Answer:
Step-by-step explanation:
[tex]\frac{2x}{x-1} -\frac{2x-5}{x^2-3x+2} =\frac{-3}{x-2} \\\frac{2x}{x-1} +\frac{3}{x-2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x(x-2)+3(x-1)}{(x-1)(x-2)} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-4x+3x-3}{x^2-2x-x+2} =\frac{2x-5}{x^2-3x+2} \\\frac{2x^2-x-3}{x^2-3x+2} =\frac{2x-5}{x^2-3x+2} \\x\neq 1,x\neq 2,x^2-3x+2\neq 0\\multiply~by~x^2-3x+2\\2x^2-x-3=2x-5\\2x^2-3x+2=0\\x=\frac{3\pm\sqrt{9-4*2*2} }{2*2} \\x=\frac{3 \pm\sqrt{-7} }{4} \\x=\frac{3 \pm \sqrt{7} i}{4}[/tex]
The solutions of the given rational equation are 13/4 and 11/4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2x/(x-1) - (2x-5)/(x² -3x+2) = -3/(x-2)
Here, 2x/(x-1) - (2x-5)/(x² -2x-1x+2) = -3/(x-2)
2x/(x-1) - (2x-5)/(x(x-2)-1(x-2)) = -3/(x-2)
2x/(x-1) - (2x-5)/((x-2)(x-1)) = -3/(x-2)
(2x(x-2)-(2x-5))/((x-2)(x-1)) = -3/(x-2)
(2x²-4x-2x+5)/(x-1)=-3
2x²-4x-2x+5= -3(x-1)
2x²-6x+5=-3x+3
2x²-6x+5+3x-3=0
2x²-3x+2=0
By using quadratic formula, we get
x=3±√(9-8)/4
x=3± 1/4
x= 3+1/4 and x=3-1/4
x=13/4 and x=11/4
Therefore, the solutions of the given rational equation are 13/4 and 11/4.
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Help
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:)))
Find the value of x in the isosceles triangle shown below.
Answer:
22.18 = x
Step-by-step explanation:
a^2 + (b)^2 = (x/2)^2
a = sqrt(74)
b = 7
x/2 = ?
(74)[^1/2]^2 = 74
b^2 = 7^2 = 49
74 + 49 = (x/2)^2 Substitute into a^2 + b^2 = c^2
123 = (x/2)^2 Combine like terms
(123^0.5) = x/2 Take the square root of both sides.
11.09 = x/2 Multiply both sides by 2
11.09*2 = x
22.18 = x The full length of the base of the triangle is 22.18
Answer: C
Step-by-step explanation: We only need to find the value of one of the x so just use Pythagorean theorem but simplified to do it in one step which is sqrt(4^2+6^2) which gives us sqrt(52).
Solve pleaseeeeeeeeeeeeee
Answer:
x > 3
Step-by-step explanation:
___________________
Please answer max 10 min, I have a test.
Given a room is 12 feet by 10 feet and we have a circular rug with a radius of 3 feet, calculate the amount of floor left uncovered by the circular area rug in a rectangular living room
Step-by-step explanation:
floor = 12*10= 120 sq ft
rug = r² = 9 Пr2
120-9π = 91.74 sq ft
What is the domain of the function y=%/x-1?
O-
o -1 < x < oo
0
O 1
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x - 1}[/tex]
Required
The domain
The given function is cubic root; there are no restrictions on cubic root functions
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
what is the mean of the data set 8, 8, 9, 11, 24
Answer:
12
Step-by-step explanation:
8+8+9+11+24=60
60/5=12
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{Well, you know that mean means average. You have to find the}\\\large\text{sum of all of the number in the data set and divide the sum by}\\\large\text{by the total numbers in the data.}[/tex]
[tex]\mathsf{\dfrac{8+8+9+11+24}{5}}[/tex]
[tex]\mathsf{8 + 8 + 9 + 11 + 24}\\\mathsf{8 + 8 = \boxed{\bf 16}}\\\mathsf{= 16 + 9 + 11 + 24}\\\mathsf{16 + 9 = \boxed{\bf 25}}\\\mathsf{= 25+11+24}\\\mathsf{25+11=\boxed{\bf 36}}\\\mathsf{36+ 24}\\\boxed{= \mathsf{\bf 60}}[/tex]
[tex]\mathsf{\dfrac{60}{5}}\\\\\\\mathsf{= \dfrac{60\div5}{5\div5}}\\\\\\\mathsf{= 60\div5\rightarrow\boxed{\bf 12}}\\\\\\\mathsf{= 5\div5\rightarrow\boxed{\bf 1}}\\\\\mathsf{\rightarrow \dfrac{12}{1}= \boxed{\bf 12}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge Your \bf {MEAN is 12}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
By visual inspection determine the best-fitting regression model for the data plot below
Answer:
Exponential
Step-by-step explanation:
By visual inspection the graph generated by the points plotted is an exponential graph as the graph curves upward. The graph is also continous and differs from either a decreasing or increasing Linear graph, which shows a straight best of fit pattern. Hence, the graph most closely represents an exponential graph from visual examination.
The best-fitting regression model for the considered data plot is given by:
Option A: Exponential.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).
Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.
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write P(x)=6x³+3x²-24x-12 as a product of (2x+1)and a quadratic formula.
pls help
Answer:
3(2x+1)( [tex]x }[/tex]-2)(x+2)
Step-by-step explanation:
3(2x+1)( [tex]x }[/tex]-2)(x+2)
3(2x+1)( [tex]x^{2}[/tex]-4)
(2x+1)(3[tex]x^{2}[/tex]-12)
The length of a rectangle is twice its width. If the area of the rectangle is
32cm2, find the perimeter.
Before we find the perimeter, first we must know length and width.
Let width = x
The question says that the length of a rectangle is twice its width. Therefore the length is 2×x or two times of width which equal to 2x.
The area of rectangle is given as 32 cm^2.
Do you remember the rectangle area formula? If not then it is:
[tex] \large \boxed{ \tt{A = width \times length}}[/tex]
Since A is area - substitute A = 32 in. As for width, we substitute in x and length in 2x.
[tex] \large{32 = x \times 2x}[/tex]
Since x multiplies by another x. It becomes x squared.
[tex] \large{32 = 2{x}^{2} }[/tex]
Next, we divide 2 by both sides since we want to solve for x.
[tex] \large{ \frac{32}{2} = {x}^{2} }[/tex]
Simplify 32/2 in simplest form.
[tex] \large{16 = {x}^{2} }[/tex]
Square both sides so we can get rid the x squared, leaving only x.
[tex] \large{ \sqrt{16} = \sqrt{ {x}^{2} } }[/tex]
Normally, when solving quadratic equation, you must write plus or minus. However, for this circumstance - we are solving a variable for length and width which cannot be negative. Therefore
[tex] \large{4 = x}[/tex]
After we solve for x. Substitute x = 4 in width = x and length = 2x.
[tex] \large{ \tt{width = x = 4}} \\ \large{ \tt{length = 2x = 2(4) = 8}}[/tex]
When we multiply these two numbers, we get 32 cm^2.
Next, we find the perimeter. The formula of perimeter for rectangle is:
[tex] \large \boxed{ \tt{P = (width + length) \times 2}}[/tex]
We know width and length which are 4 and 8 in order. Substitute in the formula.
[tex] \large{P = (4 + 8) \times 2} \\ \large{P = 12 \times 2} \\ \large \boxed{P = 24}[/tex]
Hence, the perimeter is 24.
Answer
The perimeter for the rectangle is 24.after you list the factors, you have to read the question back .. the question the length of the rectangle is twice the width .. so 4 × 8 is the correct answer .. and you do as usual to calculate the perimeter ..
How many terms are in this expression 4+3c
Answer: there are 2 terms
Step-by-step explanation: A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. ... Examples of single terms: 3x is a single term.
2 terms
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them. The number in front of a term is called a coefficient.
The Marked price of a jacket at a dealer's shop is 2400. The dealer allows a discount of 15% to the retailer. As the company's policies the marked price of the retailer should be the same as the dealer's marked price. What SP should the retailer fix for the jacket? What would its final price be if 10% VAT is imposed? What would be the actual gain of retailer?
Ans
2280,2502,240
Answer:
2400
2640
360
Step-by-step explanation:
I am not sure the description is totally clear.
my assumptions are (based on my interpretations of the text) :
the retailer buys from the dealer with 15% discount.
but the retailer has to sell the jacket for the same price as the dealer.
so, both mark the sale price as 2400.
if the customer buys from the retailer, the retailer makes 15% profit (the discount he got from the dealer).
15% = 2400 × 15/100 = 24 × 15 = 360
the retailer makes this profit no matter what other fees or taxes are added.
if the customer buys from the dealer, the dealer makes these 15% and some more (we don't know how much) profit.
now, the final price is to include also 10% VAT
100% = 2400
1% = 2400 / 100 = 24
10% = 24 × 10 = 240
so,
final price = SP + VAT = 2400 + 240 = 2640
Elsa, miguel and scott sent a total of 133 text messages over their cell phones during the weekend. Scott sent 8 fewer messages than elsa. Miguel sent 3 times as many messages as scott. How many messages did they each send?
Answer:
Scott sent 23 text, Elsa sent 16 and Miguel sent 64 test.
Step-by-step explanation:
Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 and one-half years?
$2,500
$9,159
$22,827
$23,791
Answer:
Step-by-step explanation:
The equation actually looks like this
[tex]V=P(1-r)^t[/tex] and filling in the info given:
[tex]V=25,000(1-.2)^{4.5[/tex] which simplifies to
[tex]V=25,000(.8)^{4.5[/tex]
Orders of operation tells us that we need to take care of the exponential stuff first, so
V = 25,000(.3663573) and
V = $9158.93 which rounds to what is shown as the second choice down: $9,159.
Answer:
B
Step-by-step explanation:
$9159
given parallelogram BCDE
what is the equation to find x?
what is x?
what is length of side CD?
please help
Answer:
x=3
CD = 13
Step-by-step explanation:
BE = CD in a parallelogram
1+4x = 5x -2
Subtract 4x from each side
1+4x-4x = 5x-2 -4x
1 = x-2
Add 2 to each side
1+2 = x-2+2
3 =x
The length of CD
CD = 5x-2 = 5*3 -2 = 15-2 = 13
what time did he reach ???
Answer: 2050hrs
Step-by-step explanation:
If he is going 72 km/hr and he traveled 504 km we can calculate how long he took to go by dividing the distance he went by distance per hour. That will give us the amount of hours that he took to get there. That would be [tex]\frac{504}{72}[/tex]. [tex]\frac{504}{72}=7[/tex] so it took him 7 hours to get there. 7 hours after 1350 is 2050 assuming we are using the 24 hour clock notation.
The sides of a triangle are 4, 7, and 10. The triangle is dilated by a scale factor of 3 to create a
new triangle. Find the perimeter of the new triangle.
A
21 units
B
63 units
30 units
D
25 units
Answer:
B 63 units
Step-by-step explanation:
Dilatation is an increase of shape , a larger imagine , the dilatation is 3 so times each side by three and add them all up
What is the distance between the bank and Hiroto's house on the map?
Enter the distance to the nearest quarter mile. (Each unit represents 1 mile.)
Answer:
The distance is 12 miles
Step-by-step explanation:
Given
See attachment for grid
Required
The distance
From the attached:
[tex]B = (-8,6)[/tex] --- Bank
[tex]H = (4,6)[/tex] --- Hiroto's house
Using distance formula, we have:
[tex]d = \sqrt{(x_1- x_2)^2 + (y_1 - y_2)^2}[/tex]
This gives:
[tex]d = \sqrt{(-8- 4)^2 + (6 - 6)^2}[/tex]
[tex]d = \sqrt{(-12)^2}[/tex]
[tex]d = \sqrt{144}[/tex]
[tex]d = 12[/tex]
PLEASE HELP LOL
what type of angles are <4 and <8
Answer:
C. Corresponding angles
Step-by-step explanation:
Visualize the two points of intersection and the four angles around each of them being separated. If you put the on top of each other, you can see that angle 4 corresponds with angle 8.
Answer: corresponding :)
Step-by-step explanation:
corresponding angles are angles that are in the same position relative to lines intersected by a transversal
basically theyre equal and on the same side of the transversal
hope this helps :)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer and Step-by-step explanation:
Mandy travels more miles.
We determine this by multiplying the distance from home by the number of trips.
For Mandy, she lives 10 miles away from school, and takes 9 trips. 9 times 10 is 90 miles.
For Matt, he lives 8 miles away from school, and takes 11 trips. 11 times 8 is 88 miles.
Many travels 2 more miles in total than Matt.
#teamtrees #PAW (Plant And Water)
Answer:
mandy
Step-by-step explanation:
so mandy has 10 miles and 9 trips to school matt has 8 miles and 11 trips to school so mandy is 10x9=90
and matt is 11x8=88
mandy=90
matt=88
Given any triangle ABC labeled as shown the law of sines states that:
Please help will be marked as brainliest if correct
Answer:
[tex]{ \tt{question \: 1.}} \\ { \bf{ = {}^{ + } 24}} \\ \\ { \tt{question \: 2.}} \\ { \bf{ = in \: the \: third \: quadrant}} \\ \\ { \tt{question \: 3.}} \\ { = \bf{graph \: J}} \\ \\ { \tt{ \underline{ \blue{becker \: jnr}}}}[/tex]
Please help!?
Use △DEF, shown below, to answer the question that follows: What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below
Answer:
x=63.25
Step-by-step explanation:
Hi there!
We're given ΔDEF with m<E=90°, m<D=49°, DE=55, and EF=x
we need to find the value of x
Let's use trigonometry to do it
Since we are given the measures of the 2 legs (the sides that make up the 90° angle), let's use tangent, specifically tan(49), since we are given the measure of that angle
Recall that tangent is [tex]\frac{opposite}{adjacent}[/tex]
in reference to m<D (the angle that is 49°), the opposite side is EF (x) and the adjacent side is DE (55)
so tan(49)=[tex]\frac{x}{55}[/tex]
plug tan(49) into your calculator; remember to have the calculator on degree mode
tan(49)≈1.15 (rounded to the nearest hundredth)
so that means:
1.15=[tex]\frac{x}{55}[/tex]
multiply both sides by 55 to clear the fraction
63.25=x
Hope this helps!
Diane has $814 in her checking account. If she writes five checks for a total of $287, how much does she have left
in her account?
Answer:
$527
Step-by-step explanation:
Find how much she has left by subtracting 287 from 814:
814 - 287
= 527
So, she has $527 left in her account
Find the solution to the equation 8n - 9 = 63.
Answer:
9
Step-by-step explanation:
63+9=72
72/8=9
hope this helped
Answer:
[tex]8n - 9 = 63 \\ 63 + 9 = 8n \\ 72 \div 8 = n \\ n = 9[/tex]
Chris had 3/4 of a jug of milk left. He used 2/5 of it to bake a cake how much of the jug of milk did he use in his cake
Answer:
5 pints of milk
Step-by-step explanation:
took the test
2. Si x representa la edad de Ana, ¿cómo se
escribe en simbolos "la mitad de la edad de
Ana"?
Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line. Estimate how far the hurdles are from one another. Do not include units (meters) in your answer. Round your answer to the nearest whole meter. plzzzzzzzzzzzzzzz help
Answer:
7.5 metres
Step-by-step explanation:
According to the Question,
Given,Andre is running in an 80-meter hurdle race. There are 8 equally-spaced hurdles on the race track. The first hurdle is 12 meters from the start line and the last hurdle is 15.5 meters from the finish line.Thus, the distance from the first hurdle to eighth hurdles is 80-(12+15.5) = 52.5m
Now, we have 8 Hurdle but the distance between each hurdle is equally divided in 7 parts . (Please find the diagram in Attachment)
So, 52.5 /7 ⇔ 7.5m far the hurdles are from one another.
Which decimal is equivalent to 4/3
Answer:
1.33333333333 repeating
Step-by-step explanation:
Hope this helps
Answer:
1.3333
Step-by-step explanation:
Use the explicit formula an = a + (n-1). d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
Answer:
Step-by-step explanation:
The difference is a2 - a1 = 31 - 24 = 7
n = 500
a500 = a1 + (500 - 1) * 7
a500 = 24 + 499 * 7
a500 = 24 + 3493
a500 = 3517
12. The length and width of a rectangle are in the ratio 7:3. If the perimeter is 62cm calculate: (1) the width (ii) the length of a diagonal to the nearest centimetre. (iii) the area of the rectangle.
Answer:
Step-by-step explanation:
Length = 7x
Width = 3x
Perimeter = 2L + 2W
Part A
2*7x + 2*3x = 62
14x + 6x = 62
20x = 62
x = 62/20
x = 3.1
Length = 3.1 * 7 21.7
Width = 3.1 *3 9.3
Width = 9.3
Part B
Use the Pythagorean Theorem
diagonal squared = 21.7^2 + 9.3^2
diagonal^2 = 557.38
sqrt(diagonal^2) = sqrt(557.38)
diagonal = 23.61
To the nearest cm is 24
Part C
Area = L*W
Area = 21.7 * 9.3
Area = 201.8