The volume of the cylinder is 98π cubic centimeters.
To find the volume of a cylinder, we use the formula:
Volume = π × [tex]r^2[/tex] × h
Given:
Radius (r) = 7 cm
Height (h) = 2 cm
Substituting the values into the formula, we have:
Volume = π × (7 [tex]cm)^2[/tex] × 2 cm
Calculating the values inside the parentheses:
Volume = π × 49 [tex]cm^2[/tex] × 2 cm
Multiplying the values:
Volume = 98π [tex]cm^3[/tex]
Therefore, the volume of the cylinder is 98π cubic centimeters.
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Deigo wrote 6^4*8^3=48^7. explain what his mistake was.
The index forms are of different bases and thus cannot be multiplied and their exponents added.
How to determine the valueTo determine Deigo's mistake, we need to know index forms and their rules.
Index forms are defined as mathematical forms that are used in representing numbers or variables that are too large or too small in more convenient forms.
They are also called scientific notation or standard forms.
The rules of index forms are;
Subtract the exponents when like bases are dividedAdd the exponents when like bases are multipliedFrom the information given, we have;
6⁴ × 8³ = 48⁴⁷
They are not of like bases and thus cannot be multiplied
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What is the balance after three years on a CD with an initial investment of $2,200 and a 2.95% interest rate?
The remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.
To solve this problemThe compound interest formula is as follows:
Balance = Principal * (Rate/100 + Rate * 1)Time
Where
The initial investment is the principalRate is the period-to-period interest rateThe amount of periods makes up timePrincipal (P) is equal to $2,200.
Rate (R) = 2.95% = 2.95/100 = 0.0295 in decimal form.
Time (T) = 3 years.
The following formula is substituted for the values:
Balance =[tex]$2,200 * (1 + 0.0295)^3.[/tex]
Exponent calculation:
Balance = [tex]$2,200 * (1,0295)^3[/tex]
Calculating the result:
Balance ≈ $2,200 * 1.089135
Balance ≈ $2,393.10
So, the remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.
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Mrs. Brown wants to assign eight homework
problems to her Algebra 1 class tonight. If
there are eleven problems she could choose
from, how many different homework sets
could she assign?
A
88
B
165
C
495
D
990
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
We have,
The number of different homework sets Mrs. Brown could assign can be calculated using the combination formula.
In this case, she wants to choose 8 problems out of 11 available problems. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items to choose from and r is the number of items to be chosen.
Using this formula:
C(11, 8) = 11! / (8! x (11 - 8)!)
C(11, 8) = 11! / (8! x 3!)
Simplifying the factorial expressions:
C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)
The factorial terms cancel out:
C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)
C(11, 8) = 165
Therefore,
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
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Uncle Joe made chocolate chip cookies. Michael ate 50% right away. Robert ate 50% of what was left. fourteen cookies remain. How many cookies did Uncle Joe make?
Answer:
50% ate uncle joe and 50% ate robert so, uncle joe make 14 cookies
Answer:
1. Michael ate 50% of the cookies, so the remaining cookies are 50% of the total. Let's denote the total number of cookies as T. So, after Michael ate his share, 0.5 x T cookies remained.
2. Robert then ate 50% of what was left, leaving only 50% of the cookies that were left after Michael ate. So, after Robert ate his share, 0.5 x 0.5 x T = 0.25 x T cookies remained.
3. We know that 14 cookies remained after Robert ate his share.
So, we can set up the equation 0.25 x T = 14 and solve for T:
T = 14/0.25 = 56
So, Uncle Joe made 56 chocolate chip cookies.
Step-by-step explanation:
Hope it helps!!!
Susan has two solutions that contain alcohol. She uses 100 millileters less of solution a than solution b. Solution A HAS 13% ALCOHOL AND SOLUTION b is 10% alcohol. How many milliliters of solution b is used if the resulting mixture has 102 milliliters of pure alcohol
Susan uses 500 milliliters of solution b to obtain a resulting mixture with 102 milliliters of pure alcohol.
Let's set up the equation based on the given information.
Let x represent the amount of solution b in milliliters.
Since Susan uses 100 milliliters less of solution a than solution b, the amount of solution a is (x - 100) milliliters.
We know that solution a has a concentration of 13% alcohol, which means that for every 100 milliliters, it contains 13 milliliters of alcohol.
Similarly, solution b has a concentration of 10% alcohol, which means that for every 100 milliliters, it contains 10 milliliters of alcohol.
Given that the resulting mixture has 102 milliliters of pure alcohol, we can set up the equation:
0.13(x - 100) + 0.1x = 102
Simplifying the equation, we have:
0.13x - 13 + 0.1x = 102
0.23x - 13 = 102
0.23x = 115
x = 115 / 0.23
x = 500
Therefore, Susan uses 500 milliliters of solution b to obtain a resulting mixture with 102 milliliters of pure alcohol.
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John, Rick, and Molli can paint a room working together in 5 hours. Alone, Molli can paint the room in 14 hours. If Rick works alone, he can paint the room in 10 hours. Write an equation comparing the group rate to the sum of the individual rates. Then find how long it will take John to paint the room if working alone.
It will take John approximately 2.69 hours to paint the room alone.
Let's denote the individual rates of John, Rick, and Molli as J, R, and M, respectively. We are given the following information:
John, Rick, and Molli can paint the room together in 5 hours.
Molli alone can paint the room in 14 hours.
Rick alone can paint the room in 10 hours.
To find the equation comparing the group rate to the sum of the individual rates, we can use the concept of work done. The amount of work required to paint the room is the same, regardless of who is doing the work.
The equation can be expressed as:
1/5 = 1/J + 1/R + 1/M
Now, let's substitute the given information into the equation. We know that:
M = 14 (since Molli can paint the room alone in 14 hours)
R = 10 (since Rick can paint the room alone in 10 hours)
Substituting these values, the equation becomes:
1/5 = 1/J + 1/10 + 1/14
To solve for J, we can find the least common denominator (LCD) of 10 and 14, which is 70:
14J + 7J + 5J = 70
26J = 70
J = 70/26
J ≈ 2.69
Therefore, it will take John approximately 2.69 hours to paint the room alone.
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Point A is translated 2 units up and 5 units to the right, where it now overlaps point B(3,-1)
Point A will have coordinates (-2, -3), which overlaps with the coordinates of Point B (3, -1).
To determine the new coordinates of Point A after the translation, we can start with the coordinates of Point B and apply the inverse translation.
Given that Point B has the coordinates (3, -1), we know that Point A after translation will have the same coordinates. We need to determine the inverse translation that will bring Point B back to its original position, and then apply that inverse translation to Point B.
The inverse translation of moving 2 units up and 5 units to the right is moving 2 units down and 5 units to the left. Therefore, we need to subtract 2 from the y-coordinate and subtract 5 from the x-coordinate of Point B.
Applying this inverse translation to Point B (3, -1), we have:
New x-coordinate of Point A = 3 - 5 = -2
New y-coordinate of Point A = -1 - 2 = -3
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x 7 16 25 34
5
10
20
40
y
Is the relationship linear, exponential, or neither?
Based on the given data, the relationship appears to be exponential.
To determine if the relationship between the given values is linear, exponential, or neither, we can examine the pattern in the data.
If the relationship is linear, we would expect the values of y to increase or decrease at a constant rate as the values of x increase. In other words, there would be a constant slope between the points.
If the relationship is exponential, we would expect the values of y to change by a constant factor as the values of x increase. In this case, the relationship would exhibit exponential growth or decay.
Looking at the given values of x and y, we can observe the following differences between consecutive x-values: 7, 9, 9, 9. These differences are not constant, indicating that the relationship is not linear.
To determine if the relationship is exponential, we can examine the ratios between consecutive y-values: 5/10 = 0.5, 10/20 = 0.5, 20/40 = 0.5. These ratios are constant, suggesting that the relationship may be exponential with a common ratio of 0.5.
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If 15% of the customers total is $98,880, then the sum total equals what
Answer:
Step-by-step explanation:
Are the following figures similar?
Trapezoids ABCD and EFGH are shown. Angle A equals 137 degrees, Angle B equals 90 degrees, Angle C equals 90 degrees, Angle D equals 43 degrees, Angle E equals 136 degrees, Angle F equals 90 degrees, Angle G equals 90 degrees, Angle H equals 44 degrees.
No, the trapezoids are not similar because their corresponding angles do not have the same measures.
The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.
Let's examine the angles of the trapezoids:
In trapezoid ABCD:
Angle A = 137 degrees
Angle B = 90 degrees
Angle C = 90 degrees
Angle D = 43 degrees
In trapezoid EFGH:
Angle E = 136 degrees
Angle F = 90 degrees
Angle G = 90 degrees
Angle H = 44 degrees
By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.
However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.
Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.
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What is the meaning of "A function f is one-to-one"?
A function f is said to be one-to-one, or injective, if it has the property that for any two different inputs, it produces two different outputs.
What is the meaning of "A function f is one-to-one"?More formally, a function f: X -> Y is one-to-one (or injective) if for every x1, x2 in X, if x1 ≠ x2 then f(x1) ≠ f(x2).
This means that no two different elements of the domain X map to the same element of the codomain Y. If you were to draw a horizontal line through any point on the graph of a one-to-one function in the Cartesian plane, that line would intersect the graph at most one time. This is known as the "horizontal line test" for one-to-one functions.
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What is the temperature in °C? Hint: (°F -32) ÷ 1.8 °C or °F= 1.8 °C
+32
Converting the temperature from Celsius to Fahrenheit:
Subtract the given temperature by 32 and divide it by 1.8°C.
°C = (F - 32) / 1.8°C, or use the equation °F= 1.8 °C+32
(°F-32) / 1.8°C
a) The given temperature is 60°F
substitute the given values in the above equation:
(60 - 32) / 1.8
28 / 1.8
= 15.5555 approx 16°C
60°F = 16°C
b) The given temperature is 10°F
°C = (F - 32) / 1.8°C
substitute the given values in the above equation:
(10 -32) / 1.8
-22 / 1.8
-12.222 approx -12°C
10°F = -12°C
correct question:
What is the temperature in °C, if the temperature is
a) 60F
b) 10F
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Please help me to do this i really need it.
First correct Answer gets Brainliest.
Answer:
Step-by-step explanation:
-3≤ x = graph 6
-3 > x = graph 3
x≥ 3 = graph 2
x ≤ 3 = graph 4
3 > x = graph 1
x > 3 = graph 5
the closed circles means greater/less than or equal to
the open circle means greater/less than
the direction of the arrow tells you if the number is greater than x or less than x
What is the meaning of "only under the assumption that at least one set X exists"?
The phrase "only under the assumption that at least one set X exists" means that a certain statement or conclusion holds true or can be deduced only if there is a set X that exists.
Answer to the questionIn other words, the validity or applicability of the statement is conditional upon the existence of at least one set X.
This phrase indicates that the argument or reasoning being presented depends on the existence of a specific set or group. Without the existence of such a set, the statement or conclusion being made may not hold true or may not be applicable.
It's important to note that without further context, the meaning and implications of this phrase may vary depending on the specific subject or context in which it is used.
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Find the mystery number from the following clues
It is a 2-digit number
It is a factor of 48
It is a multiple of 6
The sum of the digits is 3
Based on the given clues, the mystery number is 12.
Let's analyze the clues given to find the mystery number:
It is a 2-digit number: This means the number is greater than or equal to 10 and less than 100.
It is a factor of 48: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
It is a multiple of 6: The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, and so on.
The sum of the digits is 3: From the clues, we know that the mystery number is a 2-digit number, so let's consider the possible numbers where the sum of the digits is 3:
12 (1 + 2 = 3)
21 (2 + 1 = 3)
Now let's check which of these numbers satisfy the first three clues:
12: This number is a factor of 48 (48 ÷ 12 = 4) and it is a multiple of 6 (12 ÷ 6 = 2). The sum of the digits is 3. Therefore, 12 satisfies all the clues.
21: This number is not a factor of 48 (48 ÷ 21 ≈ 2.29), so it doesn't satisfy the second clue.
Based on the given clues, the mystery number is 12.
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Find the measure indicated.
27)
T
A) 59⁰
C) 56°
S
80°
20
Q
B) 50°
D) 37°
R
b)50
since its a Equilateral triangle, then the two base angels have the same measure
abd since both triangles are symmetric, they have the same measurements
so 180-80 = 2x
x = 50⁰
Calculate the following values.
The output value of f(-1) include the following: -13.
What is a piecewise-defined function?In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains.
Since the value of x is -1, the output value of this piecewise-defined function can be calculated by using the first function as follows;
f(x) = 3x - 10
f(-1) = 3(-1) - 10
f(-1) = -3 - 10
f(-1) = -13
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you are dealt one card from a 52-card deck. find the probability that you are not dealt a two
Answer:
Step-by-step explanation:
48 out 52 cards are not a 2:
[tex]P(not 2)=\frac{48}{52} =\frac{12}{13}[/tex]
A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 15 to 30.5 on the number line. A line in the box is at 21.5. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball. What value does 75% of the data lie above? Find the value. Lower quartile (Q1) = 14 Lower quartile (Q1) = 15 Upper quartile (Q3) = 30.5 Upper quartile (Q3) = 32
Given statement solution is :- The quartile value above which 75% of the data lies is 31.625.
To find the value above which 75% of the data lies, you can determine the third quartile (Q3) of the data set. In this case, the upper quartile (Q3) is given as 30.5.
Since the data is represented on a number line with tick marks every one-half unit, we can divide the range between Q3 and the maximum value (32) into four equal parts. Each part represents 25% of the data.
To find the value that corresponds to 75% of the data lying above, we need to determine the value that is three-fourths of the way between Q3 and the maximum value.
First, calculate the range between Q3 and the maximum value: 32 - 30.5 = 1.5.
Next, divide the range by four to find the size of one-fourth of the range: 1.5 / 4 = 0.375.
Now, multiply the size of one-fourth of the range by three to find the size of three-fourths of the range: 0.375 * 3 = 1.125.
Finally, add the size of three-fourths of the range to Q3 to find the value above which 75% of the data lies: 30.5 + 1.125 = 31.625.
Therefore, the quartile value above which 75% of the data lies is 31.625.
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How do I find the possible degree(s) of a function from the graph alone?
The possible degrees of a function from it's graph are found with the sum of the multiplicities of each root of the function.
How to obtain the x-intercepts of a function?On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.
On the graph, these are the values of x for which the graph of the function crosses or touches the x-axis.
The multiplicity of each root is given as follows:
Even multiplicity when the graph touches the x-axis.Odd multiplicity when the graph crosses the x-axis.Hence the degree is found with the sum of the multiplicities of the zeros of the function.
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using the centriod explain the relationship between point z and the triangle. justify with applicable theorem.
4. if the length of gu is 18 units, what is the length of gz?
5. if the length of zt is 4.8 units, what is the length of ot?
show all work
Length of gz = 12 units
Length of ot = 14.4 units
Given,
Triangle EGD with centroid at Z .
Now,
As we know that centroid divides the line segment in the ratio 2:1 .
Firstly calculate the length of gz,
gu = 18 unit
gz:zu = 2:1
gz = 2/3 * 18
gz = 12 units .
Secondly calculate the length of ot,
zt = 4.8 units
oz:zt = 2:1
oz = 4.8 * 2
oz = 9.6 units
ot = 9.6+ 4.8
ot = 14.4 units
Hence with the centroid length of ot and gz can be found out .
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
PLEASE ANSWER FAST!!!
A) Two equations are,
S = 18 + 4t
L = 30 + 3t
Where, "t" represents the number of weeks that have passed.
B) It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
C) when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.
Part A:
For a system of equations to represent the number of rocks in each person's collection.
Let "S" be the number of rocks in Samuel's collection and "L" be the number of rocks in Lewis's collection.
Hence, We can represent the situation as follows:
Equation 1:
S = 18 + 4t
Equation 2:
L = 30 + 3t
Where, "t" represents the number of weeks that have passed.
Part B:
To find out how many weeks it will take for Samuel and Lewis to have the same number of rocks in their collections, we need to set Equation 1 equal to Equation 2 and solve for "t".
This gives us the following:
S = L
18 + 4t = 30 + 3t
1t = 12
t = 12 weeks
Hence, It will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
Part C:
For number of rocks Samuel and Lewis will have when the amount of rocks in their collection is equal, we can substitute the value of "t" that we found in Part B into either Equation 1 or Equation 2.
Hence, substituting "t = 12" into Equation 1 gives,
S = 18 + 4(12)
S = 18 + 48
S = 66 rocks
Therefore, when the amount of rocks in their collection is equal, Samuel and Lewis will have 66 rocks each.
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While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?
13.3km/L=__________mi/gal
The rental car is getting approximately 37.56 miles per gallon.
To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:
1 km/l ≈ 2.82475 mpg
Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:
13.3 km/l x 2.82475 mpg ≈ 37.56 mpg
So, your rental car is getting approximately 37.56 miles per gallon.
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An online real estate website estimates that a fair price for Jerrold’s house would be $715,000. The market is
strong, so he is optimistic and puts the house on the market for $750,000. Two weeks later, the best offer
he’s gotten is $718,000, and so he accepts that offer. At what percent above the website’s estimate did he set
his asking price? At what percent below his asking price did he sell
Answer:
approximately 4.2667%
Step-by-step explanation:
To calculate the percentage above the website's estimate that Jerrold set his asking price, we can use the following formula:
Percentage above = ((Asking price - Website estimate) / Website estimate) * 100
Percentage above = (($750,000 - $715,000) / $715,000) * 100
Percentage above ≈ 4.895
Therefore, Jerrold set his asking price approximately 4.895% above the website's estimate.
To calculate the percentage below his asking price that Jerrold sold for, we can use the following formula:
Percentage below = ((Selling price - Asking price) / Asking price) * 100
Percentage below = (($718,000 - $750,000) / $750,000) * 100
Percentage below ≈ -4.2667
Therefore, Jerrold sold his house approximately 4.2667% below his asking price.
Select all expressions that equal 6x10(-10)
To express the value 6 × 10^(-10), you can use scientific notation or decimal notation. Here are some valid expressions that equal 6 × 10^(-10):
0.0000000006
6E-10
6 × 10^(-10)
These expressions represent the same value, which is 6 multiplied by 10 raised to the power of -10.
Decimal is a number system used in everyday arithmetic and mathematics. It is also known as the base-10 system because it uses ten digits (0-9) to represent numbers. Each digit's position in a decimal number represents a power of 10.
In a decimal number, the digits to the left of the decimal point represent whole numbers, while the digits to the right of the decimal point represent fractions or parts of a whole. For example, in the decimal number 123.45, the digit "1" represents 100, the digit "2" represents 10, the digit "3" represents 1, the digit "4" represents 0.1, and the digit "5" represents 0.01.
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Please Help
8x + 1
115⁰
Write an expression using the distributed property to dind the product of 7x63
The product of the expression 7 x 63 is 441.
We have,
To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:
7 x 63 = 7 x (60 + 3)
Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:
7 x (60 + 3) = 7 x 60 + 7 x 3
Simplifying further:
7 x 60 + 7 x 3 = 420 + 21
Therefore,
The product of 7 x 63 is 441.
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33. It's 2 years since I was last in Rome. ⇒ I haven't 34. I saw Tom last on his wedding day. ⇒ I haven't 35. I last ate raw fish when I was in Japan. ⇒ I haven't 36. It's years since Mary last spoke French. ⇒ Mary hasn't 37. It's ten weeks since since I last had a good night sleep. I haven't 38. He last paid taxes in 1970. He hasn't last taxes 39. I last ate meat 5 years ago. ⇒ I haven't since 1970 40. It's 3 months since since the windows were cleaned. The windows haven't 41. It's years since I took photographs.
34. I haven't seen Tom since his wedding day.
36. Mary hasn't spoken French in years.
37. I haven't had a good night's sleep in ten weeks.
38. He hasn't paid taxes since 1970.
40. The windows haven't been cleaned for 3 months.
41. It's been years since I took photographs.
What is a perfect tense?The perfect tense is a grammatical construction used to express actions that are completed or have happened before the present moment. It indicates that an action was performed and finished in the past but has relevance or impact on the present.
There are three main forms of the perfect tense: present perfect, past perfect, and future perfect.
1. Present Perfect Tense: This tense is used to describe an action or event that started in the past and has a connection to the present. It emphasizes the result or completion of the action.
2. Past Perfect Tense: This tense is used to describe an action or event that occurred before another action or a specific point in the past. It expresses an action completed before a specified time in the past.
3. Future Perfect Tense: This tense is used to describe an action that will be completed before a specified time or point in the future.
Each form of the perfect tense can be used with different time references to indicate the relationship between the completed action and the present or other points in time.
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} One number is 8 times another. When the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number. What are the numbers?
The numbers are 1 and 8.
We have,
Let's assume the lesser number as "x" and the greater number as "8x".
According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:
8x - x = 5x + 2
Simplifying the expression:
7x = 5x + 2
Subtracting 5x from both sides:
2x = 2
Dividing both sides by 2:
x = 1
So, the lesser number is 1 and the greater number is 8 times that, which is 8.
Therefore,
The numbers are 1 and 8.
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Solve the equation for the variable given. Solve for x
The solution for x, is x= (3m - b)/2. (Option-d)
To solve for x in the given equation, m=(2x+b)/3, we can start by isolating x on one side of the equation.
First, we can multiply both sides of the equation by 3 to get rid of the denominator:
3m = 2x + b
Next, we can subtract b from both sides of the equation:
3m - b = 2x
Finally, we can divide both sides of the equation by 2:
x = (3m - b)/2
It's important to note that this is a linear equation with one unknown variable, and we can use algebraic methods to solve for the unknown variable. This equation may arise in many fields of study, including physics, engineering, and economics, among others.(Option-d)
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