9514 1404 393
Answer:
x = 2
Step-by-step explanation:
There are no algebraic methods for solving an equation like this.
The proof of Fermat's Last Theorem demonstrates that no integer x-value can possibly exist that is greater than 2. Trial and error (or your familiarity with Pythagorean triples) tells you that x=2 is a solution for this equation. Equations like this can be solved graphically, as in the attached.
Answer:
[tex] x =2[/tex]
Step-by-step explanation:
Given :-
[tex]{3}^{x} + {4}^{x} = {5}^{x} [/tex]
And we need to find out the value of x. Well there is no specific method to solve the equation .This can be only done using the " Trial and error" Method.
We know that , 3 , 4 and 5 are Pythagorean triplets . So the sum of squares of two smallest numbers is equal to the square of the largest number . Henceforth ,[tex]\implies {3}^{2} + {4}^{2} = {5}^{2} [/tex]
Verification :-
[tex]\implies {3}^{2} + 4^2 = 9+16=25=\boxed{5^2}[/tex]
So , the value of x is 2 . We can here prove that , x does not have other roots other than 2 . For that , divide the both sides of equation by [tex]5^x[/tex] , we have ,
[tex]\implies \dfrac{{3}^{x} + {4}^{x}}{5^x} = \dfrac{{5}^{x}}{5^x} [/tex]
[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+ \bigg( \dfrac{4}{5}\bigg)^x = 1 [/tex]
Now if we take the value of x greater than 2 or less than 2 , then the value 1 will not be satisfied for the values of x greater than or less than 2 .
That is ,
If x > 2[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x > \bigg( \dfrac{3}{5}\bigg)^2 +\bigg( \dfrac{4}{5}\bigg)^2 [/tex]
Subsequently :-
[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x > 1 [/tex]
If x < 2[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x < \bigg( \dfrac{3}{5}\bigg)^2 +\bigg( \dfrac{4}{5}\bigg)^2 [/tex]
Subsequently :-
[tex]\implies \bigg( \dfrac{3}{5}\bigg)^x+\bigg( \dfrac{4}{5}\bigg)^x <1[/tex]
Thus there is no other value other than 2 for which the value of above expression becomes 1 .Hence 2 is the root of the given equation.
What is the answer to: 8+(n-4)
Darla washed 5/9 of the windows on a building, and Cindy washed 1/9 of them. How much greater was Darla's fraction of the windows than Cindy's
Answer:Darla's fraction of the windows was 4/9 greater than Cindy's.
Step-by-step explanation:
Fraction of the window washed by Darla =5/9
Fraction of the window washed by Cindy=1/9
To find How much greater Darla's fraction of the windows was than Cindy's, we subtract ,
5/9-1/9=4/9
Thetrefore, Darla's fraction of the windows was 4/9 greater than Cindy's.
Answer:
4/9
Step-by-step explanation:
The cumulative frequency table shows the heights (inches) of every student in Mrs. Torjman’s math class. What number should be written in the red box?
Answer:
The number 28 should be written in the red box.
9. In the diagram below, Angle A is 50 degrees. What is angle B?
Answer:
130
Step-by-step explanation:
Angle B = 180 - Angle A
180 - 50 = 130
Answer:
The answer is 130 degrees.
Step-by-step explanation:
A+B should be 180, so with A being 50; B has to be 130.
...........................
Answer:
1.
It has two solution because it is in quadratic form.
2.
(x-4)²-28=8
x²-8x+16-28-8=0
x²-8x-20=0
Doing middle term factorization
x²-(10-2)x-20=0
x²-10x+2x-20=0
x(x-10)+2(x-10)
(x-10)(x+2)=0
either
x=10
or
x=-2
:. x= 10 or -2
3.
2x²-5x-5=0
Comparing above equation with ax²+bx +c
we get
a=2
b=-5
c=-5
quadratic equation is
[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Substituting value
[tex]x = \frac{ 5 ± \sqrt{ {-5}^{2} - 4×2×-5} }{2×-5} [/tex]
-10x=5±[tex] \sqrt{ {25+ 40}}[/tex]
taking + ve
-10x=5+[tex] \sqrt{ {65}}[/tex]
x=-½-[tex] \frac {\sqrt{ {65}}}{10}[/tex]
taking -ve
x=-½+[tex] \frac {\sqrt{ {65}}}{10}[/tex]
Madison, Natalie, Isabella and Rebecca go shopping. Madison spent 4/5 of her money, Natalie spends 75% of her money,Isabella spends 0.68 of her money and Rebecca spends 17/20 of her money. Who has the largest percentage of their money left?
Answer:
you need common denominater so 10/10 - 9/10 =1/10 thats how much of her money she used.
Step-by-step explanation:
Solve each problem and show the work for each one.
Solve by factoring.
1. 2x^2+9x+26=-4x+5
Solve by using the quadratic formula and round to the nearest hundredth.
2. 3x^2-6x-4=0
Answer:
Solve by factoring.
1. 2x^2+9x+26=-4x+5
2x²+9x+4x+26-5=0
2x²+13x+21=0
doing middle term factorization
2x²+7x+6x+21=0
x(2x+7)+3(2x+7)=0
(2x+7)(x+3)=0
either
x=-7/2
or
x=-3.
2.
3x^2-6x-4=0
comparing above equation with ax²+bx+c=0
we get
a=3
b=-6
c=-4
By using quadratic equation
x=[tex] \frac{ - b±\sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Substituting value
x=[tex] \frac{ 6±\sqrt{ {-6}^{2} - 4*3*-4 }}{2*-4} [/tex]
x=[tex] \frac{ 6±\sqrt{ {84}}}{-8} [/tex]
x=[tex] \frac{ 6±2\sqrt{ {21}}}{-8} [/tex]
-8x=6±2√21
taking positive
-8x=6+2√21
x=[tex] \frac{6+2√21}{-8} [/tex]
x=-[tex] \frac{3+√21}{4} [/tex]
taking negative
-8x=6-2√21
x=[tex] \frac{6-2√21}{-8} [/tex]
x=-[tex] \frac{3-√21}{4} [/tex]
Name a pair of adjectives
Carry" it needed. Use the (27) 5 0 X 21
Answer:
I belive the answer will be 28,350
PLEASE HELP ME!!!
Boyle's law is :
p1 v1 = p2 v2
what happens to the pressure of a container if the volume is doubled and the temperature is kept the same?
- impossible to determine with the info provided
- the pressure will increase
- the pressure will decrease
- the pressure will stay the same
Answer:
- the pressure will decrease
(volume is doubled ,the pressure reduced by half).
Step-by-step explanation:
P_1 V_1=P_2 V_2
This equation shows that, as volume increases, the pressure of the gas decreases in proportion.
Similarly, as volume decreases, the pressure of the gas increases.
3x+5(2+x)=4x-7 help me out here?
Answer:
x = -17/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3x + 5(2 + x) = 4x - 7
Step 2: Solve for x
[Distributive Property] Distribute 5: 3x + 10 + 5x = 4x - 7[Addition] Combine like terms: 8x + 10 = 4x - 7[Subtraction Property of Equality] Subtract 4x on both sides: 4x + 10 = -7[Subtraction Property of Equality] Subtract 10 on both sides: 4x = -17[Division Property of Equality] Divide 4 on both sides: x = -17/4Answer:
x=[tex]\frac{-17}{4}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x+5(2+x)=4x−7
3x+(5)(2)+(5)(x)=4x+−7(Distribute)
3x+10+5x=4x+−7
(3x+5x)+(10)=4x−7(Combine Like Terms)
8x+10=4x−7
8x+10=4x−7
Step 2: Subtract 4x from both sides.
8x+10−4x=4x−7−4x
4x+10=−7
Step 3: Subtract 10 from both sides.
4x+10−10=−7−10
4x=−17
Step 4: Divide both sides by 4.
[tex]\frac{4x}{4}[/tex]=[tex]\frac{-17}{4}[/tex]
x=[tex]\frac{-17}{4}[/tex]
please help!!
x = ___ units
Answer:
x = 16 units
Step-by-step explanation:
BC = 32√2 / √2 = 32
x = 32/2 = 16
The students in Mabel's class got to choose between pizza and burgers for the celebration on the last day of school. 12 students picked the pizza. If there are 40 students in all in Mabel's class, what percentage of the students picked the pizza?
Answer:
30%
Step-by-step explanation:
The percentage of something can be calculated by dividing that number by the total amount. In this scenario, you divide 12 by 40
12/40 = 0.3
Or, you could do it the way without doing the math and simplifying to make it easier
12/40 = 6/20 = 3/10 = 0.3 = 30%
I need help asap
Which expression represents the volume of a cube with a side length of 6x?
a)6x^2
b)36x^2
c)36x^3
d)216x^3
Answer:
Option 4
Step-by-step explanation:
So formula of voulme of the cube is a³
We have the side length is 6x
So sub the value in formula we get 216x³
What is the product ? Sorry picture isn’t good
Answer:
840 megabytes
Step-by-step explanation:
hope this helps
four less than the sum of a number, x and nine is 35
Step-by-step explanation:
(x+9)-4=35x+9-4=35x=35-5x=30,stay safe healthy and happy..Need help please!!!!
Answer:15
Step-by-step explanation:
Multiply 5730 x (1/2)4
Answer:
no its 5_8)8_9
Step-by-step explanation:
Answer:
The answer is 11460
Hope this helps!
Solve the equation for x
Answer:
B. x = -4
Step-by-step explanation:
- 7x - 35 = -7
add 35 to both sides
-7x = 28
Divde both sides by -7
x = -4
Answer: X = -4
Step-by-step explanation:
-7x - 35 = -7
-7x = -7 + 35
-7x = 28
x = -4
1. Calculate exactly;
(b) 3/4 + 2/3 + 4/5
[tex]6 - 2x - 4(2x + 1)[/tex]
I need help with this problem.
Answer:
2 - 10x
Step-by-step explanation:
Given
6 - 2x - 4 (2x + 1) ← distribute parenthesis by - 4
= 6 - 2x - 8x - 4 ← collect like terms
= 2 - 10x
Help please and thank you
Answer:
B is correct: 3x=40
Step-by-step explanation:
just cross multiply and mark brainliest if you feel like it :)
Answer:
3x =40
Step-by-step explanation:
3 will cross multiply with x then 4 will multiply 10
Hence 3x=40
Help me with the math
Answer:
See below
Step-by-step explanation:
[tex] m\angle 1 = 180\degree - (90+39)\degree = 51\degree [/tex]
[tex] m\angle 2= 90\degree -51\degree =39\degree [/tex]
[tex] m\angle 3= 90\degree[/tex]
[tex] m\angle 4 = 180\degree - (90+39)\degree = 51\degree [/tex]
[tex] m\angle 5 = 180\degree - (129+34)\degree = 17\degree [/tex]
[tex] m\angle 6 = 90\degree +39\degree = 129\degree [/tex]
A new price of an item is $39.32. The percent increase was 16%. What was the original price?
Answer:
let x =the original price
then 116x/100=$39.32
116x=100×39.32
116x=3932
divide both sides by 116
116x/116=3932/116
x=33.89655
(2dp)
x=33.90
can someone please help me lol
thank u!
Answer:
The Slope Equation = y2 -y1 over X2 - X1
Step-by-step explanation:
1.) Pick every graph
2.) Pick any 2 point in the graph
3.) do the slope equation
4.) the answers must be equal
Find the exact value of sin v/2, given tanv=12/5 and pi
74.55 divided by 5
I’m not sure of the answer I need some help
Answer:
14.91
Step-by-step explanation:
Have a good day :)
Answer:
The answer is 14.91
Step-by-step explanation:
To find the answer we must first see how many times 5 can go into 74.55. Since 5 x 14.91 = 74.55, then it means that our answer is 14.91.
how to solve fractagons
Answer:
By using cross multiplication
Step-by-step explanation:
What are the values of Limit of g (x) as x approaches 33 minus and Limit of g (x) as x approaches 33 plus?
Answer:
D
Step-by-step explanation:
?? im conufsed please help
Answer:
B
Step-by-step explanation:
The sign means greater than or equal to and the car need to travel at least 570 miles.
Hope it helps, sorry if it's not right :>
Answer:
Step-by-step explanation:
b