Answer:
30^(1/5) is in (1, 2)45^(1/3) is in (3, 4)Step-by-step explanation:
You want to know the consecutive integers that bound the values of 30^(1/5) and 45^(1/3).
Powers and rootsThe fifth root of 30 will lie between the two integers whose 5th powers lie on either side of 30:
1^5 = 1 < 30
2^5 = 32 > 30
So, the fifth root of 30 lies between 1 and 2:
[tex]\boxed{1 < \sqrt[5]{30} < 2}[/tex]
The cube root of 45 will lie between the two integers whose cubes lie on either side of 45:
3^3 = 27 < 45
4^3 = 64 > 45
So, the cube root of 45 lies between 3 and 4:
[tex]\boxed{3 < \sqrt[3]{45} < 4}[/tex]
__
Additional comment
A calculator confirms this:
[tex]\sqrt[5]{30}\approx 1.974\\\sqrt[3]{45}\approx3.557[/tex]
Find the quotient of - 62"y' + 12x2?
15zy - 15 divided by
-3
The quotient of the expression -6x²y + 12x² + 15zy - 15 divided by -3 is 2x²y - 4x² - 5zy + 5
How to determine the quotientFrom the complete question, we have the following parameters that can be used in our computation:
quotient of -62"y' + 12x2? 15zy - 15 divided by -3
Express properly
So, we have
-6x²y + 12x² + 15zy - 15 divided by -3
To solve this question, we simply divide each term of the expression by -3
So, we have the following representation
(-6x²y + 12x² + 15zy - 15)/-3
Evaluate the quotient
2x²y - 4x² - 5zy + 5
Hence, the solution is 2x²y - 4x² - 5zy + 5
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find the highest common factor of 48 and 504
The highest common factor of 48 and 504 is 24.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The highest common factor or HCF of a group of numbers is the greatest number which divides the given numbers without remainder.
48 = 2 * 24
504 = 2 * 21 * 24
The HCF of 48 and 504 is 24
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hi la amigos y amigas what is 26 divded by 2 plus 5?
Is it possible to have a triangle with the following sides 5 cm 9 cm 10 cm?.
Yes, it is possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(5cm + 9cm) =10 cm
14 cm = 10 cm
LHS>RHS
A triangle is possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Consider this expression.
| m^2 - 7 | + n^2
When m = -2 and n = 5, the value of the expression is ___.
Type the correct answer in the box (aka the empty spot). Use numerals instead of words.
The value of the expression as given in the task content is; 28.
What is the value of the given expression?It follows from the task content that the value of the expression is to be determined given the parameters for m and n.
Since the given expression is; | m² - 7 | + n²
Therefore, when m = -2 and n = 5, we have that;
| (-2)² - 7 | + 5²
= | 4 - 7 | + 25
= | -3 | + 25
= 3 + 25
= 28.
Ultimately, the value of the expression according to the given parameters is; 28.
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How do you divide 3 digit numbers by 3 digit numbers?.
The steps for dividing the 3 digit numbers by 3 digit numbers is solved with the help of multiplication and subtraction.
The process of division is defined as the process of breaking a number up into equal parts, and finding out how many equal parts can be made.
Here we need to find the way to divide 3 digit numbers by 3 digit numbers.
The steps to solve the given division is written as,
The first steps is to take the first digit of the dividend from the left and then we have to check if this digit is greater than or equal to the divisor.
Now then we have to divide it by the divisor and write the answer on top as the quotient.
Then we have to do the subtract operation the result from the digit and write the difference below.
Then the final steps is to bring down the next digit of the dividend and this process is repeated until we get the remainder as zero.
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tell me how many tenths are equivalent to 1/2 btw this is just for fun
Answer:
5/10
Step-by-step explanation:
hi I atleast have. to have 20 characters so yeah
Answer: 5 tenths
Step by steps:
Find the perimeter or area of the figure a indicated. 5) Find the perimeter. (5x 7) meter × meter 9x meter (9x - 10) meter 8x meter 7 meter
The Area of the rectangle is (40x²+ 49x + 15)cm²
The area of a rectangle in geometry is the region covered by the rectangle in a two-dimensional plane. The area of the rectangle is the region occupied by a rectangle within its four sides or boundaries.
A rectangle is a sort of quadrilateral, a two-dimensional object with four sides and four vertices. The rectangle's four angles are all right angles or equal to 90 degrees. The rectangle's opposite sides are equal and parallel to one other.
Given that,
Length of rectangle=(8x+5)cm
Breadth of rectangle=(5x+3)cm
Area of rectangle=Length×Breadth
Area of rectangle=(8x+5)(5x+3) = (40x²+ 49x + 15)cm²
Therefore, the Area of the rectangle is (40x²+ 49x + 15)cm²
Correct question: A rectangle is (8x+5)cm long and (5x+3)cm broad.
Find its area or perimeter.
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What is the angle measure of each interior angle of a regular polygon with 42 sides?.
The interior angle measurement of a regular polygon with 42 sides is 150 degrees.
The interior angle measure of a regular polygon is determined by the formula (n-2)*180/n, where n is the number of sides of the polygon. In the case of a regular polygon with 42 sides, this formula can be expressed as (42-2)*180/42, which simplifies to 150 degrees. Therefore, the interior angle measure of a regular polygon with 42 sides is 150 degrees. This means that each interior angle of the polygon is 150 degrees. The exterior angle measure of a regular polygon with 42 sides would be 10 degrees, which can be calculated by subtracting the interior angle measure from 180 degrees. Knowing the angle measure of both the interior and exterior angles of a regular polygon with 42 sides is useful for a variety of applications, such as modeling or designing.
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IS
√21 A
RATIONAL
NUMBER? PLEASE
EXPLAIN
CLEARLY WHY IT
EITHER IS OR
ISN'T.
Answer:
√21 is irrational
Step-by-step explanation:
√21 = 4.58257569495584 which is a non-terminating decimal.
Therefore √21 is irrational.
Answer: No, it cannot be a rational number.
Step-by-step explanation:
A rational number is defined to be a whole number (ex. 1, 2, 3) or can be decimals that continuously repeat the digits after the point. In the case of a square root, they can be rational--but this only applies to perfect squares: √100, √64, √16, etc, which would give an outcome of a whole number. Therefore, √21 is not a rational number, as the decimal value is 4.57257, and is not continuous (ex. 3.666666).
The box-and-whisker plot below represents some data set. What is the value of the median?
150
The median is where the line inside the box sits. That's the halfway point between all of the data. (Halfway in terms of "if you line everything up and it's the data point in the middle.")
What is the value of f/g )( 5 )?.
Answer:270
Step-by-step explanation:
We have to find (f/g)(5). Therefore, (f/g)(5) is 270.
Which player is the median?
I need help with this question so I can get my homework done What is. 0.75n+s
N(b) =75 because p(b) =n(b) /n(s)
0.75=n(b)/100
n(b)=0.75*100=75
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
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Can someone please help me with this math problem, ASAP? It is in the picture, Thanks!
[tex]g(x) = 4x^2 + 3x[/tex]
So, [tex]g(x+a) = 4(x+a)^2 + 3(x+a)[/tex], since we're just substituting (x+a) for x.
If we clean that up a bit,
[tex]\begin{aligned}g(x+a) &= 4(x+a)^2 + 3(x+a)\\[0.5em] &= 4(x^2+2xa+a^2) + 3x+3a\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a\end{aligned}[/tex]
Now putting this all together:
[tex]\begin{aligned}g(x+a)-g(x) &= ( 4x^2+8xa+4a^2 + 3x+3a) - (4x^2+3x)\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a - 4x^2-3x\\[0.5em]&= 8xa+4a^2 +3a\end{aligned}[/tex]
Remember that [tex](x+a)^2 = (x+a)(x+a) = x^2+2xa+a^2[/tex]
During an experiment, 456 g of carbon dioxide is produced. What is the mass of carbon dioxide in kg?
Answer:
0.456 kg
Step-by-step explanation:
URGENT PLS ANSWER ASAP THANKS!
The true statement is "No, you cannot prove that the two right triangles are congruent with the information given."
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Sidewalk A and Sidewalk B intersect at a right angle. Sidewalk B extends 500 feet on either side of the intersection with Sidewalk A.As a general rule, congruent triangles would have same dimensions and angles
In the scenario, we understand that Sidewalk B and Sidewalk A form a right angle.
This and the other information does not provide information to determine the congruency because the lengths of the sides of either triangle or the angles are missing.
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Which jam recipe has more strawberry flavor?
Recipe A
3 cups strawberries
1/2 cup sugar
Recipe B
5 cups strawberries
1 cup sugar Help please
The jam recipe that has more strawberry flavor is Recipe A.
Which recipe has more strawberry flavor?In order to determine which recipe has more strawberry flavor, determine how many cups of strawberry is needed for one cup of sugar. In order to do this, divide the cups of strawberry by the cups of sugar.
Cups of strawberry needed for one cup of sugar = cups of strawberry / cups of sugar
Cups of strawberry needed for one cup of sugar in recipe A = 3 ÷ 1/2
3 x 2 = 6
Cups of strawberry needed for one cup of sugar in recipe B = 5 ÷ 1 = 5
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How do you solve inverse functions examples?.
The process of inverse the function is f⁻¹(x) = x/2.
In math the term function is known as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Here we have to explain the process of solve inverse functions with examples.
While we take the function for examples as
f(x) = 2x.
Now, we have to do the following steps to identify the inverse of the function,
Here the first steps is to replace f(x) by y in the equation describing the function, then we get
=> y = 2x
Now, we have to interchange x and y in a simple terms now we have to replace replace every x by a y and vice versa, then we get,
=> x = 2y
Then the next step is to Solve for y, here we get
=> y = x/2
Finally replace y by f⁻¹(x)
Therefore, the inverse of the function is
=> f⁻¹(x) = x/2.
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Use mathematical reasoning Two points have the same y-coordinate but different x-coordinates. Make a prediction about the slope of a line drawn through the points. Justify your prediction.
The slope of points with same y coordinate but a different x coordinate is 0
this is because change in y is zero
How to find the slope of the lineThe slope, m of the linear function is calculated using the formula
= change in y / change in x
This is represented mathematically as
m = (y₀ - y₁) / (x₀ - x₁)
In this case change in y is zero since it is same point
y₀ = y₁
And when a number in the numerator is zero the division will result to a quotient of zero and hence the line is a horizontal line
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solve this absolute value equation
[tex]|5x-12| + |x+2| = 8[/tex]
Answer: 3 , 1 1/2
Step-by-step explanation:
Solve for
x
by simplifying both sides of the equation, then isolating the variable.
Exact Form:
x
=
3
,
3
2
Decimal Form:
x
=
3
,
1.5
Mixed Number Form:
x
=
3
,
1
1
2
helphelphelphelphelp
The length of a rectangle is 5 cm more than its breadth. If the perimeter of the rectangle is 58 cm, find its dimensions.
Step-by-step explanation:
58 = 2(l+b)
58 = 2(x+x)+5
58 = 2x + 5
2x = 58-5
2x = 53
x = 53/2
x = 26.5
So, length = 26.5 + 5 = 31.5
Hence, the length and breadth are 31.5 and 26.5 respectively.
If PQRS is a rectangle, ST = 12, and mzPRS = 23°, find each measure.
SQ =
PT =
measurement of angle QPR =
Answer:
SQ = 24
PT = 12
<QPR = 23°
Step-by-step explanation:
SQ= 12+12=24
PT=12
<PRS is alternate to <QPR
<QPR=23°
PLEASE HURRY!
No false answers just for points !
The adjacent angle to ∠PSL is ∠KRM which is ∠2
what is adjacent angle?
Adjacent angles are two angles that share a common vertex and have a common side (or arm) but no common interior points. They are side by side angles and are next to each other. They are not always congruent but they share a common side, usually represented by a line. They can be acute, obtuse or right angles. They can also be complementary angles, meaning they add up to 90 degrees. For example, in a rectangle, the angles across from each other are called adjacent angles, they are both right angles.
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R = 2 + 4sin(theta)
Domain is [0,2pi)
a. Write the integral to determine the area enclosed by the inner loop. Show your work that leads to the integral.
b. Write the integral to find the area between the loops
a. The integral to determine the area enclosed by the inner loop is:
A = ∫0^2π2+4sin(θ)dθ
This integral can be solved using the substitution u = 4sin(θ). This will give us the following integral:
A = ∫0^2π2 + udu
Next, we apply the power rule to the integral and solve for A.
A = 2θ + (u^2)/2 | 0^2π
A = 2θ + (4sin(θ)^2)/2 | 0^2π
A = 2π + 4[1 - cos(2θ)]/2 | 0^2π
A = 2π + 2 - cos(2π)
A = 4π - 1
b. To find the area between the loops, we can use the following integral:
A = ∫2^4π2+4sin(θ)dθ
Using the same substitution, we have:
A = ∫2^4π2 + udu
A = 2θ + (u^2)/2 | 2^4π
A = 2θ + (4sin(θ)^2)/2 | 2^4π
A = 2π + 4[1 - cos(2θ)]/2 | 2^4π
A = 2π + 2 - cos(4π)
A = 4π + 1
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Lin's father is paying for a $20 meal. He has a 15%-off coupon for the
meal. After the discount, a 7% sales tax is applied. What does Lin's
father pay for the meal? Explain or show your reasoning.
Answer:
18.19
Step-by-step explanation:
15% of 20 = 3
20 - 3 = 17
7% of 17 = 1.19
17 + 1.19 = 18.19
Determine whether the next pair of triangles is similar. If the triangles are similar, give a reason: write AA, SSS, or SAS.
The two triangles in this problem are similar, and the reason for their similarity is given as follows: AA.
What are similar triangles?Similar triangles are triangle that share these following two features:
Congruent angle measures.Proportional side lengths.The two right triangles in this problem are similar, as they have two common angle measures, given as follows:
The right angle.The angle at the bottom left of the image.As the angles have two common angle measures, the reason is given as follows:
AA.
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Charlie and Hayden are standing outside. Charlie is 64 inches tall and casts a shadow of 30 inches. If Hayden is 68 inches tall, approximately how long is his shadow? 28 inches 32 inches 145 inches 31 inches
The length of the shadow of Hayden is approximately 32 inches.
How to find the length of Hayden shadow?Charlie and Hayden are standing outside. Charlie is 64 inches tall and casts a shadow of 30 inches.
Hayden is 68 inches tall. The length of the shadow of Hayden can be calculated as follows:
Using proportion,
64 / 30 = 68 / x
where
x = length of the shadow of Hayden
Therefore,
64 / 30 = 68 / x
cross multiply
64x = 68 × 30
64x = 2040
divide both sides by 64
x = 2040 / 64
x = 31.875
Hence,
Length of the shadow of Hayden = 32 inches
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Is 1 0 infinity or infinity?.
Since division by zero is not defined, 1/0 is not infinity, and 0/0 is not indeterminate.
We must keep in mind that, except in the case of limitations, the value of 1 divided by 0 is infinite. The phrase "infinity" denotes the size of the number. When it comes to limits, we merely presume that limit x's value tends toward something rather than being equal to anything. We thus treat it as infinite.
Since it is not a real number, infinity is only used to symbolise extraordinarily big real numbers. The result of 1 divided by infinity is 0. The quotient of nonzero real numbers that divide infinity is infinity, and the rule of thumb is that any real number divided by infinity is zero.
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