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].
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.
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
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
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.
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:
Which of the following could be a rational number
What are the options???
brainliest. please help
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:
Can someone help me?
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Answer:
1. 48ft
2. 28 inches
Step-by-step explanation:
1. 6x8=48
2. 4x7=28
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.
How to simplify 4(8n+2)
Answer:
32n +8
Step-by-step explanation:
4(8n + 2)
32n+8
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!
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.
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:
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
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
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
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
cylinder radius and height
cone radius height
sphere raduis
The question is right there please read and help I’ll give u Branliest plz
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
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
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:
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.
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°
Enter 4/5 and 1/3 as a pair of equivalent fractions with the least common denominator between the two fractions.
karrie was late to work 14 times last year if she worked 250 days last year what percent of the days were she late
11. What is the value of x?
A 48
B 30
C 60
D 36
Answer:
I think it is B
hope this helps
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
You start at (2, 8). You move up 1 unit. Where do you end?
Answer:
2,9 should be your answer
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Step-by-step explanation:
