decide which of the following statements are true based on the given triangle below. Assume the figure is drawn to scale that angle A is greater than angle B.
Answers
From the figure given, the triangle is a right triangle.
Since it is a right triangle, ∠C = 90 degrees
Assuming the figure is drawn to scale and ∠A is greater than ∠B, then we have the following:
m∠A = 90° - m∠B
Using the triangle angle sum theorem, ∠A + ∠B + ∠C = 180
since m∠C = 90°,
m∠B + m∠A = 90°
Thus, m∠A = 90 - m∠B,
Also,
\(\tan B=\frac{\sin B}{\cos B}\)Since ∠A is greater than ∠B, then ∠A = 60 and ∠B = 30
Thus,
\(\begin{gathered} \tan B=\frac{\sin B}{\cos B} \\ \\ \tan 30=\frac{\sin 30}{\cos 30} \end{gathered}\)ANSWER:
\(\begin{gathered} \tan B=\frac{\sin B}{\cos B} \\ \\ \\ m\angle A=90-m\angle B \end{gathered}\)
Related Questions
• Write this number as a fraction:178.25
Answers
Answer: 178 1/4 or 713/4
Step-by-step explanation:
178.25 = 178+0.25 = 178+25/100
gcd(25,100) = 25
178.25 = 178+(25/25)/(100/25) = 178+1/4 = 713/4
Solve the quadratic equation using factoring x2 + 3x + 2 = 0.
Ox= 1, x= 2
Ox=-1, x=-2
Ox=1, x=3
Ox=-1, x=-3
Answers
Answer:
x= -1 and also x = -2
Which agrees with the second option in your list of answers
Step-by-step explanation:
We look for two numbers whose product is "2" (constant term in your quadratic equation) and which added give "3" (coefficient in the middle term with "x"). So we find the factors 1 and 2:
1 times 2 = 2 and 1 + 2 = 3
So we use these factor to expand the middle term and then factor by grouping:
\(x^2+3x+2=0\\x^2+x+2x+2=0\\x(x+1)+2(x+1)=0\\(x+1)(x+2)=0\)
Then for this product of binomials to give zero, each binomial must be zero. That is
x= -1 and also x = -2
what is the image point of (0,8) after a translation right 3 units and down 5 units
Answers
Answer:
(3,3) because (0+3, 8-3)
Two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2 seconds , 45 cm in another next 2 seconds, etc. Find how long it takes for the particles to meet and hence, determine the distances travelled by each particle
Answers
The movement of both particles are illustrations of arithmetic progression.
Both particles meet at 1 cm, after 50 seconds
For particle 1, we have:
\(\mathbf{Particle\ 1: 97, 93, 89,.....}\)
The nth term of particle 1 is:
\(\mathbf{T_n = 97 - 4(n - 1)}\)
For particle 2, we have:
\(\mathbf{Particle\ 2: 49, 47, 45,.....}\)
The nth term of particle 2 is:
\(\mathbf{T_n = 49 - 2(n - 1)}\)
Both particles are at the same distance, when:
\(\mathbf{T_n = T_n}\)
So, we have:
\(\mathbf{97 - 4(n - 1) = 49 - 2(n -1)}\)
Subtract 49 from both sides
\(\mathbf{48- 4(n - 1) = - 2(n -1)}\)
Divide through by -2
\(\mathbf{-24+ 2(n - 1) = (n -1)}\)
Collect like terms
\(\mathbf{-24 = (n -1) - 2(n - 1)}\)
\(\mathbf{-24 = -(n -1)}\)
Divide through by -1
\(\mathbf{24 = n -1}\)
Add 1 to both sides
\(\mathbf{n = 25 }\)
Substitute 25 for n in \(\mathbf{T_n = 97 - 4(n - 1)}\)
\(\mathbf{T_{25} = 97 - 4(25 -1)}\)
\(\mathbf{T_{25} = 1}\)
This means that both particles meet at 1 cm
The time they meet is:
\(\mathbf{Time = n \times 2\ seconds}\)
Substitute 25 for n
\(\mathbf{Time = 25 \times 2\ seconds}\)
\(\mathbf{Time = 50\ seconds}\)
Hence, both particles meet after 50 seconds
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what's the result of adding these two polynomials: (2x+y+1) + (2x⁶-y+1)? I'm doing a test and the correct answer says is 4x⁶-2y+1 but I'm not very sure it is the correct one. Can someone help me? :3
Answers
Answer
\(\begin{equation*} 2x^6+2x+2 \end{equation*}\)Step-by-step explanation
Given the polynomials:
\(\begin{gathered} 2x+y+1 \\ \text{ and} \\ 2x^6-y+1 \end{gathered}\)To add them we need to add the similar terms (terms with the same variable and degree), as follows:
\(\begin{gathered} (2x+y+1)+(2x^6-y+1)= \\ =2x^6+2x+(y-y)+(1+1)= \\ =2x^6+2x+2 \end{gathered}\)What is -2 - 1 3\7 please help
Answers
Answer:
Step-by-step explanation:
To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.
To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.
Now we can add -7/7 and 3/7 to get -4/7.
Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form
Amadi is three times as old as Chima. The sum of their ages is 24
Answers
Answer:
Amadi: 20 years old
Chima : 4 years old
La probabilidad de que julio salga con carla es 0.75 , y la probabilidad de que salga con marisol es de 0.50. Si la probabilidad de que salga con carla o marisol es 0.85; calcular la probabilidad de que salga con ambas a la vez
Answers
La probabilidad de que Julio salga con Marisol y Carla al mismo tiempo es 0.40
What is the addition rule of probability for two events?For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
\(P(A) = 0.75\\\)\(P(B) = 0.50\)\(P(A \cup B) = 0.85\)To find: \(P(A \cap B)\\\)
Using the addition rule, we get:
\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\\0.85 = 0.75 + 0.50 - P(A \cap B)\\P(A \cap B) = 1.25 - 0.85 = 0.40\)
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40
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The probability that Julio will date Marisol and Carla at the same time is 0.40.
Here, we have, For two events A and B, we have:
Probability that event A or B occurs = Probability that event A occurs + Probability that event B occurs - Probability that both the event A and B occur simultaneously.
This can be written symbolically as:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given that;
The probability that Julio goes out with Carla is 0.75, and
the probability that he goes out with Marisol is 0.50.
The probability that he goes out with Carla or Marisol is 0.85
To find:
The probability that he will date both at the same time.
Let we take:
A = event that Julio goes with Carla
B = event that Julio goes with Marisol, then, the given expression is symbolically represented as:
P(A) = 0.75
P(B) = 0.50
P(A∪B)= 0.85
To find: P(A ∩ B)
Using the addition rule, we get:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.85 = 0.75 + 0.50 - P(A ∩ B)
P(A ∩ B) = 0.40
Thus, the probability that Julio will date Marisol and Carla at the same time is 0.40.
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complete question:
The probability that Julio dates Carla is 0.75, and the probability that he dates Marisol is 0.50. If the probability that he goes out with carla or marisol is 0.85; Calculate the probability that he will date both at the same time.
Choose the best explanation that describes in words what the numerical value of the slope tells you.
a. Every increase in coral growth of one centimeter will result in an average of 5.25 fewer degrees Celsius of sea surface temperature per year.
b. Every increase in coral growth of one centimeter will result in an average of 5.25 more degrees Celsius of sea surface temperature per year.
c. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 more centimeters of coral growth per year.
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.
Answers
Data for the question :
Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1
Growth 0.85 0.85 0.79 0.86 0.89 0.92
Answer:
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.
Step-by-step explanation:
Given the data :
Surface Temperature (X) : 26.7 26.6 26.6 26.5 26.3 26.1
Growth (Y) : 0.85 0.85 0.79 0.86 0.89 0.92
Using a regression calculator, we can find the model equation and extract the slope :
The regression equation obtained is :
y=5.039-0.1578x
From y = mx + c
Where m = gradient or slope
c = intercept
x and y are predictor and predicted variables respectively.
Hence, the gradient or slope (m) of the model = - 0.157. We have a negative slope, hence, increase in x will result una decrease in y.
The slope thus means: for every 1 degree increase in sea surface temperature (x), there is an average decline of about 0.1578 cm in growth per year.
write the abbreviation for each of the following: match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer.
Answers
1. The abbreviation for femtogram is - fg.
2. The abbreviation for decimeters is - dm.
3. The abbreviation for microliter is - μL or ul.
4. The abbreviation for femtosecond is - fs.
1. Femtogram (fg): A unit of mass measurement in the International System of Units (SI). It is equal to \(10^{-15}\) grams and is commonly used to measure the mass of small particles or atoms.
2. Decimeter (dm): A unit of length measurement in the International System of Units (SI). It is equal to 0.1 meters and is commonly used to measure small distances.
3. Microliter (μL or ul): A unit of volume measurement in the International System of Units (SI). It is equal to \(10^{-6}\) liters and is commonly used to measure very small volumes of liquids.
4. Femtosecond (fs): A unit of time measurement in the International System of Units (SI). It is equal to \(10^{-15}\) seconds and is commonly used to measure very short periods of time, such as in atomic and molecular physics, chemistry, and photonics.
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The complete question is -
write the abbreviation for each of the following: match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer.
1. The abbreviation for femtogram is -
2. The abbreviation for decimeter is -
3. The abbreviation for microliter is -
4. The abbreviation for femtosecond is -
In a lottery, the top cash prize was $642 million, going to three lucky winners. Players pick five different numbers from 1 to 56 and one number from 1 to 49.
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A player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 49). What is the probability of winning the minimum award?
The probability of winning the minimum award is
Answers
Total number of possible outcomes:
Number of ways to choose 3 numbers from 56 (56 choose 3): 56! / (3! * (56 - 3)!) = 22,957
Number of ways to choose 1 number from 49: 49
Total number of possible outcomes = 22,957 * 49 = 1,128,593
Number of favorable outcomes:
Number of ways to choose 1 number from 49: 1
Number of favorable outcomes = 1
Probability of winning the minimum award:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 1,128,593 ≈ 0.000000888, or approximately 0.0000888%
State if the triangles are similar. If so, how do you know they are
similar and complete the similarity statement.
STU~
Answers
Answer:
yes the triangles are similar
Step-by-step explanation:
I know this because the triangle still keeps the same shape for both triangles, one is simply scaled down to size.
Step-by-Step Explanation:
In Triangle UTS,
UT = 96
TS = 64 + 44 = 108
US = 96
Angle S (common)
In Triangle CDS,
CD = 40
DS = 44
CS = 96 - 57 = 39
Angle S (common)
Now compare the Ratios of the Corresponding Sides.
=> UT/CD = 96/40 = 12/5
=> TS/DS = 108/44 = 27/11
=> US/CS = 96/39 = 32/13
Therefore, their Sides are not in proportional ratios. So, these triangles are not similar.
Consider the following "generic rectangle" where the area of each region is given. Write equivalent
expressions that express the area of the whole rectangle as a sum and as a product.
Answers
Answer:
sum: 3x² -4x -4product: (x -2)(3x +2)Step-by-step explanation:
The areas of four regions are given. We can simply add them to find the sum. To express them as a product, we need to look at common factors.
SumThe total of the given area expressions is ...
3x² +2x -6x -4 = 3x² -4x -4 . . . . sum
ProductExtending the table to show common factors of each row and column, we have ...
\(\begin{array}{c|c|c|}&3x&2\\\cline{1-3}x&3x^2&2x\\\cline{1-3}-2&-6x&-4\\\cline{1-3}\end{array}\)
Since each cell of the table is the product of the corresponding common factors, we can write the area as the product ...
(x -2)(3x +2) . . . . product
Carol sells candles and Yankee Candle. She earns $8.50 per hour plus 6% commission on sales. Last week Carol worked 40 hours. What was Carol’s weekly gross salary if her total sales were $250?
Show work and equation and operation
Answers
Answer:
355.
Step-by-step explanation:
Basic Pay = 8.50 per hour * 40 hours
Basic Pay = 340 dollars.
Commission
Commission wage = gross sales * 6%
Commission wage = 250 * 6/100 = 15 dollars
Income = basic Pay + commission
Income = 340 + 15
Income = 355
What is the equation of the line that is perpendicular to the line through (1,-4) and (-2,2) and passes through the x-intercept of that line?
Answers
Answer:
y=-\(\frac{1}{2}\)x+\(\frac{3}{2}\)
Step-by-step explanation:
First, calculate the slope of the line that is perpendicular to the equation of line we are asked to find
m=(y2-y1)/(x2-x1)
=(2-(-4))/(-2-1)
=6/-3
=-2
in this equation the slope is 2, and to find the first equation, use y=mx+b
use the point (1, -4) to find b
-4=(2)(1)+b
-4=2+b
b=-6
the first equation of the line is y=2x-6
to find the x intercept of that line substitute 0 for y
0=2x-6
2x=6
x=3
the slope of a line perpendicular to this would be the opposite reciprocal of the slope which would be equal to -1/2
for the second equation of the line to pass thorugh the x-intercept of the first line, it must pass through (3, 0), so substitute and solve for b
y=mx+b
0=(-1/2)(3)+b
b=3/2
thus the equation of the line that is perpendicular to the line through (1,-4) and (-2, 2) and passes through the x intercept of that line is y=-\(\frac{1}{2}\)x+3/2
The equation of the line that is perpendicular to the line through (1,-4) and (-2,2) is \(y= \frac{1}{2}x+3\)
The equation of the line perpendicular to the line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
\(y-y_1=\frac{-1}{m} (x-x_1)\)
The slope m is calculated using the formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
\(m=\frac{2-(-4)}{-2-1} \\\\m=\frac{6}{-3} \\\\m=-2\)
For the line passing through the points (1,-4) and (-2,2), substitute m = -2, x₁ = 1, and y₁ = -4 into the equation \(y-y_1=\frac{-1}{m} (x-x_1)\)
\(y-1=\frac{-1}{-2} (x-(-4))\\\\y-1=\frac{1}{2}(x+4)\\\\y=\frac{1}{2}x+2+1\\\\y= \frac{1}{2}x+3\)
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Pls help, I'll give brainlest
Answers
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
When multiplying exponents, you would add the degrees.
A, B, and D's degrees add up to \(5^{-2}\) , which is equal to 1/25.
C adds up to \(5^{2}\), which is 25, therefore making it C
Gretta is saving for retirement. She deposits $125 each month at 6% annual interest for 35 years. According to her calculations, at the end of 35 years, she should have $178,088.79 in her account. How much of this did Gretta contribute and how much of this is interest?
Answers
Answer:
Gretta's Contribution = $52,500
Interest = $125,588.79
Step-by-step explanation:
Gretta contributes $125 each month, for 35 years. Therefore, to find the amount she contributed, we multiply those pieces together (12 months in each year).
125 x 12 x 35 = $52,500
Therefore, over the 35 years, Gretta contributed $52,500.
If there was $178,088.79 in her account, and she contributed $52,500, then the rest is interest.
$178,088.79 − $52,500 = $125,588.79
There was $125,588.79 in interest earned on Gretta's account.
The Emerald Bot clicks 3 times in ____ sec, and its Unit Rate is 7.5 clicks per second. Find the number of sec.
Answers
Answer: The Emerald Bot clicks 3 times in __0.4_ sec
²/₁₅ second per click × 3clicks = ²/₅ sec
Or 0.1333 × 3 = 0.3999 Round to 0.4
Step-by-step explanation: If its unit rate is 7.5 clicks per second, we can find the time, seconds per click by dividing one second by 7.5 clicks
1/7.5 = 0.13333 seconds per click.
Multiply that ²/₁₅ seconds by the 3 clicks to get the time it takes for the 3 clicks.
Negative fractions on the number line
Answers
Answer:
-1.2
Step-by-step explanation:
each mark is .20 so yeah
Pls mark brainliest!
hellppp................
Answers
Answer:
\(B)\)
\((-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x\)
OAmayOHopeO
Solve for x.
x² + 6x + 9 = 12
0 x = -9 + 2√3
0 x =
-9 ± 4√3
0 x =
−3 ± 4√3
0 x = −3+2√3
Answers
Step-by-step explanation:
= x^2 + 6x - 3 = 0
Are you familiar with the Quadratic Formula?
a = 1 b = 6 c = -3
then x = -3 ± 2 \(\sqrt{3}\)
Answer:
\(x1 = - 3 - 2 \sqrt{3} \)
\(x2 = - 3 + 2 \sqrt{3} \)
Step-by-step explanation:
\( {x}^{2} + 6x + 9 = 12\)
\( {x}^{2} + 6x + 9 - 12 = 0\)
\( {x}^{2} + 6x - 3 = 0\)
a = 1, b = 6, c = -3
\(d = {b}^{2} - 4ac = {6}^{2} - 4 \times 1 \times ( - 3) = 36 + 12 = 48 > 0\)
\(x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 6 - \sqrt{48} }{2 \times 1} \frac{ - 6 - 4 \sqrt{3} }{2} = - 3 - 2 \sqrt{3} \)
\(x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 6 + \sqrt{48} }{2 \times 1} = \frac{ - 6 + 4 \sqrt{3} }{2} = - 3 + 2 \sqrt{3} \)
Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Answers
The statements that are true are:
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Options A, B, D, E, and F.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Clayton could use the relationship (x, y) → (y, x) to find the points of the image.
This is the y = x reflection rule.
This is true.
Clayton could negate both the x and y values in the points to find the points of the image.
Reflection of (x, y) along the x-axis and y-axis consecutively will give us
(-x, -y).
This is true.
C’ will remain in the same location as C because it is on the line of reflection.
This is not true.
C’ will move because all points move in a reflection.
This is true.
The image and the pre-image will be congruent triangles.
This is true.
The image and pre-image will not have the same orientation because reflections flip figures.
This is true.
Thus,
All statements are true except the statement:
C’ will remain in the same location as C because it is on the line of reflection.
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Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often, sometimes, and seldom. Below are the results of the one-way ANOVA. Source of Variation SS df MS F Between groups 1,959.79 3 653.26 21.16* Within groups (error) 3,148.61 102 30.86 Total 5,108.41 105 (a) What are the values for N and k
Answers
Answer:
K = 4 ; N = 106
Step-by-step explanation:
Given the following :
Source of VARIATION - SS - df - - MS - - - - - F
Between groups - 1,959.79 - 3 - - 653.26 - 21.16*
Error - - - - - - - - 3,148.61 - - - - 102 - - 30.86
Total - - - - - - - - - - - 5,108.41 - 105
The degree of freedom between group (treatment) (DFT) is obtained using the formula ;
K - 1, where k = number of groups observed
DFT = K - 1 ; From the ANOVA table, DFT = 3
3 = K - 1
3 + 1 = K
K = 4
To obtain sample size (N) :
Degree of freedom of Error (DFE) is the difference between the sample size and the number of groups observed.
DFE = N - K ; From. The table DFE = 102 ; K = 4
102 = N - 4
102 + 4 = N
N = 106
explain 3 factors that should be considered in the construction of index numbers
Answers
1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.
2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.
3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`
construction of index number is also available in two parts:
1. simple
2. weighted
1. simple: the simple method is classified into simple aggregative and simple relative.
2. weighted: the weighted method is classified into a weighted aggregative and weighted average.
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Ron recently increased the size of his Jeep tires from the original P220/75R16 to the
larger P250/85R17. If Mike didn't recalibrate his speedometer, how fast is he really
going on the new tires when his speedometer shows he is traveling 60 mph?
O 54.5 mph
O 62.1 mph
66.1 mph
O 69.8 mph
Answers
Write 0.000000624 in scientific notation
Answers
Answer:
6.24 x \(10^{-7}\)
Step-by-step explanation:
0.000000624 in scientific notation is 6.24 x \(10^{-7}\)
Answer:
Step-by-step explanation:
The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.
The square root of 9999.
Answers
Answer:
99.99499987
Step-by-step explanation:
Answer:
99.99499987
Step-by-step explanation:
chingLesson 113Nomehours playing basketball games during theThe basketball team plays 114 games during the season. Each gomelasts 2 hours. How many hours does the team spend playing basketballgames during the season?The team spendsseasonCircle the most reasonable estimate of the weight of a poper ckp1 liter gram inchI militer701 x 495 =3 meters =centimetersLook at the thermometer Circle the word thatbest describes the temperature.warm cool freezing hotLesson 114A photoshop needs to develop 7,896 rolls of film over a 2-day penodThey want to develop an equal number of rolls of film each day Howmany rolls of film should the photo shop develop each day?The photo shop should developphotos each day5,608 + 8 =696 x 302 =578 676 -14what is the area of the triangle?nclude the unit of measuren your answer18 in.- To61
Answers
Given:
The total number of basketball games played during the season to be 114 games.
The number of hours spent on each games is 2 hours.
Therefore, the number of hours the team spent playing basketball game during the season is
\(114\times2hours\)Simplify
\(114\times2hours=228hours\)Hence, the team spends 228 hours playing basketball games during the season.
Given the following sets, find the set (A U B) n (AUC).
U= {1, 2, 3, ..., 10}
A=(2, 5, 7, 10}
B = {1, 2, 3)
C={1, 2, 3, 4, 5}
Answers
The set (A U B) n (A U C) is {2, 5, 7, 10}. A.
To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.
Set A U B:
The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.
A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.
A U B consists of the elements {1, 2, 3, 5, 7, 10}.
Set (A U B) U C:
Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.
Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.
Finding the intersection:
Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.
The intersection of these two sets is the combination of common elements.
The common elements are {2, 5, 7, 10}.
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Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she
sold 6 fewer books than she did on Tuesday. During the three days Rachel sold 19 books. Create an equation that can
be used to find m, the number of books Rachel sold on Monday.
Equation:
Answers
Step-by-step explanation:
1. Let the number of books sold on Monday be x.
2. And, The no. of Books sold on Tuesday be 2x , which is twice as the books sold on monday.
3. Now, The no. of books sold on Wednesday be 2x-6 ,
which is fewer than the books sold on Tuesday.
Where Total no. of books sold on 3 days is 19.
so, The equation be like: x+2x+2x-6 = 19
Answer:
m = 5
Step-by-step explanation:
On Tuesday, she sold twice as many books as she did on Monday. An equation is now formed from this:
I Tu = Mo * 2
On Wednesday, she sold 6 fewer books than she did on Tuesday. An equation is now formed from this:
II We = Tu - 6
During the three days Rachel sold 19 books. An equation is now formed from this:
III Mo + Tu + We = 19
The task says that you should just use one equation to find out how many books were sold on Monday. So take the last equation and replace Tu and We with terms in which Mo occurs.
Substitute equation I into equation III:
IIIa Mo + Mo*2 + We = 19
Replace Tu in Equation II with Equation I:
II a We = Mo * 2 - 6
Substitute equation IIa into equation IIIa:
IIIb Mo + Mo * 2 + Mo * 2 - 6 = 19
Now the equation is converted to Mo (Mo = m):
m + m * 2 + m * 2 - 6 = 19 | + 6
m + 2 m + 2 m = 25
5 m = 25 | : 5
m = 5