Answer:
0.8
Step-by-step explanation:
You are given the equation
[tex]\left(\dfrac{1}{64}\right)^{0.5x-3}=8^{9x-2}[/tex]
First note that
[tex]\dfrac{1}{64}=\dfrac{1}{2^6}=2^{-6}\\ \\\left(\dfrac{1}{64}\right)^{0.5x-3}=(2^{-6})^{0.5x-3}=2^{-6\cdot (0.5x-3)}=2^{-3x+18}\\ \\8=2^3\\ \\8^{9x-2}=(2^3)^{9x-2}=2^{3\cdot (9x-2)}=2^{27x-6}[/tex]
Now
[tex]2^{-3x+18}=2^{27x-6}\\ \\-3x+18=27x-6\\ \\-3x-27x=-6-18\\ \\-30x=-24\\ \\x=\dfrac{24}{30}=\dfrac{8}{10}=0.8[/tex]
Final answer:
To solve the given equation, we convert both sides to a common base and equate the exponents. After simplifying, we find that the solution is x = 8/11.
Explanation:
We are asked to solve the equation (1/64)^0.5x-3 = 8^9x-2. To begin, we will express both sides of the equation with the same base since 64 is 2^6 and 8 is 2^3. This transformation will allow us to use the property of exponents that states when the bases are equal, the exponents must also be equal.
First, let's rewrite the equation using base 2:
(1/2^6)^(0.5x-3) = (2^3)^(9x-2)(2^-6)^(0.5x-3) = (2^3)^(9x-2)2^(-6(0.5x-3)) = 2^(3(9x-2))Now, since the bases are the same, we can equate the exponents:
-6(0.5x-3) = 3(9x-2)-3x + 18 = 27x - 633x = 24x = 24/33x = 8/11The solution to the equation is x = 8/11. Always remember to check for extraneous solutions when dealing with exponents and roots.
which of the following properties can be used to show that the expression?
Answer:
1 3 5set/dhzhhhhhhhhhhhhhhhhhhh
The expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].
The correct option is (a).
To demonstrate that the expression[tex]\(4^5/3\) is equivalent to \(\sqrt[3]{4^5}\)[/tex], we can apply the following properties:
1. Radical to Exponent Property:
- The expression [tex]\(\sqrt[3]{4^5}\) can be rewritten as \(4^{5/3}\)[/tex].
- This property allows us to convert a radical expression to an exponent expression by raising the base to the reciprocal of the index of the radical.
2. Exponent to Radical Change Property:
- The fraction exponent [tex]\(5/3\)[/tex] can be expressed as a radical: [tex]\(\sqrt[3]{4^5}\)[/tex].
down step-by-step:
1. Start with the given expression: [tex]\(4^5/3\)[/tex].
2. Apply the **Radical to Exponent Property: [tex]\[4^5/3 = 4^{5/3}\][/tex]
3. Now, express the fraction exponent as a radical:
[tex]\[4^{5/3} = \sqrt[3]{4^5}\][/tex]
Therefore, the expression [tex]\(4^5/3\)[/tex] is indeed equivalent to[tex]\(\sqrt[3]{4^5}\)[/tex].
How do I set up the equation for this?
If your average speed is 55 mph, how long will it take you to drive 248 miles?
Answer:
Speed = Distance ÷ Time
time = distance ÷ speed
Step-by-step explanation:
248 ÷ 55 * 60 = 270.54 minutes
The formula for the perimeter of an equilateral triangle is p=3s. What is the perimeter?
In order to answer this, you have to have the unit of measurement and an illustration.
What’s the area of a 72 ft diameter circle?
Answer:
4069.44
Step-by-step explanation:
a=pie R squared
A pencil manufacturer uses 5,376 grams of rubber to make 960 pencils. If they use 64,512 grams of rubber an hour, how many pencils are made per hour?
A) 11,420 pencils per hour
B) 11,480 pencils per hour
C) 11,520 pencils per hour
D) 11,580 pencils per hour
This answer would be C because I had worked out answer good
For this case, we look for the number of pencils per gram of rubber.
[tex]\frac {960} {5,376} = 0.178571428571[/tex]
0.178571428571 pencils per gram of rubber are made
We are looking for the number of pencils per hour.
[tex]0.178571428571 \frac {penc} {g} * 64,512 \frac {g} {h} = 11,520 \frac {pen} {h}[/tex]
Thus, 11,520 pencils per hour are made.
Answer:
Option C
what is the prime fractorization of 180
Answer:
2^ .3^.5
Step-by-step explanation:
We need to obtain factors of 180 which are prime numbers
2^=4
3^=9
4.9.5 = 180
50 points An unknown number x is at most 20. Which graph best represents all the values of x? (1 point) Number line graph with closed circle on 20 and shading to the right. Number line graph with open circle on 20 and shading to the right Number line graph with closed circle on 20 and shading to the left. Number line graph with open circle on 20 and shading to the left
At most means it can either equal 20 or be less than 20.
On a number line, there would be a closed circle on the number 20 and the area to the left of 20 would be shaded.
Number line graph with closed circle on 20 and shading to the left.
what is the biggest star in the solar system
Answer:
Well we only have one star in our solar system so the Sun?
The sun is the biggest star. The sun is at the center of our solar system and is the nearest star to Earth. The sun is a huge ball of very hot, burning gas. The sun sends out heat and light into space.
what is the complete factorization of the polynomial below
Answer:
B
Step-by-step explanation:
(x+2)(x^2+1)
=(x+2)(x+1)(x+1)
Answer:
( x + i)(x -i) ( x +2).
Step-by-step explanation:
Given : x³ + 2x² +x +2.
To find : complete factorization of the polynomial below.
Solution : We have given x³ + 2x² +x +2.
On taking common x² from first two terms and 1 from last two terms .
x² ( x +2) +1 (x +2).
On grouping
(x² +1) ( x +2).
Now factor of (x² +1) become ( x + i)(x -i) in complex form .
Factors are ( x + i)(x -i) ( x +2).
Therefore, ( x + i)(x -i) ( x +2).
Geometry, Triangle in a circle. Find X show work and explain please
Answer: [tex]x=7[/tex]
Step-by-step explanation:
By the Intersecting Secants Theorem, we know that:
[tex](5)(x+5)=(6)(6+4)[/tex]
Having this, we can find the value of "x" by solving for "x":
Applying Distributive property:
[tex](5)(x+5)=(6)(24)\\5x+25=60[/tex]
Subtract 25 from both sides of the equation:
[tex]5x+25-25=60-25\\5x=35[/tex]
And finally dviding both sides of the equation by 5, we get:
[tex]\frac{5x}{5}=\frac{35}{5}\\x=7[/tex]
Answer:
35/5 it would be 35 over 5
Step-by-step explanation:
I need help please!!
Answer:
about 32.9
Step-by-step explanation:
By looking at the triangle, you can see that there is both an angle and a side provided. This allows you to use trigonometry (sin, cos, tan). You have to use tan to find the answer since it is used when you have either the opposite side or adjacent side and are solving for one of them. You take the tangent of the angle and set it equal to the opposite over the adjacent (see image attached).
I hope this helps.
Also sorry that the image is the wrong way, but it wouldn't let me attach it the right way.
QUESTION 1
Given a right triangle, the unknown side is opposite to the 35° angle.
The side adjacent to this angle is 47 units.
We use the tangent ratio to get:
[tex] \tan(35 \degree) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(35 \degree) = \frac{x}{47} [/tex]
[tex] x = 47\tan(35 \degree)[/tex]
[tex]x = 32.9units[/tex]
to the nearest tenth.
QUESTION 2
The given angle is 47°
The opposite side is x units.
The adjacent side is 40 units.
We again use the tangent ratio to obtain:
[tex] \tan(47 \degree) = \frac{x}{40} [/tex]
[tex]x = 40\tan(47\degree) [/tex]
[tex]x = 42.9units \: to \: the \: nearest \: tenth[/tex]
a bag with 10 marbles is shown below. a marble is chosen from the bag at random. what are odds in favor of choosing a black marble
Divide the number of black marbles by 10, the total number of marbles. If there is one black marble, the chances of choosing a black marble is 1/10.
60 points !!
Triangle QRS is shown on the coordinate grid. Triangle QRS is dilated with the origin as the center of dilation using the rule (x, y) → ( 1/4 x, 1/4 y) to create triangle Q'R'S'. Which statement is true? A) Triangle Q'R'S' is smaller than triangle QRS, because the scale factor is less than 1. B) Triangle Q'R'S' is larger than triangle QRS, because the scale factor is less than 1. C) Triangle Q'R'S' is larger than triangle QRS, because the scale factor is greater than 1. D) Triangle Q'R'S' is smaller than triangle QRS, because the scale factor is greater than 1.
https://lh3.googleusercontent.com/qPYvRzvroDEYvaSZbKCSiNmf-uxSPXZzCkwcqzIAnhtvrmk7zmrkSt5hQ-lftybdtUCa-A=s91
Answer:
A
Step-by-step explanation:
The triangle is being scaled down by a factor of 1/4. So Q'R'S is smaller than QRS because the scale factor is less than 1. Answer A.
Answer:\
The answer is A :) I took the assignment
What is the approximate area of the triangle below?
a)72.8
b)111.9
c)142.0
d)164.7
all in sq. cm.
I believe it’s B of joy them A
Answer:
A
Step-by-step explanation:
Got a 100
(please hurry)Consider this composite figure.
Composite Figure
Apply the formula of each shape to determine the volumes.
What is the exact volume of the composite figure?
V =
π cm³
Answer:
39pi cm 3
Step-by-step explanation:
i just did the assingment
The composite figure is the combination of the two cones. The volume of the composite figure will be 39π cm³.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The volume of the composite figure.
The composite figure is the combination of the two cones.
[tex]V = \dfrac{1}{3} \times \pi \times 3^2 \times 5 + \dfrac{1}{3} \times \pi \times 3^2 \times 8\\[/tex]
On simplifying, we have
V = 15π + 24π
V = 39π cm³
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ2
PLEASE HELP WILL MARK
Answer:
( 8.5 , 6.5 )
Step-by-step explanation:
Midpoint formula = ( x₁ + x₂ / 2 ) , ( y₁ + y₂ / 2 )
x₁ = 4
x₂ = 13
y₁ = 10
y₂ = 3
Midpoint = ( 4 + 13 / 2 ) , ( 10 + 3 / 2 )
Midpoint = ( 17 / 2 ) , ( 13 / 2 )
Midpoint = 8.5 , 6.5
Approximately how many accidents occurred between 1965 and 1970 inclusive?
Answer:
About 1,800 accidents
Step-by-step explanation:
Observing the attached figure
In 1965 ----> Approximately 260 accidents
In 1966 ----> Approximately 325 accidents
In 1967 ----> Approximately 300 accidents
In 1968 ----> Approximately 350 accidents
In 1969 ----> Approximately 360 accidents
In 1970 ----> Approximately 400 accidents
Total------> Approximately 1.920 accidents
NEED HELP FAST!!!!!!!!
i need a life fast plz
Answer:
[tex]m=0.002kg[/tex]
Step-by-step explanation:
The given formula is:
[tex]E=mc^2[/tex]
Divide both sides by [tex]c^2[/tex].
[tex]\implies \frac{E}{c^2}=\frac{mc^2}{c^2}[/tex]
Cancel out the common factors to get;
[tex]\implies \frac{E}{c^2}=m[/tex]
[tex]m=\frac{E}{c^2}[/tex]
When [tex]E=1.8\times10^{14}J[/tex] and [tex]c=300,000,000ms^{-1}[/tex], then
[tex]m=\frac{1.8\times10^{14}}{300,000,000^2}[/tex]
This simplifies to
[tex]m=0.002kg[/tex]
What’s the smallest zero for the function h(x)=4x^2-8x-60
Answer:
-3
Step-by-step explanation:
In order to find the smallest zero, we will have to find out all the zeros of the function.
In case you are wondering what a zero is, it is the x-value or the domain intersections. The points where the parabola intersects the x-axis.
4x² - 8x - 60 = 0
Why zero?
We know that the parabola intersects the x-axis and when it does, the y-value is 0. h(x) is nothing but 'y'.
4(x²-2x-15) = 0 → I took the gcd as 4 and did it accordingly.
x² - 2x - 15 = 0 → Divide on both sides with 4
Now, what multiples to -15 but adds up to -2?
-5 and 3
x² + 3x - 5x - 15 → Grouping the terms
x ( x + 3 ) - 5 ( x + 3 ) → Taking the GCD in both groups
( x - 5 ) ( x + 3 ) = 0
x = 5 , -3
The smallest one out of these zeros is -3.
Hope it helps! :)
a food truck sells tacos, burrito, and drinks.
Let event A = A customer buys a taco
Let event B = A customer buys a drink
What does P(A or B) = 0.60 mean in terms of this problem?
A) The probability that a customer buys both a taco and a drink is 60%.
B) Buying a taco and buying s drink are mutually exclusive events.
C) The probability that a customer buys either a taco or a drink is 60%.
D) The probability that a customer buys neither a taco nor a drink is 60%.
Answer:
Option C is correct.
Step-by-step explanation:
P(A or B) represents that event A has occurred or event B has occurred or both events A and B are happening.
We are given P(A or B) = 0.60 or 0.60/100 = 60%
So, Option C The probability that a customer buys either a taco or a drink is 60% is correct.
Answer: Option C
Step-by-step explanation:
For two events A and B, P(A or B) represents the probability that event A occurs, or event B occurs.
In this case, event A represents a customer buys a taco and event B represents a customer buys a drink. We know that
[tex]P (A\ or\ B) = 0.60[/tex]
So this means that the probability that a customer buys either a taco or a drink is 60%
The answer is the option C
evaluate 9!/7! PLEASE I NEED HELP
Answer:
72
Step-by-step explanation:
Remember that 9! = 7! (8)(9)
write Substitute
7!(8)(9) for 9!
7!(8)(9)/ 7!= (8)(9)= 72
Answer: 72
Step-by-step explanation:
By definition, it is important to know that the factorial of a non-negative integer "n" is the product of all positive integers less than or equal to "n". This is expressed with an exclamation symbol (!):
[tex]n![/tex]
Then, the rule for this is the following:
[tex]n! = n *(n-1)![/tex]
Therefore, knowing this, you can evalute [tex]\frac{9!}{7!}[/tex] as following:
[tex]\frac{9*8*7*6*5*4*3*2*1}{7*6*5*4*3*2*1}=\frac{362,880}{5,040}=72[/tex]
simplify x squared - 9/ x squared - 3x
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{x^2-9}{x^2-3x}[/tex]
Factorise the numerator/denominator
x² - 9 = (x - 3)(x + 3) ← difference of squares
x² - 3x = x(x - 3) ← common factor of x
The fraction simplifies to
[tex]\frac{(x-3)(x+3)}{x(x-3)}[/tex] ← cancel (x - 3) on numerator/denominator
= [tex]\frac{x+3}{x}[/tex]
What is the smallest two-digit prime number?
Answer: 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
the prime numbers (1-15 is the furthes i will go for this) are 2,3,5,7,11,13
as you can see the smallest two didget prime number is 11------------
richard wants to paint the top sides of the block column. what is the surface area he needs to cover?
First of all, you have to send the measurements; otherwise, there would not be an answer
i neeed helpppp can someone help me?
Answer:
-8/5
Step-by-step explanation:
The thing that makes lines different from other kinds of curves is their constant rate of change. We call this rate of change slope, and you usually see it represented with the letter m. We measure it as the rate our y-coordinate changes for some amount our x-coordinate changes.
We're given the two points (-1, 4), and (4, -4). From that first point to the second one, our x-coordinate increases by 5, while our y-coordinate decreases by 8, so our change in y is -8 for every 5 in the positive x direction, and we'd write our slope as
m = -8/5
20) Which rule yields the dilation of the figure RSTU centered at the origin?
A)
(x, y) → (4x, 4y)
B)
(x, y) → (0.25x, 0.25y)
C)
(x, y) → (x + 4, y + 4)
D)
(x, y) → (x + 0.25, y + 0.25)
Answer: A) [tex](x,y)\to(4x,4y)[/tex]
Step-by-step explanation:
The rule of dilating a shape by scale factor k centered at the origin is given by :-
[tex](x,y)\rightarrow (kx,ky)[/tex] [We multiply k to the coordinates of pre-image ]
It means Option C) and D) is incorrect.
From the given graph , it can be observe that quadrilateral R'S'T'U' (image) is larger than the RSTU (pre-image) .
It means the scale factor should be greater than 1. [∵ Scale factor for enlargement is k>1]
Then, Option B is also incorrect.
Hence, the rule yields the dilation of the figure RSTU centered at the origin is given by option A)
i.e. [tex](x,y)\to(4x,4y)[/tex]
brainly what is the leanth of the line segment with endpoints (-6,-8) and (7,-8)
Answer:
The length of the line segment is 13 units
Step-by-step explanation:
The line segment joining the two points is horizontal since the y co-ordinate is the same.
For a horizontal line, the length of the line segment is simply the difference between the x co-ordinate values.
In this case we have;
7 - (-6) = 7 + 6 = 13
Therefore, the length of the line segment is 13 units
Answer:
13 units
Step-by-step explanation:
We want to find the length of the line segment with endpoints (-6,-8) and (7,-8).
Observe that, the y-coordinates are the same.
We can quickly use the absolute value method to find the required length.
According to this method the length of the line segment with endpoints (-6,-8) and (7,-8) is the absolute value of the difference between the x-values.
[tex]|7--6|=|7+6|=|13|=13[/tex]
The length of the line segment is 13 units.
-4h - 6 + 15 = 17 ( I don’t understand the concept.)
the concept is to find the value of h
Answer:
it is an algebraic expression (answer is h = -2 )
Simplify the expression
−4h−6 + 15 = 17
(Combine Like Terms)
(−4h)+(−6+15)=17
−4h + 9 = 17
Step 2: Subtract 9 from both sides.
−4h + 9 − 9 = 17 − 9
−4h=8
Step 3: Divide both sides by -4.
[tex]\frac{-4h}{-4}[/tex] = [tex]\frac{8}{-4}[/tex]
h = -2
Step-by-step explanation:
What is the value of
x3 + 4, when x = 6?
I'm not sure if you meant to write 3x or [tex]x^{3}[/tex] instead of x3 but I will work out both versions just in case
In the equation 3x + 4 plug 6 in for x
3(6) + 4
Multiply 3 and 6 first
18 + 4
Add 18 and 4
22
OR
In the equation [tex]x^{3}[/tex] + 4 plug 6 in for x
[tex]6^{3}[/tex] + 4
Solve the exponent
(6*6*6) + 4
216 + 4
Add the numbers together
220
Hope this helped!
Answer:
220
Step-by-step explanation:
Im going to assume x3 equals x^3, so 6^3 is 216, add this to 4 and get 220
Two different functions are represented.
Function A:
X- 0,1,2,3,4
F(X)- 5,10,20,40,80
Function B- y=4/x
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only positive numbers.
The domain and range of both functions contain only positive numbers and zero.
Answer:
Neither function A nor function B has an x-intercept.
Step-by-step explanation:
Function A has a y-intercept at (0, 5).
Function B is defined for negative numbers as well as positive numbers, but not for x=0.
These observations eliminate all answer choices but the first one.
The statement that best compares the two functions is; Neither function A nor function B has an x-intercept.
How to Interpret Functions?A y-intercept is the point where x = 0. Now, for function A we can see that when x = 0, y = 5. Thus, it has a y-intercept.
However, we are not given the point where y = 0 which is x-intercept. Thus, function A does not have an x-intercept.
Formula for Function B is y = 4/x.
This function does not have an x-intercept because at x = 0, the function is undefined.
Read more about Functions at;https://brainly.com/question/3951754
#SPJ2