The final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.
To multiply each term by the LCD, we need to first find the LCD of the given expression. The LCD of the expression is the product of the denominators, which is x(x-4)(x-3).
Now, we can multiply each term by the LCD to get rid of the denominators:
A[x(x-4)(x-3)]/(x) * x(x-4)(x-3) = A(x-4)(x-3)
B[x(x-4)(x-3)]/((x-4)) * x(x-4)(x-3) = B(x)(x-3)
C[x(x-4)(x-3)]/((x-3)) * x(x-4)(x-3) = C(x)(x-4)
Now, we can combine the terms to get the final expression:
A(x-4)(x-3) + B(x)(x-3) + C(x)(x-4) = (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC
So, the final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.
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The table for the quadratic functions f(x) and g(x) are given.
x f(x) g(x)
−6 36 4
−3 9 1
0 0 0
3 9 1
6 36 4
Determine the type of transformation and the value of k.
1. g(x) = 3f(x)
2. g(x) = f(3x)
3. g of x equals one third times f of x
4. g of x equals f of one third times x
The value of k is 1, which is the value of g(x) (and f(x)) when x = -3 or x = 3.
We can determine the type of transformation and the value of k for each of the aforementioned functions using the tables provided for f(x) and g(x).
g(x) = 3f(x) (x)
Here, there occurs a vertical stretch/compression transformation. The function g(x) is a three-fold vertical expansion or contraction of f(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(3x) (3x)
Here, there occurs a horizontal stretch/compression transformation. A horizontal stretch or compression of f(x) by a factor of 1/3 results in the function g(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
g(x) = (1/3)f(x) (x)
Here, there occurs a vertical stretch/compression transformation. A vertical stretch or compression of f(x) by a factor of 1/3 results in the function g(x). G(x) has a value of 4, which is identical to the value of k, whether x = -6 or = 6.
g(x) = f(x/3)
Here, there occurs a horizontal stretch/compression transformation. The function g(x) is a three-fold horizontal stretching or compression of f(x). When x = -3 or x = 3, the value of k is 1, which is also the value of g(x) and f(x).
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In triangle ABC, Angle C is a right angle. Find the value of the trig function. Find the Tan A if c=7√10 and a=21
Answer:
tan A= 8/15
draw triangle where A and B are legs and C is hypotenuse
A=8 and C=17, meaning that you need to find B by using Pythagorean theorem (a^2+b^2=c^2)
8^2+b^2=17^2
64+b^2=289
b^2=225
b=15
tan= opposite/adjacent
tan A=8/15
Match the cylinder in the left column with its surface area in the right column
Show work please!! I need this ASAP
The surface area of the cylinder is 502.4 in², 602.88 in² and 175.84 in² respectively
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The surface area of a cylinder is:
Surface area = 2πr(r + h)
where r is the radius and h is the height
1) r = 5 in., h = 11 in. and π = 3.14, hence:
Surface area = 2πr(r + h) = 2(3.14)(5)(5 + 11) = 502.4 in²
2) r = 6 in., h = 10 in. and π = 3.14, hence:
Surface area = 2πr(r + h) = 2(3.14)(6)(6 + 10) = 602.88 in²
3) r = 2 in., h = 12 in. and π = 3.14, hence:
Surface area = 2πr(r + h) = 2(3.14)(2)(2 + 12) = 175.84 in²
The surface area of the cylinder is 502.4 in², 602.88 in² and 175.84 in² respectively
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HELP PLEASE THIS IS SOO HAARD!!!!!!!!
If a car is going at 75 mph, how far would you get in one hour?
Answer: 75
Step-by-step explanation:
MPH stands for Miles per hour
So the car drives 75 miles per hour
Annabel sent 39 text messages to her brother during the last 13 days. How many text messages did she send her brother each day if she sent him the same number of text messages each day?
Answer: 3
Step-by-step explanation:
39 divided by 13 is equal to 3
there are 39 days, and if you divide it by how many days (13), you would get how many messages were sent each day which is 3
Well It’s Really Simple You’ve Could Have A Calculator. 52 Fifty- Two
If the constant of variation is 12 and y = 36 and they vary directly, what does x equal?
If the constant of variation is 12 and y = 36 and they vary directly, then x equals 3.
Direct variation is when two quantities, x and y, are related in such a way that the ratio of their values is always the same. This means that y = kx, where k is the constant of variation.
In this case, we are given that k = 12 and y = 36. We can plug these values into the equation to find x:
36 = 12x
To solve for x, we can divide both sides of the equation by 12:
36/12 = 12x/12
This simplifies to:
3 = x
Therefore, x equals 3.
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0.12x= 1 I need help on this please
Answer:
x=8.3 recurring
Step-by-step explanation:
1÷0.12=8.3 recurring
x=8.3 recurring
or as a fraction 8 1/3
Solve Show all steps
(x^3/2)^6/5 =x^a
[tex](x^{3/2} )^{6/5}[/tex]
= [tex]x^{9/5}[/tex]
The value of a after solving through exponents = 9/5
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. The number of times a number has been multiplied by itself is the exponent, so to speak.
For instance, the result of multiplying the number 6 by itself four times is:
6 × 6 × 6 × 6. You can write this as
Now here,
[tex](x^{3/2} )^{6/5}[/tex]
= [tex]x^{9/5}[/tex]
Therefore, the value of a = 9/5.
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Arrange these in descending order
0. 68
0. 5
0. 345
0. 99
Math question 5 help
Calculate the expected value of the scenario.
xi P(xi)
11 0.24
22 0.31
33 0.01
44 0.15
55 0.29
The expected value of this scenario is 4.19.
The Expected value (EV), which is based on a random variable's probability distribution, describes the long-term average level of that variable. The expected value of a stock or other investment is a crucial factor in investing and is taken into account while performing scenario analysis.
To calculate the expected value, we need to multiply each outcome xi by its respective probability P(xi), and then add up all of these products. So, we have:
Expected value = 1(0.24) + 2(0.22) + 3(0.31) + 4(0.01) + 5(0.16) + 6(0.29)
Expected value = 0.24 + 0.44 + 0.93 + 0.04 + 0.80 + 1.74
Expected value = 4.19
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Solve each system of equations by substitution. Clearly identify your solution.
y=3x+19
y=5x+33
Answer:
(x, y) = (-7, -2).
Step-by-step explanation:
To solve the system of equations:
y = 3x + 19
y = 5x + 33
We can use the substitution method, which involves solving one equation for one variable and substituting that expression into the other equation. Then we can solve for the remaining variable.
From the first equation, we can solve for y in terms of x:
y = 3x + 19
From the second equation, we can solve for y in terms of x:
y = 5x + 33
Now we can substitute the expression for y from the first equation into the second equation:
3x + 19 = 5x + 33
Simplifying this equation by subtracting 3x from both sides:
19 = 2x + 33
Subtracting 33 from both sides:
-14 = 2x
Dividing both sides by 2:
x = -7
Now that we have the value of x, we can substitute it back into either equation to find the value of y:
y = 3x + 19
y = 3(-7) + 19
y = -21 + 19
y = -2
The solution to the system of equations is (x, y) = (-7, -2).
What is the product of (−2)(18)(−8)?
Pls do this
Answer:
288
Step-by-step explanation:
-2 x -8 =16
16 x 18 = 288
Answer:
288
is the answer
Step-by-step explanation:
please mark brainiest
Question 2 of 10
Solve the inequality for x and identify the graph of its solution.
|x+3|< 2
Choose the answer that gives both the correct solution and the correct graph.
A. Solution: x < -5 or x>-1
411
O
-8 -7 -6 -5 -4 -3 -2 -1 0 12
B. Solution: x>-5 and x < -1
+
O11
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
OC. Solution: x>-5 and x < -1
O
-8-7-6 -5 -4 -3 -2 -1 0 1 2
OD. Solution: x < 1 or x>5
O
-2 -1 0 1 2 3
3
4
O
5 6 7 8
The solution of the inequality |x+3| < 2 is -5 < x < -1.
And the graph is given in the image below.
The correct option is C.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
To solve the inequality |x+3| < 2, we need to consider two cases:
Case 1: x+3 ≥ 0
In this case, the inequality simplifies to x+3 < 2, which gives us x < -1.
Case 2: x+3 < 0
In this case, the inequality simplifies to -(x+3) < 2, which gives us -x-3 < 2, or -x < 5, or x > -5.
Combining the results from both cases, we get the solution:
-5 < x < -1
To graph the solution, we draw an open circle at x=-3
(since the absolute value is less than 2, not less than or equal to), and shade the region between -5 and -1.
Therefore, the solution is -5 < x < -1.
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2+2+??= 4,000
helppppppppppppppppppppppp
Answer:
2 + 2 + ?? = 4,000
?? = 3996
Step-by-step explanation:
You're welcome.
The sum of two number is 40. The larger number is 8 more than the smaller number. What are the numbers?
Answer:
16 + 24
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!
The value of m and n is 5√2 and 5 respectively.
What is Pythagoras' theorem?The hypotenuse side of a right-angled triangle's square is equal to the sum of the squares of its other two sides, according to Pythagoras' Theorem.
A right-angled triangle.
A 45° angle is found in a triangle.
The triangle is therefore a right-angled isosceles triangle.
Hence, n = 5.
To find m:
Apply Pythagoras' theorem,
m = √{n² + 5²}
m = √(25 + 25)
m = √50
m = 5√2
Therefore, m = 5√2.
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Subtract. (7)/(12vx^(2))-(3)/(8v^(2)x) Simplify your answer as much as possible.
Subtracting the expression (3)/(8v²x) from the expression (7)/(12vx²) will result to the expression (14v - 9x)/(24v²x²).
To subtract the two fractions, we need to find a common denominator. The least common denominator (LCD) is the least common multiple of the denominators of two or more fractions, and it is used to find a common denominator so that we can perform operations on them. The LCD of 12vx² and 8v²x is 24v²x². We can then multiply each fraction by the LCD to get the same denominator and subtract the numerators.
(7)/(12vx²) x (24v²x²)/(24v²x²) - (3)/(8v²x) x (24v²x²)/(24v²x²) = (14v)/(24v²x²) - (9x)/(24v²x²) = (14v - 9x)/(24v²x²)
So the simplified answer is (14v - 9x)/(24v²x²).
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An architect is designing a covered bridge to be placed over a ravine. In the diagram BF and BG represent the sides of the ravina, FIG represents the road surface of the bridge, and AC represents the of covering the bridge. Would these
urements ensure the roof is parallel to the road of the bridge? Explain
Therefore, it would be necessary to take the measurements in a manner that would guarantee that these requirements are met.
what is parallel ?Two or more lines, dotted lines, or planes that remain the same distance apart and never cross, even if they are extended indefinitely in both directions, are referred to as parallel in mathematics. The sign "||" stands for parallel lines. There are many significant characteristics of parallel lines. The fact that a transversal line—a line that crosses two or more parallel lines—always forms equal angles is among the most significant.
given
If two lines are drawn, one from the highest spot on the roof to the surface and the other from the lowest point, they must be parallel to one another. Those lines must also be parallel to one another if we sketch one from the leftmost point on the roof to the surface and another from the rightmost point on the roof to the surface.
Therefore, it would be necessary to take the measurements in a manner that would guarantee that these requirements are met.
To ensure that the measurements are precise and that the roof is built at the right angle to be parallel to the road, this may require using a level or other instruments.
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PLEAAAASEEEE HELPP!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!
1. The y-intercept of y = -3/2x - 4, is -4, which would be marked at y = -4 on the y-axis.
2. The slope (m) = 3; y-intercept (b) = -86;
The equation for the situation is: y = 3x - 86
3. Median of class A = 40; Median of class B = 8
The difference is: 32
What is the Y-intercept of a Linear Equation?In a linear equation, the y-intercept is the point at which the graph of the equation intersects the y-axis. It is the value of y when x is equal to zero.
1. The y-intercept of the equation, y = -3/2x - 4, is -4. This means the y-intercept on the graph would be at when y = -4 on the y-axis.
2. The slope (m) = unit rate = 3 degrees every hour
The starting value = y-intercept (b) of the situation = -86
To write an equation for the situation substitute m = 3 and b = -86 into y = mx + b:
y = 3x - 86
3. Median is the middle value of a data set, therefore:
Median of class A = 40
Median of class B = 8
The difference between the medians of the class = 40 - 8 = 32
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James spent 2/5 of his pocket money on snacks and 1/4 of the remaining amount on snacks a) Calculate the fraction of his pocket money spent on snacks. b)calculate his pocket money if he still has$9.00 left
Answer: about 26.00
Step-by-step explanation:
a pair of pants usually sells at 500.00 during a sale , it is being sold at a 40% discount how much is the discount?how much will u pay for a pair of pants during the sale?
estimate the product of 3.8 and 11.9 by rounding
The product or multiple of 3.8 and 11.9 by rounding off (simplification) is equal to 45.22.
What is simplification in mathematics?Simplification means keeping it simple. In mathematics, it simplifies or simplifies formulas/fractions/problems into simpler forms. Simplify the problem with calculations and solutions.
Simplification generally means finding answers to complex calculations involving division, multiplication, square roots, cube roots, plus and minus numbers.
Why do we use simplification?Simplicity complicates deadpan, making it easier to understand and solve. Here are some advantages of solving a problem or equation by simplification.
It helps you solve your problem in fewer steps. Complex problems can be reduced to simpler forms by following the rules of simplification
According to the question:
3.8×11.9 = (38/10)×(119/10)
= 4522/100
= 45.22
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solve this
please i need help with this
Answer:
45
Step-by-step explanation:
You want the area of triangle RST using the area formula A=1/2bh, given the points R(-2, 7), S(-5, 1), and T(7, -5).
Side lengthsA plot of the points is shown in the first attachment. By counting grid squares, you can see that segment RS has a "rise" of 2 grid squares for each 1 to the right. The total (run, rise) is ...
R -S = (-2, 7) -(-5, 1) = (-2 +5, 7 -1) = (3, 6)
The length of RS is found using the Pythagorean theorem (distance formula). It is ...
RS = √(3² +6²) = √45 = 3√5
Similarly the length of segment ST is ...
T -S = (7, -5) -(-5, 1) = (7 +5, -5 -1) = (12, -6)
ST = √(12² +(-6)²) = √180 = 6√5
SlopesWe note that the slopes of these segments are opposite inverses of each other:
slope RS = 6/3 = 2
slope ST = -6/12 = -1/2
This means the segments are at right angles. One of them can be considered to be the "base" and the other the "height" of the triangle.
AreaUsing the area formula, we find the area to be ...
A = 1/2bh
A = 1/2(6√5)(3√5) = (1/2·6·3)(√(5·5)) = 9·5 = 45
The area of ∆RST is 45 square units.
__
Alternate solution
When the coordinates of a polygon are given, there are several other ways to find its area. One of these is illustrated in the second attachment.
The method illustrated here computes successive "determinants", then finds the area as half the absolute value of their sum. (The sign of the sum will depend on the order in which the points are listed around the figure. Here, it is counterclockwise.) As you can see, we get the same result. You can also see that a spreadsheet is useful for doing the repetitive math.
Area ∆RST = 45 square units
__
Additional comment
The distance formula for the length of the segment between two points is ...
d = √((x2-x1)² +(y2-y1)²)
Above, we calculated the differences (x2-x1, y2-y1) separately, then used the "root sum squares" formula for the distance. This has the advantage that (y2-y1)/(x2-x1) is the slope of the segment, and we needed to make sure the segments were perpendicular.
Caleb needs to place a ground cover
under a tent. The floor of the tent measures 82 feet by 92 feet.
He purchases a ground cover that states that it covers 90 square
feet. Will the ground cover be able to be used under the tent?
Explain your reasoning.
One cover is not enough to cover tent, Caleb will need at least 84 ground covers to cover the entire floor of the tent.
How to find the Cover area of the tent?To determine if the ground cover will be sufficient, we need to calculate the area of the tent floor and compare it with the area covered by the ground cover.
The area of the tent floor is:
82 feet x 92 feet = 7544 square feet
The area covered by one ground cover is:
90 square feet
To determine the number of ground covers needed to cover the tent floor, we can divide the area of the tent floor by the area covered by each ground cover:
7544 square feet ÷ 90 square feet ≈ 84
Therefore, Caleb will need at least 84 ground covers to cover the entire floor of the tent. As the number of ground covers required is greater than one, we can conclude that the ground cover will be able to be used under the tent.
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A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 49° and AB = 8. 9. Calculate the length of AC rounded to 3 SF
Answer:
/AC/=10.2
Mark as brainliest
(a)Let Q be the quotient of the ring R=Z*Z by the ideal I= 2Z*2Z.
What is Q four elements?
(b) Use the Fundamental Homomorphism Theorem to show Q is
equivalent to Z2*Z2?
By the Fundamental Homomorphism Theorem, Q is isomorphic to Z2*Z2.
a) Q is the quotient ring R/I, which has four elements: [0]_I, [1]_I, [2]_I, and [3]_I. Here, [x]_I is the equivalence class of x in R/I.
b) Using the Fundamental Homomorphism Theorem, we can show that Q is equivalent to Z2*Z2. Since I is a normal subring of R, the quotient ring Q can be written as Q = R/I. Then the homomorphism defined by φ: R → Z2*Z2, where φ(r) = (r mod 2, r mod 2) is onto and I is the kernel of φ. Thus, by the Fundamental Homomorphism Theorem, Q is isomorphic to Z2*Z2.
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a ice cream truck driver figured out that the number of ratio of vanilla to chocolate ice cream cones sold was 5 to 2 if 125 vanilla cones were sold how many chocolate cones were sold?
Answer: 50 chocolate cones
Step-by-step explanation: if 5 is 125 vanilla then 125/5= 25 so every 1=25 and that means 2*25= 50
Answer:
50. There were 50 chocolate cones sold.
Step-by-step explanation:
so we do it like this: see the attachment for the work i did to solve
*Baige=Vanilla*
*brown=chocolate*
when you cross multiply you get 50
Someone please help me with this I got 0 clue what I'm doing with it
Answer:
3rd choice down
f(x) = -1/2x + 8
Step-by-step explanation:
find the slope of the line using the 2 given points:
slope = m = (8-14) / (0--12) = -6/12 = -1/2
read the y intercept right off the graph at point (0,8):
b = 8
f(x) = mx + b = -1/2x + 8
Which graph shows the solution to the inequality? x + 2 < -3 A) A B) B C) C D) D
Therefore , the solution of the given problem of inequality comes out to be the inequality x -5 is option B.
What does inequality imply in reality?Regardless of the equal symbol, a connection or group of numbers variables can be an inequality in mathematics. Equilibrium is always followed by equity. Inequality happens when ideals are still incompatible. Differences exist between inequality expression and fairness. We chose to utilize the most prevalent symbol because elements aren't always similar or comparable (). No mater how few or many variations there are, they can all be used to evaluate values.
Here,
Option B) B is the proper response.
We must isolate x on one side of the inequality in order to answer the inequality x + 2 -3. By taking 2 away from both edges, we arrive at:
=> x < -5
According to this inequality, x is any integer that is less than -5. Since x cannot equal -5,
we must create an open circle at this point on the number line and shade to the left of it to represent all the different values of x that could be used.
Looking at the available choices, we can see that the only graph that accurately depicts the inequality x -5 is option B) B.
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