The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).
The lowest integer that unites all of the fractions in a given collection is known as the least common denominator (LCD).
Given that,
The equation x+2/3x - 1/x-2 = x-3/3x is being multiplied by the least common denominator (LCD)
So, further solving this equation,
x+2 / 3x - 1/x-2 = x-3/3x
Here, the least common denominator (LCD) is (3x)(x-2). so we multiply the whole equation by the least common denominator (LCD).
(3x)(x-2) (x+2/3x - 1/(x-2) = x-3 / 3x)
We multiply each term by the least common denominator (LCD).
(3x)(x-2) (x+2/3x) - (3x)(x-2)(1/(x-2)) = (3x)(x-2)(x-3 / 3x)
Thus, we get (x-2) (x+2)-1(3x) = (x-3) (x-2).
Therefore,The resulting equation is (x-2) (x+2)-1(3x) = (x-3) (x-2).
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Answer:
D
Step-by-step explanation: answer is d
Solve the system of equations using substitution.
=================================================
Work Shown:
Plug the first equation into the second equation.
2x - y = 5
2x - (3x-1) = 5
2x - 3x+1 = 5
-x+1 = 5
-x = 5-1
-x = 4
x = -4
Use this to find the value of y.
y = 3x-1
y = 3*(-4)-1
y = -12-1
y = -13
The solution is (x,y) = (-4,-13)
This points to choice A as the final answer.
You can use graphing software like Desmos or GeoGebra to confirm that the two lines intersect at (-4,-13).
What are the coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1), and C(2, 5)
The coordinates of the circumcenter of a triangle with vertices A(0,1),
B(2, 1) , and C(2, 5) is (1,3).
What is circumcenter of triangle?
The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).
Given: A triangle with vertices A(0,1), B(2, 1) , and C(2, 5).
Using distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB = 2 units
BC = 4 units
AC = √20 units
The midpoint of AC:
[tex]= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\\= (\frac{2+0}{2}, \frac{5+1}{2}) \\= (\frac{2}{2} , \frac{6}{2})\\ = (1, 3)[/tex]
The midpoint of AC is (1, 3).
Hence, The coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) is (1,3).
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The difference of twice a number and 9 is at least -25.
Answer:
x≥-8
Step-by-step explanation:
Because we don't know the first number mentioned, we can name it as x
Since the problem starts off with "twice a number" so we mark it as 2x and then it states to take the difference of that number and 9. So the new problem we have is 2x-9=?. Now, the answer that we have is at least -25, so the answer is no longer an equal sign, but a greater-than or equal-to sign. Making our new equation 2x-9≥-25. Now we can act as if its a normal equation, adding 9 to both sides making it 2x≥-16, divide both sides by 2 to get x≥-8.
An extra step to ensure our answer is more than or equal to -8 is by plugging in -8 AND another number that is more than -8. 2(-8)-9=? which we would find that ? is -25. A number that is greater than -8 could be -1, which we would test by doing 2(-1)-9=?. ? would be equal to -11 so we know that our final answer of x≥-8 is correct.
The table shows the distance why in meters that a person runs an ex seconds graph the line that passes through the points in a table then write an equation that represents the line (1,4.5),(2,9),(3,13.5).
!!!!GIVING EXTRA BRAINLIST!!!!
Use the area model to multiply(½f-49).
First, find the partial products. Write numbers as integers, decimals, or simplified proper or
improper fractions.
38
f
BE
Now, write the product.
-4g
Video
Answer:
[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g
Step-by-step explanation:
[tex]\frac{3}{8}[/tex] ( [tex]\frac{1}{2}[/tex] f - 4g )
multiplying each of the terms inside the parenthesis by [tex]\frac{3}{8}[/tex]
[tex]\frac{3}{8}[/tex] × [tex]\frac{1}{2}[/tex] f
= [tex]\frac{3(1)}{8(2)}[/tex] f
= [tex]\frac{3}{16}[/tex] f
and
[tex]\frac{3}{8}[/tex] × - 4g ( cancel 4 and 8 by 4 )
= [tex]\frac{3}{2}[/tex] × - g
= - [tex]\frac{3}{2}[/tex] g
combining the 2 products, gives
[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g
Answer:
[tex]\textsf{Orange partial product}=\dfrac{3}{16}\;f[/tex]
[tex]\textsf{Pink partial product}=-\dfrac{3}{2} \;g[/tex]
[tex]\textsf{Product}=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)[/tex]
Calculate the partial products then add these together to find the product of the given expression.
Orange partial product
[tex]\implies \dfrac{3}{8} \times \dfrac{1}{2}f[/tex]
[tex]\implies \dfrac{3 \times 1}{8\times 2}\;f[/tex]
[tex]\implies \dfrac{3}{16}\;f[/tex]
Pink partial product
[tex]\implies \dfrac{3}{8} \times (-4g)[/tex]
[tex]\implies \dfrac{3 \times -4}{8} \;g[/tex]
[tex]\implies \dfrac{-12}{8} \;g[/tex]
[tex]\implies -\dfrac{\diagup\!\!\!\!4 \times 3}{\diagup\!\!\!\!4 \times 2} \;g[/tex]
[tex]\implies -\dfrac{3}{2} \;g[/tex]
Product:
[tex]\implies \dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]
How many and what type of solutions does 4x² 12x 9 0 have?
The equation [tex]4x^2+12x+9=0[/tex] has only one solution, and the type of solution is rational.
Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal. When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used. Let's go over each method for solving an equation in detail one by one.
Here steps for solving an equation are given below.
[tex]4x^2+12x+9=0\\4x^2+6x+6x+9=0\\2x(2x+3)+3(2x+3)=0\\(2x+3)(2x+3)=0\\2x=-3\\x=\frac{-3}{2}[/tex]
Here both solutions are same so the equation [tex]4x^2+12x+9=0[/tex] has only one solution and the type of solution is a rational solution.
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a cell phone plan has a basic charge of $45 a month. the plan includes 500 free minutes and charges 10 cents for each additional minute of usage. write the monthly cost c (in dollars) as a function of the number x of minutes used.
The cost function is [tex]C(x)=[/tex] [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex] .
The application of the idea of kinds of functions is the foundation of this issue. We will create and classify the sort of function we have using the provided information.
According to the given information, the cell phone plan has a basic charge of $45 a month. The plan includes 500 free minutes and charges 10 cents for each additional minute of usage.
Let t be the number of minutes the cell phone is used.
So, for 0≤t≤500 it will cost only the basic charge of $45.00
For an additional minute of usage, it costs 10 cents or $0.1 in addition to the basic charge. So, our function looks like:
f(x)=45+0.1(t-500)=45+0.1t-50 = (0.1t-5), for 500 ≤ t ≤ 700.
Thus, the cost function looks like:
C(x) = [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex]
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X^2 + _x + 100
Find all possible values for the missing number that make the expression the square of a binomial.
Answer: The expression X^2 + _x + 100 is the square of a binomial if the missing number is -b/2 and b^2 - 4ac = 0.
Step-by-step explanation: The general form of the square of a binomial is (x + b)^2 = x^2 + 2bx + b^2.
In this case, the missing number is -b/2, and the expression becomes X^2 - x + 100.
Now to find the value of x, we can use the equation b^2 - 4ac = 0
The equation becomes x^2 - 41100 = 0
Which gives x^2 - 400 = 0
So x = ± 20.
So the possible values for the missing number that make the expression the square of a binomial is -20/2 = -10 and 10.
Answer:
To find the missing number in the given expression, we will see the operation used. Step 1: Recall the concept of addition. We need to find the first addend. Step 2: Think of the number which when added to 3 gives the sum equal to 8. Step 3: 5 + 3 = 8. So, the missing number is 5. Step 4: Write the missing number: 5 + 3 = 8.
Step-by-step explanation:
Supplementary angles are two angles that have measures with a sum of 180°. Angles 1 and 2 are supplementary and the measure of angle 2 is 3° more than twice the measure of angle 1.
Write a system of equations and use substitution to find the measures of angles 1 and 2.
100 characters remaining
Answer:
Step-by-step explanation:
180 total
180-3=177
ratio of angle 1 to angle 2:
2:1
we need to divide 177 by 3 since there are 3 parts in the ratio above
177/3=59
angle 1 = 59x2=118
angle 1=118 degrees
angle 2=59+3=62
angle 2 =62 degrees
we can check by adding 62 and 118
62+118=180
Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.
How to illustrate the triangle?Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.
A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
In this case, the correct option is A.
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How to find the answer
s= 7; 6s²
Answer:
294
Step-by-step explanation:
We will take our equation, and substitute in 7 for s, wherever we see it, so we have:
[tex]6 * 7^{2}[/tex]
Simplifying, we have:
[tex]6 * 49[/tex]
Which finally we multiply to:
6 * 49 = 294
So, your answer is 294.
Hope this helped!
four marbles are chosen from the jar with replacement. what is the probability that they are all white?
The probability that four marbles are chosen from the jar with the replacement and that they are all white is p^4 (p raised to the fourth power).
If four marbles are chosen from a jar with replacement, the probability that they are all white is (probability of drawing a white marble)^4.
If the marbles are chosen with replacement, the probability of choosing a white marble on any one draw is the same as the proportion of white marbles in the jar. Let's call this probability p. The probability that all four marbles chosen are white is p^4 (p raised to the fourth power).
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Determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
–x+y= –5
3x+5y=15
Answer:
(5, 0)
Step-by-step explanation:
The slope of the first line is -(-1 / 1) = 1.
The slope of the second line is -(3 / 5) = -3/5.
Since the lines have different slopes, they intersect at a single point. Therefore, there is only one solution. To find it, solve the system of equations.
Using elimination, multiply the first equation by 3 and add it to the second.
-3x + 3y = -15
3x + 5y = 15
-------------------
8y = 0
y = 0
Using substitution, find x:
-x + 0 = -5
x = 5
The solution is (5, 0).
An ordinary (fair) die i a cube with the number 1 through 6 on the ide (repreented by painted pot). Imagine that uch a die i rolled twice in ucceion and that the face value of the two roll are added together. Thi um i recorded a the outcome of a ingle trial of a random experiment. Compute the probability of each of the following event. Event : The um i greater than 6. Event : The um i diviible by 5 or 6 (or both)
The required values of the events are P(Sum > 5) = 0.72 , P (sum is even) = 0.5.
What is Probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
According to question:We have,
According to empirical or relative frequency probability, probabilities are determined by dividing the total number of potential outcomes of an experiment by the number of ways an event could occur.
There are a total of 36 possible results when a fair die is rolled twice consecutively, which is
(1,1), (1, 2), (1,3), (1,4), (1, 5), (1, 6)
(2,1), (2, 2), (2, 3), (2,4), (2,5), (2,6)
(3, 1), (3,2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4,2), (4,3), (4, 4), (4, 5), (4, 6)
(5, 1),(5, 2), (5, 3), (5,4), (5,5), (5, 6)
(6,1), (6, 2), (6,3), (6,4), (6,5), (6,6)
Event A: The total exceeds 5. We find 26 numbers in the table that are bigger than 5, so
P(A) = P(Sum > 5) = 0.72 Event
B: The results of the total are even from the table are 18
P(B) = P (sum is even) = 0.5
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The hypothesis becomes the basis of
what?
A. as atistical analysis
B. the data to interpret
C. alw
4
D. the experiment
Answer:
D. the experiment
Step-by-step explanation:
The hypothesis becomes the basis of the experiment.
Kent multiplies both sides of the equation below by an expression. Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now
The equation must satisfies the Kent calculation is k² - 8k + 12 = 0
The term equation in math is called as a mathematical expression that contains an equals symbol.
Here we have given that Kent multiplies both sides of the equation below by an expression.
And then he moves all the terms to one side of the equal sign in the resulting equation.
Here we have the given equation is
=> k+12/k= 8
When we multiply both sides by k.
=> k² + 12 = 8k
Now we have to subtract 8k from both sides to move all the terms to one side of the equal sign then we get
=> k² + 12 - 8k = 0
Hence the required equation is k2 - 8k + 12 = 0.
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what is the answer for the probability question?
Answer:
0.15
Step-by-step explanation:
Factors of 12 are 1, 2, 3, 4, and 6.
Only 5 is not a factor of 12.
The probability of rolling a 5 is 15 / 100, or 0.15, or 15%.
You saved 17 dimes and your brother saved 8 dimes. How many more dimes did you save? Your answer is (?).
Answer:
p
Step-by-step explanation:
no of dimes you have =17
no of dimes your brother have=8
now
no of dimes more you have save =17-8
=9
hence you have saved 9 more dimes
If x = 11 , evaluate the following expression: x + 4
Answer:
Substitute x = 11 to x + 4, you get,
11 + 4 = 15
Thanks
[tex]x+4[/tex] when x is equal to 11
Evaluate:
[tex](11)+4[/tex]
[tex]=15[/tex]
urgent help needed w this pls
Answer:
Based on the given information, we know the following:
Solid A is formed by joining one hemisphere to the frustum of a cone.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.
The volume of solid A is 6 times the volume of solid B.
We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.
The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.
The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.
The volume of a cone is (1/3)πr^2h
Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r
We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)
After simplifying, we get:
2h = 12r + 12Rh + 6Rr
We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:
2h = 12r + 12rk + 6rk^2
Solving for h, we get:
h = 6rk + 6rk^2
So h is expressed in terms of k and r.
Graph the system of equations 8x+8y=64 2x-2y=-4
To graph a system of equations, you can first solve each equation for y, and then plot the solutions on the same coordinate plane.
For the first equation, 8x + 8y = 64, we can solve for y by subtracting 8x from both sides, which gives us 8y = 64 - 8x. Then we divide both sides by 8 to get y = (64 - 8x)/8.
For the second equation, 2x - 2y = -4, we can solve for y by adding 2x to both sides, which gives us 2y = 2x - 4.
So the solutions for y in the first equation are:
y = (64 - 8x)/8
and in the second equation are:
y = 2x - 4
We can now plot these two lines on the same coordinate plane. The point of intersection of these two lines will be the solution of the system of equations
Answer is attached in the graph.
Step by step
The easiest way to solve these is to graph on an internet or app graphing calculator.
To graph by hand you need to simplify them and arrange in slope intercept form y=mx + b
(#1)
8x + 8y = 64 all are divisible by 8
8/8x + 8/8y = 64/8
Simplify
x + y = 8
Arrange in slope intercept form
subtract x from both sides to isolate y
x - x + y = -x + 8
y = -x + 8
We plot the first point of y intercept of 8 (0,8) and plot the 2nd point by slope of -1/1 or
( 1, -1). Draw your line
(#2)
2x - 2y = -4 are all divisible by 2
2/2x - 2/2y = -4/2
Simplify
x - y = -2
Arrange in slope intercept form
subtract x from both sides to isolate y
x - x - y = -x -2
Simplify
-y = -x -2
Change the signs by multiplying all by -1
y= x +2
We plot the first point of y intercept
of 2 (0, 2) and plot the 2nd point by slope of 1/1 or ( 1, 1). Draw your line
Now you can find the solution is where the lines intersect. At (3, 5)
See my attached graph for your two line equations below
y = x + 2
y = -x + 8
bc pills are about 99% effective in perfect use, about how effective are they in typical use (because people may forget to take them at the same time every day and other reasons due to human error)?
The tablet is 99% effective if used correctly.
However, since individuals make mistakes and it's easy to forget or overlook pills, the actual effectiveness of the pill is only about 93%. Accordingly, 7 out of every 100 women who take pills annually become pregnant.
Depending on the type of pills you're utilizing and when you start taking them. The birth control pill can be started on any day of the month. However, for up to 7 days, you might need to use a backup birth control method, such as condoms, depending on when you start and the type of pill you're taking.
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Your team scores 10 points in the first game, 3 points in the second game, 2 points in the third game, 5 points in the fourth game, and 0 points in the fifth game. What was the mean number of points your team scored for all 5 games?
The mean number of points for all 5 games is 4 points.
What is arithmetic mean?The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
As per the question,
Here, n = 5
⇒ ∑x = Sum of Observations
⇒ ∑x = 10 + 3 + 2 + 5 + 0 = 20
Mean = ∑x/n
Mean = 20/5
Mean = 4
Hence, the mean of the given data is 4.
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pedro bought 4 pounds of chopped meat for a barbecue party. he plans to make 1/5 pound burgers for his guests. how many guests can he feed?
Answer:
20
Step-by-step explanation:
4 ÷ 1/5 Multiply by the reciprocal (turn the fraction upside down)
4 x 5 = 20
What are acute triangles called?
Answer: acute-angled triangles.
Step-by-step explanation:
Equilateral Acute Triangle. An equilateral acute triangle is that type of acute triangle that has all its interior angles measuring 60°.
Isosceles Acute Triangle.
Scalene Acute Triangle
What is the quotient?
Make y the subject of the formula.- A=r(y + 2 ) / 5
[tex] \frac{5a}{r} \: - 2 = y[/tex]
Step-by-step explanation:
A = r(y +2) /5
A×5 = r(y+2)
(5A)/r = y+2
(5A)/r - 2 = y
•: y = (5A)/r - 2
(only applicable when
[tex]a = \frac{ry + 2r}{5} [/tex]
expand)
You need to get to the mall to buy some new shoes, but you're not sure how to get there. Your city is a nxm rectangular grid of blocks, where you home is located at the coordinates (x1, y1) and the mall's location is (x2, y2).
To get to the mall, you'll need to find the shortest path from your home to the mall.
The Manhattan Distance formula is an efficient way to calculate the shortest path between two points on a rectangular grid. The formula is as follows:
MD = |x1-x2| + |y1-y2|
Where MD is the Manhattan Distance, x1 and y1 are the coordinates of your home, and x2 and y2 are the coordinates of the mall.
To find the shortest path, simply plug in the coordinates for your home and the mall into the formula and calculate the Manhattan Distance. The result is the shortest number of blocks you need to travel to get to the mall.
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If you dissolved 50g of sugar in 30g of water, what would the sugar concentration be
Another soccer team had tryouts for the fall season. This team had 60 players show up for the tryouts and had 9 players return for a second evaluation. What percent of the players at the tryout were asked back for a second evaluation? part = whole = percent= Substitute and solve:
