The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.
What is LCM?The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We must find the lcm of the rational algebraic equation.
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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Hello! I need some help with this homework question, please? The question is posted in the image below. Q11
A one-to-one function means that there are no two elements in the domain of the function that corresponds to the same element in the range,
Mathematically since
[tex]\begin{gathered} x\text{ is the input or the domain, then} \\ f(x)\text{ is the output} \end{gathered}[/tex]A one-to-one follows that
[tex]\text{if }x_1\text{ and }x_2\text{ are two different inputs of a function }f,\text{ then }f(x_1)\neq f(x_2)[/tex]Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?
Answer:
63 i think!
Step-by-step explanation:
71-53 is 18. 18+45 is 63!
Im so so so sorry if im wrong, have a nice day friend!: )
The Product of twice a number and six is the Same as the difference of eleven times the number and 5/7. Find the number
The number x = - 5/7 .
How do you frame an equation?The following steps are necessary to construct a linear equation in one variable from the provided word problem:
Step I: Read the problem attentively and make separate notes for the provided and necessary quantities.
Step II: Use 'x', 'y', 'z', etc. to represent the unknowable quantities.
Step III: Next, convert the issue into a mathematical formulation or statement.
Step IV : Utilizing the conditions provided in the problem, form a linear equation in one variable in
Step V: Verify the equation for the unknown quantity
Let the number be x
Thus according to the question :
( twice a number) × 6 = 11 (number) - 5/7
(2x)6 = 11 x - 5/7
12x = 11 x- 5/7
x= - 5/7
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A cylinder with a radius of 1 yd and a height of 2 yd
URGENT!!!!!!!!!
Thank you to whoever solves it right!
Answer:
D
Step-by-step explanation:
The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.
Hope that helps
Can you please explain? I have the other options also.
Given
[tex]f(x)=\frac{1}{3}\lvert x+4\rvert-4[/tex]The graph
Bill owns land but has no access to water so he has to pay for well water from Jim.
Jim charges him $8 per month plus $0.80 per gallon.
During any given summer month, his water bill costs between $48 and $72.
Write and solve a compound inequality to determine how much water Bill is using.
Please see image attached on using the diagram to name the ray
Given:
Find - Name of rays
Sol:
Ray:- In geometry, a ray can be defined as a part of a line that has a fixed starting point but no endpoint can extend infinitely in one direction. On its way to infinity, a ray may pass through more than one point.
So rays is
[tex]=\vec{AE}[/tex]Find the value of x in the diagram. ΔPQR ~ ΔSTU
45.6 divided by 0.03
Answer:
1,520
Step-by-step explanation:
Elsa is saving money to buy a game. So far she saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Elsa is saving money to buy a game.
So far she saved $24, which is two-thirds of the total cost of the game.
let the cost of the game is $x
Then, two -third of the total cost = 2/3 x
Since, it is given that 24 is the two-thirds of the total cost of the game.
i.e.
[tex]\frac{2}{3}x=24[/tex]Simplify the expression for x;
[tex]\begin{gathered} \frac{2}{3}x=24 \\ \text{ Apply cross multiplication;} \\ 2x=24\times3 \\ x=\frac{24\times3}{2} \\ x=12\times3 \\ x=36 \end{gathered}[/tex]x = 36
Total cost of the game is $36
....
Hello! I need some assistance with this homework question, pleaseQ16
we have the function
[tex]y=\sqrt[]{x}[/tex]shifted down 10 units, is the same that apply the rule
(x,y) -----> (x,y-10)
therefore
the new function is
[tex]y=\sqrt[]{x}-10[/tex]The answer is the first optionGiven that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.
The Solution.
Given that
[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]The conditional probability P(A/B) is given as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]But for independent events, we have that
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence, it follows that
[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for sales and research combined is 75,000,000. What is the total annual budget?
$150,000
1) In that pie chart, we can tell that the Sales and Research department combined responds to 50% (35%+15% =50%)
2) Thus, we can tell that:
[tex]\begin{gathered} 0.35x+0.15x=75000 \\ 0.5x=75000 \\ x=\frac{75000}{0.5} \\ x=150,000 \end{gathered}[/tex]So, since 50% of that budget corresponds to $75,000 we can tell that 100% (the total budget) corresponds to twice that figure, which yields 150,000
8x – 12y = – 24 a. x-intercept: b. y-intercept: 10+ C. graph 9 8 7 6 5 4 13 2 -10 -9 -8 -7 -6 -5 -4 -B-2 -1 2 15 4 SI 6 8 9 10 -2 3 -6 -7 -8 9 10 Clear All Draw:
To determine the x- and y-intercepts is best to write the equation in slope-intercept form.
Given
[tex]8x-12y=-24[/tex]-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 8x-8x-12y=-8x-24 \\ -12y=-8x-24 \end{gathered}[/tex]-Divide both sides of the equal sign by -12
[tex]\begin{gathered} \frac{-12y}{-12}=\frac{-8x}{-12}-\frac{24}{-12} \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]So the equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]a) The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is equal to zero. To determine the x-coordinate of the intercept, you have to equal the equation to zero and calculate the corresponding value of x:
[tex]0=\frac{2}{3}x+2[/tex]-Subtract 2 to both sides of the equal sign
[tex]\begin{gathered} 0-2=\frac{2}{3}x+2-2 \\ -2=\frac{2}{3}x \end{gathered}[/tex]-Multiply both sides of the expression with the reciprocal fraction of 2/3
[tex]\begin{gathered} (-2)\frac{3}{2}=(\frac{2}{3}\cdot\frac{3}{2})x \\ -3=x \end{gathered}[/tex]The x-intercept is (-3,0)
b) The y-intercept is the point where the line crosses the y-axis, at this point, the x-coordinate is equal to zero. To determine the y-intercept, replace the equation with x=0 and calculate the corresponding value of y:
[tex]\begin{gathered} y=\frac{2}{3}x+2 \\ y=\frac{2}{3}\cdot0+2 \\ y=2 \end{gathered}[/tex]The y-intercept is (0,2)
c) To graph the line, plot both intercepts on the coordinate system and then link both points with a line:
Find the equation (in terms of x) of the line through the points (-3,-3) and (4,-2) II
Given:
The coordinates of the points through which the line passes,
(x1, y1)=(-3, -3).
(x2, y2)=(4, -2).
The two point form of the equation of a line can be expressed as,
[tex]y-y1=\frac{y2-y1}{x2-x1}(x-x1)[/tex]Substitute the known values in the above equation.
[tex]\begin{gathered} y-(-3)=\frac{-2-(-3)}{4-(-3)}(x-(-3)) \\ y+3=\frac{-2+3}{4+3}(x+3) \\ y+3=\frac{1}{7}(x+3) \\ 7(y+3)=x+3 \\ 7y+7\times3=x+3 \\ 7y+21=x+3 \\ 7y=x+3-21 \\ 7y=x-18 \\ y=\frac{1}{7}x-\frac{18}{7} \end{gathered}[/tex]Therefore, the equation of the line is,
[tex]y=\frac{1}{7}x-\frac{18}{7}[/tex]determine the domain of each function yx-3x=3y-1
Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.
What is a domain?The dependent variable and the independent variable are the two types of variables used to define a function.
The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.
Despite x=0, the domain of g(x)=1/x can contain any real number.
The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:
Domain → Function → Range
We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.
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13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.
Answer:
The equation is true when x = 2.25
Explanation:
On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:
3*(-x) + 10*(1)
-3x + 10
For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:
5*x + 8*(-1)
5x - 8
Now, we can write the equation as:
-3x + 10 = 5x - 8
So, solving for x, we get:
-3x + 10 + 3x = 5x - 8 + 3x
10 = 8x - 8
10 + 8 = 8x - 8 + 8
18 = 8x
18/8 = x
2.25 = x
Therefore, the equation is true when x is equal to 2.25
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. Work out the probability that tina takes two blue counters in fraction.
Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. The probability that tina takes two blue counters in fraction is 15/72
What is the probability?Given parameters:
Bag A= 5 red + 3 blue
Bag B = 4 red + 5 blue
Hence,
Total counters in bag A = 5 +3 = 8
Total counters in bag B = 4 + 5 = 9
Now let determine the probability that she takes two blue counters
Probability = 3 /8 × 5 /9
Probability = 15 / 72
Therefore 15 / 72 is the probability that two blue was taken.
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Justin places a bet on the giants to win the superbowl. the odds are 2:3. a) Are the giants expected to win? why or why not?b) Find P(Giants win)=
To convert the odds to a probability, we can divide the odds by one plus the odds.
then, in this case we have the following:
[tex]\begin{gathered} \text{odds:} \\ 2\colon3=\frac{2}{3} \\ \Rightarrow1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]then, we have that the probability is:
[tex]\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2\cdot3}{5\cdot3}=\frac{2}{5}[/tex]thus, the probability that the Giants will win the superbowl is 2/5=0.4=40%
As we can see, we cannot expect for sure that the giants will win
Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2
Answer: √x−2,−√x−2
Step-by-step explanation:
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
Step-by-step explanation:
Answer:
lol no
Step-by-step explanation:
The radius of a circle is 6 centimeters. What is the area of a sector bounded by a 150 degree arc?Give the exact answer in simplest form._____ square centimeters
Concept
[tex]\text{Area of a sector = }\frac{\theta}{360}\text{ }\times\text{ }\pi r^2[/tex][tex]\begin{gathered} \theta\text{ is the angle subtend at the center} \\ r\text{ is the radius} \end{gathered}[/tex]Step 1: List the given data
[tex]\begin{gathered} \theta=150^o \\ r\text{ = 6cm} \\ \pi\text{ = }\frac{22}{7} \end{gathered}[/tex]Step 2: Substitute the values to find the area of the sector.
[tex]\begin{gathered} \text{Area of the sector = }\frac{150}{360}\text{ }\pi\text{ }\times6^2 \\ =\text{ }\frac{150\text{ }\pi\text{x 36}}{360\text{ }} \\ =15cm^2 \end{gathered}[/tex]Ok
find the reciprocal -16/5
Remember that the reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).
Thereby, the reciprocal of
[tex]-\frac{16}{5}[/tex]is
[tex]-\frac{5}{16}[/tex]What is the completely simplified form of the expression 2(1 - 3x) - (5x + 1)?
A) -11x + 1
B) -8x + 1
C) -11x + 3
D) -8x + 3
Answer:
A
Step-by-step explanation:
2(1-3x)-(5x+1)
=2-6x-5x-1
=1-6x-5x
=1-11x/-11x+1
4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a
Answer:
D: x > a
Step-by-step explanation:
We have 5x - 2a > 2x-a
We can rewrite this equation by subtracting 2x on both sides, which gives:
5x - 2x -2a > 2x - 2x - a,
so 3x - 2a > a
We now add 2a on both sides, which gives:
3x -2a + 2a > a + 2a, so 3x > 3a
We nog divide both sides by 3, which gives:
3x/3 > 3a/3, so x>a
The correct answer is D
A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.
We are given the following information
Perimeter of the rectangular room = 24 meters
The rectangular room is 4 meters longer than it is wide.
Let L be the length and W be the width of the rectangular room.
[tex]L=4+W[/tex]The perimeter of a rectangular shape is given by
[tex]P=2(L+W)[/tex]Substitute P = 24 and L = 4 + W into the above equation
[tex]\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ \frac{16}{4}=W \\ W=4\;m \end{gathered}[/tex]So, the width of the rectangular room is 4 meters.
[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]So, the length of the rectangular room is 8 meters.
Length = 8 meters
Width = 4 meters
Example Problem:
Suppose that perimeter is 1055 meters.
The length is 45 meters longer than the width of the rectangle.
[tex]L=45+W[/tex]Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.
[tex]\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=\frac{965}{4} \\ W=241.25\;m \end{gathered}[/tex]So, the width of the rectangle is 241.25 meters.
[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]So, the length of the rectangle is 286.25 meters
two trains travel at a constant speed. Train a travels 1400 miles in 5 hours and train b travels 2100 miles in 7 hours. Which train travels faster?
Martin eats 3/8 of a pizza. Felix eats 2/5of a pizza of
same size. Who eats more pizza? How much more pizza
does he eat?
all the odd numbers from 51 to 5001 are written what is the total number of digits used
Answer:
9404 digits
Step-by-step explanation:
The numbers written:
51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]
101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]
1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]
Total:
50 + 1350 + 8004 = 9404 digits