The concept:
We are given the equation:
[tex]5^{x(x-1)} = 1[/tex]
Which can be simplified as:
[tex]5^{x^{2} - x} = 1^{1}[/tex]
Since any number to the power '0' is 1
x² - x must be equal to 0 for the given equation to be true
Solving for x:
x² - x = 0
x(x-1) = 0
now, we can divide both sides by either x OR x-1
So we will see what we get for either choice:
x = 0/(x-1) x-1 = 0/x
x = 0 x = 1
Hence, the value of x is either 0 or 1
Of the total school population of 800 students, 200 live outside the student limits. What percentage of students live outside the city limits?
Answer:
1/4 population
Step-by-step explanation:
Answer: 25%
Step-by-step explanation: 200/800=0.25
Move the decimal places of 0.25 two spaces to the right so is 25.
Please help.
Click on the picture for better view!
Answer:
D. (-3;-3)
Step-by-step explanation:
2x-3y<9
A. 2×6-3×(-4)=24 FALSE, because 24>9
B. 2×(-1)-3×(-9)=25 FALSE, because 25>9
C. 2×2-3×(-5)=11 FALSE, because 11>9
D. 2×(-3)-3×(-3)=9 TRUE, because 3<9
solve for x under the assumption that x<0. Enter your answer in interval notation using grouping symbols
Step-by-step explanation:
x² + 9x < -20
x² + 9x + 20 < 0
(x + 4)(x + 5) < 0
Therefore -5 < x < -4 / (-5,-4)
PLS HELP DUE AT 12:00!
pls explain too
A salesman made a trip of 480 miles by bus and train. He traveled 4 hours by
bus and 4 hours by train. On the average, the train was 20 mph faster than
the bus. Find the rate of each.
Answer:
bus = 50mph and train = 70mph
Step-by-step explanation:
4b + 4t = 480
t = b + 20 [replace the "t" in the next step to solve]
4b + 4(b + 20) = 480
4b + 4b + 80 = 480
8b + 80 = 480 [subtract 80 from both sides of the equation]
8b = 400 [divide by 8 on both sides of the equation]
b = 50 and if the train is 20mph faster, t = 70
4(50) + 4(70) = 480
Answer:
480
Step-by-step explanation:
Helppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
-5, -2, 1, 3.
Step-by-step explanation:
This is how you would put them in order from least to greatest.
Answer:
-5,-2,1,3
Step-by-step explanation:
Hope it helps
I need help, can someone tell me the answer to 13x + 3 - 7x - 1? Please and thank you.
Answer:
6x+2 is the answer
Step-by-step explanation:
.......
Chapter 1:Qua
END-OF-CHAPTER REVIEW EXERCISE 1
1
A curve has equation y = 2xy + 5 and a line has equation 2x + 5y = 1.
The curve and the line intersect at the points A and B. Find the coordinates of the midpoint
of the line AB
Answer:
(¹/₂, 0)Step-by-step explanation:
2x + 5y = 1 ⇒ 2x = 1 - 5y
y = 2xy + 5
y = (1 - 5y)y + 5
y = y - 5y² + 5
5y² = 5
y² = 1
y₁ = 1 ∨ y₂ = -1
2x₁ = 1 -5(1) 2x₂ = 1 - 5(-1)
2x₁ = 1 - 5 2x₂ = 1 + 5
2x₁ = -4 2x₂ = 6
x₁ = -2 x₂ = 3
Midpoint:
[tex]M=\left(\frac{x_1+x_2}2\ ,\ \frac{y_1+y_2}2\right)=\left(\frac{-2+3}2\ ,\ \frac{1+(-1)}2\right)=\left(\frac12\ ,\ 0\right)[/tex]
The coordinates of the midpoint of the line AB is (0, 1/2).
The equation of the curve is given by y = 2xy + 5.
The equation of the line is given by 2x + 5y = 1.
We have to first find the point of intersection between the curve and the line and then find the coordinates of the midpoint of line AB where A and B is the point of intersection between the curve and the line.
What is the formula for finding the coordinates of a point that divides a given line in the ratio m:n?If C(x, y) divides a line AB in m:n then we have,
[tex]x = \frac{mx_2 +nx_1}{m+n},~~~y =\frac{my_2+ny_1}{m+n}[/tex]
And if C(x,y) is the midpoint then m = n.
we have,
[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}[/tex]
Where x and y are the coordinates of the midpoint o the line AB.
Find the point of intersection between the line and the curve.
y = 2xy + 5............(1)
2x + 5y = 1..............(2)
From (2) we have,
2x = 1 - 5yx = (1-5y) / 2..........(3)
Substituting (3) in (1).
[tex]y =2\frac{(1-5y)}{2}y + 5\\\\y =\frac{2y-10y^2}{2} + 5\\\\2y = 2y - 10y^2 + 10\\\\10y^2 = 10\\\\y^2 = 1[/tex]
So we have,
y = 1 and y = -1
Puttin y = 1 in (3) we get,
x = (1 - 5) / 2 = - 4 / 2 = -2
Puttin y = -1 in (3) we get,
x = {1-5(-1)} / 2 = (1+5) / 2 = 6 / 2 = 3
Now we have two points of intersection A( 1, -2 ) and B( -1, 3 ).
Finding the coordinates of the midpoint of the line AB.
we have,
[tex]A(1, -2) = A (x_1, y_1)~~and~~B(-1, 3) = B(x_2, y_2)[/tex]
Substituting in the given equation.
[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\\\\x = \frac{-1 +1}{2},~~~y =\frac{3+(-2)}{2}\\\\x = 0,~~~y=\frac{1}{2}[/tex]
So the coordinates of the midpoint is (x,y) = ( 0, 1/2 ).
Learn more about the midpoint of a given line here:
https://brainly.com/question/24493570
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Jason wants to buy flowers for his wife. He is going to buy a combination of daisies and sunflowers. Daisies are $2 each and roses are $3 each. Jason has $25 to spend on a combination of the flowers. Write an inequality to represent this situation.
Answer:
naygas
Step-by-step explanation:
awdwadjhwyajsdudjHASGVJX wvjbhdaes,cvmdjh,bkn,cdblajnkcdbvhjksnam ,bchbdjkns.a d,cbjhkna.djbc
answer: B
What is the expansion of (a + b)4?
o A. a4 + a3b + a2b2 + ab3 + 64
B. a4 + 4a3b + 6a2b2 + 4ab3 + b4
C. a4 + 2a²b + 3a2b2 + 2ab3 + b4
D. a4 + 4a3b - 6a2b2 + 4ab3 – 64
Answer:
option B
Step-by-step explanation:
[tex](a+b)^4\\\\=(a+b)^2(a+b)^2\\\\=(a^2+2ab+b^2)(a^2+2ab+b^2)\\\\=a^2(a^2+2ab+b^2)\\\\+2ab(a^2+2ab+b^2)\\\\+b^2(a^2+2ab+b^2)\\\\=a^4+2a^3b+a^2b^2\\\\+2a^3b+4a^2b^2+2ab^3\\\\+a^2b^2+2ab^3+b^4\\\\=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex]
I need help is it a, b, c, or d
Which expression is the best estimate of One-fourth times 31.3?
One-fourth times 24
One-fourth times 28
One-fourth times 32
One-fourth times 36
Answer:
One-fourth times 32
Step-by-step explanation:
Yes, I know...31.3 rounded is 31, not 32. But it's closer than any other number.
BRAINLEST to whoever answer correctly FIRST
These triangles
are congruent by
the triangle
congruence
postulate [ ? ].
Dan earns £367 over the course of a five day week. How much is that per day?
is x^2 + 1/x = 4 a quadratic equations
Answer:
[tex]\large\boxed{\pink{ \leadsto The \ given \ equation \ is \ not \ a \ Quadratic \ equation . }}[/tex]
Step-by-step explanation:
Given equation to us is ,
[tex]\green{\implies x^2+\dfrac{1}{x}=4 }[/tex]
So , a equation is said to be a quadratic equation if the highest degree of the variable is 2 . On simplifying the Equation ,
[tex]\implies x^2 +\dfrac{1}{x}=4 [/tex]
Taking x as LCM ,
[tex]\implies \dfrac{x^2.x + 1 }{x}= 4 [/tex]
Transposing x to RHS .
[tex]\implies x^3 + 1 = 4x [/tex]
Putting all terms in LHS
[tex]\boxed{\bf \implies x^3 - 4x - 1 = 0 }[/tex]
Since here the highest degree of the variable is 3 not 2 . So its a cubic equation and not a quadratic equation .
Hence the given equation is not a quadratic equation .PLEASE HELP ASSP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
0.96% or 1% to the nearest whole ( use the whole as for your answer )
Step-by-step explanation:
825-817 = 8
8 / 825 = 0.00969696....
x 100 = 0.96%
Use the arc length formula and the given information to find r. s = 12 cm, 0 = 360; r = ?
Arturo worked a 40 hour week at $12 per hour. He then received a raise of one dollar per hour and worked 830 hour week. How much more money did he receive for the first week of work than the second
Answer:
nobody can work 830 in one week; there are only 168 hours in a week
Step-by-step explanation:
Margo spent $5.00 of the $8.00 in her wallet. Which decimal represents the fraction of the $8.00 Margo spent?
Answer:
is it 3.00
Step-by-step explanation:
Answer:
0.625.
Step-by-step explanation:
To find the decimal of what Margo spent we have to divide the part ($5.00) by the whole ($8.00). Like this:
(5)/(8) = 0.625
Therefore, the decimal that represents the fraction is 0.625.
I hope this helps!!
- Kay :)
please help me out! determine the range of the following graph
Answer:
[-9,-4]
Step-by-step explanation:
The highest and lowest points this graph gets to on the y axis are -4 and -9 respectively.
This means the range is [-9,-4].
Brackets are used since -9 and -4 are seemingly included.
A plane is flying at a heading of 125° at a speed of 320 mph. The wind is blowing from due North at a speed of 35 mph. Find the ground speed and the course of the plane. (Note: The course must be between 0° and 360°, where due North corresponds to a course of 0°, due East to a course of 90°, due South to a course of 180°, and due West to a course of 270°.)
Answer:
[tex]301.29\ \text{mph}[/tex]
[tex]119.5^{\circ}[/tex]
Step-by-step explanation:
[tex]v_p[/tex] = Velocity of plane = 320 mph
[tex]v_w[/tex] = Velocity of wind = 35 mph
[tex]\theta[/tex] = Angle between wind and plane directions = [tex]125^{\circ}[/tex]
From triangle law we have resultant
[tex]v_r=\sqrt{v_p^2+v_w^2+2v_pv_w\cos\theta}\\\Rightarrow v_r=\sqrt{320^2+35^2+2\times 320\times 35\cos125^{\circ}}\\\Rightarrow v_r=301.29\ \text{mph}[/tex]
Direction is given by
[tex]\phi=\tan^{-1}\dfrac{v_p\sin\theta}{v_w+v_p\cos\theta}\\\Rightarrow \phi=\tan^{-1}\dfrac{320\sin125^{\circ}}{35+320\cos125^{\circ}}\\\Rightarrow \phi=-60.46^{\circ}=180-60.46=119.5^{\circ}[/tex]
The magnitude of the plane is [tex]301.29\ \text{mph}[/tex] moving at an angle of [tex]119.5^{\circ}[/tex].
Write an equation to represent this situation: Kelly earns $9.50 per hour that she baby-sits. Use T to represent total earned and h to represent hours worked.
(2x+3)^5 expanded using binomial theorem
Answer:
[tex]32 {x}^{5} + 240 {x}^{4} + 720 {x}^{3} + 1080 {x}^{2} + 810x + 243[/tex]
the sum of the first nine terms of an arithmetic series is 162, and the sum of the first 12 terms is 288. Determine the first five terms of the series.
Answer:
[tex]\boxed{\pink{\tt \leadsto Sum \ of \ first \ five \ terms \ is \ 50 . }}[/tex]
Step-by-step explanation:
Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.
[tex]\boxed{\red{\bf \bigg\lgroup For \ answer \ refer \ to \ attachment \bigg\rgroup }}[/tex]
Related Information :-• The sum of n terms of an AP is
[tex]\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}[/tex]
• nth term of an AP is given by ,
[tex]\boxed{\blue{\sf T_n = a+(n-1)d }}[/tex]
A singing competition is auditioning 32 contestants each hour for the next h hours. Which equation can be used to find the total number of contestants, C, that audition in h hours?
a) write √3 × √6 in the form b√2 where b is an integer
Answer: 3√2
√3 . √6 = √(3.6) = √(9.2) = √(3².2) = 3√2
Step-by-step explanation:
Answer:
b = 3
Step-by-step explanation:
[tex] \sqrt{6} [/tex]can be written as [tex] \sqrt{3} \times \sqrt{2} [/tex]
So, lets arrange it.
[tex] \sqrt{3} \times \sqrt{6} = \sqrt{3} \times \sqrt{3} \times \sqrt{2} = 3 \sqrt{2} [/tex]
Hence b = 3.
how do l convert 320 pounds into tons
Answer:
0.16 tons
Step-by-step explanation:
I need help: number 19
Answer:
y=x+2
Step-by-step explanation:
the standard form is y=mx+b where m is the slope and b is the y intercept
TO FIND THE SLOPE: we take the x and y intercepts as a fraction. in this case the line touches the y axis (vertical) at point/value 2 and the x axis at point 2 as well. This means the slope is 2/2x which can be simplified to 1x or just x.
TO FIND THE Y INTERCEPT: we find where the line touches the y axis at point 2.
the slope is plugged into the m of the equation and the y intercept is plugged into the b of the equation.
HELP ME PLEASE!!!!!!
Which values of a, b, and c correctly represent the answer in simplest forrn?
Answer:
The equation becomes
[tex]1\frac{7}{19}=a\frac{b}{c}[/tex]
Therefore,
a = 1b = 7c = 19Hence, option (C) is true.
Step-by-step explanation:
Given the expression
[tex]3\frac{1}{4}\div 2\frac{3}{8}\:=a\frac{b}{c}[/tex]
Solving the L.H.S of the equation
[tex]3\frac{1}{4}\div \:2\frac{3}{8}=\frac{13}{4}\div \:2\frac{3}{8}[/tex]
[tex]=\frac{13}{4}\times \frac{8}{19}[/tex]
[tex]=\frac{13\times \:2}{1\times \:19}[/tex]
[tex]=\frac{26}{1\times \:19}[/tex]
[tex]=\frac{26}{19}[/tex]
Converting improper fraction to a fixed number: [tex]\frac{26}{19}=1\frac{7}{19}[/tex]
[tex]=1\frac{7}{19}[/tex]
Thus, the equation becomes
[tex]1\frac{7}{19}=a\frac{b}{c}[/tex]
Therefore,
a = 1b = 7c = 19Hence, option (C) is true.