Answer:
yes
Step-by-step explanation:
it's hard but you'll figure it out so don't worry
2^x - 3^x = √(6^x - 9^x)
[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]
[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]
For [tex]x=0[/tex], our initial equation is obviously true.
Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].
Answer to the miscellaneous equation, is x=0 and x=-1.71
Miscellaneous equation are the equations which are not polynomial
The question can be solved by:
Factorising Splitting the terms to find the required solution
Completing the squares, etc
2ˣ - 3ˣ = √(6ˣ - 9ˣ)
Squaring both sides,
2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ
2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0
Factorising the terms,
2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0
(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0
Equating the braces to zero,
Either,
2ˣ=3ˣ
x=0
or
2ˣ=2.3ˣ
Taking log on both sides
xln2=ln2+xln3
x=ln2/(ln2-ln3)
=-1.71
Therefore, x=0 and x=-1.71 is the only solution
Learn more about miscellaneous equation: https://brainly.com/question/121433
#SPJ10
Unit 8:Right triangles & Trigonometry
Answer:
[tex]24\sqrt{5}[/tex]
Step-by-step explanation:
So for this problem you can use the law of sines which states
[tex]\frac{a}{sin A} = \frac{b}{sin B}\\[/tex]
Since the angle is a right triangle we can find the hypotenuse by plugging in the values.
[tex]\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}\\[/tex]
we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)
Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
| x - 57 | = 3
Step-by-step explanation:
Since the house is on the 57th block, Jamaal must stop walking on the 54th block or the 60th block.
Use the given graph to determine the limit, if it exists.
The limit in the given graph [tex]\lim_{x \to \ 2^{-} } f(x)[/tex] is 3 and [tex]\lim_{x \to \ 2^{+} } f(x)[/tex] is -2
Given graph of a function and we have to determine the limits when x tends to 2 minus and when x tends to 2 plus.
When we see the graph we can find that the graph is not of the linear function because it is not straight line.
From x=2 and onwards it gives values values of only -2 because it is parallel to x-axis at y=-2.From x=2 and leftwards it gives values values of only 3 because it is parallel to x-axis at y=3.
Hence the limit of the function whose graph is shown is 3 and -2.
Learn more about limits at https://brainly.com/question/27517662
#SPJ10
A=(3+[tex]\frac{a+\sqrt{a} }{\sqrt{a}+1 }[/tex])(3-[tex]\frac{a-5\sqrt{a} }{\sqrt{5}-5 }[/tex])
The simplification of the given algebra we see is; 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
How to Simplify Algebra?We are given the algebra expression;
A = [3 + ((a + √a)/(√a + 1))][3 - ((a - 5√a)/(√5 + 5))]
When we multiply out, we will get;
9 + 3((a + √a)/(√a + 1)) - 3((a - 5√a)/(√5 + 5)) - [((a + √a)/(√a + 1)) * ((a - 5√a)/(√5 + 5))]
⇒ 9 + 3((a√a + a - a + √a)/(a - 1)) - ³/₂₀((√5 - 5)(a - 5√a)) - (a² - 4a√a - 5a)/((√a + 1)*√5 + 5))
Read more about Algebra at; https://brainly.com/question/4344214
#SPJ1
Area of a triangular prism
Answer:
if you mean the formula it is (1/2) · b · (6 · h + sqrt(3) · b)
Step-by-step explanation:
In 2000, the number of people with a home phone in Indiana was 3,286,000. If the number of home phones have decreasing by 4% each year,
how many Hoosiers will have a home phone in 2011? Round to two-decimal places.
Hoosiers
Pause test
3286000x4/100=131440
131440x11=1445840
3286000-1445840=1840160
Answer: 1840160
this is the answer I got but for some reason the answer didn't turn out to be in decimal :( but I sware this is the answer I got
A building 190 feet tall casts a 90 foot long shadow. if a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building
Answer:
About 64.65 degrees
Step-by-step explanation:
[tex] \tan(x) = \frac{190}{90} [/tex]
[tex]x = { \tan}^{ - 1} \frac{190}{90} = 64.65[/tex]
Make sure your calculator is in degree mode.
divided it by 7 and added 25. the result was 34 what was my number?
25. the result was 34 what was my number?
Answer:63
Step-by-step explanation:
63/7+25=34
Answer:
x = 63
Step-by-step explanation:
we know that...
(x will be the stand-in for "your number")
x ÷ 7 + 25 = 34
(x ÷ 7) + 25 = 34
To find x, we have to isolate x
first, we can subtract 25 from both sides (remember, if you do an action on one side, you must do the same action on the other side)
{why are we subtracting? we need to do the opposite of a sign to get rid of it. By subtracting, we are undoing addition; by multiplying we are undoing division (and vice versa) }
(x ÷ 7) + 25 = 34
- 25 - 25 (subtract 25)
x ÷ 7 = 9
× 7 ×7 (multiplying by 7 to get rid of the "÷7")
x = 63
now, we can test out our x-value:
(63 ÷ 7) +25 = 34
( 9 ) + 25 = 34
34 = 34
because this equation is true, we can be certain that x = 63
hope this helps!
What is the area of Vivian’s garage door?
The area of Vivian’s garage door is 62.5 square feet
Area of composite shape.The Vivian garage is made up of a trapezoid and a rectangle. The area of the door is expressed as;
Area = Area of rectangle + area of trapezoid
Area = (5 * 8) + 0.5(7 + 8)*3
Area= 40 +22.5
Area = 62.5 square feet
Hence the area of Vivian’s garage door is 62.5 square feet
Learn more on composite shapes here: https://brainly.com/question/8370446
#SPJ1
Please help! To solve the equation 1.75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
Answer:
C
Step-by-step explanation:
1.75n = 7 ( to isolate n divide both sides by 1.75 )
n = [tex]\frac{7}{1.75}[/tex] = 4
Answer:
c.) Divide by 1.75
Step-by-step explanation:
Given equation:
⇒ 1.75n = 7
Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.
When done so:
⇒ 1.75n/1.75 = 7/1.75
⇒ n = 4
he height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent?
the number of seconds after the rocket is released
the initial height of the rocket
the initial velocity of the rocket
the height of the rocket after t seconds
Answer: the number of seconds after the rocket is released
i do not now these questions
Using proportions, it is found that:
a) 5 people are needed.
b) Yes.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Item a:
Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:
150/32 = 4.6875.
However, an integer number is needed, hence 5 people are needed.
Item b:
With 30 hours, the number of people needed is given by:
150/30 = 5.
Which remains the same.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
vincent mows 8 lawns in 2 hours. how many lawns are mowed in 5 hours .
Answer:
20 lawns
Step-by-step explanation:
For the graph below, what should the domain be so that the function is at least 300? (1 point) graph of y equals minus 2 times the square of x plus 50 times x plus 300 a x ≥ 0 b −5 ≤ x ≤ 30 c 0 ≤ x ≤ 25 d all real numbers
The function is a quadratic function, then the domain will be all real numbers. Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = -2x² + 50x + 300
Then the function is a quadratic function, then the domain will be all real numbers.
Then the correct option is D.
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ1
Using the following image, solve for JI.
J
2x + 28
x + 22
5
H
In the given image, the length of JI is 6
Solving linear equationsFrom the question, we are to solve for JI
From the given image, we can write that
JI + IH = JH
Then,
2x + 28 + 5 = x + 22
Solving for x
2x + 28 + 5 = x + 22
First, collect like terms
2x - x = 22 - 28 - 5
Simplifying
x = -11
But,
JI = 2x + 28
∴ JI = 2(-11) + 28
JI = -22 + 28
JI = 6
Hence, the length of JI is 6
Learn more on Linear equations here: https://brainly.com/question/27979747
#SPJ1
What is the circumference of the circle shown below? (Round your answer to the nearest tenth.) A. 33.0 B. 66.0 C. 346.4 D. 206.2
Answer:
B. 66.0
Step-by-step explanation:
The formula for circumference is 2*π*r where r is the radius. MS and MR are both radii, so we can plug in 10.5 to the formula to get 2* π*10.5, which would be about 65.97, which rounds to 66.0. Hope this helps!
Tomas learned that the product of the polynomials
(a + b)(a ab + bf) was a special pattern that would
result in a sum of cubes, a3 + b3. His teacher
put four
products on the board and asked the class to identify
which product would result in a sum of cubes if a =
2x and b = y
The product that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).
Product that would result in a sum of cubesGiven:
Product of polynomials=(a + b)(a²- ab + b²)
Sum of cubes=a³+ b³
Hence,
a³+ b³ = (a + b) (a²-ab + b²)
When:
a=2x
y=b
So,
a³+ b³= (2x + y ) [ (2)² - (2x) (y) + y²)
a³+ b³= (2x + y ) [ 4x² - 2xy + y²]
a³+ b³ = (2x + y)(4x² – 2xy + y²)
Therefore the product that would result in a sum of cubes if a =2x and b = y is: (2x + y)(4x² – 2xy + y²).
Learn more about product that would result in a sum of cubes here:https://brainly.com/question/14305581
#SPJ1
City worker drain a community pool that contains 403,920 gallons of water. The pump they use removes water at a rate of 40 cubic feet per minute. One cubic foot of water contains 7.48 gallons how long in hours will it take to remove all the water from the pool
Answer:
22.5 hours
Step-by-step explanation:
One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have
299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours
The tables represent the functions f(x) and g(x). f(x) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g(x) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions? x = -3 O x = -1 x = 0 Ox=1 The tables represent the functions f ( x ) and g ( x ) . f ( x ) -5 -2 -1 0 1 2 -3 -1 1 3 w 5 X -3 -2 -1 0 1 2 g ( x ) -13 -9 -5 -1 3 7 Which input value produces the same output value for the two functions ? x = -3 O x = -1 x = 0 Ox = 1
Answer:
x=1
Step-by-step explanation:
There are two functions (f & g), each of which have a table of inputs and outputs. The same list of inputs is given to both functions, but the outputs are different.
Imagine that you asked your Father 6 questions, (weirdly instead of numbered 1 through 6, numbered -3 through 2), and that he gave you a list of answers.
Imagine that you asked your Grandfather the same 6 questions, and you got a list of answers from him.
On which question did they give the same answer?
It was on question number "1", (really the 5th question, but as we've numbered things from -3 to 2, it's question "1").
Since the "questions" were the input, "x", x=1.
Pls help me solve this equation
Answer:
a
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, 4 ) into the partial equation
4 = 2 + c ⇒ c = 4 - 2 = 2
y = [tex]\frac{1}{3}[/tex] x + 2 ← equation of line
Sofia is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Sofia's test score (out of 100) if she got 8 questions wrong? What would be her score if she got xx questions wrong?
Score with 8 questions wrong:
Score with xx questions wrong:
need answer quickly
Answer:
60 points
100 - 5x
Step-by-step explanation:
If she got 8 questions wrong she missed (8 * 5) points or 40 points. This means she only got 60 points
This can be further generalized by simply subtracting the amount of questions someone got wrong by 5 from the total available points of 100
100 - 5x
copy machine can make 250 copies in 4 minutes. Represent
rate of change in copies per minute.
Answer:
62.5 copies per minute
Step-by-step explanation:
Note that the word "per" means divide. So, a rate of change in "copies per minute", means a number of copies divided by a number of minutes
If the copy machine can make 250 copies in 4 minutes, then the number of copies is 250 copies, and the number of minutes is 4 minutes:
[tex]\text{rate of change in copies per minute}=\dfrac{\text{number of copies}}{\text{number of minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=\dfrac{\text{250 copies}}{\text{4 minutes}}[/tex]
[tex]\text{rate of change in copies per minute}=62.5\dfrac{\text{copies}}{\text{minute}}[/tex]
the diagram shows a logo
Answer:
where is the digram may i see the digram
which is NOT an arithmetic sequence
-7,0,7,14
0,5,1,1.5
10,6,2,-2
2,4,8,16
Answer:
2,4,8,16
Step-by-step explanation:
2,4,8,16
difference is multiplied by 2
Luis and Raul are playing Odds or Evens. Both friends flip a coin. If both coins land on heads or if both coins land on tails, then Luis wins both coins. If one coin lands on hea
No, the game is not fair because Raul has a higher probability of winning than Luis.
Yes, the game is fair because both friends have an equal probability of winning.
No, the game is not fair because Luis has a higher probability of winning than Raul.
Yes, the game is fair because the friends do not have an equal probability of winning.
Answer:
B
they both have equal probability of winning as both of them have a 50/50 chance of winning
Step-by-step explanation:
Yes, the game is fair because both friends have an equal probability of winning.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The game of Odds or Evens is not fair because Raul has a higher probability of winning than Luis.
In this game, the probability of both coins landing on heads or both coins landing on tails is 1/2 * 1/2 = 1/4.
Therefore, there is a 1/4 probability that Luis will win both coins.
However, there is a 1/2 probability that one coin will land on heads and the other will land on tails. In this case, Raul will win both coins because he chose "evens" and the sum of the numbers is even.
The sum of two random coin flips has an equal probability of being even or odd, so the probability of Raul winning both coins is 1/2.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ2
7 is what percent of 154?
Answer: 10.78
Step-by-step explanation:
if(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers
Answer:
a = 4/3 and b = 0============================
Given expression:[tex]\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}[/tex]
Simplify it in steps:Step 1Bring both fractions into common denominator:
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]
Step 2Simplify:
[tex]\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]
[tex]\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =[/tex]
[tex]\dfrac{4\sqrt{14} }{7-4} =[/tex]
[tex]\dfrac{4}{3} \sqrt{14} }[/tex]
Step 3Compare the result with given expression to get:
a = 4/3 and b = 0The function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x). Which represents
g(x)?
O g(x) = (x + 9)² + 4
O g(x) = (x + 9)²-4
Og(x)=(x-4)² +9
Og(x) = (x+4)² +9
Answer:
g(x) = (x-4)² +9
Step-by-step explanation:
If f(x) is moved up 9 units, it becomes x² + 9, as only the 'y' value is changed by 9. Then, if it is moved 4 units to the right, it becomes (x+4)² +9, as only the 'x' value is changed by -4.
The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Now, To translate the function f(x) = x² with 9 units up and 4 units to the right, we need to use the following formula:
⇒ g(x) = f (x - 4) + 9
Substituting f(x) with its equivalent form:
⇒ g(x) = ( x - 4 )² + 9
Therefore, The function g(x) that represents the translation of f(x) = x² with 9 units up and 4 units to the right is,
⇒ g(x) = (x-4)² + 9.
Learn more about transformation visit:
https://brainly.com/question/30097107
#SPJ5
Sarah bought snacks for her team's practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost before tax was $33.96. Write and solve an equation which can be used to determine j, how much each bottle of juice cost.
The equation is 1.56 + 20x = 33.96 and the value of x is 1.62.
What is Equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here, Based on the given conditions, formulate: 1.56 + 20 × x = 33.96
Rearrange unknown terms to the left side of the equation: 20x = 33.96-1.56
Calculate the sum or difference: 20x = 32.4
Divide both sides of the equation by the coefficient of variable: x = 32.4/20
Calculate the product or quotient: x = 1.62
get the result: x = 1.62
Thus, the equation is 1.56 + 20x = 33.96 and the value of x is 1.62.
Learn more about Equation from:
https://brainly.com/question/2263981
#SPJ1
