Question 1:
No, \(x^3 \cdot x^3 \cdot x^3\) equals \(x^9\), while \(x^3 \cdot 3 \cdot 3\) equals \(9x^3\), representing different operations and values.
Question 2:
Incomplete. The expression \(1/x^3\) can be rewritten as \(x^{-3}\) using negative exponents.
Question 3:
Incorrect. The product of \(\sqrt{x}\) and \(4\sqrt{x}\) equals \(4x\), not \(5x\). Use exponents to simplify.
Question 4:
The expression \(x^{5/6} \cdot x^{1/6}\) simplifies to \(x\). Show the steps of exponent addition.
Question 5:
Unjustified. Determine equivalent expressions by simplifying each and comparing results. Justify based on mathematical properties.
Here's a review of your work:
Question 1:
Your reasoning is incorrect. The expressions are not equivalent because they represent different operations. \( x^3 \cdot x^3 \cdot x^3 \) means \( x \) multiplied by itself 3 times, which is \( x^9 \). \( x^3 \cdot 3 \cdot 3 \) is a multiplication of constants, which equals \( 9x^3 \). So, the expressions are not equivalent because they result in different values.
Question 2:
Your answer is incomplete. It seems like you've provided a template for simplifying radicals, but you haven't actually applied it to the given expression. To simplify \( \frac{1}{x^3} \), you can rewrite it as \( x^{-3} \).
Question 3:
Your answer is incorrect. The product of \( \sqrt{x} \) and \( 4\sqrt{x} \) is not simply \( 5x \). To rewrite it in simplest rational exponent form, you should use the property of exponents which states that \( \sqrt{a} = a^{1/2} \). So, \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and \( 4\sqrt{x} \) is equivalent to \( 4x^{1/2} \). Multiplying these expressions together, you get \( 4x^{1/2} \cdot x^{1/2} = 4x^{1/2 + 1/2} = 4x^1 = 4x \).
Question 4:
You haven't shown your process for simplifying \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} \). To simplify, use the property of exponents which states that when you multiply two terms with the same base, you add their exponents. So, \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} = x^{\frac{5}{6} + \frac{1}{6}} = x^{\frac{6}{6}} = x^1 = x \).
Question 5:
You haven't justified which expressions are equivalent. To determine equivalence, you need to simplify each expression and compare them to each other.
6% of what number is 2.36
Answer:
39.3
Step-by-step explanation:
100 / 6 is about 16, 16.66667 to be exact:
2.36 * 16.66667 = approx. 39.3
Final answer:
To determine 6% of what number is 2.36, divide 2.36 by 0.06, resulting in an answer of approximately 39.33.
Explanation:
To find 6% of what number equals 2.36, we set up an equation where 6% (or 0.06) multiplied by a number 'x' equals 2.36. The equation looks like this: 0.06x = 2.36. To solve for 'x', you divide both sides of the equation by 0.06, which yields x = 2.36 ÷ 0.06. After calculating, you get that x equals 39.33. Therefore, 6% of 39.33 is 2.36.
Identify which is NOT a Pythagorean triple.
A)5, 12, 13B)7, 24, 25C)8, 15, 16D)11, 60, 61E)12, 35, 37
Answer:
C) 8, 15, 16 is NOT Pythagorean TRIPLET.
Step-by-step explanation:
There numbers a, b and c are said to be a PYTHAGORAS TRIPLET if
[tex](a) ^2 + (b)^2 = (c) ^2[/tex]
Now, here in the given options:
A)5, 12, 13
[tex](5)^2 + (12)^2 = 25 + 144 = 169 = (13)^2\\\implies (5) ^2 + (12)^2 = (13) ^2[/tex]
Hence, 5, 12, 13 is a Pythagorean TRIPLET.
B)7, 24, 25
[tex](7)^2 + (24)^2 = 49 + 576= 625 = (25)^2\\\implies (7) ^2 + (24)^2 = (25) ^2[/tex]
Hence, 7, 24, 25 is a Pythagorean TRIPLET.
C)8, 15, 16
[tex](8)^2 + (15)^2 = 64 + 225= 289 \neq (16)^2 = 256\\\implies (8) ^2 + (15)^2 \neq (16) ^2[/tex]
Hence, 8, 15, 16 is NOT Pythagorean TRIPLET.
D)11, 60, 61
[tex](11)^2 + (60)^2 = 121 + 3600 = 3721 = (61)^2\\\implies (11) ^2 + (60)^2 = (61) ^2[/tex]
Hence, 11, 60, 61 is a Pythagorean TRIPLET.
E)12, 35, 37
[tex](12)^2 + (35)^2 = 144 + 1225 = 3721 = (37)^2\\\implies (12) ^2 + (35)^2 = (37) ^2[/tex]
Hence, 12,35 , 37 is a Pythagorean TRIPLET.
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either [Choose...] g or [Choose...] g.
The scale is likely to show the mass is either 270.9g or 245.1g
Step-by-step explanation:
Actual mass = 258g
Percent error = 5% = ±0.05
Mass shown by scale = Actual mass*percent error
[tex]Mass\ shown\ by\ scale=258*(\±0.05)\\Mass\ shown\ by\ scale=\±12.9g[/tex]
Therefore,
Mass shown by scale = 258+12.9 , Mass shown by scale = 258-12.9
Mass shown by scale = 270.9g , Mass shown by scale = 245.1g
The scale is likely to show the mass is either 270.9g or 245.1g
Keywords: error, percentage
Learn more about percentages at:
brainly.com/question/11286417brainly.com/question/11566221#LearnwithBrainly
Answer:
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either
245.1
g or
270.9
g.
Step-by-step explanation:
I copied an pasted from k-12
how do i write this inequality
You must be at least 42 inches tall to ride the bumper cars at an amusement park. Write an inequality that represents this situation. Let x represent the heights of people who are allowed to ride the bumper cars.
The inequality for the given condition is x ≥ 42 inches
Solution:
Given that, the condition is you must be at least 42 inches tall to ride the bumper cars at an amusement park.
We have to write an inequality that represents this situation.
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =
Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥
Let "x" represent the heights of people who are allowed to ride the bumper cars
Height of people who are allowed to ride the bumper cars should be at least 42 inches
Height of people ≥ 42 inches [ since at least condition holds even at 42 value also ]
x ≥ 42 inches
Hence, the inequality for the given condition is x ≥ 42 inches
) What number makes the equation true?
-5+__=7 1/3
Shawn is buying his first home. At closing he brought a check for $7570. The
closing costs were as follows:
Title Fee
Processing Fee
Appraisal
No. of Points
$545
$2100
$695
Based on this information, how much did the house cost?
Answer:It cost 2100 dollars
Step-by-step explanation:I did the math on calculator very very simple buddy
12. What's
written as a fraction with a denominator of 42?
O C. 42/42
O D.742
Mark for review (Will be highlighted on the review page)
<< Previous Question
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Answer:
C.)
Step-by-step explanation:
Denominator is the bottom part of a fraction
In a large city, the heights of 10-year-old children are approximately normally distributed with a mean of 53.7 inches and standard deviation of 7 inches.
(a) What is the probability that a randomly chosen 10-year-old child has a height that is less than than 38.2 inches? Round your answer to 3 decimal places.
(b) What is the probability that a randomly chosen 10-year-old child has a height that is more than 40.3 inches? Round your answer to 3 decimal places
Answer:
(A) 40.67
(B) 57.98
Step-by-step explanation:
I did it in my head
there are two green Skittles out of every five what percent are green
Answer:
40%Step-by-step explanation:
2 green of every 5:
[tex]\dfrac{2}{5}[/tex]
Convert to the percent:
[tex]\dfrac{2}{5}\cdot100\%=\dfrac{200}{5}\%=40\%[/tex]
What is a non-example of unit rate
Answer:
60 calories per day
Step-by-step explanation:
example: 60 calories per serving so obviously the non example is the opposite
How do you determine the slope of a line
Answer:
To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). There are three steps in calculating the slope of a straight line when you are not given its equation.
Step-by-step explanation:
Step One: Identify two points on the line. Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
What is an equation of the line that passes through the points (0,2) and (5,8)
The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The point given that lie on the line are mentioned below.
(0, 2) and (5, 8)
Then the equation of the line that passes through the points (0, 2) and (5, 8) will be given as,
(y - 2) = [(8 - 2) / (5 - 0)](x - 0)
y - 2 = (6/5)x
y = (6/5)x + 2
The equation of the line that passes through the points (0, 2) and (5, 8) will be y = (6/5)x + 2.
More about the line passing through two points link is given below.
https://brainly.com/question/12740817
#SPJ3
Final answer:
To find the equation of the line passing through (0,2) and (5,8), we calculate the slope as 6/5 and use the y-intercept of 2 to write the equation as y = (6/5)x + 2.
Explanation:
To find an equation of the line that passes through the points (0,2) and (5,8), we need to calculate the slope and use one of the points to write the equation in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
First, let’s find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (8 - 2) / (5 - 0), which simplifies to m = 6 / 5. This is the slope of the line.
Now, we can use the slope and one of the points to find the y-intercept. Since the line passes through (0,2), we know that the y-intercept b is 2. Therefore, the equation of the line is y = (6/5)x + 2.
In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, form an equation in terms of x and solve it.
Answer:
[tex]x=\frac{8}{3}\ cm[/tex]
Step-by-step explanation:
we know that
The area of the right triangle ABC is equal to
[tex]A=\frac{1}{2}(AB)(BC)[/tex]
we have
[tex]A=17\ cm^2[/tex]
[tex]AB=(3x-2)\ cm[/tex]
[tex]BC=(x+3)\ cm[/tex]
substitute the values
[tex]17=\frac{1}{2}(3x-2)(x+3)[/tex]
[tex]34=(3x-2)(x+3)[/tex]
[tex]34=3x^2+9x-2x-6[/tex]
[tex]3x^2+7x-6-34=0[/tex]
[tex]3x^2+7x-40=0[/tex]
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^2+7x-40=0[/tex]
so
[tex]a=3\\b=7\\c=-40[/tex]
substitute in the formula
[tex]x=\frac{-7(+/-)\sqrt{7^{2}-4(3)(-40)}} {2(3)}[/tex]
[tex]x=\frac{-7(+/-)\sqrt{529}} {6}[/tex]
[tex]x=\frac{-7(+/-)23} {6}[/tex]
[tex]x=\frac{-7(+)23} {6}=\frac{16}{6}=\frac{8}{3}[/tex]
[tex]x=\frac{-7(-)23} {6}=-5[/tex]
therefore
The solution is
[tex]x=\frac{8}{3}\ cm[/tex]
A scale has a percent error of 5%. The actual mass of a rock is 258 g.
Select from the drop-down menus to correctly complete the statement.
The scale is likely to show the mass is either [Choose...] g or [Choose...] g.
Please help, I have an F in math and the semesters almost over. Im doing over due so I can try to bring my grade up to a C. Please help, Ill give brainlyest.
Multiply the weight by 5%, then subtract that from the weight for the lower value and add it for the higher value:
258 x 0.05 = 12.9g
Lower value: 258 - 12.9 = 245.1g
Higher value: 258 + 12.9 = 270.9g
Solve for k
7k+2m = kr + 4m + 3
Answer:
[tex]\large\boxed{k=\dfrac{2m+3}{7-r}\ \text{for}\ r\neq7}[/tex]
Step-by-step explanation:
[tex]7k+2m=kr+4m+3\qquad\text{subtract}\ 2m\ \text{from both sides}\\\\7k+2m-2m=kr+4m-2m+3\\\\7k=kr+2m+3\qquad\text{subtract}\ kr\ \text{from both sides}\\\\7k-kr=kr-kr+2m+3\\\\7k-kr=2m+3\qquad\text{distribute}\\\\k(7-r)=2m+3\qquad\text{divide both sides by}\ (7-r)\neq0\\\\k=\dfrac{2m+3}{7-r}[/tex]
Jordan can run a mile in 8.4 minutes. How long would it take to run 6.21 miles
Final answer:
To find how long it takes Jordan to run 6.21 miles, multiply the per-mile time (8.4 minutes) by the total miles (6.21), resulting in approximately 52.164 minutes.
Explanation:
To calculate how long it would take Jordan to run 6.21 miles based on the information that Jordan can run a mile in 8.4 minutes, we use the following steps:
Multiply the time it takes to run one mile by the total number of miles.Time for 1 mile = 8.4 minutes
Total distance = 6.21 miles
Total time = 8.4 minutes/mile × 6.21 miles
Total time = 52.164 minutes
Therefore, it would take Jordan approximately 52.164 minutes to run 6.21 miles. This straightforward multiplication provides a precise estimate, illustrating the application of the mile pace to calculate the overall running time for the specified distance.
What is 889 divided by 17
Answer:
The answer is 52.2
Step-by-step explanation:
One number is
= of another number. The sum of the two numbers is
12. Find the two numbers. Use a comma to separate your answers.
Answer:
Two such numbers are 10 , 2 .
Step-by-step explanation:
Here, the question is INCOMPLETE.
Here is the Complete question:
One number is 1/5 of another number. The sum of the two numbers is 12. Find the two numbers. Use a comma to separate your answers.
We can solve the given problem as follows:
Here, : One number is 1/5 of another number.
Let one such number = m
⇒ The other number = 1/5 (m)
Sum of both the given number = 12
[tex]\implies m + \frac{1}{5} m = 12\\\implies \frac{5m + m}{5} = 12\\\implies \frac{6m}{5} = 12[/tex]
or, 6 m = 12 x (5) = 60
or, m = 60 / 6 = 10
or, m = 1 0
Hence, the first number = m = 10
Second number is [tex]\frac{1}{5} m = \frac{1}{5} \times 10 = 2[/tex]
Hence, two such numbers are 10 , 2 .
LiAnn works in the Olde Tyme Soda Shopee. The shop sells milkshakes, double milkshakes, and triple milkshakes. A shake uses 1/8 cup of syrup, a double shake uses 1/4 cup of syrup, and a triple shake uses 3/ 8 cup of syrup. How many shakes of each kind could she make with 3 cups of syrup?
Answer:
[tex]\large \boxed{24; 12; 8}[/tex]
Step-by-step explanation:
1. Calculate the number of milkshakes
[tex]\text{Number of milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each milkshake}} = 3 \div \dfrac{1}{8}[/tex]
Invert the denominator and change division to multiplication
[tex]3\div\frac{1}{8} = 3\times \dfrac{8}{1} = \mathbf{24}\\\\\text{LiAnn can make $\large \boxed{\mathbf{24}}$ milkshakes}[/tex]
2. Calculate the number of double milkshakes
[tex]\text{Number of double milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each double milkshake}} = 3 \div \dfrac{1}{4}[/tex]
Invert the denominator and change division to multiplication
[tex]3\div\dfrac{1}{4} = 3\times \dfrac{4}{1} = \mathbf{12}\\\\\text{LiAnn can make $\large \boxed{\mathbf{12}}$ milkshakes}[/tex]
3. Calculate the number of triple milkshakes
[tex]\text{Number of triple milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each triple milkshake}} = 3 \div \dfrac{3}{8}[/tex]
Invert the denominator and change division to multiplication
[tex]3\div\dfrac{3}{8} = 3\times \dfrac{8}{3}[/tex]
Cancel the 3s
[tex]3\times \dfrac{8}{3} = \mathbf{8}\\\\\text{LiAnn can make $\boxed{\mathbf{8}}$ triple milkshakes}[/tex]
(5x)(-2x)(3x) is equal to?
What is the volume of a sphere that has a 64 m radius
Answer:
V=349525.333*pi
Step-by-step explanation:
Volume of a sphere: V=(4/3)*pi*r^3 where r=radius.
r=64
V=(4/3)*pi*(64)^3=(4/3)(262144)pi=349525.333*pi
How do you answer this?
Answer:
The simplified form would be [tex]6x^5[/tex]
Step-by-step explanation:
Given:
[tex]\frac{(3x^4)(12x^2)}{6x}[/tex]
Now multiplying the numbers and variable we get,
[tex]\frac{(3x^4)(12x^2)}{6x}\\\\\frac{(36x^{2+4})}{6x}\\\\\frac{36x^6}{6x}[/tex]
Now Dividing 36 by 6 we get,
[tex]\frac{6x^6}{x}=6x^6\times x^{-1} = 6x^{6-1}= 6x^5[/tex]
Hence the simplified form would be [tex]6x^5[/tex]
What is the solution to the equation
1+1
Answer:
2
Step-by-step explanation:
but I would personally say FISH
Answer: Like I really told you what I just had said, "The answer to this basic math question with the given basic math expression is [tex]1+1=2.[/tex]"
Step-by-step explanation: Seriously, like I really told you what I just had said, "This seems extremely too simple and easy for me and the users of The Brainly in order to answer to this basic math question with your own given the basic math expression, there is just only 1 of the basic step-by-step explanation for the basic math question with the given basic math expression for me and the users of The Brainly in order to solve it that looks in the equation form like this: [tex]1+1=2.[/tex]"
So, anyway, I hoped that my own given quoted with my own given quoted basic answer and my own given quoted basic step-by-step explanation is being very helpful to your own basic math question with the given basic math expression what I've been just said and have a great rest of the weekend! :D
Sincerely,
Jason Ta,
The Ambitious of Brainly And The Role of The TDSB And WHCI Student of The High School.
find the area of the figure.
12 ft
18 ft
18 ft
36 ft
The area of the given figure is 864 square feet.
To find the area of the given figure, we can break it down into two rectangles and then sum their areas.
The figure consists of two rectangles with dimensions:
1. The first rectangle has a length of 36 ft and a width of 18 ft.
2. The second rectangle has a length of 12 ft and a width of 18 ft.
The area (A) of a rectangle is calculated using the formula: [tex]\(A = \text{length} \times \text{width}\).[/tex]
For the first rectangle:
[tex]\[ A_1 = 36 \, \text{ft} \times 18 \, \text{ft} = 648 \, \text{ft}^2 \][/tex]
For the second rectangle:
[tex]\[ A_2 = 12 \, \text{ft} \times 18 \, \text{ft} = 216 \, \text{ft}^2 \][/tex]
Now, add the areas of both rectangles to find the total area (A) of the figure:
[tex]\[ A = A_1 + A_2 = 648 \, \text{ft}^2 + 216 \, \text{ft}^2 = 864 \, \text{ft}^2 \][/tex]
The question probable maybe :-
Find the combined area of two rectangles with side 36 ft 18 ft ,12 ft
18 ft respectively .
Label each pair of triangles with the postulate or theorem that proves the triangles are congruent.
Answer:
We can conclude that Δ GHI ≅ Δ JKL by SAS postulate.
Step-by-step explanation:
Δ GHI and Δ JKL are congruents because:
1. Their sides GH and JK are equal (9 units = 9 units)
2. Their included angles ∠G and ∠J are equal (62° = 62°)
3. Their sides GI and JL are equal (17 units = 17 units)
Now, we can conclude that Δ GHI ≅ Δ JKL by SAS postulate.
One-Step Equations:
1. x - 3.5 + 14.9
2. x - 2.8 = 9.5
3. x - 8.5 = -2.1
4. z - 9.4 = -3.6
5. -5/6 + x = -11/12
6. x - 1/9 = 5/18
7. x + 6 = -3
8. z - 7 = 11
9. -1 = x - 8
(I will be trying to figure these out as well)
Leonard wants to save $100 in the next 2 months. He knows that in the
second month, he will be able to save $20 more than the first month.
How much should he save each month?
1 st
2nd
total
+
Answer:
$40,$60
Step-by-step explanation:
Let the money in the first month be x.
2x+20=100
x=40
In a different plan for area codes, the first digit could be any number from 0 through 6 , the second digit was either 7 or 8, and the third digit could be any number except 0 or 6. or 6. With this plan, how many different area codes are possible?
112 different area codes can be made.
Solution:Given, In a different plan for area codes, the first digit could be any number from 0 through 6 ,
So, total 7 digits are possible for 1st place (i.e. 0 1 2 3 4 5 6)
The second digit was either 7 or 8,
So, total 2 digits are possible for 2nd place (i.e. 7 8)
And the third digit could be any number except 0 or 6.
So, total possible digits are 8 for 3rd place (i.e. 1 2 3 4 5 7 8 9)
With this plan, we have to find how many different area codes are possible?
[tex]\text { total possible combinations }=7 \text { possibilities for } 1 \text { st place } \times 2 \text { for } 2 \text { nd place } \times 8 \text { for } 3 \text { rd place }[/tex]
[tex]\text { Total possible area codes }=7 \times 2 \times 8=14 \times 8=112[/tex]
Hence, 112 different area codes can be made.
Help with number 15 with the graph
Answer:
I believe it is 7
Step-by-step explanation:
Carlotta has 12 2/3 yd of ribbon to be divided among 19 girls in the cheerleading squad.how much ribbon will each girl get if it is divided equally among the 19 girls
Answer:
Each girl gets 2/3 yd of ribbon.
Step-by-step explanation:
12 2/3=38/3
(38/3)/19
(38/3)(1/19)
(2/3)(1/1)=2/3