Answers
Answer:
1. x = -2 , 3
2. x = - 1, 5
3. -1, 6/5
4. - 0/3, 1.3
Step-by-step explanation:
1.
[tex]ln(x+5)=ln(x-1)+ln(x+1)\\\\x+ 5 = (x-1)(x+1)\\\\x + 5 = x^2 - 1\\\\x^2 - x - 6 = 0 \\\\x^2 - 3 x + 2 x - 6 =0 \\\\x(x-3)+2(x-3)=0\\\\x = -2 and 3[/tex]
2.
[tex]e^{x^{2}}=e^{4x +5}\\\\x^2 - 4x - 5 = 0 \\\\x^2 - 5x + x - 5 = 0 \\\\x (x-5)+1 (x-5)=0\\\\x = -1 and 5[/tex]
3.
[tex]log_{4}(5x^2 +2)=log_{4}(x +8)\\\\5x^2 - x - 6 = 0 \\\\5 x^2 - 6 x + 5x- 6 = 0 \\\\5 x (x + 1)-6(x+1)=0\\\\x = -1 and \frac{6}{5}[/tex]
4.
[tex]log(x-1)+log 5x = 2\\\\5 x (x-1) =2 \\\\5x^2 - 5x -2 = 0 \\\\x = \frac{5\pm\sqrt{25+40}}{10}\\\\x = \frac{5\pm 8}{10}\\\\x = 1.3, - 0.3[/tex]
Related Questions
HELPPP ME OUTTTT!!!!!
Answers
Answer:
Measure of the unknown angle is 21°.
Step-by-step explanation:
In the given question,
Measure of opposite side and the measure of hypotenuse have been given.
Therefore, we will use the trigonometric ratio for the unknown angle which has the ratio of opposite side and the hypotenuse.
[tex]\text{sin}\theta=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]=\frac{13}{36}[/tex]
[tex]=0.36111[/tex]
[tex]\theta \approx \text{sin}^{-1}(0.36111)[/tex]
[tex]\theta \approx 21.17[/tex]
[tex]\theta \approx 21^{\circ}[/tex]
Therefore, measure of the unknown angle is 21°.
How much water should be added to 90ml of 45 percent acid solution to dilute it to 25 percent acid solution
Answers
Answer:
72 ml
Step-by-step explanation:
Let
x = amount of water that should be added
45% acid solution = 45/100 = 0.45
25% acid solution = 25/100 = 0.25
The equation is
90(0.45) = 0.25(x + 90)
40.5 = 0.25x + 22.5
40.5 - 22.5 = 0.25x
18 = 0.25x
Divide both sides by 0.25
x = 18/0.25
= 72
x = 72 ml
The length of a rectangle is three times the width. The area of the rectangle is 108 sq. inches what’s the triangles width?
Answers
Answer:ÑÑÑÑÑÑÑÑÑññÑÑÑÑññññññÑÑÑÑÑÑÑÑÑñÑÑÑÑññ
Step-by-step explanation:
HELP PLEASE HURRY
THANKS
Answers
Answer:
Step-by-step explanation:
Please hurry I will mark you brainliest
The length of a rectangle is 5 less than 4 times the width. The perimeter is 136 m. Determine the dimensions of the rectangle. Write an equation and the “let statements”
Answers
Answer:
l = 14.6 m
b = 53.4 m
Step-by-step explanation:
Let breadth be x
Let lenght be 4x-5
so,
perimeter = 2(l+b)
136 = 2(4x-5+x)
or, 136 = 2(5x-5)
or, 136 = 10x - 10
or, 136 + 10 = 10x
or, 146 = 10x
or, x = 146/10
so, x = 14.6 m
so, breadth(x) = 14.6
so, lenght = 4x - 5
= (4×14.6)-5r
= 53.4m
Linear equation: -1
2
(6x + 10) = 13
Step 1: –3x – 5 = 13
Step 2: –3x = 18
Step 3: x = –6
Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
Answers
Answer:
see below
Step-by-step explanation:
-1/2 * (6x + 10) = 13
Distribute -1/2
–3x – 5 = 13
Add 5 to each side
-3x-5+5 = 13+5
–3x = 18
Divide each side by -3
-3x/-3 = 18/-3
x = -6
nolan uses 7 inches of string to make each bracelet. if nolan makes 3 bracelets, how many inches of string will he use?
Answers
Answer:
21 inches
Step-by-step explanation:
We can write a ratio to solve
7 inches x inches
------------- = -------------------
1 bracelet 3 bracelets
Using cross products
7*3 = 1x
21 = x
21 inches
Answer:
21 inches
Step-by-step
This can be solved two ways: addition or multiplication.
Addition: Since there are three bracelets you could add 7 three times
7+7+7
= 14+7
= 21
Multiplication: Simply multiply 7 x 3= 21
Select the correct location in the expression.
Consider this expression.
4x^4-6x^3+6x+3/x-3
Which term in the quotient of this expression contains an error?
Answers
Answer:
78
Correct term:60
Step-by-step explanation:
We are given that
[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]
The quotient of this expression is given by
[tex]4x^3+6x^2+18x+78+\frac{183}{x-3}[/tex]
We have to find the term in this expression which contains an error.
[tex]\frac{4x^4-6x^3+6x+3}{x-3}[/tex]
The quotient of this expression is given by
[tex]=4x^3+6x^2+18x+60[/tex]
[tex]Dividend=Divisor\times quotient+ remainder[/tex]
Using the formula
[tex]4x^4-6x^3+6x+3=(x-3)(4x^3+6x^2+18x+60)+\frac{183}{x-3}[/tex]
We can see that in the given expression there is 60 in place of 78.
The error in the expression of quotient is 78.
Correct term is 60.
On a pie chart, a category representing 20% of the whole should correspond to a central angle of 20°.
Answers
Answer:
No! 20% does not correspond to a central angle 20°.
Step-by-step explanation:
The central angle for pie chart is 360°.
So, a category represents 20% is 20%(360) for central angle.
Let's simplify it to get the angle,
[tex]\frac{20}{100} * 360[/tex]
Simplify it,
72°
So, 20% does not correspond to a central angle 20°.
Edwin hiked to a famous point with a beautiful view. It took 2 hours and 55 minutes to hike to the viewpoint and 25 minutes to hike back. Edwin spent 25 minutes enjoying the view at the top. He finished the hike at 11:45 A.M. What time did Edwin start the hike to the viewpoint?
Answers
Answer:
= 8:00 A.M.
Step-by-step explanation:
▪You first find the total time taken which will be :
2 hrs 55 min + 25 min
= 3 hrs 20 min + 25 min
= 3 hrs 45min
▪ Beginning time = Arrival time - Time taken
= 11:45 - 3:45
= 8:00 am
¿
Did I do this right?
Answers
Answer:
it must be yes!
Step-by-step explanation:
Calculate the axis of symmetry in the equation Y = (x+1) (x-4)
Come on anyone please helppppppp.
Answers
Answer:
Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points
x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation
y=(x+1)(x-4)
=x^2-3x-4
a is 1,b is -3 and c is -4
x= -(-3)/2(1)
=1.5
and y=x^2-3x-4
=1.5^2-3(1.5)-4
= -6.25
therefore the axis of symmetry is (1.5,-6.25)
I hope this helps
what is 8/9 divided 2/3
Answers
Answer:
4/3
Step-by-step explanation:
8/9 ÷ 2/3
Copy dot flip
8/9 * 3/2
Rewriting
8/2 * 3/9
4 * 1/3
4/3
Write 42 as a product of primes use index notation
Answers
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
please show steps!!
Answers
Answer:
x = 0, π/3, 2π/3, π, 4π/3, 5π/3
Step-by-step explanation:
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
x
The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
4cos^4(x) – 5cos^2(x) + 1 = 0 from [0, 2π)
so, we get,
4cos^4(x) – 5cos^2(x) + 1 = 0
(4cos^2(x) - 1)(cos^2(x) - 1) = 0
When 4cos^2(x) - 1 = 0
cos^2(x) = 1/4
cos x = +/-1/2
so x = π/3, 2π/3, 4π/3, 5π/3.
When cos^2x - 1 = 0
cos x = +/- 1
x = 0, π.
Hence, The solution is : x = 0, π/3, 2π/3, π, 4π/3, 5π/3.
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The range of cells in column D and rows 1 to 10 is represented as:
1:10 D1:D10 D:D
Answers
Answer:
how?
Step-by-step explanation:
I didnt get question
f(x) = 275
1. Find the inverse of f(x) and its domain.
Answers
Answer:
y = 1/(x+1) -5
X cannot be -1 because the denominator would go to zero
Step-by-step explanation:
f(x) = 1/(x+5) -1
y = 1/(x+5) -1
Exchange x and y and solve for y
x = 1/(y+5) -1
x+1 = 1/(y+5)
Multiply by (y+5)
(x+1) (y+5) = 1
Divide by (x+1)
y+5 = 1/(x+1)
Subtract 5
y = 1/(x+1) -5
X cannot be -1 because the denominator would go to zero
What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5)=g(8)=−9. (Do not include "c=" in your answer.)
Answers
Answer:
[tex]\displaystyle c = \frac{20}{3}[/tex]
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to x:
[tex]\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right][/tex]
Differentiate:
[tex]g'(x) = -21x^2+182x-280[/tex]
Let g'(x) = 0:
[tex]0 = -21x^2+182x-280[/tex]
Solve for x. First, divide everything by negative seven:
[tex]0=3x^2-26x+40[/tex]
Factor:
[tex]0=(x-2)(3x-20)[/tex]Zero Product Property:
[tex]x-2=0 \text{ or } 3x-20=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=2 \text{ or } x = \frac{20}{3}[/tex]
Since the first solution is not within our interval, we can ignore it.
Therefore:
[tex]\displaystyle c = \frac{20}{3}[/tex]
What is the area of the triangle? A) 6 squared inches B) 7 1/2 square inches. C) 10 square inches. D) 12 square inches
Answers
Answer:
A) 6 square inches.
Step-by-step explanation:
A(Triangle) = 1/2bh
b = base length
h = height length
A(Triangle) = 1/2(4)(3) = 6
Therefore, the area of the triangle is 6 in².
Plot each angle on the unit circle below. You will need to draw additional radius segments
○ 0, 30, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330
Determine the radian measure for each angle
Determine the Sin, Cos, Tan for each angle
Use 0 as an example
Upload your completed circle in the dropbox provided.
Answers
Solution :
Trigonometric angles :
The trigonometric angles are defined as the angles that are obtained by the ratios of trigonometric functions. It shows the relationship between the sides of the triangle and the angles between them. These values of the trigonometric angles ranges from 0 to 36 degrees.
Below attached shown are the angles on a unit circle which shows the angles for each value of sin, cos and tan, and also the radian measure for each of the angles.
What is the value of X?
Answers
Answer:
x=2
Step-by-step explanation:
A line that intersects a circle in two points is called a secant line, and this is the case for both line DE and AE.
For two secant lines that intersect outside of the circle, such as the ones here, we can say that
CE * DE = BE * AE
Therefore, we need to then define these lines.
CE is x+4, BE is x+1, AE = (BE + AB) = 11+x+1 = 12+x, and DE = (CE + DC) = 1+x+4 = 5+x
We then have
(x+4) * (5+x) = (x+1) * (12+x)
expand
5x + x² + 20 + 4x = 12x+x²+12+x
x²+9x + 20 = x²+13x+12
Next, we want to congregate all values to one side so we can solve for x. This can be done by subtracting both sides by (x²+13x+12) to get
-4x + 8 = 0
subtract 8 from both sides to isolate the x and its coefficient
-4x = -8
divide both sides by -4 to isolate the x
x = 2
Explanation: I just took a test on it
help please summer school sucks!!!
Answers
Answer:
X =30
Step-by-step explanation:
= 60+90
=150
angle sum property
x+150=180
x=180- 150
x= 30
Answer:
Step-by-step explanation:
90 + 60 = 150
(right angles = 90)
There is 180 degrees in a triangle, therefore,
180 - 150 = 30
Therefore, x = 30
p.s. Are you good at history?
p.p.s I dont like summer school either =)
Which of the following is the correct factorization of the polynomial below?
x3 + 10x2 + 25x
A. x(x + 5)(x - 5)
B. (x2 + 2x - 5)(x-10)
C. (x2 + 5x - 2)(x-10)
D. x(x + 5)2
Answers
Answer:
x(x+5)^2
Step-by-step explanation:
x^3 + 10x^2 + 25x
Factor out x
x(x^2+10x+25)
What 2 numbers multiply to 25 and add to 10
5*5 = 25
5+5 =10
x(x+5)(x+5)
x(x+5)^2
Answer:
D
Step-by-step explanation:
Given
x³ + 10x² + 25x ← factor out x from each term
= x(x² + 10x + 25) ← perfect square
= x(x + 5)²
What is the answer I need help ASAP be truthful
Answers
Answer:
your closest number should be A
Answer:
A.√99
Step-by-step explanation:
10^2 = 100
Or vise versa √100 = 10
The closest number to 100 is 99
So √99 is closest to 10
A civil servant had a salary of Rs 9600. Tax up to Rs 85000 per year would be exempted. If he paid Rs 4530 as a tax, how much percent of tax was imposed?
Answers
Answer:
4%
Step-by-step explanation:
Yearly salary = 9600 * 12 = Rs. 115200
Tax = Rs . 4530
[tex]Tax \ percent = \frac{4530}{115200}*100[/tex]
= 3.93 = 4%
i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!
Answers
Answer: D
Step-by-step explanation:
Given TVW,MZV = 90°, TV = 14, and VW= 9,
which of the following choices is used to find mZW?
Answers
here's the answer to your question
THIS HURTS MY HEAD SO I CANT FOCUS, PLEASE HELP!
find the missing part of the pattern:
69388966938896?988963
Answers
Answer:
6
Step-by-step explanation:
The probability that Dan buys a sandwich is 0.2.
The probability that Dan gets the bus is 0.9.
Assuming the events are independent, what is the probability that Dan buys a sandwich
and gets the bus?
Answers
Answer:
0.18
Step-by-step explanation:
Find the probability that both independent events occur by multiplying the individual probabilities by each other:
0.2(0.9)
= 0.18
So, the probability is 0.18
What is the rate of change of the amount earned with respect to hours worked for this function?
A) 1/13 hours per dollar
B) 2/5 hours per dollar
C) 3 dollars per hour
D) 13 dollars per hour
Answers
The rate of change of the amount earned with respect to hours worked for this function is D. 13 dollars per hour.
What is rate of change?The rate of change for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x₂, y₂)
Point b = (2, 26) = (x₁, y₁)
Calculating the gradient or slope :
Rate of change = (y₂ - y₁) / (x₂ - x₁)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
Rate= 13 dollars per hour
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Complete question
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
