Justify [tex] \sqrt[3]{8} \times \sqrt[3]{8} = 16[/tex]using the properties of exponents in at least two different ways.
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EXPLANATION
Given the cubic root:
[tex]\sqrt[3]{8}\cdot\sqrt[3]{8}[/tex]Rewriting 8 as 2^3:
[tex]=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}[/tex]Applying the property of roots:
[tex]\sqrt[3]{a^3}=a[/tex][tex]=2\cdot2=4[/tex][tex]\sqrt[3]{8}\cdot\sqrt[3]{8}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]Related Questions
If z=13 which equation is true?
A) 3z + 16 = 55
B) 2(23 + z) = 70
C) 3( 18 + z) = 85
D) 2z - 5 = 20
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Select all the ratios equivalent to 8:6.A. 4:3B. 6:8C. 16:12D. 10:8E. 7:5
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Dividing the given ratio by 2, we get
8:6 = 8/2 : 6/2 = 4:3
Multiplying the given ratio by 2, we get
8:6 = 8*2 : 6*2 = 16:12
Then, the correct choices are A and C
0.08 is 30%?TrueFalse
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A number can be expressed in percent form or in decimal form.
For example, 0.3
a frame is 9 inch wide and 6 inch tall. if it is reduced to a width of 3 inch the how tall will it be?
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The height of the frame will remain the same.
The height of the frame is 6 inch
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
A frame:
The frame can be considered as a rectangle.
Wide = 9 inch
Height = 6 inch
_______
| |
| | 6-inch (height)
| |
|_______|
9-inch (wide)
If wide = 3 inches the height remains the same.
Thus,
The height of the frame will remain the same.
The height of the frame is 6 inch
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Circle describe and correct each error.X-int = (0,-2)Y-int = (-4,0)
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First, we solve for y in the expression:
[tex]\begin{gathered} 4x+2y=-8\Rightarrow2y=-4x-8 \\ \\ \Rightarrow y=-2x-4 \end{gathered}[/tex]So, the y-intercept is (0, -4).
The error is that you are given the wrong y-intercept and the wrong x-intercept; they are swapped in the place of writting.
Match each graph with the correct equation from the equation bank not all equations will be used. (pls help) questions 6,7,8,10.
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The linear functions for each graph are given as follows:
6. y = -1/3x + 3.
7. y = 1/3x + 1.
8. y = x + 3.
10. y = -2x.
How to define linear functions?The definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, which is by how much y changes when x changes by 1.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis.For item 6, we have that:
The function crosses the y-axis at y = 3.When x increases by 3, y decays by 1, hence the slope is of -1/3.Then the equation is:
y = -1/3x + 3.
For item 7, we have that:
The function crosses the y-axis at y = 1.When x increases by 3, y increases by 1, hence the slope is of 1/3.Then the equation is:
y = 1/3x + 1.
For item 8, we have that:
The function crosses the y-axis at y = 3.When x increases by 1, y increases by 1, hence the slope is of 1Then the equation is:
y = x + 3.
For item 10, we have that:
The function crosses the y-axis at y = 0.When x increases by 1, y decreases by 2, hence the slope is of -2.Then the equation is:
y = -2x.
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Find the GCF and LCM for 24 & 30.
GCF-
LCM-
Answers
Answer:
The GCF of 24 & 30 would be 6. The LCM of 24 & 30 would be 120.
Step-by-step explanation:
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What is the measure of angle X to the nearest degree?
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Using a trigonometric relation we will see that the correct option is B, 24°.
What is the measure of angle X?On the image we can see a right triangle, where the length of the hypotenuse and of one leg (the opposite cathetus to angle X) are known.
We can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Then we can write:
sin(X) = 9/22
If we apply the inverse sine function in both sides, we will get:
X = Asin(9/22) = 24.15°
Then the correct option is B.
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Annie purchased a season pass for the new aquarium at a cost of $110. if she uses the pass 10 times this year , what is the unit rate in cost per visit?
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If she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
In the given question,
Annie purchased a season pass for the new aquarium at a cost of $110.
If she uses the pass 10 times this year then we have to find the unit rate in cost per visit.
We have to find the unit rate.
Unit rate means finding the value of one object, that means we have to find the cost of one visit.
The cost of season pass is $110.
She visit aquarium 10 times.
We find the unit rate cost per visit by dividing the total cost of season pass for the new aquarium by total times she visits in the new aquarium.
10 times = $110 cost
Divide by 10 on both side
10/10 times = $110/10 cost
1 times = $11 cost
Hence, if she uses the pass 10 times this year then the unit rate in cost per visit is $11 unit per visit.
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if the population standard deviation were 10 instead of 5, what effect would this new standard deviation have on margin of error?
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If the population standard deviation were 10 instead of 5,Margin of error would rise as a result. A broader width of the confidence interval and a larger margin of error would be the outcomes of a higher standard deviation.
Define margin of error.The margin of error (MOE) for a survey indicates how closely the survey results should be compared to the actual population value. For instance, a poll with a 3% margin of error shows that 72% of respondents prefer Brand A over Brand B.
Given,
If the population standard deviation were 10 instead of 5,
Margin of error would rise as a result. A broader width of the confidence interval and a larger margin of error would be the outcomes of a higher standard deviation. The margin of error diminishes as sample size grows, to be precise. The margin of error rises as population variability does as well. The margin of error grows as the confidence level does.
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Find the slope of a line that is a) parallel and b) perpendicular to the given line.– 3x – 4y = 1
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The line is:
[tex]-3x-4y=1[/tex]Which is equivalent to:
[tex]\begin{gathered} \Rightarrow4y=-3x-1 \\ \Rightarrow y=-\frac{3x}{4}-\frac{1}{4} \end{gathered}[/tex]Thus, the slope of the line is equal to -3/4
a) Every line parallel to that one has the same slope, then the answer is -3/4
b) On the other hand, if m_1 and m_2 are the slopes of two perpendicular lines, then:
[tex]m_1\cdot m_2=-1[/tex]Therefore, since the slope of our line is equal to -3/4, the slope of any line perpendicular to that one is:
[tex]\begin{gathered} m_1\cdot(-\frac{3}{4})=-1 \\ \Rightarrow m_1=\frac{4}{3} \end{gathered}[/tex]Hence, the answer is 4/3
5.
Write the equation for this line
Answers
Answer:
y = 3x - 6 is the correct equation. The slope is 3, and the y-intercept is at -6.
Students in mrs smiths class must complete at least 40 math problems for homework every week. the table shows the progress of four students on Wednesday. Which list shows the names of students in order from the greatest amount of homework complete to the least amount of homework completed? A Katie, Jonah, D’Angelo. Grace B D’Angelo, grace, Jonah, Katie C Katie, Jonah, grace, D’Angelo D Jonah, Katie, D’Angelo, grace
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Answer: the anwser is B
Step-by-step explanation:
Answer:
Grace, jonah,D'angelo,then Katie.
First,Grace because she finished it 100%
Next,it's Jonah because he finished it 2/3 the way meaning about around 70% of the work.
Then, D'angelo because he completed five more than Katie.
Last,Katie because she was less than jonah.She had 40 but D'angelo had five more than her
F(2-k)=8-5(2-k) evaluating functions
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Answer:
f = 5k−2/−k+2
200,000 divided by 2,800
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8373+01274+93738939x937x058+938484
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94We need to solve the next operation.
We need to take into consideration the rules of operations:
1. Parentheses
2. Exponents
3. Multiplication
4. Divison
5. Addition
6. Subtraction
Then, solve the given expression:
8373+01274+93738939*937*058+938484
Solve the multiplication 93738939*937*058
[tex]\begin{gathered} 93738939 \\ x\text{ }937 \\ ------------ \\ =87833385843 \\ \end{gathered}[/tex][tex]\begin{gathered} 87833385843 \\ x\text{ }058\text{ } \\ ------------ \\ =5094336378894 \end{gathered}[/tex]Now, make the next sum 8373+01274+ +938484:
[tex]\begin{gathered} 938484 \\ 001274 \\ 008373 \\ ------------ \\ 948131 \end{gathered}[/tex]Finally, make the next sum operation:
[tex]\begin{gathered} 5094336378894 \\ 0000000948131 \\ ------------- \\ 5094337327025 \end{gathered}[/tex]Hence, the result of the operation is 5094337327025.
Which of the following equations is equivalent to 4x + 2y = 12? A. 2y = -4x + 12 B. y=-2x + 6 C. y = 2X - 6 D. y = 8x + 24
Answers
Let's find the equivalent equation to:
4x + 2y = 12
2y = 12 - 4x
Dividng by 2 at both sides:
2y/2 = 12/2 - 4x/2
y = 6 - 2x
We can see that choices B and C are not correct because the signs.
If we multiply by 2 at both sides, we have:
2y = 12 - 4x
We can see that if we change the order at the right side of the equation, we have:
2y = -4x + 12
I think now you are ready to select the correct choice, Deppreso.
A rectangle has a length of 17 inches less than 7 times its width. If the area of the rectangle is 2204square inches, find the length of the rectangle.
Answers
SOLUTION
We are told that the length of the rectangle is 17 inches less than 7 times its width.
Now, let the letter L represent the length and the letter w represent the width of the rectangle.
This statement can be represented algebraically as
[tex]L=7w-17[/tex]So, Area =
[tex]\text{Area = L x w}[/tex]We are also told the Area A of the rectangle = 2204. Now
[tex]\begin{gathered} 2204=L\times w \\ \\ 2204=(7w-17)\times w \end{gathered}[/tex]We have to find the width, then we find the length L
[tex]\begin{gathered} 2204=(7w-17)\times w \\ 2204=7w^2-17w \\ 7w^2-17w-2204=0 \\ \\ \text{Solving the quadratic equation } \\ \\ w=19\text{ or w = -16.57} \end{gathered}[/tex]Since the width cannot be negative, w = 19 inches
The length becomes
[tex]\begin{gathered} L=7w-17 \\ L=7\times19-17 \\ L=133-17 \\ L=116\text{ inches } \end{gathered}[/tex]question 1A.) 4, 8, 12B.)6, 10, 26C.) 2, 6, 22D.) 1, 2, 6
Answers
Answer
Option C is correct.
a₁, a₂ and a₃ = 2, 6 and 22 respectively.
Explanation
We have been told that
a₀ = 1
And any term after that is given as
[tex]a_{i+1}=4a_i-2[/tex]So,
a₁ = 4a₀ - 2
a₁ = 4 (1) - 2
a₁ = 4 - 2
a₁ = 2
a₂ = 4a₁ - 2
a₂ = 4 (2) - 2
a₂ = 8 - 2
a₂ = 6
a₃ = 4a₂ - 2
a₃ = 4 (6) - 2
a₃ = 24 - 2
a₃ = 22
Hope this Helps!!!
For each shape in the table list three examples of real world objects that could be modeled by the shape use your experiences, the Internet, newspapers, magazines, or other resources to uncover examples1.) rectangular prism2.) triangular prism3.) cylinder4.) cone5.) pyramid6.)sphere
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1. A rectangular prism is a figure that has the following shape:
A real-world example of a figure that has this shape is a rectangular box.
2. A triangular prism is a figure that has the following shape:
8. If two lines are cut by a transversal so that consecutive interior angles are (congruent, supplementary, complementary), then the lines are parallel
Answers
Supplementary angles add up to 180°
If two lines are cut by a transversal so that consecutive interior angles are ( supplementary,, then the lines are parallel
The rule for a relation is y= (x+1) ^2. The domain is ( -2, -1,0,1,2,3). Is the relation a function?
Answers
No, this rule for a relation is not a function because the input variable (domain) are not uniquely mapped to an output variable (range).
What is a function?In Mathematics, a function is a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).
When x = -2, the range (output) of this function is given by:
y = (x + 1)²
y = (-2 + 1)²
y = (-1)²
y = 1.
When x = -1, the range (output) of this function is given by:
y = (x + 1)²
y = (-1 + 1)²
y = (0)²
y = 0.
When x = 0, the range (output) of this function is given by:
y = (x + 1)²
y = (0 + 1)²
y = (1)²
y = 1.
Based on the integers shown above, we can reasonably infer and logically deduce that this rule for a relation does not represent a function because the value of "1" is mapped to more than one domain element i.e -2 and 0.
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Please help!!!!!!!!!!!!!!!! please
Answers
Answer:
yes they are congruent
Step-by-step explanation:
Find the domain and range and intercepts.g of x = 3 / x-4
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a) Domain; all real numbers except 4
b) Range; all real numbers except y = 0
c) Y-intercept = -0.75
d) x-intercept does not exist
Here, we want to find the domain, range and intercepts
The domain refers to the possible x-values
From the question, the function will hold for all values of x, except x = 4, where we will have an undefined expression
Thus, the domain is all real numbers, except x= 4
For the range, we are referring to the possible y-values
From the given equation the possible y values are all real numbers except y = 0
To find the intercepts, let us write g(x) as y
The equation is thus;
[tex]\begin{gathered} y\text{ = }\frac{3}{x-4} \\ \end{gathered}[/tex]To get x-intercept, substitute y = 0
By doing this, we have no x-intercept
To get the y-intercept, we simply substitute x = 0
That means;
[tex]\begin{gathered} y\text{ = }\frac{3}{0-4} \\ y\text{ = }\frac{3}{-4} \\ y\text{ = -0.75} \end{gathered}[/tex]If x squared minus 6x plus 7 equal k(2x-3) has real equal roots find the possible values of K
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We will have the following:
[tex]\begin{gathered} x^2-6x+7=k(2x-3)\Rightarrow x^2-6x+7=2kx-3k \\ \\ \Rightarrow x^2-6x-2kx+7+3k=0 \end{gathered}[/tex]Now, we want to operate like terms and take to "solve for x" using the quadratic expression, that is:
[tex]\Rightarrow x^2+(-6-2k)x+(7+3k)=0\Rightarrow x=\frac{-(-6-2k)\pm\sqrt{(-6-2k)^2-4(1)(7+3k)}}{2(1)}[/tex]No, in order to determine the possible real values for "k" we have to analyze the value under the root, so:
[tex]\begin{gathered} \sqrt{(-6-2k)^2-4(1)(7+3k)}\Rightarrow(-6-2k)^2-4(1)(7+3k)\ge0 \\ \\ \Rightarrow36+24k+4k^2-28-12k\ge0\Rightarrow8+12k+4k^2\ge0 \end{gathered}[/tex]Now, we will have to use the quadratic expression again to determine the values for "k" that make the inequality true, that is:
[tex]\begin{gathered} k=\frac{-(12)\pm\sqrt{(12)^2-4(4)(8)}}{2(4)} \\ \\ \Rightarrow k\leq-2 \\ \\ and \\ \\ \Rightarrow k\ge-1 \end{gathered}[/tex]So, the values for which the inequality and thus the expression under the root are true are then given by:
[tex]k\leq-2\wedge x\ge-1[/tex]In other notation:
[tex](-\infty,2]\cup[-1,\infty)[/tex]Aiden ran a total of 8 miles over the course of 2 track practices. How many track practices would it take for Aiden to run 16 miles? Assume the relationship is directly proportional.
Answers
Answer:
4
Step-by-step explanation:
8 miles over 2 practices so double that
Find the surface area of the pyramid. 4.33 m 5 m 5 m The surface area is (Type a whole number or a decimal
Answers
Answer:
43.3 m²
Explanation:
The surface area of the pyramid can be calculated as 4 times the area of one face.
So, the area of one face is equal to:
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base of the triangles and h is the height. So, replacing b by 5 m and h by 4.33 m, we get:
[tex]\begin{gathered} A=\frac{1}{2}\cdot5\text{ m }\cdot4.33\text{ m} \\ A=10.825m^2 \end{gathered}[/tex]So, the surface area is equal to:
[tex]A=4(10.825)=43.3m^2[/tex]Therefore, the answer is 43.3 m²
Divide 12x5 − 36x4 − 6x3 by 3x2. 4x2 + 12x + 2 4x2 − 12x − 2 4x3 + 12x2 + 2x 4x3 − 12x2 − 2x
Answers
The correct option is D that is 4x³-12x²-2x when 12x⁵-36x⁴-6x³ will be divided by 3x² as the definition of polynomial says, "A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division".
What is polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division. Polynomials are sums of kxn terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines terms such as degree, standard form, monomial, binomial, and trinomial. According to this definition, the number ten is not a polynomial. However, people frequently use the symbol 10 to represent the polynomial (10,0,0,...). This is an example of a symbol being "overloaded," which occurs occasionally in mathematics. Here,
(12x⁵-36x⁴-6x³)/3x²
take 3x² from numerator,
3x²(4x³-12x²-2x)/3x²
=4x³-12x²-2x
When 12x⁵-36x⁴-6x³ is divided by 3x², the correct option is D, which is 4x³-12x²-2x . According to the definition of polynomial, "a polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division."
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Answer: 4x³-12x²-2x
Step-by-step explanation:
360 2 kg G 10. A yogurt tub contains 1 liter of yogurt. Nancy and her friends' eat 425 milliliters of yogurt. How much yogurt is left? Datab 425 s 75 you
Answers
The amount of 1 litre is equivalent yo 1000 milliliter.
Determine the amount yogurt left by subtraction of 425 from 1000.
[tex]1000-425=575[/tex]So 575 milliliter of yogurt is left.
3) Calculate the volume
4 cm
5 cm
3 cm
9 cm
Answers
Answer:
57cubic sm
Step-by-step explanation:
4 x 3= 12
5 x 9= 45
12 + 45 = 57