[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]
Applying the laws of indices mentioned above,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]
= [tex]5^{3} .( 5 )[/tex] = [tex]5^{3 + 1}[/tex]
= [tex]5^{4} = 625.[/tex]
Thus, [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
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3z - 7.1 = -4.1
What dose Z =
Answer:
4.1
Step-by-step explanation:
madookoo doo doo
7x(92+7) = (7x92)+(7x_)
Answer:
34
Step-by-step explanation:
hutbjj jugo uva bombom
For each set of values, determine which is greater without using a calculator. √10 or √2 + √3
√10 is greater than √2 + √3 .
First we assume that √10 is greater than √2 + √3. Then we check if this relation is true.
So suppose that √10 > √2 + √3
On squaring both sides and using the algebraic identity [tex](a+b)^2=a^2+b^2+2ab[/tex],
⇒ 10 > 2 + 3 + 2√6
⇒ 10 > 5 + 2√6
Subtracting 5 from both sides, we get,
⇒ 5 > 2√6
Again squaring on both sides,
⇒ 25 > 4 x 6
⇒ 25 > 24
This is a true relation. So our assumption that √10 is greater than √2 + √3 was right.
Therefore, √10 > √2 + √3
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Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning.
Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.
The diagonals of quadrilateral PQRS bisect each other
No valid conclusion drawn from the statements.
You can "detach" the hypothesis from the conclusion using the law of detachment. More specifically, if p and p -q are known to be true, we can infer that q is true. On the other hand, we can cram conditional statements together using the law of syllogism. When p-q and q-r are known to be true, they can be combined to form p-r. After all, it would be silly-gism to go through q when we can just go from p to r.
P = quadrilateral has diagonals
Q = quadrilateral diagonals bisect each other
R= the quadrilateral is a parallelogram
Statement P is true because all quadrilaterals have 2 diagonals that runs from one edge to another eg square, rectangle, parallelogram, kite etc
Statement Q is False because not all quadrilateral's diagonals bisect each other as in the case of trapezium, likewise quadrilateral whose diagonals bisects each other are not only parallelogram, kite, square and rectangle diagonals bisect each other.
Statement R is False because a quadrilateral whose diagonals bisect each other is not only parallelogram. Square, rectangle and Kite diagonals also bisect each other, and they are also parallelogram.
Therefore, no valid conclusion made from the statements because parallelogram is not the only quadrilateral whose diagonals bisect each other and not all quadrilateral's diagonals bisect each other.
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What quartic polynomial equation has roots 2-3 i, 8,2 ?
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
Given,
Zeros are: x = 2, x = -3, x = 8, and x = 2
That is: x + 2 = 0, x - 3 = 0, x + 8 = 0, and x + 2 = 0
So the factors are: (x + 2) (x - 3) (x + 8) (x + 2) = 0
Multiply two at a time:
(x + 2)(x - 3) = x² - x - 6
(x + 8)(x + 2) = x² + 10x + 16
Now multiply those polynomials together using distributive method:
x² (x² + 10x + 16) - x(x² + 10x + 16) - 6(x² + 10x + 16)
= x⁴ + 10x³ + 16x² + x³ + 10x² + 16x - 6x² - 60x - 96
= x⁴ + 11x³ + 20x² - 44x - 96
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
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A polygon is shown on the graph:
Type A Correct answer or i will report brainliest will be given
.
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. (5 points)
The translation of the polygon 3 units down and 4 units left is;
A''(-2, -4)
B"(-3, -7)
C"(-1, -8)
D"(1, -6)
What is the transformation of the object?We are given the coordinates of the polygon as;
A(2, -1), B(1, -4), C(3, -5), D(5, -3)
Now, we are told that all points are translated 3 units down and 4 units left. Thus, the new coordinates are;
A'(2, -1 - 3) = A'(2, -4)
B(1, -4 - 3) = B'(1, -7)
C(3, -5 - 3) = C'(3, -8)
D(5 , -3 - 3) = D'(5, -6)
Translation of 4 units left is now;
A''(2 - 4, -4) = A''(-2, -4)
B"(1 - 4, -7) = B"(-3, -7)
C"(3 - 4, -8) = C"(-1, -8)
D"(5 - 4, -6) = D"(1, -6)
The translation of the polygon 3 units down and 4 units left is;
A''(-2, -4)
B"(-3, -7)
C"(-1, -8)
D"(1, -6)
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14. The nth term of a quadratic sequence is n²+ 3n-2
(a) Find the fourth term of this sequence.
Here are the first five terms of a different quadratic sequence.
1, 7, 17, 31, 49
(b) Find, in terms of n, an expression for the nth term of this sequence.
Step-by-step explanation:
14a)
the 4th term = 4² + 3×4 - 2 = 16 + 12 - 2 = 26
b)
1, 7, 17, 31, 49
s1 = 1
s2 = s1 + 6
s3 = s2 + 10
s4 = s3 + 14
s5 = s4 + 18
the added term d grows with every step by 4. starting with a constant "+ 2" on top of -1 to create s1.
d1 = 2
d2 = d1 + 4
d3 = d2 + 4
dn = dn-1 + 4 = d1 + 4(n-1)
s1 = -1 + d1
s2 = s1 + d2 = -1 + d1 + d1 + 4
s3 = s2 + d3 = -1 + d1 + d1 + 4 + d1 + 4 + 4
s4 = s3 + d4 = -1 + d1 + d1 + 4 + d1 + 4 + 4 + d1 + 4 + 4 + 4
sn = -1 + n×d1 + sum(4(n - 1)) = -1 + 2n + 4n(n - 1)/2 =
= -1 + 2n + 2n(n - 1) = -1 + 2n(1 + n - 1) = -1 + 2n² =
= 2n² - 1
Using the graph below which of the following is a gas
A: NaCI
B: KCI
C: NaNO3
D: Ce2(SO4)3
Using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
What is a gas?A gas is a state of matter with no fixed shape or volume.
What is solubility?Solubility of a substance is the amount of solute that can dissolve in unit volume of solvent at a given temperature.
Which of the following compounds is a gas?Note that the solubility of a substance depends on the temperature
For gases, the solubility decreses with incresing temperatureFor liquids, temperature has no effect on solubility and For solids, the solubility increases with temperature if the reaction is endothermixc and dedreases with temperature if the reaction is exothermic.From the graph above, we see that the compound with the least solubility is Ce₂(SO₄)₃. Since the solubility of gases derease with increasing temperature, thus Ce₂(SO₄)₃ is a gas
So, using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
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Which point is located at (5,-2)?
-7-8-54
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point A
point B
point C
point D
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8
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4
3-
2-
4
7 7 3 7 8 9
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Mark this and return
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Based on the attached graph, the point that is located at (5,-2) is point F
How to determine which point is located at (5,-2)?The graph that completes the question is added as an attachment
The point located at (5,-2) implies that the coordinates of the point are
x-coordinate = 5
y-coordinate = -2
From the attached graph, we can see that the point F has the following properties
x-coordinate = 5
y-coordinate = -2
This means that the point F is located at (5,-2)
Hence, the point that is located at (5,-2) is point F
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What is each expression written as a single logarithm?
b. 2 log₄6- log₄9
The single logarithm for the given expression (2 log₄6 - log₄9) is 1.
The given logarithmic expression is 2 log₄6 - log₄9.
Use the ability rule of the logarithm logₐ(Xⁿ) = n logₐ(X), to get 2
log₄6 - log₄9= log₄6² - log₄9
= log₄36 - log₄9 (Since 6² = 36)
Use the quotient rule of the logarithm logₐ(X/Y) = logₐ(X) - logₐ(Y), to get:
log₄36 - log₄9= log₄(36/9) = log₄(4)
(Dividing 36 by 9, to get, 36 ÷ 9 = 4)
= 1 (Since logₐ(a) = 1)
Therefore, the one logarithm for the given logarithmic expression (2 log₄6 - log₄9) is 1
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Two objects are similar if they have.
the same shape. a)different shapes. b)the same shape and size. c)different shapes and sizes.
Answer: Pretty sure its B. The same shape and size.
Step-by-step explanation:
Multiply and simplify. ∛9 . ∛9
Radical expression containing third root terms will be first multiplied and then simplified to its simplest form.
A radical expression is a mathematical expression containing a radical symbol (√). A radical expression contains three distinct parts:
1. A radical symbol which is the square root sign.
2. A radicand which is a component inside the radical,
3. A degree which is the root represented by the radical.
In the given expression, the radicand is 9 while the degree is 3.
As the degree is the same for both the terms, we can multiply the radicand.
Multiplying the radicand terms,
∛(9*9)=∛81
Simplifying the radicand,
∛(3*3*3*3)
Taking the cube root and simplifying,
3∛3
Hence, ∛9.∛9 = 3∛3
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2. Denesha is thinking of a number that is divisible by both 9 and 7. What is the smallest number Denesha could be thinking of?
Answer:
63
Step-by-step explanation:
Numbers divisible by 9:
18, 27, 36, 45, 63, 72, 81, 90 and 99.
Numbers divisible by 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.
Least common multiple=63
The range of f(x) = |x| is y ≥ 0. If a < 0 for g(x) = a|x|, what is the range of function g?
the range of the function g(x) will be y ≤ 0.
What is the range of g(x)?We know that the absolute value function g(x) can be written as:
g(x) = a*|x|
Remember that the range of f(x) = |x| is y > 0, and a is a negative number, so the function is reflected over the horizontal axis.
Then the maximum value will be when x = 0, then:
g(0) = a*|0| = 0, that is the maximum.
And then the function opens downwards. Then the range will be y ≤ 0.
So the range of the absolute value function g(x) is the set of all real values equal to or smaller than zero.
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Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
Answer: |81 - (-29)|==> C
Step-by-step explanation:
h=high temperature
h=81
l=low temperature
l=-29
d=difference in high and low temperature
h-l=d
81-(-29)=d
81+29=d
d=110 ==> |81 - (-29)|=|81 +29|=|110|=110
|81 - (-29)|==> C
|81 -29|=|52|=52
-29 + 81=81-29=52
12. is the set of real numbers closed under addition? explain why or why not. if it is not closed, give an example
Yes , the set of real numbers closed under addition because on adding them we get a new number .
A set is closed (under associate operation) if and on condition that the operation on any 2 components of the set produces another part of a similar set.If the operation produces even one part outside of the set, the operation isn't closed.
The set of real numbers is closed below addition. If you add 2 real numbers, you'll get another complex quantity. there's no chance of ever obtaining something apart from another complex quantity.
5 + 12 = 17
2.5 + 3.4 = 5.9
As , we get another quantity on adding real number , hence it is closed under addition.
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If the liquid continues to cool at the same rate , what will the temperature be at 3pm pls i need this answer
The temperature of the liquid at 3PM will be -7.5 °C
The initial temperature of the liquid at 9 AM = 0°C
Given that the temperature changes by -5/4 °C each hour.
That is the rate of change of temperature = -5/4 °C
We have to find the temperature of the liquid at 3 PM.
Let x denote the number of hours.
Then the temperature after x hours, t = 0 + ( -5/4)x = -(5/4)x is the linear equation modelling this set up.
So from 9 AM to 3PM, the number of hours = 6 hours
Put x = 6 .
Then, t = (-5/4) x 6
= -7.5
Therefore, the temperature of the liquid at 3 PM = -7.5°C
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SOMEONE TELL ME IF IM CORRECT AND TELL ME HOW MUCH TO COLOR IN!!!!
Answer:
Seems correct. I would never use pen for a math assignment though ;-;
Here’s the answer sheet lol.
Step-by-step explanation:
A cube has a side length of 3x^6 units. a smaller cube has a side length of x^2. how many smaller cubes will fit in the larger cube
[tex]27x^{12}[/tex] smaller cubes will fit in the larger cube.
Given,
Side length of the smaller cube = [tex]x^{2}[/tex] units.
Side length of the larger cube = [tex]3x^{6}[/tex] units.
We have to find the number of smaller cubes that can be fitted in the larger cube.
Volume of cube is given by the formula,
Volume = (side)³
Volume of the larger cube = [tex](3x^{6} )^{3}[/tex] = [tex]27x^{18}[/tex]units³
Volume of the smaller cube = [tex](x^{2} )^{3}[/tex] = [tex]x^{6}[/tex] units³
Let the number of smaller cube that can be fitted in the larger cube = n
Volume of n cubes = [tex]nx^{6}[/tex] units³
If space inside the larger cube will be occupied by 'n' smaller cubes,
volume of n smaller cubes = Volume of a larger cube
[tex]nx^{6}[/tex] = [tex]27x^{18}[/tex]
n = [tex]27x^{12}[/tex]
Therefore, [tex]27x^{12}[/tex] smaller cubes can be fitted in the larger cube.
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I don't understand this question
The probabilities of all possible outcomes must sum to 1. So the missing probability is
1 - 1/2 - 3/10 - 1/20 = (20 - 10 - 6 - 1)/20 = 3/20
The formula F(C) = 9/5C + 32 calculates the temperature in degrees Fahrenheit, given a temperature in degrees Celsius.
You can find an equation for the temperature in degrees Celsius for a given temperature in degrees Fahrenheit by finding the function’s
The function C(F) to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit will be equal to [tex][(\frac{5}{9}F) -\frac{160}{9}][/tex]
As per the question statement, the formula [F(C) = 9/5C + 32] is to calculate the temperature in degrees Fahrenheit for a given a temperature in degrees Celsius.
We are required to determine the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit.
Since, [F(C) = 9/5C + 32],
[tex]or, [F = \frac{9}{5} C + 32]\\or, (F-32)= \frac{9}{5} C\\or, \frac{9}{5} C=(F-32)\\or,C=\frac{5}{9} (F-32)\\or,C=\frac{5}{9}F-\frac{160}{9}[/tex]
That is, the function to calculate the temperature in degrees Celsius for a given temperature in degrees Fahrenheit is [tex]C(F)=[(\frac{5}{9}F) -\frac{160}{9}][/tex].
Function: In Mathematics, a function is an operator, which when fed with a input, will perform a specific set of operations on the input and then produce a certain output.To learn more about Functions, click on the link below.
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Answer:
inverse
C(F)=5/9F-106/9
check all
Step-by-step explanation:
23
Write each logarithmic expression as a single logarithm. 3 log a-2 log b
The logarithmic expression as a single logarithm is log. a³/b²
What is defines as the logarithmic functions?A logarithmic and even sometimes log function is the inverse of an exponential function. We could employ a log function to find an exponent.
We should be able to transform between logarithmic as well as exponential forms in order to calculate earthquake magnitudes and otherwise correlate the magnitudes of two distinct earthquakes.
Let's use this information to make our log. Here is the logarithmic function:
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as for the represented expression;
= 3 log a-2 log b
Using the power rule in both of the terms.
= log a³- log b²
Now, applying the Quotient Rule,
= log a³/b²
Therefore, the obtained single logarithm for the given logarithmic expression is log a³/b².
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5/7x + 1/7 = 3
please simplify!!
Answer:
x=4 that is it i believe and bc i did it
Use the proportion d / 180° = r radians/πradians . Find the equivalent degree measure or radian measure 415°
Answer:
the answer is the 235⁰ ok that
Factory workers can make 18 items in 15 hours. How many hours will it take
to make 12 items at this rate?
Answer:
10 hours
Step-by-step explanation:
Unit rate 18 items / 15 hrs = 1.2 items pe hour
12 items / 1.2 items / hour = 10 hours
The postal service charges $2 to ship packages up to 5 ounces in weight, and $0.20 for each additional ounce up to 20 ounces. After that, they charge $0.15 for each additional ounce.
Using it's concept, the domain of the relation is given as follows:
x ≥ 0.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.From the graph, we have that the weights of the packages assume all values to the right of 0, hence the domain of the relation is given as follows:
x ≥ 0.
What is the missing information?The relation is incomplete, and is given by the graph at the end of the answer.
The question asked is the domain of the relation.
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Use the graph to answer the following question.
The figure shown was transformed from Quadrant II to Quadrant IV .
Which of the following BEST represents this transformation?
reflection over the x-axis followed by a dilation of scale factor 2
rotation 90° clockwise followed by a reflection over the y-axis
reflection over the y-axis followed by a translation down 6 units
reflection over the x-axis followed by a translation right 5 units
The transformation is rotation 90° clockwise followed by a reflection over the y-axis
How to use the graph to answer the question?The question is given as
Which of the following BEST represents this transformation?
From the question, we have the figure shown to be
A transformation of a figure from Quadrant II to Quadrant IV
From the figure, we can see that the shapes in both quadrants have the same dimensions
This means that the shapes are not dilated
However, the orientation of the figures are difference
Because of the positioning of the shapes, we can conclude that the transformaton is rotation 90° clockwise followed by a reflection over the y-axis
Hence, the transformation is rotation 90° clockwise followed by a reflection over the y-axis
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(6x2-6x+4)-(x2-5x-9)
Find the total cost of 901 computers that cost $508 each.
6. application jeremy has a job at the movie theater.
his hourly wage is $7.38. suppose 15% of his income
is withheld for taxes and social security
a. what percent does jeremy get to keep?
b. what is his hourly take home wage?
a) Jeremy get to keep 85%
b) $6.273 is Jeremy's hourly take home wage.
Given,
Jeremy has a job at the movie theatre.
Hourly wage of Jeremy = $7.38
The % of income withheld for taxes and social security = 15%
7.38 × (15/100) = 1.107
That is, $1.107 from Jeremy's income is withheld for taxes and social security.
a) Percentage of income Jeremy get to keep:
= 100% - Withheld percentage
= 100 - 15
= 85
So, Jeremy gets 85% of his income to keep with him.
b) Jeremy's hourly take home wage:
Total income - Withheld amount
7.38 - 1.107 = 6.273
That is, Jeremy's hourly take home wage is $6.273.
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