Therefore, the volume of the larger cylinder is 44.8. [tex]m^{3}[/tex], which is closest to option (c) 437.5. [tex]m^{3}[/tex].
What is volume?Volume is a measure of the amount of space occupied by an object or substance. It is a three-dimensional quantity that is usually measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or gallons (gal).
Given by the question.
The ratio of the volumes of two similar solids is the cube of the ratio of their corresponding side lengths. In this case, the ratio of the scale factor of the cylinders is 5:2, so the ratio of their volumes is (5/2) ^3 = 125/8.
If the volume of the smaller cylinder is 28 m^3, then we can set up the following equation to solve for the volume of the larger cylinder:
(125/8) * V = 28
where V is the volume of the larger cylinder.
Simplifying this equation, we get:
V = 28 * (8/125) * 125
V = 224/5
V = 44.8 [tex]m^{3}[/tex]
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(5)/(x+6)=(7)/(5x+30)-2 If there is more than one solution, separate If there is no solution, click on "No solution" x
The solutions are x ≈ -2.744 and x ≈ -17.106.
To solve this equation, we need to get rid of the fractions by multiplying each term by the least common multiple (LCM) of the denominators. The LCM of x+6 and 5x+30 is (x+6)(5x+30).
Multiplying each term by the LCM gives us:
(5)(x+6)(5x+30)/(x+6) = (7)(x+6)(5x+30)/(5x+30) - 2(x+6)(5x+30)
Simplifying the fractions and distributing the terms gives us:
5(5x+30) = 7(x+6) - 2(x+6)(5x+30)
Expanding and simplifying the terms gives us:
25x + 150 = 7x + 42 - 10x^2 - 180x - 360
Combining like terms and rearranging gives us:
10x^2 + 198x + 468 = 0
Using the quadratic formula, we can find the values of x:
x = (-198 ± √(198^2 - 4(10)(468)))/(2(10))
Simplifying gives us:
x = (-198 ± √(39204 - 18720))/(20)
x = (-198 ± √20484)/(20)
x = (-198 ± 143.126)/(20)
The two solutions for x are:
x = (-198 + 143.126)/(20) ≈ -2.744
x = (-198 - 143.126)/(20) ≈ -17.106
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What is the difference in area betwee circle with its of 10 centimeters a square inscribed in it, to the neares whole?
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is 114 cm².
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.
First, calculate the area of the circle using the formula
A = πr²,
where A is the area and r is the radius.
A = π(10)² = 100π ≈ 314.16 square centimeters
Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.
Using the Pythagorean theorem, we can find the side length of the square:
s² + s² = (20)²
2s² = 400
s² = 200
s ≈ 14.14 centimeters
The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.
Finally, subtract the area of the square from the area of the circle to find the difference:
314.16 - 199.97 ≈ 114.19 square centimeters
To the nearest whole, the difference in area is 114 square centimeters.
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15. \( x=-5, \quad x=4, \quad x=-\frac{1}{2} \) factored form standard form 16. \( x=3, \quad x=-7, \quad x=0 \) (multiplicity of 2) factored form standard form
\[ \text { 17. } x=\frac{2}{3} \text {
The standard form to this equation is x=2/3.
This equation is in the form of a linear equation in one variable, where the variable is x.
The equation is written as x=2/3, meaning that the value of x is equal to 2/3.
The equation can be interpreted as the ratio of two numbers, 2 and 3. The numerator, 2, represents the number of parts, and the denominator, 3, represents the total number of parts.
This equation can be used to solve for the fraction of the total number of parts represented by the numerator. In this case, the fraction is 2/3, or 2 parts out of a total of 3 parts.
The equation can also be interpreted as a proportion. If we make the numerator the unknown value, x, then the equation becomes x/3 = 2/3. This equation can be solved using the cross-multiplication method.
By multiplying the denominators together and setting them equal to each other, then solving for x, we get x = 2/3. This equation shows that the value of x is equal to 2/3 of the total number of parts.
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Miguel has started training for a race. The first time he trains, he runs 0. 5 mile. Each subsequent time he trains, he runs 0. 2 mile farther than he did the previous time.
a) What is the arithmetic series that represents the total distance Miguel has run after he has trained n times?
b) A marathon is 26. 2 miles. What is the least number of times Miguel must run for his total distance run during training to exceed the distance of a marathon?
Answer:
hope this helps.
Step-by-step explanation:
Given \( f(x)=5 x \) and \( g(x)=7 x^{2}+6 \), find the following expressions. (a) \( (f \circ g)(4) \) (b) \( (g \circ f)(2) \) (c) \( (f \circ f)(1) \) (d) \( (g \circ g)(0) \) (a) (fog)(4) = (Simplify your answer.)
(b) (go f)(2) = (Simplify your answer.)
(c) (fo f)(1) = (Simplify your answer.)
(d) (go g)(0) = (Simplify your answer.)
By following this process, we were able to evaluate each expression and get the answers of 590, 181, 25, and 6 respectively.
a) (fog)(4) = (f(g(4)) = f(7(4)^2+6) = 5(7(16)+6) = 5(118) = 590
b) (gof)(2) = (g(f(2)) = g(5(2)) = 7(5)^2+6 = 7(25)+6 = 181
c) (fof)(1) = (f(f(1)) = f(5(1)) = 5(5) = 25
d) (gog)(0) = (g(g(0)) = g(7(0)^2+6) = 7(0)+6 = 6
To find the expressions given, we need to first use the definition of a function composition. This means that when we have a function \(f\) composed with a function \(g\), this is represented by \(f\circ g\). When we use a function composition, we evaluate the function \(g\) first, then plug the result into the function \(f\).
For example, in part (a) we have the expression \(f\circ g(4)\). We need to first evaluate \(g(4)\), which gives us \(7(4)^2+6\). Then we plug this result into the function \(f\) to get \(f(7(4)^2+6)= 5(7(4)^2+6) = 590\). We can repeat this process for the rest of the parts. For part (b) we have \(g\circ f(2)\). Evaluating \(f(2)\) gives us \(5(2)\), which we then plug into \(g\) to get \(g(5(2))= 7(5)^2+6 = 181\).
For part (c) we have \(f\circ f(1)\), so evaluating \(f(1)\) gives us \(5(1)\) and then plugging this into \(f\) gives us \(f(5(1))= 5(5) = 25\). Finally, for part (d) we have \(g\circ g(0)\), so evaluating \(g(0)\) gives us \(7(0)^2+6\), which we plug into \(g\) to get \(g(7(0)^2+6) = 7(0)+6 = 6\).
In conclusion, we can use function composition to find the expressions given. We start by evaluating the inner function, then plugging the result into the outer function.
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Javier took out a loan for $2700 at 12% interest, compounded annually. If he
makes yearly payments of $320, will he ever pay off the loan?
OA. No, because $320 is greater than the amount of interest he is
charged per year
OB. No, because $320 is less than the amount of interest he is
charged per year
OC. Yes, because $320 is less than the amount of interest he is
charged per year
OD. Yes, because $320 is greater than the amount of interest he is
charged per year
The correct statement regarding the monthly payments is given as follows:
D. Yes, because $320 is greater than the amount of interest he is
charged per year.
What is the monthly payment formula?The monthly payment formula is defined by the equation as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed as follows:
P is the initial amount, which will be paid/divided over a period of time.r is the interest rate, as a decimal.n is the number of payments, in the period through which the monthly payments will be paid.The parameter values for this problem are given as follows:
P = 2700, r = 0.12, n = 12.
Hence:
r/12 = 0.12/12 = 0.01.
Hence the monthly payment is calculated as follows:
A = 2700 x 0.01 x (1.01)^12/(1.01^12 - 1)
A = $240.
The interest is less than $320, hence he will manage to pay off the loan.
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How do the average rates of change for the pair of functions compare over the given interval?
f(x)x
g(x)x
x
Question content area bottom
Part 1
The average rate of change of f(x) over x is
enter your response here. The average rate of change of g(x) over x is
enter your response here. The average rate of change of g(x) is
enter your response here times that of f(x). (Simplify your answers. Type integers or decimals. )
The average rate of change of g(x) over the interval [2, 5] is -2.1.
The formula to calculate the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
slope = (y₂ - y₁) / (x₂ - x₁)
Using this formula, we can calculate the slopes of the two secant lines for f(x) and g(x) over the interval [2, 5]. Let's start with f(x):
slope_f = (f(5) - f(2)) / (5 - 2)
= (-0.1(5)² - (-0.1(2)²)) / (5 - 2)
= (-0.1(25) + 0.1(4)) / 3
= (-2.5 + 0.4) / 3
= -2.1 / 3
= -0.7
Therefore, the average rate of change of f(x) over the interval [2, 5] is -0.7.
Now, let's calculate the average rate of change of g(x):
slope_g = (g(5) - g(2)) / (5 - 2)
= (-0.3(5)² - (-0.3(2)²)) / (5 - 2)
= (-0.3(25) + 0.3(4)) / 3
= (-7.5 + 1.2) / 3
= -6.3 / 3
= -2.1
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Complete Question:
how do the average rates of change for the pair of functions compare over the given interval
f(x)= -0.1x²
g(x)= -0.3x²
2≤x≤5
PLEASEEEE HELP A GIRL OUTTTTTTTT 17 POINTSSSSSSS!!!!!!!!!
Answer: B
Step-by-step explanation:
Ava was playing a game online. She had a great first round and the second round she increased her point total by 25%. On the third round she decreased her point total by 3/5. She had a great fourth round increasing her total points by 75%. On the fifth and final round she lost 2/7 of her total ending the game with 50 points. How many points did Ava have at the end of round one?
To find out how many points Ava had at the end of round one, we need to work backwards from the end of the game using probability. Here are the steps to do so:
Step 1: At the end of the game, Ava had 50 points. This was after she lost 2/7 of her total points in the fifth round. Let's call the number of points she had before the fifth round X. So:
50 = X - (2/7)X
Step 2: Solve for X by combining like terms:
50 = (5/7)X
Step 3: Multiply both sides of the equation by 7/5 to isolate X:
X = 70
Step 4: Now we know that Ava had 70 points before the fifth round. This was after she increased her total points by 75% in the fourth round. Let's call the number of points she had before the fourth round Y using probability. So:
70 = Y + (75/100)Y
Step 5: Solve for Y by combining like terms:
70 = (175/100)Y
Step 6: Multiply both sides of the equation by 100/175 to isolate Y:
Y = 40
Step 7: Now we know that Ava had 40 points before the fourth round. This was after she decreased her point total by 3/5 in the third round. Let's call the number of points she had before the third round Z. So:
40 = Z - (3/5)Z
Step 8: Solve for Z by combining like terms:
40 = (2/5)Z
Step 9: Multiply both sides of the equation by 5/2 to isolate Z:
Z = 100
Step 10: Now we know that Ava had 100 points before the third round. This was after she increased her point total by 25% in the second round. Let's call the number of points she had before the second round A using probability. So:
100 = A + (25/100)A
Step 11: Solve for A by combining like terms:
100 = (125/100)A
Step 12: Multiply both sides of the equation by 100/125 to isolate A:
A = 80
Step 13: Now we know that Ava had 80 points before the second round, which means she had 80 points at the end of the first round.
Therefore, the answer is 80 points using probability.
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5.22. Exercise. Make a ruler-and-compass construction of a line thru a given point that is perpendicular to a given line.
This construction is also known as the "perpendicular bisector" construction.
To construct a line through a given point that is perpendicular to a given line using a ruler and compass, you will need to follow these steps:
Place the point of the compass on the given point.Open the compass to a width that is wider than the distance between the given point and the given line.Draw an arc that intersects the given line at two points.Without changing the width of the compass, move the point of the compass to one of the intersection points and draw another arc.Move the point of the compass to the other intersection point and draw another arc that intersects the first arc.Use the ruler to draw a line through the given point and the intersection of the two arcs. This line will be perpendicular to the given line.By following these steps, you have used the ruler and compass to construct a line through a given point that is perpendicular to a given line. This construction is also known as the "perpendicular bisector" construction.
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A jet flying at 200 m/s north accelerates at a rate of 18.2 m/s² for 15 seconds. What is the jet's final velocity?
The final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.
What is meant by velocity?When observed from a specific point of view and as measured by a specific unit of time, velocity is the direction at which an item is moving and serves as a measure of the pace at which its position is changing. How quickly or slowly an object is travelling can be determined by its velocity and speed. Being a vector quantity, we need to define velocity in terms of both magnitude (speed) and direction. A body is considered to be accelerating if the magnitude or direction of its velocity changes.
Given,
The initial velocity u = 200 m/s
Acceleration of jet a = 18.2 m/s²
Time taken t = 15s
We are asked to find the final velocity v of the jet.
W can use the following formula to find the final velocity.
v = u+ at
= 200 + (18.2) × 15
= 473 m/s (north)
Therefore the final velocity of the jet flying in the north direction after accelerating for 15s is 473 m/s.
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Solve the rational equation 5 over X plus X +5 over X +2 equals -11 over X to the 2nd+ 2X
After solving the equation, the solution if the equation is -2 and -11/5.
To solve the rational equation we first express the given statement in the form of mathematical equation. After that we solve the equation.
As the statement is 5 over X + 2. It can be written as 5/(x + 2)
Then the second statement is -11 over X to the 2nd + 2X which is written as -11/(x² + 2x).
There have equal sign between both expression. So the expression is
5/(x + 2) = -11/(x² + 2x)
Now solve it.
Multiply by (x² + 2x) on both side, we get
5(x² + 2x)/(x + 2) = -11
Multiply by (x + 2) on both side, we get
5(x² + 2x) = -11(x + 2)
Now simplify using the distributive property
5x² + 10x = -11x - 22
Add 11x on both side, we get
5x² + 21x = - 22
Add 22 on both side, we get
5x² + 21x + 22 = 0
Now we factor the equation
5x² + (11 + 10)x + 22 = 0
5x² + 11x + 10x + 22 = 0
x(5x + 11) + 2(5x + 11) = 0
(5x + 11)(x + 2) = 0
Now equating equal to 0.
5x + 11 = 0 x + 2 = 0
5x = -11 x = -2
x = -11/5
The solution if the equation is -2 and -11/5.
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The complete question is:
Solve the rational equation 5 over X + 2 equals -11 over X to the 2nd + 2X.
Ver en español
Felix and his friends attended the opening of the new community center at Forest Ridge Park. The mayor unveiled a parallelogram-shaped decorative plaque at the entrance to the park with the date of the special event. Its bottom edge is 9 inches long, and its area is 126 square inches.
Which equation can you use to find how tall the plaque is, h?
How tall is the plaque?
Write your answer as a whole number or decimal. Do not round.
inches
The answer to this question is as follows The plaque measures 14 inches equation tall as a result.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Because we are aware that the plaque has a parallelogram shape, we may determine its height using the formula for a parallelogram's area. The formula for a parallelogram's area is:
Base area x height
In this instance, we are aware that the area is 126 square inches, and the base (the bottom border) is 9 inches. Thus, we can enter those values into the formula to find the height:
126 = 9h
h = 126/9
h = 14
The plaque measures 14 inches tall as a result.
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PLEASE HELP
A cylinder-shaped container is used to store water. The container has a height of 6 feet and
diameter of 3 feet.
About how much water is in the container when it is 3/4 full?
o 127 cubic feet
o 42 cubic feet
o 32 cubic feet
o 14 cubic feet
Answer:
32 cubic feet
Step-by-step explanation:
The formula for a cylinder is [tex]\pi r^{2} h[/tex].
The radius of the cylinder is equal to 1.5 feet, since it is [tex]\frac{diameter}{2}[/tex].
Plugging in, the cylinder's full volume is [tex]6\pi 1.5^2[/tex] which is approximately 42.4 cubic feet.
To find the amount of water when it is 3/4 full, multiply 42.4 x .75, to get around 31.8, and 32 when rounded
What Is 1 + 1 ?
A. Window
B. Two
C. Eleven
Correct Answer Gets Brainliest!
Answer: B -_-
Step-by-step explanation:
0 0=2
pls asnwer
due in 10 mins
give simple working
Step-by-step explanation:
a = 55° because angles on a straight line (around a single point on one side of the line) add up to 180°.
b = 75° because alternate angles (with parallel lines) are equal.
c = 50°, because alternate angles (with parallel lines) are equal.
d = 50°, because corresponding angles (with parallel lines) are equal.
5 boys and girls are running in a marathon. How many ways can the first finishen complete the marathon it: a) the first 2 finishers must have different genders? b) Chantal must finish the race before David?
There are 8 possible ways for the first 2 finishers to complete the marathon with different genders. There are 20 possible ways for Chantal to finish the race before David.
There are a couple of different ways to approach this problem, but one common method is to use the multiplication principle, which states that if there are A ways to do one thing and B ways to do another, then there are A*B ways to do both. We can apply this principle to both parts of the question.
a) If the first 2 finishers must have different genders, then we can think about the possible combinations of boys and girls. There are 2 options for the first finisher (either a boy or a girl), and then there are 4 options for the second finisher (either a boy or a girl, but not the same gender as the first finisher).
So, using the multiplication principle, we can find the total number of ways for the first 2 finishers to complete the marathon with different genders:
2 * 4 = 8
Therefore, there are 8 possible ways for the first 2 finishers to complete the marathon with different genders.
b) If Chantal must finish the race before David, then we can think about the possible positions for Chantal and David. There are 5 possible positions for Chantal (first, second, third, fourth, or fifth), and then there are 4 possible positions for David (second, third, fourth, or fifth, but not before Chantal).
So, using the multiplication principle, we can find the total number of ways for Chantal to finish before David:
5 * 4 = 20
Therefore, there are 20 possible ways for Chantal to finish the race before David.
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Question 13 Evaluate the limit: lim−(x−>9)(7x−63)/(x^2−2x−63)=
Use the result of Example 1.3 to verify the formulas it Prove that x+y divides x^2n+1+y^2n+1 for n≥0. Cher then n is a positive integer, so also is (n^3
The limit of the given function can be evaluated by simplifying the expression and then substituting the value of x.
First, we can factor the numerator and denominator of the expression:
lim−(x−>9)(7x−63)/(x^2−2x−63)=lim−(x−>9)(7(x−9))/((x−9)(x+7))
Next, we can cancel out the common factor of (x-9) from the numerator and denominator:
lim−(x−>9)(7)/(x+7)
Now, we can substitute the value of x=9 into the expression:
lim−(x−>9)(7)/(x+7)=7/(9+7)=7/16
Therefore, the limit of the given function is 7/16.
As for the second part of the question, we can use the result of Example 1.3 to verify the formulas. According to Example 1.3, if x+y divides x^n+y^n for n≥0, then x+y also divides x^(n+1)+y^(n+1). Using this result, we can prove that x+y divides x^2n+1+y^2n+1 for n≥0 by induction.
Base case: n=0
x^2(0)+1+y^2(0)+1=x+y, which is divisible by x+y.
Inductive step: Assume that x+y divides x^2n+1+y^2n+1 for some n≥0. We need to show that x+y divides x^2(n+1)+1+y^2(n+1)+1.
x^2(n+1)+1+y^2(n+1)+1=(x^2n+1+y^2n+1)(x^2+y^2)
Since x+y divides x^2n+1+y^2n+1 by assumption, and x+y divides x^2+y^2 by Example 1.3, x+y also divides (x^2n+1+y^2n+1)(x^2+y^2) by the distributive property. Therefore, x+y divides x^2(n+1)+1+y^2(n+1)+1 for n≥0.
Finally, for the third part of the question, we can use the fact that n is a positive integer to show that (n^3) is also a positive integer. Since n is a positive integer, n^3 is also a positive integer because the product of three positive integers is a positive integer. Therefore, (n^3) is a positive integer.
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5 3/10 = 5 ?/50
If anyone can please help me with the rest
Answer:
See explanation
Step-by-step explanation:
50 is 5*10, so multiply 3 by 5 also to get 5 and 15/50. First answer is 15
5 and 15/50 is also equal to 4 and 65/50. second answer is 65
carry the numerator on the second line to get 30 for the third answer.
finally, subtract 3 from 4 to get 1, and subtract 30 from 65 to get 35/50.
last two answers are 1, and 35.
Half Challenge! Taxpayer Name: Bob Tax Bracket Information: Money earned between $0 and $200, 10% tax Money earned between $200 and $500, 20% tax Money earned after $500, 40% tax Finances:
Income: $750 Adjusted Income:
Expenses: $100 Adjusted Expenses: Deductible: $150
Return:
Bob Returned $120 Did Bob commit Tax Fraud? YES NO Bob's Net Income:
Bob did not commit tax fraud based on the given information.
To calculate Bob's net income, we need to start with his adjusted income, which is his income minus his expenses and deductible:
Adjusted Income = Income - Expenses - Deductible
Adjusted Income = $750 - $100 - $150
Adjusted Income = $500
Next, we need to determine the amount of tax that Bob owes based on his tax bracket information:
Tax Owed on first $200 = $200 * 0.10 = $20
Tax Owed on next $300 ($200 to $500) = $300 * 0.20 = $60
Tax Owed on remaining $0 ($500 and above) = $0 * 0.40 = $0
Total Tax Owed = $20 + $60 + $0 = $80
Now, we can calculate Bob's net income by subtracting his tax owed from his adjusted income:
Net Income = Adjusted Income - Tax Owed
Net Income = $500 - $80
Net Income = $420
Finally, we can compare Bob's returned amount to his tax owed to see if he committed tax fraud:
Returned Amount - Tax Owed = $120 - $80 = $40
Since Bob's returned amount is less than his tax owed, he did not commit tax fraud. His net income after taxes is $420.
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write three rations that are equivalent to 6/9
Answer:
12/18, 2/3, and 18/27.
Step-by-step explanation:
In order to find ratios that are equivalent to a certain fraction they must have common divisibles.
In this case...
[tex]\frac{6}{9}[/tex]
If the common divisible is two....
[tex]6\times2=12[/tex]
[tex]9\times2=18[/tex]
[tex]=\frac{12}{18}[/tex]
You could also simplify the ratio:
[tex]\frac{6}{9} \div3=\frac{2}{3}[/tex]
[tex]=\frac{2}{3}[/tex]
If the common divisible is three:
[tex]6\times3=18[/tex]
[tex]9\times3=27[/tex]
[tex]=\frac{18}{27}[/tex]
Multiplicative property of equality with whole numbers Solve for u. 78=6u Simplify your answer as much as possible. u
The multiplicative property of equality states that the same number can be added to or multiplied by both sides of an equation to obtain an equivalent equation. In this case, dividing both sides by 6 gives us u = 78/6 = 13.
The multiplicative property of equality states that if two numbers are equal, then multiplying both sides of the equation by the same number will also result in an equation that is still equal. In other words, if a=b, then ac=bc. We can use this property to solve for the variable u in the equation 78=6u.
To isolate the variable on one side of the equation, we can divide both sides by 6. This will give us:
78/6 = 6u/6
Simplifying the equation gives us:
13 = u
So the solution for u is 13.
In conclusion, the multiplicative property of equality with whole numbers was used to solve for the variable u in the equation 78=6u. The solution is u=13.
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kierna is starting a lawn-mowing buisness in her neighborhood. she creats a graph to help her determine what to charge customers per lawn to maximize her profits. she uses c to represent the number of lawns she mows and y to represent her profit in dollars.
The profit is maximum when 40 lawns are mowed.
What is function?A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given is that Kieran is starting a lawn-mowing buisness in her neighborhood. She creates a graph to help her determine what to charge customers per lawn to maximize her profits. She uses {c} to represent the number of lawns she mows and {y} to represent her profit in dollars.
The profit is maximum when 40 lawns are mowed as at this point the the peak of the parabola occurs.
Therefore, the profit is maximum when 40 lawns are mowed.
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The angle of elevation of the top of the building at a distance of 55 m from its foot on a
horizontal plane is found to be 60°. Find the height of the building rounded to the nearest
tenth of a meter.
The height of the building is _______ meters.
Need help
The height of the building, given the angle of elevation and the distance from the top of the building, is such that he height of the building is 95 meter.
How to find the height ?We shall assume that the building, the distance from the foot and the angle, are in a right - angled triangle.
This means that the height of the building is the opposite side and the given distance is the adjacent side.
The relevant operation would be Tan.
The height of the building would be:
Tan ( 60 ° ) = Height / 55 m
Height = Tan ( 60 ° ) x 55
Height = 95 meters
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select the 2 linear functions A) (y=6x+14), B) (y= x/4 + 1), C) (y=x^3), D) (y=3/x +2)
The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Let's check all the options, then we have
A) y = 6x + 14, the equation is a linear equation because the degree is one.
B) y = x/4 + 1, the equation is a linear equation because the degree is one.
C) y = x³, the equation is a cubic equation because the degree is three.
D) y = 3/x +2, the equation is a non-linear equation because the degree is negative one.
The two linear equations are y = 6x + 14 and y = x/4 + 1. Then the correct options are A and B.
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what smaller 5.75 or 9/7
Answer:
9/7 is smallerrrr
i need help 16 divided by 6032 full solution
Answer:
0.00265251989
Hope this helped.
A (-1,6)
Work out the length of AB.
Give your answer to 3 significant figure
O
B (5, 3)
thagoras' Theorem - Line on a Graph
8
X
Answer:
AB = 6.71
Step-by-step explanation:
The vertical leg of the right triangle
= absolute value of difference in y-coordinates between A(-1, 6) and B(5, 3)
= |6 - 3| = |3|
= 3
The horizontal leg of the right triangle
= absolute value of difference in x-coordinates between A(-1, 6) and B(5, 3)
= |- 1 - 5|
=|- 6|
= 6
By the Pythagorean theorem, the hypotenuse AB is related to each of these two legs by the formula
AB² = 3² + 6²
AB² = 9 + 36
AB² = 45
AB = √45
or
AB = 6.7082039324
= 6.71 significant to 3 significant figures
Significant figures means number of digits excluding leading and trailing zeros
In order for following to be consistent,
-3x +4y +7z =-4
-11x +24y +kz = -45
2x -5y -8z =9
solve for k≠ ?
please show full steps
In order for the system of equations to be consistent, k must not be equal to 31.6087.
In order for the system of equations to be consistent, the determinant of the coefficient matrix must not be equal to zero. The coefficient matrix is:
| -3 4 7 |
| -11 24 k |
| 2 -5 -8 |
The determinant of this matrix is:
(-3)(24)(-8) + (4)(k)(2) + (7)(-11)(-5) - (7)(24)(2) - (4)(-11)(-8) - (-3)(k)(-5)
Simplifying this expression gives:
576 + 8k + 385 - 336 - 352 + 15k = 0
Solving for k gives:
23k = 727
k = 727/23
k ≈ 31.6087
Therefore, in order for the system of equations to be consistent, k must not be equal to 31.6087.
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Distance (Yards)
Races
60
20-
(1, 12)
(2,24)
Mario & Peach 4
Time (Seconds)
6
Can you create the two equations for Mario and Peach
in y = mx + b form?
Mario
Submit
Peach
12
The linear functions of the scenario are y = 12x and y = 24/2x
How to determine the linear functionsFrom the question, we have the following parameters that can be used in our computation:
(1, 12) and (2,24)
From the question, we understand that the function is a linear function
A linear function is represented as
y = mx + c
Using the above as a guide, we have the following equations
m + c = 12
2m + c = 24
Subtract the equations
m = 12
Substitute 12 for m in m + c = 12
12 + c = 12
Evaluate
c =0
So, the equation is y = 12x
An equivalent equation is y = 24x/2
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