Simplify each number. 4¹/₂
The simplified form of number is 2
To find the simplified form of the number, we will find the number whose square is equal to 4. As per the known fact, only 2 is the number whose square is 4.
Firstly rewriting the number -
Number = [tex]4^{1/2}[/tex]
Now, rewriting the number with base as 2 and exponent also as 2, as stated in theory above -
Number = [tex]2^{2(1/2)}[/tex]
Cancelling 2 from the exponent as it is present in both numerator and denominator. Rewriting the number with 2 as base and 1 as exponent to find the simplified form of the number.
Number = 2
Hence, the simplified number is 2
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Which best explains the relationship between the two triangles below?
Answer:1.
Step-by-step explanation: 1. because , and Step-by-step explanation:We have been given two triangles and . We are asked to find the relationship between these triangles.By angle sum property let us find measure of angle C of triangle ADC.Let us find measure of angle T of triangle RTS.We can see that , and . Therefore, and 1st option is the correct choice.
pls help guys i have no clue whats going on
Answer:D
Step-by-step explanation:Hope that helped
Determine whether each function is an example of exponential growth or decay. Then, find the y -intercept. y=25/7(7/5) x
y = 25x / 5 is each function is an example of exponential growth or decay.
What does exponential growth look like in math?
A typical illustration of exponential expansion is population increase. Take a population of bacteria as an example. It seems sense that the rate of population increase would be inversely correlated with the population's size. After all, the number of bacteria grows more quickly the more there are for them to reproduce.y= 25/7(7/5) x
y = 25/5 x
y = 25x / 5
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what is the missing value in x^2 y^8 times x^3 y^? = x^5 y^5?
Hence , the missing value y in x^2 y^8 times x²y⁸ x³ y = x⁵ y⁵ is -3 .
Definition of law of exponents
- one in every of a collection of rules in algebra: exponents of numbers are additional once the numbers are increased, subtracted once the numbers are divided, and increased once raised by still another exponent: a^m × aⁿ = a^(m+n)
We have given an expression x²y⁸ x³ y = x⁵ y⁵ .
LHS = x²y⁸ x³ yⁿ
Let the power of y in LHS be "n" .
On using exponents rule , we get
LHS = x⁵y⁹⁺ⁿ
RHS = x⁵ y⁵
As LHS = RHS
x⁵y⁹⁺ⁿ = x⁵ y⁵
On comparing power of y , we get
9 + n = 5
n = -3
Hence , the power of y in LHS is -3 .
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The area of a blue circle is 15 square yards less than five times the area of a tan circle. The blue circle has an area of 1,335 square yards. Use approximation to find the radius of the tan circle.
Based on the given task content, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.
Area of a circleArea of the tan circle = xArea of the blue circle = (5x - 15) Area of blue circle = 1,335 square yards1,335 = 5x - 15
Add 15 to both sides1,335 + 15 = 5x
1,350 = 5x
divide both sides by 5x = 1350/5
x = 270 square yards
Area of the tan circle = πr²
270 = 3.14 × r²
270 = 3.14r²
divide both sides by 3.14r² = 270 / 3.14
r² = 85.98726114649681
r = √85.98726114649681
Approximately,
r = 9.27 yards
Therefore, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.
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On a fantasy football team the Titans score is 11.15 points and a running back score is 11.75 points a wide receiver score is 1.05 points less than the run pack how many total points do three players scored
Answer: The total would be 33.6 points.
Step-by-step explanation:
Titans Score: 11.15
Running Back Score: 11.75
Wide Receiver: 1.05 less than Running Back (11.75 - 1.05), which would be 10.7 points.
11.15 + 11.75 + 10.7 = 33.6 total points
Answer: the problem was a little confusing but I'm assuming the answer is 10.7 making the final answer 32.97
Step-by-step explanation: if the titans scored (11.15) points and the running back scores (11.75) points and the wide receiver scores 1.05 points less then the running back it would be...
11.75 (the running backs points)
- minus
1.05
__________
=10.07(how many points the wide receiver had)
Then 10.07+ 11.15+ 11.75=32.97
Hope I got it right! <3
Write each expression as a single natural logarithm. ln 9+ln 2
We have expression ln 9+ln 2 as a single natural logarithm ln 18
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to express ln 9+ln 2 as a single natural logarithm.
⇒ ln 9 + ln 2
⇒ ln (9) = ln (2)
Use the quotient property of logarithms
⇒ ln (9 × 2)
⇒ ln 18
Finally, we have expressed ln 9+ln 2 as a single natural logarithm ln 18
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what is the gravity of someone falling down
Answer: free fall
Step-by-step explanation: A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name.
1. Which equation is not an example of a direct variation?
5
A. y = x + 1
B.y = -x
C. y = 4x
D.y = -9x
3
16
Answer: D
Step-by-step explanation:
Please help me out please please please
How many minutes have passed, m, when Tank A contains the following amounts of water?
a. 151 liters
b. 191.5 liters
c. 270.25 liters
d. p liters
The minutes that have passed, m, when Tank A contains the following amounts of water will be:
151 liters = 3 minutes
191.5 liters = 7.5 minutes
270.25 liters = 16.25 minutes
p liters = (p-124) / 9 min
How to calculate the minutes?It should be noted that for 151 lit = (151 - 124)/9 = 3 min
Also, for 191.5 lit = (191.5-124) /9
= 67.5/9 = 7.5 min = 7 min 30 sec
It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec
For p lit = (p-124) / 9 min
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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
p liters
Follow • 1
what would be 12+3.4x-5.4x-x simplified?
Answer:
12−3x
Step-by-step explanation:
12+3.4x−5.4x−x
Combine 3.4x and −5.4x to get −2x.
12−2x−x
Combine −2x and −x to get −3x.
12−3x
After simplification of given expression. We get, the value of x is 4.
To simplify this 12 + 3.4x - 5.4x - x,
12 + 3.4x - 5.4x - x = 0
3.4x - 5.4x = - 2x
12 - 2x - x
-2x - x = -3x
-3x + 12 = 0
-3x = -12,
x = 4
Therefore, the value of x is 4.
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in science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution
When zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature, the change in temperature is 1/2 degree.
How to illustrate the information?It should be noted that from the information, science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 9/10 degrees as the. ending temperature.
Therefore,the change in temperature will be the subtraction of the temperature given. This will be illustrated as:
= 1/5 - (-3/10)
= 1/5 + 3/10
= 2/10 + 3/10
= 5/10
= 1/2
The change on temperature is 1/2 degree.
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In science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature. What was the change in temperature?
Death valley is a desert in northern california with many place of interest. one such place is the badwater basin, the elevation is
-282 feet. at another location, salt creek trail, the elevation is-220 feet. write an inequality to compare the elevations and state
which elevation is closer to sea level.
The inequality comparing the elevations is -220 > -282 and -220 feet is closer to sea level.
The elevation of Bad Water Basin = -282 feet
The elevation of the Salt Creek = -220 feet
We are asked to compare the elevations and find which is greater than the other.
So we know that on a number line -220 is greater than -282.
This can be understood in the same sense that -1 > -2 on the number line.
So the inequality comparing the elevations is -220 > -282.
Now consider the sea level as 0 on the number line.
Then clearly -220 is closer to 0 on number line.
Hence the elevation closer to the sea level = -220 feet.
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What is the remainder when 316 is divided by 13?
Answer:
24 reminder 4
Step-by-step explanation:
Reminder is 4
316/13 = 24 R 4
Write the ratio that compares the championships won by Australia to the total number of championships. Then explain it's meaning
The ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.
According to the question we have been given that,
Total number of championship = 41
Total number of championship won by Australia = 6
Thus we need to find the ratio that compares the championship won by Australia to the total number of championship.
For this the ratio will be : [tex]\frac{number of championship won by Australia}{Total number of championship }[/tex]
= 6/41
Hence the ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.
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Solve each equation.
3x⁺²=27²x
After solving the equation, x = 2/5 is the value of x in [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = ((3)^3)^{2x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ x+2 = 6x
⇒ 2 = 6x - x
⇒ 2 = 5x
⇒ x = 2/5
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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3. Kaitlin has two puppies. Puppy A
weighs 12 pounds and is gaining
1.5 pounds each week. Puppy B
weighs 18 pounds and is gaining
0.75 pounds each week. How
many weeks, x, will it take for
the two puppies to weight the
same amount? put in a equation or inequality
Answer:
X = 8
Step-by-step explanation:
Simplify each radical expression. Use absolute value symbols when needed. ∛-0.027
The simplified form is -0.3.
As an instance, 3√(8) method to locate the diced root of 8. If there may be no superscript range, the novel expression is asking for the rectangular root. The term underneath the unconventional image is referred to as the radicand.
An intensive expression is an expression containing a rectangular root. Radicand - a variety of expressions in the radical symbol. Radical equation - An equation containing radical expressions with variables inside the radicands.
A few examples of radicals are √7, √2y+1, etc. an intensive also can be associated with the subsequent terms: An equation this is inside a radical is referred to as a thorough equation. An expression that lies interior a rectangular root is referred to as an intensive expression.
Applying radical rule,
[tex]\sqrt[n]{-a} =-\sqrt[n]{a} \\\sqrt[3]{-0.027}=-\sqrt[3]{0.027}\\ = -0.3[/tex].
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What does the 150 in the equation represent?
What does the 9 in the equation represent?
Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|. Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
What is Equation?
Two expressions with equal sign is called as equation.
Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|.
Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
Therefore Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.
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Domain-Functions
state the domain and range of the function
The domain of the function is [-2, 2] and the range of the function is [-1, 2].
If there is a function y = x + a, then the domain is the set of all values that x can take and the range is the set of all the values that y can take for the function to exist.
Here, we are given a function as shown in the graph.
As we can see the function is defined only for the given points, that is, it has 2 endpoints.
Just by looking at the graph we can see that x can take values from -2 to 2. Thus, the domain of the function is [-2, 2].
We use closed brackets as x can be -2 and 2 as well. Similarly, we can see that y can take values from -1 to 2.
Thus, the range of the function is [-1, 2].
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The two triangles displayed are scaled copies of one another. Find the scale factor.
Answer: 6
Step-by-step explanation:
5. What is the additive inverse of 3/4
Answer:
Step-by-step explanation:
0.75
11. Chris buys six guppies. Every month his guppy population doubles. [4]
a) How many guppies will there be after 1 month? 2 months? 3 months?
b) Create a formula that would express the statement above. In your formula let n
equal the number of months, and G equal the total population of guppies.
c) How many guppies will there be after 6.5 months?
d) Can the fish population continue to grow at this rate? Explain
Answer:
G = 6(2)^n
Step-by-step explanation:
a) At 1 month he will have 12 guppies, at 2 months he will have 24 guppies and at 3 months he will have 48 guppies.
b) G = 6(2)^n
This is following the exponential formula.
c) G = 6(2)^6.5 = 543 guppies
d) At this rate, there will be no room for the guppies to continue growing.
Let athe event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event
Answer: do you have a pic??
Step-by-step explanation:
ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Which graph best represents the solution set of y ≤ 3/4x − 4?
The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the graph of the inequality expression?The inequality expression is given as
y ≤ 3/4x − 4
The inequality symbol in the above inequality expression is
≤
This implies that the inequality expression is a less than or equal to
When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line
Also, the inequality symbol implies that the bottom part is shaded
Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)
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How much should you invest in an account that pays 6 % annual interest compounded continuously if you want exactly $ 8000 after four years? Show your work.
We must invest $6294.256 if we want exactly $ 8000 after four years.
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously, after t years is-
[tex]A = Pe^{rt}[/tex]
Here, we are given that rate of interest = 6% and we need exactly $8000 after four years.
Thus r = 6/100 = 0.06 and t = 4
Putting the values in the compound interest formula we get,
8000 = P[tex]e^{(0.06*4)}[/tex]
8000 = P[tex]e^{(0.24)}[/tex]
P[tex]e^{(0.24)}[/tex] = 8000
[tex]e^{(0.24)}[/tex] = 1.271
⇒ 1.271P = 8000P
= 8000/ 1.271P
= 6294.256
Thus, we must invest $6294.256 if we want exactly $ 8000 after four years.
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What is the greatest common factor of 9 and 48?
Answer:
3 is the greatest common factor that can go into 9 and 48
The greatest common factor of 9 and 48 is 3.
What is the greatest common factor?The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.
For example, the GCF of 12 and 18 is 6, beca
To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.
We can start by listing the factors of each number:
9: 1, 3, 9
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.
Therefore, the GCF of 9 and 48 is 3.
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Write each logarithmic expression as a single logarithm.
(2logbx/3 + 3logby / 4) - 5logbz
The value of logarithmic expression (2logbx/3 + 3logby / 4) - 5logbz is logbx/3^2(by / 4)^3/logbz^5.
By considering the given logarithmic expression
(2logbx/3 + 3logby / 4) - 5logbz
logb(x/3)^2 +log(by / 4)^3-log(bz)^5
logb(x/3)^2(by / 4)^3-logbz^5
logbx/3^2(by / 4)^3/logbz^5
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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