Given:
The equation is:
[tex]\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}[/tex]
To find:
The value of x.
Solution:
Formulae used:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex](a-b)(a+b)=a^2-b^2[/tex]
We have,
[tex]\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}[/tex]
Taking LCM, we get
[tex]\dfrac{(x+1)^2-(x^2-1)^2}{(x-1)(x+1)}=\dfrac{7}{12}[/tex]
[tex]\dfrac{x^2+2x+1-(x^2-2x+1)}{x^2-1^2}=\dfrac{7}{12}[/tex]
On cross multiplication, we get
[tex]12(x^2+2x+1-x^2+2x-1)=7(x^2-1)[/tex]
[tex]12(4x)=7x^2-7[/tex]
[tex]48x=7x^2-7[/tex]
[tex]0=7x^2-48x-7[/tex]
Splitting the middle term, we get
[tex]7x^2-49x+x-7=0[/tex]
[tex]7x(x-7)+1(x-7)=0[/tex]
[tex](7x+1)(x-7)=0[/tex]
[tex]x=-\dfrac{1}{7},7[/tex]
Therefore, the values of x are [tex]-\dfrac{1}{7}[/tex] and [tex]7[/tex].
ABCD is an isosceles trapezoid.
measure of angle B=
measure of angle C=
measure of angle D=
Answer:
Angle b= angle c =83degree
Angle d =97degree
Step-by-step explanation:
Since isosceles:
Angle b =angle c
Angle a= angle d
Angle d =a=97
Sum of quadrilateral inner degrees:360
(360-2x97)/2=b=c=83
Answer:
Answer:
Angle b= angle c =83degree
Angle d =97degree
Step-by-step explanation:
Since isosceles:
Angle b =angle c
Angle a= angle d
Angle d =a=97
Sum of quadrilateral inner degrees:360
(360-2x97)/2=b=c=83
Step-by-step explanation:
The length of a rectangular swimming pool is exactly three times as long as its width. If the pool has a perimeter of 400m find the width of the pool.
Answer:
50m
Step-by-step explanation:
let the width be x
length=3x
3x+3x+x+x=400
8x=400
x=400÷8
x=50
Enter 4/5 and 1/3 as a pair of equivalent fractions with the least common denominator between the two fractions.
Which of the following could be a rational number
What are the options???
2)
A line passes through the points (0.5) and (-6,3). A second line passes through
(-15, 0) and (-21, -2).
A) Do the lines intersect? Show work to prove it! Grcle YES or
NO
Answer:
Step-by-step explanation:
Find the slope of each line. If the slopes are the same, the lines are parallel. Otherwise, the lines intersect.
Slope of line passing through (x₁, y₁) and (x₂, y₂) = (y₂-y₁)/(x₂-x₁)
Slope of line passing through (0, 5) and (-6, 3) = (3-5)/(-6-0) = ⅓
Slope of line passing through (-15, 0) and (-21, -2) = (-2-9)/(-21-(-2)) = 11/19
The lines intersect.
How to simplify 4(8n+2)
Answer:
32n +8
Step-by-step explanation:
4(8n + 2)
32n+8
help please in this question?
Answer:
see explanation
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and are supplementary, sum to 180° , so
5x + x + 54 = 180 ← equation to solve to find x
6x + 54 = 180 ( subtract 54 from both sides )
6x = 126 ( divide both sides by 6 )
x = 21
Then
∠ 1 = 5x = 5 × 21 = 105°
∠ 2 = x + 54 = 21 + 54 = 75°
Write an equation of a line in slope-intercept form that has a slope of -5 and passes through the point (-3, -4).
Answer:
y = -5x - 19
Step-by-step explanation:
y = -5x + b
-4 = -5(-3) + b
-4 = 15 + b
-19 = b
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Answer:
cylinder radius and height
cone radius height
sphere raduis
plsss helppppp I need it right now plss :(
deadline now until 6:00pm and its 5:30pm here so plsss :(
Answer:
a) IJ is median
IJ = 1/2(HG + EF)IJ = 1/2(8 + 12) = 10 cmb) I is midpoint of HE, therefore, HI = IE
Substitute values and solve for x:
10 = x - 4x = 10 + 4x = 14 cmAnswer:
a) IJ is median
IJ = 1/2(HG + EF)
IJ = 1/2(8 + 12) = 10 cm
b) I is midpoint of HE, therefore, HI = IE
Substitute values and solve for x:
10 = x - 4
x = 10 + 4
x = 14 cm
Step-by-step explanation:
Solve.
A standard coffee mug has a capacity of 16 fluid ounces.
If Annie needs to fill 10 mugs with coffee, how many total quarts of coffee does she need?
Annie needs
quarts of coffee.
Answer: Annie needs 13 quarts of coffee
Step-by-step explanation:
find the measure of each interior angle of a regular polygon with the following number of sides 10
Answer:
a regular polygon has all angles measure sum up to 360 degrees so each interior angle = sum of alll angles/no.of sides so it is 360/10= 36 degrees hope its clear now
Step-by-step explanation:
karrie was late to work 14 times last year if she worked 250 days last year what percent of the days were she late
Jared made a scale drawing of his classroom for his tech project. He used a scale of 1 cm = 3.5 ft. If the length of his classroom on the drawing measured 30 cm, What is the actual length of his classroom?
Answer: 105ft
Step-by-step explanation: If 1cm is 3.5ft then you should multiply 3.5ft by 30 cm to get 105ft.
the number that makes the ratio equivalent to 1:9.
7:
Answer:
63. so it'll be 7:63
Step-by-step explanation:
1:9
7:x
(we multiplied 1 by 7 to get 7 so multiply 9 by 7)
9*7= 63
please help!! I’m doing 13 points since it’s sorta tricky!!
Answer:
c 10
Step-by-step explanation:
2units each and there are five spaces , this 10
For a party, Tyler gets four different kinds of soda. He buys a 6-pack of each
kind. At home, he divides the sodas evenly among three coolers. How many
sodas are in each cooler?
Answer:
8 sodas/cooler
Step-by-step explanation:
4 · 6 = 24
24/3 = 8
Mr. Smith's class has 28 students. They all put in an equal amount of money to get Mr. Smith an end of year gift. If they collected $168 altogether, how much money did each student give. For each question, define a variable (Let statement), write and solve an equation
Answer:
Step-by-step explanation:
28 students all give $128
so,
[tex]\sqrt[28]{128}[/tex]= v v=6
Each student gave 6 dollars. This is true due to the fact that
[tex]\sqrt[28]{128}[/tex]=6
28X6=128
The question is right there please read and help I’ll give u Branliest plz
Just the answer please I need you
Answer:
A = 33.6 sq units
Step-by-step explanation:
A (trapezoid) = 1/2(4)(14+2) = 2(16) = 32
A (semi-circle) = π(1)/2 = 1.57
I need this Done tonight. Plz help me.
Answer is 15 miles
This is because:
1 inch- 5 miles
3 inches- 15 miles
3x5=15 miles
Hope this helps!
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Answer:
1. 48ft
2. 28 inches
Step-by-step explanation:
1. 6x8=48
2. 4x7=28
Solve 5x + 2y = 7 10x + 4y = 14 (1 point) (1,1) (2,3) No solution Infinitely many solutions
Step-by-step explanation:
if you do 14 divided by 7 gives you 2 am I right
You start at (2, 8). You move up 1 unit. Where do you end?
Answer:
2,9 should be your answer
Answer:2 Answers By Expert Tutors ... You end at (-2, 1-4+8), which is point (-2,5). ... Moving down and up would indicated that we are moving along the y- ...
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Step-by-step explanation:
11. What is the value of x?
A 48
B 30
C 60
D 36
Answer:
I think it is B
hope this helps
A rectangle has a length of y^2+3y+7 and a width of y-3. How much longer is the length?
Given:
The length of the rectangle = [tex]y^2+3y+7[/tex]
Width of the rectangle = [tex]y-3[/tex]
To find:
How much longer is the length?
Solution:
We need to find the difference between length and width of the rectangle.
[tex]Difference=Length-Width[/tex]
[tex]Difference=y^2+3y+7-(y-3)[/tex]
[tex]Difference=y^2+3y+7-y+3[/tex]
[tex]Difference=y^2+(3y-y)+(7+3)[/tex]
[tex]Difference=y^2+2y+10[/tex]
Therefore, the length of the rectangle is [tex]y^2+2y+10[/tex] much longer than the width.
list some values that would make this inequality -2x>10
Answer:
-6,-9,-20,-25.
Step-by-step explanation:
You need to multiply a negative to make it positive as a negative multiplied by a negative equals a positive. But anything besides -1,-2,-3,-4,-5 and all positves can be placed.
Can someone help me?
brainliest. please help
Sandra bought a pair of leather boots that were marked down by 20%. The original cost of the boots was $150. What did Sandra pay for the boots
Answer:
130 maybe
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
It is 120 because if you do 20% of 150 that's 30 so subtract that with 150 leaving you 120.