Sam says that 2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten as 2/21 to the power of 7 sarah says it can be rewritten as 2/21 to the power of 10 steve says it cannot be rewritten as either of these expressions who is correct explain
If Sam says that 2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten as 2/21 to the power of 7 Sarah says it can be rewritten as 2/21 to the power of 10 Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.
Expression2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten or express as [(2/7²)× (1/3^5)].
This implies that both Sam and Sarah are wrong, Only Steve is correct because 2/7 to the power of 2 times 1/3 to the power of 5 can either of the two expression that was mentioned by Sam and Sarah.
Therefore if Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.
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Expand each logarithm.
logb √x√3 /y² √6z²
After expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa.
The basic form of the logarithm function can be written as .
[tex]log_ax =N[/tex]
where, a is the base of function or equation
x define expression
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log_c (a) +log_c (b) = log (a b)log a/b = log a - log blog a^x = x log alog a^a = 1The given expression can be written as,
[tex]log_b\frac{\sqrt{x} \sqrt{3} }{y^2 \sqrt{6z^2} } \\\\= log_b \sqrt{x} \sqrt{3} - log_b {y^2 \sqrt{6z^2} }\\\\= log_b\sqrt{x} + log_b\sqrt{3} - log_by^2 - log_b \sqrt{6z^2} \\\\= \frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - \frac{1}{2} log_b{(6z^2)} \\\\=\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]
Thus, after expanding logarithm is [tex]\frac{1}{2} log_bx + \frac{1}{2} log_b3 - 2log_b(y) - log_b{(\sqrt{6}z )}[/tex]
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8.
Calculate the midpoint of the line segment
formed with the endpoints shown.
Show your work.
(2, 4) and (5, -1)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +2}{2}~~~ ,~~~ \cfrac{ -1 +4}{2} \right) \implies \left(\cfrac{ 7 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies \left(3\frac{1}{2}~~,~~1\frac{1}{2} \right)[/tex]
2. What is the VOLUME of the rectangular prism? Consider the rectangle on the top/bottom as the base.
I need Area of Base
height and
Volume
Area of base = 52
height = 5
Volume = 260
To find the volume of a rectangular prism all you need to do is multiply the length * width * height.
the area of base is the length * width = 13 * 4 = 52
then you multiply that by the height = 52 * 5 = 260
Which expression is NOT equivalent to 6√81x⁴y⁸ ?
(f) (3 x y²)²/₃ (g) (3 x)²/₃ y⁴/₃ (h) (3 x²y²)¹/₃ (i) ∛9 x² y⁴
None of the given option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex].
What are square and square roots?squares are the products of numbers which comes out when the no. is multiplied by itself twice .
and square root helps to find the no. which is multiplied twice to get that no. inside the root.
CALCULATION6 [tex]\sqrt81x^{4}y^{8}[/tex]
= 6 * 9 [tex]x^{2} y^{4}[/tex]
= 54 [tex]x^{2} y^{4}[/tex]
Since from the given option none of the option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex]
because you can see that all of the option are given in cube roots but the question is in square root .
so , there are two possibilities that maybe the question is typed wrong or the options are incorrect . But if everything present in the question is correct then none of the given values are equivalent to the given expression.
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Can someone answer this plssss
Answer:
It is Perpendicular
Simplify each expression.
49¹/₂
The question is testing on indices. Write 49 in its prime factors. By power rule (a^m)^(1/n)=a^(m/n). By factors, 49 = 7×7
49^(1/2)
(7^2)^(1/2) = 7^(2×1/2) = 7
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Example 1:
If f(x) = 3x-4, find each value. Show all work.
a) ƒ(4)
b) f(-5)
c) f(2-x)
Answer: f(4) = 8, f(-5) = -19, f(2-x) = -3x+2
Step-by-step explanation:
Let's start by analyzing what we are given:
f(x)=3x-4
In this equation, f is the name of the function.
The number in the parentheses represents x.
The 3x-4 tells us what the equation does. In this instance, we multiply x by 3 and then subtract 4.
Let's start with (a).
f(4)
Since we have established that the number in the parentheses is x, we can plug 4 in for x into the equation f. We must abide by the order of operations. Therefore, we can obtain the following:
f(4) = 3(4) -4
f(4) = 12 -4
f(4) = 8
We can continue this for part (b).
f(-5) = 3(-5) -4
f(-5) = -15-4
f(-5) = -19
Part (c) is slightly different, but applies the same principles we established previously. On this part, we must recall the distributive property. The 3 multiples the 2 and the x. We must also remember to combine like terms.
f(2-x) = 3(2-x) -4
f(2-x) = 6 - 3x -4
f(2-x) = -3x +2
If f(1)=1 and f(n)=f(n-1)-1 then find the value of 4
The scatter plot and a line of best fit show the relationship between the hours spent sleeping and the hours spent watching TV.
Which statement describes the relationship between the hours spent sleeping and the hours spent watching TV?
For every hour spent watching television, the amount of time spent sleeping drops by an Graph hour.
Graph: A graph is a visual representation, such as a picture or diagram, that shows information or values in a structured way.
The relationships between two or more items are frequently represented by the points on a graph.
Various Graph Types
Pictograph
The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects.
Line Graph:
In a line graph, dots are connected by lines to depict changes over time.
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Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
y = 2.2x
y = 3x
y = 1.4x
y= 1/2x
The equations which could represent Relationship B which has a greater rate than Relationship A as described in the task content are; y = 2.2x and y = 3x.
Which equations could represent Relationship B?It follows from the task content that the equation which could represent Relationship B given that it has a greater rate than Relationship A be determined.
It can be evaluated from the graph given that the slope of relationship A which is a measure of it's rate is;
Slope, m = (y2 - y1)/(x2 - x1)
m = (8 -4)/(4-2)
m = 4/2
m = 2.
Ultimately, since the rate of Relationship A is 2, and the rate of Relationship B has to be greater, it follows that the equations which are required are;
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Find the height and area of the base of a rectangular pyramid with a volume of 70 cubic centimeters, length of 7 centimeters, and width of 6 centimeters
The height of the rectangular pyramid will be 5 centimeters.
What is volume?The volume of any solid body is defined as the space covered by the object in the three-dimensional space. For a rectangular pyramid, the volume will be the space covered by a pyramid in a three-dimensional space.
Given that the volume of 70 cubic centimeters, length of 7 centimeters, and width of 6 centimeters.
The height of the rectangular pyramid is calculated by using the formula:-
V = ( l w h ) / 3
70 = ( 7 x 6 x h ) / 3
h = 70 / 14
h = 5
Therefore, the height of the rectangular pyramid will be 5 centimeters.
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If your original network address with prefix is 172.16.0.0/16, what should your new network address with prefix be if you need 16 subnets?
172.16.0.0/20 is the required network address with a prefix if you need 16 subnets.
Given that,
If you require 16 subnets, your new network address with a prefix should be something different from the old one, which is 172.16.0.0/16. To determine the prefix corresponding to the 16 subnets.
Here,
Original network address with a prefix = 172.16.0.0/16,
After 16 subnets the address would become,
New network address with the prefix with 16 subnets = 172.16.0.0/20.
172.16.0.0/20 is the required new address with prefix be if you need 16 subnets.
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Pre-Calc: Find all the zeros of the function.
The zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i and the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the zeros of the polynomial?The polynomial equation is given as
f(y) = 625y^4 - 256
Express the terms as an exponent of 4
So, we have
f(y) = (5y)^4 - 4^4
Express the terms as an exponent of 2
So, we have
f(y) = (25y^2)^2 - 16^2
Apply the difference of two squares
So, we have
f(y) = (25y^2 - 16)(25y^2 + 16)
Apply the difference of two squares
So, we have
f(y) = (5y - 4)(5y + 4)(25y^2 + 16)
Set the equation to 0
So, we have
(5y - 4)(5y + 4)(25y^2 + 16) = 0
Expand the equation
So, we have
5y - 4 = 0, 5y + 4 = 0 and 25y^2 + 16 = 0
This gives
5y = 4, 5y = -4 and 25y^2 = -16
Solve the factors of the equation
So, we have
y = 4/5, y = -4/5 and y = ±4/5√i
Hence, the zeros of the polynomial function are y = 4/5, y = -4/5 and y = ±4/5√i
How to write the polynomial as a product of the linear factors?
In (a), we have
The polynomial equation is given as
f(y) = 625y^4 - 256
Express the terms as an exponent of 4
So, we have
f(y) = (5y)^4 - 4^4
Express the terms as an exponent of 2
So, we have
f(y) = (25y^2)^2 - 16^2
Apply the difference of two squares
So, we have
f(y) = (25y^2 - 16)(25y^2 + 16)
Apply the difference of two squares
So, we have
f(y) = (5y - 4)(5y + 4)(25y^2 + 16)
Hence, the polynomial as a product of the linear factors is f(y) = (5y - 4)(5y + 4)(25y^2 + 16)
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PLEASE HELPPP MEEEEEEEEE
The value of the variable x and y are 12 and 31 respectively.
How to find the value of a variable?Line a and b are parallel lines.
These parallel lines are cut by a transversal.
The traversal forms angle relationship as follows:
5x - 7 = 3x + 17 (alternate angles)
The variable x and y can be found as follows
5x - 7 = 3x + 17
5x - 3x = 17 + 7
2x = 24
x = 24 / 2
x = 12
Therefore,
4y + 3 + 3x + 17 = 180
4y + 3 + 3(12) + 17 = 180
4y + 3 + 36 + 17 = 180
4y = 124
y = 124 / 4
y = 31
Therefore, the value of the variable x and y are 12 and 31 respectively.
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Joseph removes 5/8 gallons of white paint from a can. Then he adds 5/8 gallons of blue paint to the can.
Write and then evaluate a subtraction expression to find the overall increase or decrease in the amount of paint in the can.
Answer: Change = - 2.8 gallons
Step-by-step explanation:
Let X be the starting amount of paint in the can, in gallons.
"Removes 5/8 gallon" can be written -(5/8)gal
"Adds 3/8 gallon" becomes +(3/8)gal
The result is : X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)
Consolidating: Remaining (gallons) = X - (2/8)gal
If we want the overall increase/decrease, subtract the initial volume:
Initial - Remaining = Change in amount of paint in can
Change = (X-(2/8)gal) - X = - (2/8) gallons
if chips cost 2.00 for 5 bags how much will it cost for 308 people
Answer:
$123.20
Step-by-step explanation:
Hey there!
To find the price for 308 bags of chips FOR 308 people, we need to first know what the price for 1 bag is
It says that it is 2 dollars for 5 bags
Now, we need to divide 2 by 5 to see how much money 1 bag is
2/5 is 0.4 and in this case 0.40 since we're dealing with money
Now that we know this, all we need to do is multiply 0.40 by 308 because we are buying for 308 people
0.40 x 308 is 123.2
This means that for 308 people, it would cost $123.20 to supply them all with a bag of chips!
7+(8-3*2) what would be the answer for 50-[20+{50-40}]
Answer:
So the answer would be 20 for 50-[20+[50-40]]
Step-by-step explanation:
50 - 40 =10 and 20 +10 = 30 so we 50 minus 30 which is 20
If its the other one it is 9 because 3 times 2 is 6 and 8 minus 6 is 2 and 7 plus 2 equals 9
Write each expression as a single logarithm.
log 8-2 log 6+log 3
The expression as a single logarithm is log (2/3).
In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.
The general properties of logarithm for a fixed base are:
logₐa=1logₐx+logₐy=logₐxylogₐx-logₐy=logₐ(x/y)logₐxⁿ=n logₐxlogₓy=(logₐy)/(logₐx)Now from the above properties of logarithms we can calculate:
log 8-2 log 6+log 3
=log 8 + log 3 - 2log6
We know that logₐx+logₐy=logₐxy and logₐxⁿ=n logₐx
∴log(8×3) -log(6²)
=log 24 - log 36
Again we know that logₐx-logₐy=logₐ(x/y)
=log(24/36)
=log(2/3)
Therefore the given expression written as a single logarithm is log(2/3).
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A data set related to finding a job contains many variables. Some of the varia
job title, starting salary (in dollars), education required (number of years posts
experience, and location. Classify each variable as categorical or quantitative
column
Categorical variable: job titles, location
Quantitative variable: starting salary, number of years post-experience
Categorical variables represent many data kinds that can be grouped. Race, sex, age, and educational level are a few examples of categorical variables.
In addition, categorical variables are any variables where the data represent groups, as opposed to quantitative variables, which are any variables where the data indicate amounts, such as height, weight, or age.
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What is a Euler Equations?
Answer: a set of quasilinear partial differential equations governing adiabatic and inviscid flow.
Step-by-step explanation:
that the definition of a Euler Equation.
Su Young borrows $2,900 from the bank for a new deck and some outdoor patio furniture. The interest rate is 5.5% per year. How much simple interest will she pay if she takes 15 months to repay the loan? Round to the nearest cent.
The simple interest that Su Young paid for borrowing $2,900 for 15 months at 5.5% per year is $199.375.
What is simple interest?Simple interest is interest that is not compounded.
Compounding involves adding earned interests to the principal when computing the next period's interest.
Data and Calculations:Principal = $2,900
Period = 15 months or 1.25 years
Interest Rate = 5.5%
Simple interest amount = Principal x Period x Rate
= $199.375 ($2,900 x 1.25 x 5.5%)
Thus, based on simple interest, Su Young paid $199.375.
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SOMEONE PLEASE HELP MEEEEEE
The answer should be parallel to each other
step by step
from plotting the graph line AB is parallel to Line DF
Answer: AB and DF are parallel.
Step-by-step explanation:
A=(-2,-11)
B=(6,5)
D=(-7,-10)
F=(2,0)
Slope (AB)=5-(-11) =
6-(-2) =2
Slope (DF)=8-(-10)=
2-(-7) =2
Slope of AB=Slope of DF
AB and DF are parallel.
HELP ME WITH THIS QUESTION HURRY!!!!DUE IN A FEW MINS
LVL- 8th
Answer:
I think the length remains the same
Step-by-step explanation:
If your coefficient is a negative number, what would that indicate for a real life scenario?
the starting amount is positive
the initial quantity is decreasing
the starting amount is negative
the initial value is increasing
It should be noted that if your coefficient is a negative number, this indicates for a real life scenario that C. the starting amount is negative.
A negative coefficient means what?A negative coefficient indicates that the dependent variable tends to drop as the independent variable rises. The coefficient value is the amount that a one-unit change in the independent variable affects the mean of the dependent variable while keeping all other model variables constant.
If the correlation coefficient is negative, the two parameters you evaluated may have an inverse relationship.
Therefore, it should be noted that if your coefficient is a negative number, this indicates for a real life scenario that the starting amount is negative
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A company stock was selling at 28$ a share. A month later, it was selling at 21$ a share what is the percentage loss
The percentage loss is 25 %.
Percent change is the difference between subtracting the old value from the new value, dividing by the old value, and multiplying the final result by 100, expressed as a percentage. Generally, to convert a fraction to a percentage, multiply by 100. Similarly, the fraction (ratio) of the amount difference from the initial value is multiplied by 100 to get the percentage change. The formula for the percentage change is defined as the ratio of the difference of final value and initial value to the initial value. The formula of percentage change is mathematically expressed as [tex]Percentage=\frac{Final - Initial}{Initial} \times100\\[/tex] ..(1)It is given that initial value of company stock is $28 and final value is $21 . Put these values in equation (1) , we get
[tex]Percentage=\frac{21 - 28}{28} \times100\\\\Percentage=\frac{-7}{28} \times100\\\\Percentage=-25 \%[/tex]
Negative sign indicates loss in the percentage.
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Due today! Help, please! Will give brainly! 25 pts
The measures of the angles are
TLN = 51, NLM = 129 and MZQ = 129JZQ = TLN = 99LMO= ZMR = 34 and LMR = y = 166How to determine the measures of the angles?1. Angle TLN, MZQ and NLM
The angles TLN and NLM are supplementary angles
So, we have
TLN + NLM = 180
This gives
3x - 18 + y = 180
Also, we have
TLN + MZQ = 180
So, we have
3x - 18 + 5x + 14 = 180
Evaluate the like terms
8x -4 = 180
This gives
8x = 184
Divide
x = 23
Substitute x = 23 in 3x - 18 + y = 180
3 x 23 - 18 + y = 180
Evaluate
51 + y = 180
So, we have
y = 129
The above computations imply that:
TLN = 3 x 23- 18 = 51
NLM = y = 129
MZQ = 5 x 23 + 14 = 129
2. Angle JZQ and TLN
The above means that
JZQ = TLN
So, we have
9x + 9 = 8x + 19
Evaluate
x = 10
So, we have
JZQ = TLN = 9 * 10 + 9
JZQ = TLN = 99
3. Angle ZMR, LMO and LMR
The angles ZMR and LMO are congruent angles
So, we have
ZMR = LMO
This gives
x + 14 = 2x - 6
Evaluate
x = 20
Also, we have
LMR + LMO = 180
So, we have
y + 2x - 6 = 180
y + 2 x 10 - 6 = 180
y + 14 = 180
So, we have
y = 166
The above computations imply that:
LMO= ZMR = 20 + 14 = 34
LMR = y = 166
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Greatest perfect square number between 250 and 300
Answer:
69
Step-by-step explanation:
Describe the difference between an equation and an expression. Give an example!
The primary difference between expression and equation has an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.
What is Expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases.
The primary difference between expression and equation is an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.
For example
ax2+by+c is an expression.
4x+3y+8=5 is an equation.
Therefore expression and equation both are different.
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What is the answer for this question?
The radical expression ∛24 is between integers 2 and 3
How to determine the two integers?The expression is given as
∛24
The above expression is a radical expression .
So, we have:
Express 24 as the product of 8 and 3
So, we have
∛24 = ∛(8 * 3)
Take the cube root of 8
So, we have
∛24 = 2∛3
Take the cube root of 3
So, we have
∛24 = 2 * 1.44
Evaluate the product
∛24 = 2.88
2.88 is between integers 2 and 3
Hence, the radical expression ∛24 is between integers 2 and 3
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