If y is a positive integer, for how many different values of y is sqrt ^ 3 144 / y a whole number?
Answers
Answer: second option.
Step-by-step explanation:
We need the remember that:
[tex]\sqrt[n]{a^n}=a[/tex]
Therefore, the radicand (In this case [tex]\frac{144}{x}[/tex]) must be a perfect cube in order to get a whole number.
Remember that a perfect cube are the numbers that have exact cube roots. Therefore, "y" must be a factor of 144.
Now, we need to descompose 144 into its prime factors:
[tex]144=2*2*2*2*3*3=2^4*3^2[/tex]
Then, the factors of 144 are: [tex]1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144[/tex]
Substitute values into [tex]\frac{144}{x}[/tex] to check:
[tex]\frac{144}{1}=144[/tex]
[tex]\frac{144}{2}=72[/tex]
[tex]\frac{144}{3}=48[/tex]
[tex]\frac{144}{4}=36[/tex]
[tex]\frac{144}{6}=24[/tex]
[tex]\frac{144}{8}=18[/tex]
[tex]\frac{144}{9}=16[/tex]
[tex]\frac{144}{12}=12[/tex]
[tex]\frac{144}{16}=9[/tex]
[tex]\frac{144}{18}=8[/tex] (Perfect cube: [tex]8=2^3[/tex])
[tex]\frac{144}{24}=6[/tex]
[tex]\frac{144}{36}=4[/tex]
[tex]\frac{144}{48}=3[/tex]
[tex]\frac{144}{72}=2[/tex]
[tex]\frac{144}{144}=1[/tex] (Perfect cube: [tex]1=1^3[/tex])
Therefore, for 2 different values of "y" ([tex]y=18[/tex] and [tex]y=144[/tex]) [tex]\sqrt[3]{\frac{144}{y} }[/tex] is a whole number.
Answer:
B) 2
Step-by-step explanation:
Edge 2020
Related Questions
which inequality symbols do i use for a-d if can help please comment picture of how number line will look
Answers
Answer:
a. <
b. >
c. >
d.<
Step-by-step explanation:
6 1/4 is less than 6 2/3
-3 is greater than -4
-5 is greater than -5.2
-5 is lesson that -4.8
15 - 2(3 - 2x) = 46
Answers
Answer:
x=33
Step-by-step
subtract 15 and 2 you get 13
13 times 3 =39
subtract 39 with 39 and 46 with 39
at the end you will get -26x=7
reverse negative into positive and then add -26 with 26 and you will be left with x and then you add 7 with 26 and your answer is
x=33
-2 (3-2x) = 31
3-2 = -31/2
-2x = -31/2 - 3
-2x = -37/2
X = 37/2/2
X = 37/2 x 2
X= 37/4
Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. 2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank. Which statement is true about angles 3 and 5? They are acute. They are congruent. They are complementary. They are supplementary.
Answers
Answer:
"They are supplementary" ⇒ last answer
Step-by-step explanation:
* Look to the attached figure
- Two parallel horizontal lines are intersected by a third line
- The angles formed form intersection are labeled on the figure
- From the two parallel lines and
∠5 ≅ ∠1 ⇒ corresponding angles
m∠5 = m∠1
- A linear pair is two angles that are adjacent and form a line and
they are supplementary
∠1 and ∠3 form a line
∠1 and ∠3 are linear pair
* lets prove that ∠3 and ∠5 are supplementary
∵ m∠1 = m∠5 ⇒ corresponding angles
∵ ∠1 and ∠3 form a linear pair
∵ Linear pair are supplementary
∴ m∠1 + m∠3 = 180°
- By substitute ∠1 by ∠5
∴ m∠5 + m∠3 = 180
∴ ∠5 and ∠3 are supplementary
* The true statement is "They are supplementary"
Angles 3 and 5 are congruent because they are alternate interior angles formed by a transversal intersecting two parallel lines. This is supported by the Alternate Interior Angles Theorem.
To determine the relationship between angles 3 and 5 when two parallel lines are intersected by a transversal, we can use the properties of alternate interior angles.
Given that angles 1 and 5 are congruent, we identify that they are alternate interior angles formed by the transversal intersecting two parallel lines. By the Alternate Interior Angles Theorem, since the lines are parallel, angles 1 and 5 are congruent.Angles 3 and 5 in this setup are also alternate interior angles, and by the same theorem, they are congruent.
This leads us to the conclusion that:
Angles 3 and 5 are congruent.
In a class of 20 students, 17 of the students
passed a prerequisite skills quiz What percent of
the students passed the quiz?
Answers
Answer = 85%
The correct answer is [tex]\(\frac{17}{20} \times 100\%\)[/tex].
To find the percentage of students who passed the quiz, we need to divide the number of students who passed by the total number of students, and then multiply by 100 to convert the fraction to a percentage.
Given that 17 students passed out of 20, the calculation is as follows:
[tex]\[ \text{Percentage of students who passed} = \left( \frac{\text{Number of students who passed}}{\text{Total number of students}} \right) \times 100\% \][/tex]
[tex]\[ \text{Percentage of students who passed} = \left( \frac{17}{20} \right) \times 100\% \][/tex]
This fraction can be simplified to a decimal or a mixed number if necessary, but it is most accurate and precise in its fractional form as given above. To convert it to a decimal, one would divide 17 by 20 and then multiply by 100, which would yield 85%. Thus, 85% of the students passed the quiz.
Evaluate this exponential expression.
4. (2 + 5)2 - 52 =
A. 46
B. 144
c. 8
D. 171
Answers
Answer:
B
Step-by-step explanation:
Given
4(2 + 5)² - 52
Evaluate the parenthesis
4 × 7² - 52 ← evaluate the exponent
4 × 49 - 52 ← evaluate the multiplication
= 196 - 52 ← evaluate the subtraction
= 144 → B
Answer: D 171
Step-by-step explanation:
Find x please!!!!!!!!!
Answers
write a linear equation in slope -intercept form that passes through the points (-8,4) (1,-5)
Answers
[tex]\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}}\implies \cfrac{-9}{1+8}\implies \cfrac{-9}{9}\implies -1[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-8)}]\implies y-4=-(x+8) \\\\\\ y-4=-x-8\implies y=-x-4[/tex]
1.) Michelle works at Bloomingdale's and earns a 20% commission for her daily sales. Yesterday, Michelle
sold $2,235 worth of merchandise. What was her commission?
Answers
Answer:
$447
Step-by-step explanation:
2,235 multiplied by .20
2235(1.25)=2682
2682-2235=447
Answer Michelle’s commission was $447
positive whole numbers less than 9
Answers
0 is a negitave number
4 can be one too because its less than 9 and its a whole number
Hope it helps :)
Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3. What is the length of line segment LJ? 9 units 12 units 15 units 18 units
Answers
Answer:
[tex]LJ=15\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the length side KJ
In the right triangle JKM
Applying the Pythagoras Theorem
[tex]KJ^{2}=JM^{2}+KM^{2}[/tex]
we have
[tex]JM=3\ units[/tex]
[tex]KM=6\ units[/tex]
substitute
[tex]KJ^{2}=3^{2}+6^{2}[/tex]
[tex]KJ^{2}=45}[/tex]
[tex]KJ=\sqrt{45}\ units[/tex]
simplify
[tex]KJ=3\sqrt{5}\ units[/tex]
step 2
Find the value of cosine of angle MJK in the right triangle JKM
[tex]cos(JKM)=JM/KJ[/tex]
substitute the values
[tex]cos(JKM)=\frac{3}{3\sqrt{5}}[/tex]
simplify
[tex]cos(JKM)=\frac{\sqrt{5}}{5}[/tex] -----> equation A
step 3
Find the value of cosine of angle MJK in the right triangle JKL
[tex]cos(JKM)=KJ/LJ[/tex]
we have
[tex]KJ=3\sqrt{5}\ units[/tex]
[tex]cos(JKM)=\frac{\sqrt{5}}{5}[/tex] ----> remember equation A
substitute the values
[tex]\frac{\sqrt{5}}{5}=\frac{3\sqrt{5}}{LJ}[/tex]
Simplify
[tex]LJ=5(3)=15\ units[/tex]
Answer:
The answer would be option C. 15 units :)
Step-by-step explanation:
Did it on edge :D
Hope this helps!
write an equation for the line parallel to y= -2x+1 that contains (-2,5)
Answers
Answer:
y = - 2x + 1
Step-by-step explanation:
Parallels line have the same slope, when an equation is in the form y= mx + b, m is the slope. In this problem slope = - 2
Now with the slope what is missing is the y-intercept, the problem says that the line contains the point (-2, 5), replacing that point in the equation you can solve it to find the y-intercept
y = mx + b
5 = (-2)(-2) + b
5 = 4 + b
1 + b
y = - 2x +1
How do I get from this guy 3/2/(15/4) to 2/5?
Answers
[tex]\bf \cfrac{~~\frac{3}{2}~~}{\frac{15}{4}}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix}2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{5}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{2}{5}[/tex]
To simplify the expression 3/2/(15/4), first convert the division of fractions to multiplication by the reciprocal, giving (3/2) * (4/15). Multiply the numerators and denominators and then reduce the fraction by dividing both by their greatest common divisor. The simplified result is 2/5.
To simplify the expression 3/2/(15/4), you would follow these steps:
Understand that dividing by a fraction is the same as multiplying by its reciprocal. In this case, 15/4 is the divisor, so we take its reciprocal which is 4/15.Multiply the original fraction 3/2 by the reciprocal of 15/4 which is 4/15.Perform the multiplication: (3/2) * (4/15).First, simplify by multiplying the numerators together and the denominators together: 3 * 4 = 12 and 2 * 15 = 30.So, you have 12/30, which can be reduced. Divide both the numerator and denominator by their greatest common divisor (GCD), which is 6.12 / 6 = 2 and 30 / 6 = 5, therefore the fraction simplifies to 2/5.Following these steps results in the original expression 3/2/(15/4) simplifying to 2/5.
Which of the following values is the solution to the equation -35x = -105 ? 3 -3
Answers
Answer:
3.
Step-by-step explanation:
-35x = -105
Divide both sides by -35:
x = -105/-35
= 3.
The solution to the equation is x = 3.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is -35x = -105.
Solve the equation as follows:
-35x = -105
35x = 105
x = 105/35
x = 3
Hence, the solution to the equation is x = 3.
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What is the solution to the equation 3/7(x+3)+5=3x+2?
Answers
Answer:
5/3
Step-by-step explanation:
i added a picture that will help you solve it.
The solution to the equation[tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] when "x" is an unknown variable is [tex]\dfrac{5}{3} .[/tex]
Two algebraic expressions separated by an equal symbol between them and with the same value are called equations.
Example = 2x +4 = 12
here, 4 and 12 are constants and x is variable.
To solve the equation[tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] we can follow these steps:
Multiply \dfrac{3}{7} into the brackets or inside the parentheses
[tex][\dfrac{3}{7}x + \dfrac{3}{7}\times3] + 5 = 3x + 2[/tex]
[tex]\dfrac{3}{7}x +\dfrac {9}{7} + 5 = 3x + 2[/tex]
On solving we get,
[tex]\dfrac{3x+9}{7} = 3x +2-5[/tex]
[tex]\dfrac{3x+9}{7} = 3x -3[/tex]
On cross multiplication we get,
[tex]{3x+9} = 7(3x -3)[/tex]
Opening the parenthesis we get
[tex]{3x+9} = (21x -21)[/tex]
Taking the variables to one side and constants on the right side we get,
[tex]{9+21} = (21x -3x)[/tex]
On further solving we get,
30 = 18 x
Simplify and solve for x:
Divide both sides by 18, and we get
[tex]\dfrac{30}{18} = x[/tex]
Now, in standard form
[tex]\dfrac{5}{3} = x[/tex]
In decimals, we get 1.66666.
Therefore, the solution to the equation [tex]\dfrac{3}{7}(x+3)+5=3x+2[/tex] is [tex]\dfrac{5}{3}[/tex].
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What is the slope of the line passing through the points
(-1,7) and (4,-1)
Answers
Answer:
(5 , -18)
Hope this helps.
From your vro Que
Answer: [tex]\dfrac{-8}{5}[/tex]
Step-by-step explanation:
The slope of a line passing through points (a,b) and (m,n) is given by :-
[tex]\text{Slope}=\dfrac{n-b}{m-a}[/tex]
Given points : (-1,7) and (4,-1)
Then, the slope of the line passing through the points (-1,7) and (4,-1) will be :-
[tex]\text{Slope}=\dfrac{-1-7}{4-(-1)}\\\\=\dfrac{-8}{4+1}\\\\=\dfrac{-8}{5}[/tex]
Hence, the required slope = [tex]\dfrac{-8}{5}[/tex]
solve this problem y=(x-3)^2 when x=9
Answers
it basically says y=(9-3)^2
which is y=6^2
which is then y=36
4. Thirty divided by seven times a number
A. 30 + 7n
B. in
30
30(7n)
None of the above
30:7.
Answers
Answer:
30/7n
Step-by-step explanation:
let n be the no.
seven times a no. is 7n
so ans is 30/7n
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes. x+y=6
Answers
Answer:
x-intercept = 6 → (6, 0)y-intercept = 6 → (0, 6)Step-by-step explanation:
x + y = 6
x-intercept is for y = 0. Substitute:
x + 0 = 6
x = 6
y-intercept is for x = 0. Substitute:
0 + y = 6
y = 6
Sketch a cube with 3 cm
Answers
Answer:
Step-by-step explanation: is This what you want?
Simplify: 7 exponent9 7 exponent3
Answers
Answer:
7^9= 40,353,607
7*7*7*7*7*7*7*7*7=40,353,607
7^3 =343
7*7*7=343
Identify the rule for the following pattern:
99, 90, 81...
Answers
- 7(2-1) = 28
The solution is?
Answers
Answer:
Is there a x somewhere or is that litteraly how the equation is?
If so, -7 multiplied by 2 is -14,
-1 times -7 is 7,
add it together and you get
-7=28,
you could add 7 to both sides or subtract 28 from both sides and you'll get either 0=35 or -35=0
which would make the solution false since both sides are not the same
Draw a quick picture of 3 hundreds, 5 tens and 7 ones. What number does your quick picture show? Write in the three different ways
Answers
Answer:
The table represents the start of the division of
Step-by-step explanation: instgram mack.thrasher
In the figure attached, the quick picture can be seen. See the second picture for clarification.
Another way to represent that number is in a table format, as:
Hundreds tens ones
3 5 7
Finally, 3 hundreds 5 tens and 7 ones are equal to 300 + 50 + 7 = 357
solve each compound inequality (show your work!)
[tex] - 6 < 2x - 4 < 12[/tex]
[tex]4x \leqslant 12 \: and - 7x \leqslant 21[/tex]
[tex]15x > 30 \: or \: 18x < - 36[/tex]
Answers
Answer: -1 < x < 8
x = 3
x ≠ 2
Step-by-step explanation:
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
+4 +4 +4
-2 < 2x < 16
÷2 ÷2 ÷2
-1 < x < 8
**************************************************************************
Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
÷4 ÷4 ÷-7 ÷-7
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? when x = 3
****************************************************************************
Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
÷15 ÷15 ÷18 ÷18
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
Represent the geometric series using the explicit formula.
12, −36, 108, −324, …
f(n) = f(n − 1) ⋅ (−3)
f(n) = f(n − 1) ⋅ (3)
f(n) = 12 ⋅ (−3)(n−1)
f(n) = 12 ⋅ (3)(n−1)
Answers
The explicit formula for the geometric sequence 12, -36, 108, -324, ... is f(n) = 12 * (-3)^(n-1), where 'n' is the term number.
Explanation:The series provided is a geometric series. In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio, denoted by 'r'. In our given series 12, -36, 108, -324, ..., you can determine that the common ratio (r) is -3. Now, using the formula for a geometric sequence given by f(n) = a * r^(n-1), where 'a' is the first term (12 in this case) and 'n' is the term number, we can write the explicit formula as
f(n) = 12 * (-3)^(n-1).
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The geometric series is represented by the explicit formula f(n) = 12 * (-3)^(n-1)
Explanation:The given sequence is an example of a geometric progression where each term is found by multiplying the previous term by a constant ratio. In this case, the common ratio is -3.
The explicit formula for a geometric series is given by f(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio. In this sequence, the first term (a) is 12 and the common ratio (r) is -3.
Plugging in the values into the formula, we can write the explicit formula for this geometric series as f(n) = 12 * (-3)^(n-1).
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which is greater 8.2 or 8.23
Answers
8.23 because of you add 0 after the 8.2 that will make it 8.20.
Hope it makes sense :)
Solve 6+2x^2-3x=8x^2
Answers
Answer: 6x^2+3x-6
Step-by-step explanation:
6+2x^2-3x=8x^2
-2x^2. -2x^2
6-3x=6x^2
= 6x^2+3x-6
Answer:
Step-by-step explanation:
Determine the slope and the y intercept. Y= -2. Then use the slope and the y- intercept to graph the equation
Answers
Answer:
y-intercept: [0, -2]; 0 = m
Step-by-step explanation:
Anything set to equal y is what is known as a zero rate of change [slope] because it is a horizontal line.
I am joyous to assist you anytime.
is √10 rational or irrational
Answers
√10 is irrational because a rational number is a number that is a/b where a and b are integers and b is a nonzero number.√10 does not follow this.
If you need a better explanation just as in the comments.
Happy to help! Please mark as BRAINLIEST! Thanks
Rational numbers are numbers that can be expressed as a ratio (or divided by one)
The price of an item has been reduced by 60%. The original price was $55. What is the price of the item now?
Answers
55x.60=33 is the correct answer
Answer:
Step-by-step explanation:
55*.60=$33
SO, 55-33=22THE ITEM IS $22 NOW