Answers
Step-by-step explanation:
Taking the provided equation ,
[tex]\implies \dfrac{3x+4}{5}-\dfrac{2}{x+3} =\dfrac{8}{5} [/tex]
1) Here denominator of two fractions are 5 and x +3 . So their LCM will be 5(x+3)
[tex]\implies \dfrac{(x+3)(3x+4)-(2)(5)}{5(x+3)}=\dfrac{8}{5} [/tex]
2) Transposing 5(x+3) to Right Hand Side . And 5 to Left Hand Side .
[tex]\implies 5(3x^2+4x+9x+12 -10) = 40(x+3)[/tex]
3) Multiplying the expressions.
[tex] \implies 5(3x^2+13x+2) = 40x + 120 [/tex]
4) Opening the brackets .
[tex]\implies 15x^2+ 65x + 10 = 40x + 120 [/tex]
5) Transposing all terms to Left Hand Side .
[tex]\implies 15x^2 + 65x - 40x + 10 - 120 = 0 \\\\\implies 15x^2 +25x - 110 = 0[/tex]
6) Solving the quadratic equation .
[tex]\implies 5(3x^2+5x -22) = 0 \\\\\implies 3x^2+13x-22 = 0 \\\\ \implies x = \dfrac{-b\pm \sqrt{b^2-4ac}}{4ac} \\\\\implies x = \dfrac{-5\pm \sqrt{5^2-4(-22)(3)}}{2(3)} \\\\\implies x = \dfrac{-5\pm \sqrt{289}}{6}\\\\\implies x =\dfrac{-5\pm 17}{6} \\\\\implies x = \dfrac{17-5}{6},\dfrac{-17-5}{6}\\\\\implies x = \dfrac{12}{6},\dfrac{-22}{6} \\\\\underline{\boxed{\red{\bf\implies x = 2 , \dfrac{-11}{3}}}}[/tex]
Answer:
[tex]x=2\\x=-\frac{11}{3}[/tex]
Step-by-step explanation:
Solve the rational equation:
[tex]\displaystyle \frac{3x+4}{5}-\frac{2}{x+3}=\frac{8}{5}[/tex]
To eliminate denominators, multiply by 5(x+3) (x cannot have a value of 3):
[tex]\displaystyle 5(x+3)\frac{3x+4}{5}-5(x+3)\frac{2}{x+3}=5(x+3)\frac{8}{5}[/tex]
Operate and simplify:
[tex]\displaystyle (x+3)(3x+4)-5(2)=(x+3)(8)[/tex]
[tex]\displaystyle 3x^2+4x+9x+12-10=8x+24[/tex]
Rearranging:
[tex]\displaystyle 3x^2+4x+9x+12-10-8x-24=0[/tex]
Simplifying:
[tex]\displaystyle 3x^2+5x-22=0[/tex]
Rewrite:
[tex]\displaystyle 3x^2-6x+11x-22=0[/tex]
Factoring:
[tex]\displaystyle 3x(x-2)+11(x-2)=0[/tex]
[tex]\displaystyle (x-2)(3x+11)=0[/tex]
Solving:
[tex]x=2\\x=-\frac{11}{3}[/tex]
Related Questions
Find the value of k so that the remainder is -26 for
(x^4+kx^3-7x^2 +8x-10)+(x+4).
Answers
578 because yea yea yea yea yea
What is the distance formula?
Answers
Answer:
B
Step-by-step explanation:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
d = distance
(x1, y1) = coordinates of the first point
(x2, y2) = coordinates of the second point
I REALLY NEED HELP!!!!!!!!!!!!
Answers
Answer: 64 centimeters squared.
Step-by-step explanation: This shape is a parallelogram. And the area of a parallelogram is just the base multiplied by the height. Here, the base is 10 cm and the height is 7 cm. So you might think the the area is just 70 centimeters squared. But here's the catch. There is a rectangular region in this parallelogram that is not shaded. But you can still easily solve this problem. All you need to do is find the area of that rectangular region and you already know the length and the width of this region. And, remember, the area of a rectangle is just the length and the width multiplied. So here, the area of that rectangular region is just 2 cm multiplied by 3 cm. Which will give you 6 centimeters squared. Now, all that's left to do is subtract the area of that rectangular region, 6 centimeters squared, from the total area of the parallelogram, 70 centimeters squared. And that should give you 64 centimeters squared as your final answer. I really hope this makes sense and is helpful.
The table below represents a function. Write a number from the given values below to complete the table of values.
Answers
The answer is -3/-1/2
Tap on a clip to paste it in the text box.
Consider the systems of equations below.
System A)
X^2 + y = 17
Y = -1/2x
System B)
Y = x^2 - 7x + 10
Y = -6x + 5
System C)
Y = -2x^2 + 9
8x - y = -17
Determine the number of real solutions for each system of equations.
System A) ____
SystemB) ____
System C) ____
Answers
Based on the systems of equations given, the number of real solutions for each system is:
System A - 2 solutions. System B - 0 solutions. System C - 1 solution. How many solutions will the systems of equations give?To find out the number of solutions, you should plot the equations on a graph.
When system A is plotted as shown attached, you notice that line y = 1/2x intersects x² + y² = 17 twice. It therefore has two solutions.
When system B is plotted, y = -6x + 5 does not intercept y = x² + 7x + 10 which means that there are no real solutions.
System C shows only one real solution because 8x - y = -17 intercepts y = -2x² + 9 once.
Find out more on real solutions at https://brainly.com/question/4526506.
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Identify the correct logical reason for the next step in solving this equation
Answers
Answer:
Distributive property of equality
Step-by-step explanation:
The first thing to do in an equation is to distribute.
Answer:
Distributive property of equality
Step-by-step explanation:
apply the distributive property to create an equivalent expression
7(4p + 2q +3r) =
Answers
hope this helps !
you just multiply the parentheses by 7
Isaiah has $20 to spend on bowling. He has four bowling alleys to choose from, and the price each charges for a game is shown in the table. Prices at Four Bowling Alleys Bowling Alley Price per Game A $4.25 B $5.25 C $3.75 D $3.50 Which can he afford? 4 games at bowling alley B 5 games at bowling alley C 5 games at bowling alley A 6 games at bowling alley D Mark this and return
Answers
Answer:
b is correct
Step-by-step explanation:
Answer:
B: 5 games at bowling alley C
Step-by-step explanation:
Is this good led me know pl
Give GHJ=XJZ find each missing measure
Answers
Answer/Step-by-step explanation:
Given that ∆GHJ is congruent to ∆XYZ, this:
<G = <X,
<H = <Y = 38°
<J = <Z,
GH = XY = 27 ft
HJ = YZ = 27 ft (two sides of an isosceles ∆ are the same)
GJ = XZ = 18 ft
a. GJ = 18 ft
b. XY = 27 ft
c. ZY = 27 ft
d. m<H = m<Y (corresponding angles)
m<H = 38° (substitution)
e. m<Z = (180 - 38)/2 (base triangles of an isosceles ∆ are equal)
m<Z = 142/2
m<Z = 71°
f. m<J = m<Z (corresponding angles)
m<J = 71° (substitution)
PLEASE I NEED HELP WITH THE MATH HOMEWORK. I NEED EXPLANATION TOO!!
QUESTION: find the value of the varible
Answers
Answer:
Step-by-step explanation:
A+B+C=180
2x+x+90=180 ( the 90 comes from the right angle in the given triangle)
3x=90
x=30°
:) these are all kinda the same strategy.. notice?
Marla made an error when solving the equation shown. What was her error ,and how should she fix it?
Answers
In Step 1, she used the Distributive Property incorrectly. She should have distributed the 3 to the 2. The equation should have been
3x + 6 + 1 = 24.
ANYONE PLEASE THIS IS DUE IN 2 HOURS !
Answers
Answer:
I think 21
Step-by-step explanation:
Can someone put a website to help me understand this?
Im sure its not hard I just don't know how to do it
Answers
Answer:
67
Step-by-step explanation:
Since the diagonals in a rectangle are congruent, AC=BD and
7x+18=10x-3
We need to separate x -- to do that, we can first subtract 7x from both sides, resulting in
18=3x-3
Next, add 3 to both sides to get
21=3x
Divide both sides by 3 to get
x=7
Then, we just plug x into 10x-3 to get BD = 7*10-3 = 67
If it takes 4 hours to cook a 7-pound turkey, how many hours will it take to cook a 19-pound turkey?
Answers
Answer:
Roughly 11 to 11 and 1/2 hours
Step-by-step explanation:
Roughly 11 to 11 and 1/2 hours.
Hope this helps, if so please mark the brainliest, peace and love
Answer:
it would take 28 hours
Step-by-step explanation:
Angle A and Angle B are supplementary angles. If the measure of angle A = (6x + 10)° and the measure of angle B = (4x +30), then find the measure of angle B.
Answers
Answer:
86°
Step-by-step explanation:
Given:
A = (6x + 10)°
B = (4x +30)°
Two angles are supplementary if they sum up to 180° ;
A + B = 180°
Now insert the parameters and solve;
6x + 10 + 4x +30 = 180
10x + 40 = 180
10x = 140
x = 14
So;
B = (4x +30)° = 4(14) + 30 = 86°
A company has actual unit demand for three consecutive years of 124, 126, and 135. The respective forecasts for the same three years are 120, 120, and 130. Which of the following is the resulting MAD value that can be computed from this data? A. 3 B. 5 C. 15 D. 123
Answers
Answer:
B. 5
Step-by-step explanation:
Computation for Which of the following is the resulting MAD value that can be computed from this data
Using this formula
MAD Value=[(Actual unit demand-Respective forecasts)/Number of years]
Let plug in the formula
MAD Value = [(124 - 120) + (126 - 120) + (135 - 130)]/3 years
MAD Value =(4+6+5)/3 years
MAD Value = 15/3 years
MAD Value = 5
Therefore the MAD value that can be computed from this data is 5
serena invests the $2500 for 3 years and earns $255 what was the rate intrest
Answers
Answer:
idek
Step-by-step explanation:
Which statement best describes the function represented by the graph
Answers
Answer:
Where is the graph?
Step-by-step explanation:
Two out of three balls in a Multi-colored package are pink. How many balls in a package of 21 will be pink?
_____________ Pink Balls
Answers
Answer:
14 pink balls
Step-by-step explanation:
you would devide 21 by 3 and that would be 7, then you multiply by 2 and you get 14.
A certain forest covers an area of 4000km squared. Suppose that each year this area decreases by 3.75percent. What will the area be after 14 years
Answers
Answer:
After 14 years, the area will be 2342.4 km squared.
Step-by-step explanation:
Since the area is decreasing, we can use the decaying exponential function
[tex]y = A(1 - r)^{t}[/tex]
where
A represents the initial area.r represents the rate at which the area changest is the time periodGiven
Initial Area A = 4000 km squared
Rate r = 3.75% = 3.75/100 = 0.0375
Time period t = 14
To Determine
The Area after 14 years = y = ?
Plug in the values in the formula
[tex]y = A(1 - r)^{t}[/tex]
[tex]y\:=4000\left(1\:-\:0.0375\right)^{14}[/tex]
[tex]y=4000\cdot \:0.9625^{14}[/tex]
[tex]y=2342.4[/tex] km squared
Therefore, after 14 years, the area will be 2342.4 km squared.
A study conducted on American families shows that 18% of these families have medical bills of more than $10,000. Find the probability that among 5 randomly selected American families, at least one has medical bills of more than $10,000.
Answers
Answer:
the probability is 0.6293
Step-by-step explanation:
The computation of the probability is shown below:
Given that
n = 5
P = 0.18
As it represents the binomial distribution
P(X = x) = [tex]^NC_x[/tex]× p^x × (1 - p) ^(n - x)
P(X > 1) = 1 - P(X < 1)
= 1 - P(X = 0)
= 1 - ( [tex]^5C_0[/tex]× (0.18) ^0 × (0.82) ^5)
= 1 - 0.3707
= 0.6293
hence, the probability is 0.6293
S-95-5
34
A pair of running shoes that usually sells for $125 has been reduced by 15%. The special
sale sign says " take an additional 20% off.” What is the final selling price of the running
shoes? What is the total percentage decrease in the price?
Answers
Answer:
Solution in photo
Step-by-step explanation:
What is the slope of the line that passes through points (0,7) and (-3, 0)? O A Α. 7 ОВ. 7 O C. 13 OD 3
Answers
Answer:
[tex]m=\frac{7}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (0, 7)
Point (-3, 0)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute [SF]: [tex]m=\frac{0-7}{-3-0}[/tex]Subtract: [tex]m=\frac{-7}{-3}[/tex]Simplify: [tex]m=\frac{7}{3}[/tex]What is the factored form of the polynomial?
x +9x +20
Answers
Answer: (x - 5)(x + 4)
Answer:
(x+5)(x+4)
Step-by-step explanation:
A boat travels at a rate of 18 kilometers per hour from its port. A second boat is 34 kilometers behind the
first boat when it starts traveling in the same direction at a rate of 22 kilometers per hour to the same port.
Let d represent the distance the boats are from the port in kilometers and t represent the amount of time
in hours. The system of equations ⎧
⎨
⎩
d = 18t + 34 d = 22t
can be used to represent this situation. How many
hours will it take for the second boat to catch up to the first boat? How far will the boats be from their
port? Use the substitution method to solve this real-world application.
Answers
The number of hours taken should be 8.5 hours
And, the distance should be 187 km.
Important information:The equation is d = 18t + 34 and d = 22t.The calculation is as follows:d = 18t + 34
d = 22t
Put the d value in the above equation
22t = 18t + 34
22t - 18t = 34
4t = 34
t = 8.5 hours
Now the distance is
= 22(8.5)
= 187 km
Find out more information about the Distance here :brainly.com/question/21470320?referrer=searchResults
Which can be used to prove angle 3 is congruent to angle 6
Answers
Answer:
alternate interior angle
Step-by-step explanation:
PLZ PLZ PLZ HELP ME I AM TIMEDDDDDDDDDDDDDDDDDDDDDDDD
Answers
Answer:
The answer is A
Step-by-step explanation:
If you look at the bottom it is near -6 so if you reflect it it would be at 6 but it was 2 units down at 4
Answer:
its the last one
Step-by-step explanation:
the shape is across the x axis so you don't do 2 or 3 then you do it and it is 2 units different not 1 so it is the last one
Which of the given expressions results in 0 when evaluated at x = 5?
ОА.
5x(x-7)
OB. (x + 7)(x-2)
OC. (x-8)(x - 5)
OD
(x + 5)(x-8)
Answers
Answer:
C (x-8)(x-5)
Step-by-step explanation:
(5-8) = -3
(5-5) = 0
-3 x 0 = 0
2 sides equations
1. 15x-8x= 5x +48
2. 4-2y= 4y
3. 4-5x= 3+x
4. 2x+8=2x-5
5. 4y+9= 4y+9
Answers
Answer:
15x-8x-5x=48
3x=48
or X=16
4=4y+2y
or 4= 6y
or 4/6=y
or y=2/3
4-5x= 3x
or 4=5x+3x
or 4=8x
or 4/8=X
or X=2
2x=2x-5+8
or,2x= 2x-13
or 2x+2x=13
or 4x=13
or X= 13/4
or X =3.25
4y=4y+9-9
or 4y=4y+0
or 4y-4y=0
or 0=0
The table shows test scores for six students. Do the data show a positive or a negative correlation? Can the data be used to show causation?