, if the mixture is 6 L of 52% juice and 9 L of 12% juice.
JuiceThe total amount of juice in the 6+9 = 15 L of mix is ...
0.52·(6 L) +0.12(9 L) = 3.12 L +1.08 L = 4.2 L
Then the fraction of the mix that is fruit juice is ...
(4.2 L)/(15 L) = 0.28 = 28%
The percent of the mixture that is fruit juice is 28%, choice B.
__
Additional comment
Effectively, the fraction is the weighted average of the fractions of the constituents. The weights are the number of liters of each constituent.
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Question 25 of 40
The linearized regression equation for an exponential data set is log ý = 0.14x
+0.4, where x is the number of years and y is the population.
What is the predicted population when x = 20? Round your answer to the
nearest whole number.
A. 112,590
B. 1585
C. 630
D. 3
Answers
Answer:c
Step-by-step explanation:
Answer: B 1585
took the test
how to convert 90% to a decimal point
Answers
Answer:
0.90
Step-by-step explanation:
Just like a decimal to a percentage number, you must multiply by 100. By converting a percentage number to a decimal point, you must divide it by 100. Which means, the decimal must move 2 times.
For example,
0.90 x 100 = 90%
This is decimal to percentage number, but in this case it is percentage to decimal.
90%.
Since the number ended at 0, put the decimal there and move it 2 times to get to your decimal point.
.90 = 0.90
There you'll get your answer! ^^
90% = 0.90
The equations of three lines are given below.
3
Line 1: y=x+7
Line 2: 2y=3x+5
Line 3: 6x-4y=4
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: O Parallel O Perpendicular
Neither
Line 1 and Line 3: O Parallel O Perpendicular O Neither
Line 2 and Line 3:
O Parallel O Perpendicular O Neither
X
Answers
Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.
To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):
2y = 3x + 5
y = (3/2)x + 5/2
Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes (coefficients of x) of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.
Line 1 and Line 3:
To determine whether these two lines are parallel or perpendicular, we can convert Line 3 into slope-intercept form (y = mx + b):
6x - 4y = 4
-4y = -6x + 4
y = (3/2)x - 1
Comparing this equation to the equation of Line 1 (y = x + 7), we see that the slopes of the two lines are not equal, nor are they negative reciprocals of each other. Therefore, the lines are neither parallel nor perpendicular.
Line 2 and Line 3:
To determine whether these two lines are parallel or perpendicular, we can convert Line 2 into slope-intercept form (y = mx + b):
2y = 3x + 5
y = (3/2)x + 5/2
Next, we can rearrange Line 3 into the slope-intercept form:
6x - 4y = 4
-4y = -6x + 4
y = (3/2)x - 1
Comparing the equations of the two lines, we can see that they have the same slope (3/2). Therefore, the lines are parallel.
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please help quickly
Answers
Answer: B
Step-by-step explanation:
First, you have to know that a straight line is equal to 180 degrees. They gave you 115 degrees in part of a line, so the other part or the angle not given must be equal to 65 degrees. Another thing is that a triangle has 180 degrees. 65+80 degrees is equal to 145 degrees, leaving angle 1 to be equal to 35 degrees. Another thing to know is that reflective angles have the same measurement. If the original angle was equal to 65 after subtraction 115 from 180, we know that the second triangle's angle would also be equal to 65. 65+86 is 150, and 180-150 is 30. Thus, the answer is B.
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Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 2.1%
B. 21%
C. 3%
Answers
The percentage of saline solution in brand B is 3%. Then the correct option is C.
Let x be the percent of saline solution in brand B.
Since Danielle combined brands A and B to create a total of 18 gallons of 8% saline solution, we know that the total volume of saline solution in the combination is 18% of 6 gallons + x% of (18 - 6) gallons.
Thus, we can set up the equation:
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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which expression is equivalent to n+n-0.18n
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
Answers
Answer:
Simplifying the expression `n + n - 0.18n`, we get:
n + n - 0.18n = 2n - 0.18n
Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.
Looking at the answer choices:
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.
Therefore, the answer is d. 2n - 0.82.
Step-by-step explanation:
The volume of a cube depends on the length of its sides. This can be written
in function notation as v(s). What is the best interpretation of v(9) = 277
A. A Gube with a volume of 3 cubic feet has side lengths of 27 feet.
B. 3 sides of the cube have a total length of 27 feet.
6. A cube with side lengths of 3 feet has a volume of 27 cubic feet
D. 3 of these cubes will have a total volume of 27 cubie feet.
Answers
The best interpretation of v(9) = 277 is a cube with side lengths of 9 feet has a volume of 277 cubic feet
What is the best interpretation of v(9) = 277From the question, we have the following parameters that can be used in our computation:
The volume of a cube depends on the length of its sides.
And this is represented in function notation as v(s)
The function notation v(s) means
The volume of cube with side length s is v
Using the above as a guide, we have the following:
A cube with side lengths of 9 feet has a volume of 277 cubic feet
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Answer:
19.1
I found it out after I got the ansewer wrong on IXL
√² +13
Simplify
63x
real numbers and p and q are rational.
01
1
1
1/3
1/3
+
+
13
6
< Previous
-.Write the answer in the form ax² + bx without using radicals. a and bare
13x¹/3
6
13
1/3
+ -x-1/3
6
Next ▸
Answers
Answer:
third answer option
Step-by-step explanation:
[tex] \sqrt[3]{ {x}^{2} } = {x}^{ \frac{2}{3} } [/tex]
[tex] \sqrt[3]{x} = {x}^{ \frac{1}{3} } [/tex]
[tex] \frac{1}{ {x}^{ \frac{1}{3} } } = {x}^{ - \frac{1}{3} } [/tex]
[tex] \frac{ {x}^{ \frac{2}{3} } }{6 {x}^{ \frac{1}{3} } } = \frac{1}{6} \times {x}^{ \frac{1}{3} } [/tex]
[tex] \frac{13}{6 {x}^{ \frac{1}{3} } } = \frac{13}{6} \times {x}^{ - \frac{1}{3} } [/tex]
so, the result is
[tex] \frac{1}{6} \times {x}^{ \frac{1}{3} } + \frac{13}{6} \times {x}^{ - \frac{1}{3} } [/tex]
Emma has half of her investments in stock paying a 10%
dividend and the other half in a stock paying 14% interest. If her total annual interest is $600, how much does she have invested?
Answers
Emma has $5,000 total invested.
Let's call the total amount Emma has invested "x".
Emma has half of her investments in stock paying a 10% dividend, so that portion of her investment earns 0.10(x/2) = 0.05x in annual interest.
The other half of her investments are in a stock paying 14% interest, so that portion of her investment earns 0.14(x/2) = 0.07x in annual interest.
The total annual interest Emma earns is $600, so we can set up the following equation:
0.05x + 0.07x = 600
0.12x = 600
x = 5000
Therefore, Emma has a total of $5000 invested.
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10 cm The diagram above, not drawn to scale, shows a circle within a semicircle with a diameter of 10cm. Find the area of the shaded region. Seni
Answers
The area of the shaded region is equal to 12.5π or 39.27 square centimeters.
How to calculate the area of the shaded region?In Mathematics and Geometry, the area of a semicircle can be calculated by using this formula:
Area of semicircle, As = πr²/2
Where:
r represents the radius of a circle.
Note: Radius = diameter/2 = 20/2 = 10 centimeters.
By substituting the radius into the formula for the area of a semicircle, we have the following;
Area of semicircle = 1/2 × π × 10²
Area of semicircle = 50π square centimeters.
For the circle, we have:
Area of circle, Ac = πr²
Area of circle, Ac = π(10/2)²
Area of circle, Ac = 25π square centimeters.
Now, we can determine the area of the shaded region as follows;
Area of shaded region = (As - Ac)/2
Area of shaded region = (50π - 25π)/2
Area of shaded region = 12.5π or 39.27 square centimeters.
Read more on area of semicircle and circle here: https://brainly.com/question/28697311
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Answers
Answer: 6(a) - 6(3)
Step-by-step explanation:
Answer: Its B
Step-by-step explanation:
The expression 6(a-3) can be simplified by applying the distributive property of multiplication over addition, which gives 6a - 18. Therefore, the expression is equivalent to 6a - 18. The answer is (b) –2. All other options do not simplify to the same expression as 6(a-3). For example, 18a is not equivalent to 6(a-3) and neither is 6(a)-6(3). Option (d) 1 simplifies to 6a - 18a + 18, which is not equivalent to the original expression. Similarly, 6(a)-3 simplifies to 6a - 3, which is also not equivalent.