The value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
How to solve the equation?The equation is given as:
[tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex]
Start by taking the LCM
[tex]\frac{4x(x - 2) - 5x(x - 1)}{(x - 1)(x -2)} = \frac{2}{x^2 - 3x + 2}[/tex]
Expand the denominator
[tex]\frac{4x(x - 2) - 5x(x - 1)}{x^2 -3x +2} = \frac{2}{x^2 - 3x + 2}[/tex]
Cancel out the common factor
4x(x - 2) - 5x(x - 1)= 2
Expand
[tex]4x^2 - 8x - 5x^2 + 5x = 2[/tex]
Evaluate the like terms
[tex]-x^2 - 3x = 2[/tex]
Rewrite as:
[tex]x^2 + 3x + 2 = 0\\[/tex]
Expand
[tex]x^2 + 2x + x + 2 = 0[/tex]
Factorize
x(x + 2) + 1(x + 2) = 0
Factor out x + 2
(x + 1)(x + 2) = 0
Solve for x
x = -1 or x = -2
Hence, the value of x in the equation [tex]\frac{4x}{x - 1} - \frac{5x}{x -2} = \frac{2}{x^2 - 3x + 2}[/tex] is x = -1 or x = -2
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What is the y-intercept of the line shown?
-1
0
1
Answer:
-1
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis.
Answer:
[tex]\huge\boxed{\sf y-intercept = -1}[/tex]
Step-by-step explanation:
Y-intercept is the point of the line of the equation where:x = 0the line of the equation passes through the y-axis.Here,
y-intercept = -1Since, this is the point where x = 0 and where the line passes through the y-axis.
[tex]\rule[225]{225}{2}[/tex]
The difference between two positive integers is two if the smaller is added to the square of the larger the sum is 70
Step-by-step explanation:
ATTACHED IS THE SOLUTION.Tell me if you have any questions.An experiment consists of rolling a standard six-sided die once. Event A is "rolling a 5{}^{\prime\prime} and event B is "rolling an odd number." Are the events dependent or independent? Why? Select the option that correctly answers both questions.
O Events A and B are independent, because P(B) = P(B|A) = 1/2.
O Events A and B are independent, because P(A) = P(B|A) = 1/12.
O Events A and B are dependent, because P(A) =/ P(B|A).
O Events A and B are dependent, because P(B) =/ P(B|A).
Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.
Is event B independent of event A?Events are independent if P(B) = P(B|A)
The probability of event B is:
= 3 odd numbers / 6 numbers
= 1 / 2
The probability of A is:
= 3 prime numers / 6
= 1/2
P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)
= 1/2
So P(B) = P(B|A) = 1/2.
The events are independent.
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Copy and complete the workings to find the value of each expression when m=2 and p=-4
Answer:
- 24
Step-by-step explanation:
4(m + 2p) ← substitute m = 2 and p = - 4 into the expression
= 4(2 + 2(- 4) )
= 4(2 - 8)
= 4(- 6)
= - 24
GIVING 100 POINTS PLEASE HELP!! Consider the expression 3+(−4)−2−(−1). answer these three questions.
How many balloons should you add? How many should you remove?
How many weights should you add? How many should you remove?
What is the final answer?
Answer:
Step-by-step explanation:
12 becuase you have to read the equasion and do the problem
The solution to an inequality is graphed on the number line.
A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5.
What is another way to represent this solution set?
{x | x < 4.5}
{x | x ≤ 4.5}
{x | x > 4.5}
{x | x ≥ 4.5}
The correct answer is option B which is {x | x ≤ 4.5}
What is a number line?
A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.
Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.
A solid dot on a number means that that number is included in the solution set.
In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.
Therefore the correct answer is option B which is {x | x ≤ 4.5}
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What is the difference? startfraction x over x squared minus 16 endfraction minus startfraction 3 over x minus 4 endfraction startfraction 2 (x 6) over (x 4) (x minus 4) endfraction startfraction negative 2 (x 6) over (x 4) (x minus 4) endfraction startfraction x minus 3 over (x 5) (x minus 4) endfraction startfraction negative 2 (x minus 6) over (x 4) (x minus 4) endfraction
The difference of the fractions as given in the task content is; (4-2x) / (x²-16).
What is the difference of the two fractions?According to the task content, the fractions whose difference is to be evaluated are as indicated below;
[tex] \frac{x}{( {x}^{2 } - 16)} - \frac{3}{x - 4} [/tex]
Hence, the LCM of the denominators of both fractions can be evaluated as;
x -3(x+4)/(x²-16).
(4-2x) / (x²-16)
Hence, the difference of the two fractions is; (4-2x) / (x²-16).
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ayuda porfaaa JHAKJAH es para hoy y no entiendo un klo
A) Hala los números que hagan verdadera la adición.
a) +2 + ? = 29
b) ? + (-13) = -17
c) -17 + ? = -38
d) ? + (25) = 13
e) ? + 12 = -2
B) Encuentra el resultado de las siguientes adiciones.
a) +5 + (-12) =
b) -10 + (-13) =
c) 20 + (-17) =
d) -80 + 10 =
e) 40 + (-60) =
vence hoy:(
The measure of central angle QRS is 8pi/9 radians. What is the area of the shaded sector?
The area of the shaded sector must be 144π units².
What is the area of the circle?The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = [tex]\pi r^{2}[/tex]
We know that the angle measurement of central angle QRS is less than π radians.
for r = 18 units
The area of the circle = π18² = 324π units²
The area of the half of a circle = 324π /2 = 162π units²
The area of a quarter of a circle = 324π /4 = 81π units²
so
The area of the shaded sector < 162π units²
and
The area of the shaded sector > 81π units²
Hence the answer must be 144π units²
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Please explain how it is simplified. Thank you. No random or inexperienced mathematicians please
Answer:
[tex]\fbox {Work is attached below.} \downarrow[/tex]
Step-by-step explanation:
Someone help me pleaseee
Answer:
A.) 588329.896
B.) 274300
C.) 1657.18474
D.) 1.002
(All answers unrounded.)
Explanation:
I converted each unit to the unit used in the other number (E.g., for question A I converted tons to kilograms, and then finished solving.)
Which is the graph of y = 3√x+1-2?
Answer:
I'm not sure how to interpret "y = 3√x+1-2."
I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2
Step-by-step explanation:
Use the free online app DESMOS. Either enter the equation, or make a table of individual points and plot them as ordered pairs.
GRAPH: See attached image
PLOT: Calculate a few points, mark them on the graph and then connect the dots. I selected a few values of x and calculated y from the equation. Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected. Note that x values less than -1 result in a value of y that includes i, an imaginary number. So the graph ends abruptly at that point.
There was a bag of counters. 45 were large! For every large counters 3/5 were small! The green was 300% than yellow, there were 12 small yellow counters. How many were large green counters?
Answer:
12 is the correct answer
Two students were asked to graph a rational number -7.1. Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6 how can you determine which student is correct?
Amy is correct, -7.1 is between -7 and -8.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Two students were asked to graph a rational number -7.1.
Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.
In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.
But -7.1 has a whole number of 7 then it is in between -7 and -8.
Thus, Amy is correct, -7.1 is between -7 and -8.
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Which equation best represents the line
y = 3x + 3
y = 1 over 2x − 3
y = 1 over 2x + 3
y = 3x + 1 over 2
Answer:
C
Step-by-step explanation:
The y intercept is 3, so eliminate B and D.
Also, the slope is less than 1, so this eliminates A.
This leaves us with C.
{
5x−y=19
13x−3y=51
Can anybody help me to understand this equation ASAP
Answer:
×=-3
y=-4
Step-by-step explanation:
13×-3y=51
(-) 5×-y=19
-5×+y=-19
13×-3y=51
8×-2y=32
2/8x-2y=32
4x-y=16
4×-y=16
-5×+y=-19
-×=-3
×=3
Answer:
x = 3
y = -4
(3,-4)
Step-by-step explanation:
Hello!
We can use the Elimination Method to solve the system.
To eliminate, we want atleast one variable to have the same coefficients on both equations. To do that, we can multiply the first equation by 3 to get -3y.
[tex]5x - y = 19[/tex][tex]3(5x - y = 19)[/tex][tex]15x - 3y = 57[/tex]Now, we can vertically subtract them to eliminate -3y.
[tex]-\left \{ {{15x - 3y = 57} \atop {13x - 3y = 51}} \right.[/tex][tex]2x + 0 = 6[/tex]Solve for x
[tex]2x + 0 = 6[/tex][tex]2x = 6[/tex][tex]x = 3[/tex]The value of x is 3.
To solve for y, we can plug in 3 into the original first equation and solve for y.
Solve for y
[tex]5x - y = 19[/tex][tex]5(3) - y = 19[/tex][tex]15 - y = 19[/tex][tex]-y = 4[/tex][tex]y = -4[/tex]The value of y is -4.
The solution to the system is (3,-4).
[tex]f(x) = \sqrt{9 - {x}^{2} } [/tex]
I have a doubt. I know that the domain will be [-3, 3] because this is a real function. But what will be the range. Everywhere it is given as [0, 3]. But shouldn't it be [-3, 3].
For example let x = 0, then f(x) = √9, and it can be either -3 or 3. Why are we considering just the positive value?
Please explain.
Answer:
range of f is [0,3]
Step-by-step explanation:
The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function. As a result, it only has a single output because functions must only have a single output for each input.
Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.
When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property. The square root property says that to find both solutions, one must look at both the positive and the negative of the square root. So, to solve:
[tex]x^2=25[/tex]
Apply square root property...
[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]
[tex]x=\sqrt{25}[/tex] or [tex]x=-\sqrt{25}[/tex]
[tex]x=5[/tex] or [tex]x=-5[/tex]
In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].
Find the HCF of
x^2y and x
The highest common factor of [tex]x^2 y[/tex] and [tex]x[/tex] is [tex]\boxed{x}[/tex]
Please answer this I would really appreciate it
Answer:
Step-by-step explanation:
Ratio and proportion:
[tex]\sf \dfrac{x}{3}=\dfrac{6}{9}\\\\ x = \dfrac{6*3}{9}\\\\x = 2[/tex]
[tex]\sf \dfrac{8}{y}=\dfrac{6}{9}\\\\Cross \ multiply,\\\\y*6=9*8\\\\y=\dfrac{9*8}{6}\\\\y=3*4\\\\\bf y = 12[/tex]
[tex]\sf \dfrac{a}{15}=\dfrac{6}{9}\\\\a =\dfrac{6}{9}*15\\\\a=2*5\\\\\bf a = 10[/tex]
pls help me with this question
Answer:
D, C
Step-by-step explanation:
for part a, there is a negative slope with the graph shifted two units upwards
for part b, if you plug in C, you get an answer that works
Consider the graph of the function f(x)=-(2)^x + 4
I have linked a picture with the intervel.
What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
Answer:
60 ft
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
AD = 60 ft
The sum of 16 and a number is less than 24. Which of the following inequalities
expresses the solution?
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The complete question is:
The sum of 16 and a number is less than 24. Which of the following inequalities expresses the solution?
x<8
x>8
x=8
x<-8
Given the sum of 16 and a number is less than 24. Let the number be represented by x, therefore,
16 + x < 24
x < 24 - 16
x < 8
Hence, the correct option is A.
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Select the correct answer.
Which expression is equivalent to √48x5, if x > 0?
OA. 12x³√3x
B. 4x³√3
OC. 4x²√3x
OD. 12x²√
Answer: C
Step-by-step explanation:
[tex]\sqrt{48x^{5}}=\sqrt{16x^{4}} \sqrt{3x}=\boxed{4x^{2}\sqrt{3x}}[/tex]
PLEASEEE HELPPPP IM BEGGIN U
[tex]Y=x^4-x^3-28x^2-20x+48[/tex]
a. How many possible negative real zeros, positive real zeros, and non-real zeros does this equation have? Explain how you determined this.
b. Graph the equation in your calculator or in a graphing app. What is the general shape of the graph and how does the graph’s shape relate to the function? What are the zeros of the graph?
c. Create a table* of synthetic substitution for various values of x.
d. Using synthetic division, show* the way to divide this equation by one of its factors.
I already finished A and B but I am stuck on the synthetic division part of the question. Thanks!
Answer:
a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)
b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.
c, d) See attached
Step-by-step explanation:
Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.
Synthetic division is essentially polynomial long division with some modifications:
the variables are omitted ("place value" is used instead)the constant in the divisor is negated so its product with the partial quotient can be added to obtain the new dividendthe divisor binomial is assumed to have a leading coefficient of 1.__
a)The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.
When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.
Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.
The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.
__
b)The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.
Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.
__
c)The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)
Maybe this is the table you want:
[tex]\begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}[/tex]
__
d)The second attachment shows synthetic division by the factor (x+4).
_____
Additional comment
The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.
The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.
Trihao is driving from cambridge to london Assume the distance between cambridge and london is 100 km Given that trihao drives at an average speed of 80km/h work out his journey time
average speed equals distance over time 100/80 will give you 5/4
Find the area of a rectangle whose length is 18.60m and breadth is 7.05m.
Answer:
131.13
To find the area do w (width) times l (length/breadth) so the equation to find the area would be L*W=A
Suppose you know the slope of a linear relationship and one of the points that it’s graph passes through how can you determine if the relationship is proportional or not?
Answer:
I exactly don't have or know the answer
Use the point-slope equation to identify the slope and the coordinates of a point on the line y - 4 = 7 (x-1). The slope of the line is A point on the line is
Answer:
slope is 7 and point on line is (1, 4 )
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
given line A has equation in point- slope form of
y - 4 = 7(x - 1) , then
slope of line is 7 and a point on the line is (1, 4 )
Help please this is khan academy
Answer:
9800 cm^2
Step-by-step explanation:
The area of a square is just the length of one of the sides squared. In the first image it's given that one of the sides is 70 cm and the shape is also a square pyramid so the base is going to be a square. So the area the base is (70 cm) ^ 2 = 4,900 cm^2. The area of a triangle is 1/2 bh. The base is given in the first image which is 70 cm and the height is also given which is 140 cm. This gives you the equation 0.5 * 140 cm * 70 cm = 4900 cm^2. Adding these two values gives you 9800 cm^2