Given:
The equation is:
[tex]\dfrac{x-3}{x+2}+\dfrac{3x-3}{(x+1)(x+2)}=\dfrac{x}{x+1}-\dfrac{x-2}{x+2}[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\dfrac{x-3}{x+2}+\dfrac{3x-3}{(x+1)(x+2)}=\dfrac{x}{x+1}-\dfrac{x-2}{x+2}[/tex]
Taking LCM on both sides, we get
[tex]\dfrac{(x-3)(x+1)+3x-3}{(x+1)(x+2)}=\dfrac{x(x+2)-(x+1)(x-2)}{(x+1)(x+2)}[/tex]
[tex](x-3)(x+1)+3x-3=x(x+2)-(x+1)(x-2)[/tex]
[tex]x^2+x-3x-3+3x-3=x^2+2x-(x^2-2x+x-2)[/tex]
[tex]x^2+x-6=x^2+2x-x^2+2x-x+2[/tex]
On further simplification, we get
[tex]x^2+x-6=3x+2[/tex]
[tex]x^2+x-6-3x-2=0[/tex]
[tex]x^2-2x-8=0[/tex]
Splitting the middle term, we get
[tex]x^2-4x+2x-8=0[/tex]
[tex]x(x-4)+2(x-4)=0[/tex]
[tex](x+2)(x-4)=0[/tex]
[tex]x=-2,4[/tex]
But [tex]x\neq -2[/tex] because for [tex]x=-2[/tex] the given equation is not defined.
Therefore, the only solution of the given equation is [tex]x=4[/tex].
Please tell me if I got it right
Answer:
1/9
Step-by-step explanation:
1/3 / 3 = 1/9
she will run 1/9
jog 1/9
and walk 1/9
to check all of them equal 1/3
1/9+1/9+1/9 = 3/9 = 1/3
Students in 4th and 5th grade took a survey regarding their favorite cafeteria food. What percent of the students selected pizza as their favorite food? (Will give brainlt plus 50 points if correct)
A) 30%
B) 40%
C) 60%
D) 20%
(Teachers Hint: "For this one you need to set up a proportion. Start by finding the total amount of kids asked (60 + 110 + 120 + 10 = 300). Then set up the proportion:
pizza % 60 x
_____ = _____ ____ = ____
Total 100 300 100
Cross multiply and divide to get your answer!")
Answer:
where the pic
Step-by-step explanation
lol
What is sin(sec^-1 (u))
Answer:
i think
Step-by-step explanation:
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 60 cm, find its length and width.
length: 7 cm
Х
?
width: 1
cm
Answer:
The length of the rectangle is 25 cm, while the width is 5 cm.
Step-by-step explanation:
Given that the length of a rectangle is five times its width, to find its length and width, knowing that the perimeter of the rectangle is 60 cm, the following calculation must be performed:
(5X x 2) + (X x 2) = 60
10X + 2X = 60
12X = 60
X = 60/12
X = 5
5x5 = 25
Thus, the length of the rectangle is 25 cm, while the width is 5 cm.
What is the measure of n?
Please help!!
Answer:
70°
Step-by-step explanation:
n+20=90° [being a right angelled triangle]
or, n=90°-20°
therefore n=70°
I guess this is the answer but please confirm first.
Catherine got 9 3/8 pounds of cherries from her tree this year last year she only got 6 1/4 pound how many times more pounds did she get this years than last year
Answer:
Answers and steps are in picture.
the area of a rectangle whose length is twice its width
Answer:
is there anything else that gose with this question
Step-by-step explanation:
Gary tried to solve an equation step by step.
Answer:
2.5 x 4 = 10 not 8
so step 2
Answer:
B, Step 2
Step-by-step explanation:
Gary did, in fact, made a mistake. In step 2, 2.5*4 does not equal 8. In fact, 2.5*4 = 10
The average monthly mortgage payment for all homeowners in a city is $2870. Suppose that the distribution of monthly mortgages paid by homeowners in this city follow an approximate normal distribution with a mean of $2870 and a standard deviation of $470. Find to 4 decimal places the probability that the monthly mortgage paid by a randomly selected homeowner from this city is
Answer:
The probability that the monthly mortgage is between 2300 and 3140 is: 0.23167
Step-by-step explanation:
Given
[tex]\mu = 2870[/tex] --- the average
[tex]\sigma = 470[/tex] --- the standard deviation
Required [Missing from the question]
Monthly mortgage is between 2300 and 3140
This is represented as:
[tex]P(2300 < x < 3140)[/tex]
This is calculated as:
[tex]P(a< x < b) = P(z_a < Z < z_b)[/tex]
[tex]P(2300< x < 3140) = P(z_b < Z < z_a)[/tex]
Calculate the z scores
[tex]x = 3140[/tex]
[tex]z = \frac{3140 - 2850}{470}[/tex]
[tex]z = \frac{290}{470}[/tex]
[tex]z = 0.6170[/tex]
[tex]x = 2300[/tex]
[tex]z = \frac{3140 - 2300}{470}[/tex]
[tex]z = \frac{840}{470}[/tex]
[tex]z = 1.7872[/tex]
So, we have;
[tex]P(2300< x < 3140) = P(1.1787 < Z < 0.6170)[/tex]
This is then calculated as:
[tex]P(a < Z < b) = P(Z < a) - P(Z <b)[/tex]
[tex]P(a < Z < b) = P(Z < 1.1782) - P(Z <0.6170)[/tex]
[tex]P(2300< x < 3140) = P(Z < 1.1782) - P(Z <0.6170)[/tex]
Using the z table:
[tex]P(Z<0.6170) =0.73138[/tex]
[tex]P(Z<1.7872) =0.96305[/tex]
[tex]P(2300< x < 3140) = 0.96305 - 0.73138[/tex]
[tex]P(2300< x < 3140) = 0.23167[/tex]
Find the solution set for this inequality. SHOW YOUR WORK OR NO CREDIT
-2x+4>-4x+8
Answer:
Below
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x >2
Interval Notation: ( 2, ∞)
Hope this helps:)
Which point on the number line is closest to the product of the numbers graphed at points R and T? Explain your answer.
Answer Point R = 7/10
and Point T = 9/10
7/10 · 9/10 = 63
63/100
6 /10 = point Q.
Step-by-step explanation:
write 75 as a product of prime factors
How many lines of symmetry does the figure below have?
Answer:
4
Step-by-step explanation:
straight (1)
horizontal (1)
both diagonals (2)
Add seven to a product of a number and ten
Answer:
17
Step-by-step explanation:
10+7 = 17
the point is (5,-2) and the slope is 1/-5
Answer:
y = 1/-5x - 1
Step-by-step explanation:
y+2 = -1/5(x-5)
y+2 = -1/5x+1
y = -1/5x -1
Evaluate A2-B2 for A = 3 and B = -4.
O-2
0-7
Lenovo
Answer:
3×2+(-4)×(-2)=6+8=14
Classify ∠1 and ∠2 using all names that apply
Step-by-step explanation:
complementry
since the angle 1 and 2 both measures 90⁰
Answer: Choice 2 Adjacent and Choice 4 Supplementary
Step-by-step explanation:
Here, we are given four choices, and I will be defining each of them.
Vertical angles: two angles that are opposite to each other which was formed by two intersecting lines.Adjacent angles: two angles that share one common vertex and "arm"Complementary angles: two angles that add up to 90°Supplementary angles: two angles that add up to 180°-----------------------------------------------------------------------------------------------
We can see from the figure given
Both angles are 90°, so ∠1+∠2=90+90=180°
Which is supplementary.
We can see from the figure given
Both angles share a common arm and vertex
Which is adjacent
Hope this helps!! :)
Please let me know if you have any questions
Use the commutative property write an equivalent expression.
7 + 8 =
Answer:
8 + 7
Step-by-step explanation:
By the commutative property,
7 + 8 = 8 + 7
a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3
Answer:
2/3
Step-by-step explanation:
Which of the following is the solution to the compound inequality below?
5 + x 23
or
6x+1<-29
A. X2-2 or X<-5
O B. x2 - 22 or xc - 14
C.X22 or X<5
14
D. 28
or X
Answer:
[tex]x \ge -2[/tex] or [tex]x < -5[/tex]
Step-by-step explanation:
Given
[tex]5+x\ge3[/tex] or [tex]6x+1<-29[/tex]
Required
The solution
[tex]5+x\ge3[/tex]
Solve for x
[tex]x \ge 3 - 5[/tex]
[tex]x \ge -2[/tex]
[tex]6x+1<-29[/tex]
Solve for 6x
[tex]6x < -29 - 1[/tex]
[tex]6x < -30[/tex]
Solve for x
[tex]x < -30/6[/tex]
[tex]x < -5[/tex]
Hence, the solution is:
[tex]x \ge -2[/tex] or [tex]x < -5[/tex]
Mount McKinley in Alaska is North America’s highest mountain. The mountain is 20,320 feet high. To the nearest mile, find the distance from the summit to the horizon at sea level.
Answer:
4 miles
Step-by-step explanation:
3.8484848 rounded is 4
10 You are planning a party for a group of friends. The cost of
the party will be $30 to rent the room plus $5 per person.
You have a budget of $75. Which inequality gives you the
best estimate of the number of people p that you can invite
to your party?
Answer:
30+5p ≤ 75 (C)
Step-by-step explanation:
Well ”p” is amount of people and every person costs 5 dollars do 5p. 30 dollars for a single room so that s a one time fee, 30+5p
Now the budget can’t be greater than 75 and 75 is the greatest number so we use a less then or equal to sign
5p+30≤75 or (C)
What is the equation of a vertical line passing through the point (3, −5)? y = −5 x = −5 y = 3 x = 3
Answer:
Step-by-step explanation:
x = 3
Hailey made the following statement
"It is impossible to build a rectangular prism with a volume of 40 units it one side measures 5 units."
Key
represents
1 cubic unit
Select the two figures below that prove Hailey's statement is false
Answer:
D
Step-by-step explanation:
Joey compared the cost of 9 different toys.
$2, $8, $4, $7, $8, $5, $8, $4, $6
What is the median cost of the books?
Question 1 options:
$8
$5
$6
Answer:
6$
Step-by-step explanation:
$2, $8, $4, $7, $8, $5, $8, $4, $6
2, 4, 4, 5,6,7,8,8,8
6$
pls answer this plssssssssssss
Answer:
Angle C = 160° [given]
Angle A =?
Angle A = Angle C [Vertically Opposite Angles]
Angle A = 160° [option 1]
Please help if u know
Answer:
On the second step when he multiplied distributed (x+1) (x+2) he forgot to multiply x*1 and x*2 (check red arrows in attachment below)
Step-by-step explanation:
i hope that helps please lmk if you need for help
whats the are and perimeter for this pls help
Answer:
the area is 64 the perimeter is 30
Step-by-step explanation:
The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
Answer:
Yes
Step-by-step explanation:
3²+4²=5²
9+16=25
25=25
Which of these choices are square roots of 144? Check all that apply.
Answer:
E
Step-by-step explanation: