Find the length of side a in simplest radical form with a rational denominator.

Answer:

15

Step-by-step explanation:

Given the expression:
[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5}[/tex]

We can apply the law of exponent of:

[tex]\displaystyle{\left(a^m\right)^n = a^{mn}}[/tex]

Therefore, we will have:

[tex]\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{\frac{5}{5}}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15^{1}}\\\\\displaystyle{\left(15^{\frac{1}{5}}\right)^5 = 15}[/tex]

Hence, the value of expression is 15.

Answer:

(2/5)

Step-by-step explanation:

(-2/5) = -(2/5)

|-(2/5)| = (2/5)

If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

What is Quadratic Equation ?

Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0 .

Nature of Roots depending upon Discriminant

in step with the value of discriminant, we shall discuss the subsequent cases about the character of roots.

Case 1: D = 0

If the discriminant is same to 0 (b2 – 4ac = zero), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = zero, are real and equal. In this case, the roots are x = -b/2a. The graph of the equation touches the X axis at a single point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), a, b, c are actual numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are actual and unequal. The graph of the equation touches the X-axis at two unique points.

Case 3: D < 0

If the discriminant is less than 0 (b2 – 4ac < 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax2 + bx + c = 0, are imaginary and unequal. The roots exist in conjugate pairs. The graph of the equation does not touch the X-axis.

Case 4: D > zero and perfect square

If D > zero and an excellent square, then the roots of the quadratic equation are actual, unequal and rational.

Case five: D > 0 and now not an excellent square

If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

Therefore, If D > 0 and not an excellent square, then the roots of the quadratic equation are real, unequal and irrational.

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A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly has coordinate (1.7, 0.6). The distance of the fly from the corner of the room is 1.8 meters.

Suppose we have a point having coordinate (x,y). Then the horizontal axes, vertical axis,  and the distance from the origin form a right triangle which its base is x and y.

Hence, we can find the distance of the point (x,y) from the origin using the Pythagorean Theorem.

In this case, the origin is a certain corner of the room. The coordinate of the fly is (1.7, 0.6) meters.

Using the Pythagorean Theorem:

distance = sqrt (1.7² + 0.6²)

distance = sqrt (2.89 + 0.36)

distance = sqrt (3.25)

distance = 1.8 meters

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Coordinates of the vertices of the octagon after dilation by scale factor 3 are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).

Original coordinates of the vertices of an octagon are :

(-4, 2), (-2,5), (1,5), (3, 2), (3, -6), (1, -3), (-2, -3), and (4, -6).

Scale factor is equal to 3

Figure transformed using dilation of scale factor of 3 with center of dilation at the origin.

Coordinates of the new vertices after dilation of the octagon.

(-4×3, 2×3) = ( -12, 6)

(-2 ×3,5×3) = ( -6 , 15)

(1 ×3,5×3) = ( 3 ,15)

(3×3, 2×3) = ( 9,6)

(3×3, -6×3) = ( 9, -18)

(1 ×3, -3×3) = ( 3 , -9)

(-2×3, -3×3) = ( -6 , -9)

(4×3, -6×3) = (12, -18)

Therefore, the new coordinates of the vertices after dilation are (-12, 6), (-6,15), (3,15), (9, 6), (9, -18), (3, -9), (-6, -9),and (12, -18).

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Answer:

14S -93

Step-by-step explanation:

(4s+7 -2S) +4 (3s-5^2)

= 2S +7 +12S -4*25

=14S -93

The total number of four-digit parity-monotonic integers is 432*1 = 24.

We can solve this problem by counting the number of parity-monotonic integers in each of the four digits individually and then multiplying the counts together.

By counting the possible values of [tex]$a_1$[/tex], [tex]$a_2$[/tex], [tex]$a_3$[/tex] and [tex]$a_4$[/tex] independently, we have:

Thus, the total number of four-digit parity-monotonic integers is 432*1 = 24.

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Answer:

6 Tables

Step-by-step explanation:

48 tables divided by 8 paintbrushes equals 6 tables.

According to the elimination method, the solution of the system of equation has infinite number of solutions.

In math the term elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables

Here we know that the equations are

=> 6x - 2y = 8 ---------------(1)

=> -3x + y = -4 ------------------(2)

when we simplify the equation (1) by dividing the terms by 2, then we get

=> 3x - y = 4

Now, we have to add the two equation then we get the result as,

=> (-3x + 3x) +( -y + y) = (-4 + 4)

=> 0 + 0 = 0

Hence the system has an infinite number of solutions.

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Answer:

1250g

Step-by-step explanation:

1.25 kg × 1000 = 1250g

Answer: +8

Step-by-step explanation:

yes, it is going to be a positive product, since two negative signs multiply to give a positive sign.

⇒(4)(-0.5)(8)(-2/4)

⇒+8 ..Answer

hope that helps...

The graph of f(t) crosses the y-axis at t = 0, which represents the initial temperature of the ice cream (81°C below room temperature).

The graph of f(t) crosses the y-axis at y=81, which represents the initial temperature of the ice cream, 81°C below room temperature. This is the starting point of the graph, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. As time passes, the temperature of the ice cream decreases, and the graph of f(t) illustrates this change.

The y-intercept of a graph measures the initial value of the function. In this case, the initial temperature of the ice cream is 81°C below room temperature. As the time passes, the temperature of the ice cream decreases at a rate of 0.83°C per minute. This rate of decrease is represented by the slope of the graph, which is 0.83.

The point where the graph of f(t) crosses the y-axis illustrates the initial temperature of the ice cream, and all subsequent points on the graph represent the temperature of the ice cream as time progresses. This is a helpful visual representation of the rate at which the temperature of the ice cream is decreasing. The graph of f(t) is a useful tool for understanding how the temperature of the ice cream changes over time.

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From the given example we can say that , the given expression is in the form of quotient of a powers property.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression,

3^9 / 3^4

= 3^(9-4)

= 3^(5)

So,

if a^m / a^n = a^(m-n)

Its in the form of quotient of powers property.

And from above we can say that, The given expression also in the form of quotient of powers property.

Hence, From the given example we can say that , the given expression is in the form of quotient of a powers property.

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-1

Slope describes the rise over run for a graph.

Slope Formula

Slope is the change in y over the change in x. To find the slope of any line from two points we can use the slope formula. The slope formula is [tex]\displaystyle\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We can plug the points we are given into this formula.

This equals [tex]\frac{3}{-3}[/tex] which is simply -1. The slope of the line is -1.

Counting the Change

The formula above just represents the changes in the y-values divided by the changes in the x-values. So, we can count that the y-values increase by 3. Then, the x-values decrease by 3. This creates the slope [tex]\frac{3}{-3}[/tex] (remember that increases are positive and decreases are negative). Once again this gives the slope of -1.

Using the subtraction operation, the new long-life tire with 3/8 inches depth is deeper than the more typical 7/32 inches by 5/32 inches.

Subtraction operations involve the minuend, the subtrahend, and the result called the difference.

It is one of the four basic mathematical operations, including addition, multiplication, and division.

The depth of the new long-life tire = 3/8 inches

The depth of the old tire = 7/32 inches

The difference = 5/32 inches (3/8 - 7/32)

Thus, the depth difference between the new long-life tire and the typical tire is 5/8 inches.

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The decimal 8. 33 written as a fraction is 8 3/10

A fraction can be defined as the part of a whole number, variable, element,

The several types of fractions are;

Examples of mixed fractions: 2 4/5, 7 1/2

Examples of simple fractions: 1/3, 1/4

Examples of improper fractions: 6/4, 7/5

Example of proper fractions: 2/3, 4/5

From the information given, we have that;

8.33

This is represented as;

8 3/10

Hence. the value is 8 3/10

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The probability that the number of first graders who have liked the hot dog is 15

In math the term probability is defined as a number that reflects the chance or likelihood that a particular event will occur

Here we have know that in a survey of 50 first graders, and then 30% said their favorite food is hot dog.

Here we have to find the probability that the number of first graders who have liked the hot dog

As we know that the number of first graders is 50.

And here we also know that 30% of them are liked the hot dog.

Then it can be calculated as,

=> 50 x 30%

=> 50 x 30/100

=> 15.

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Both equations are equivalent, which means that the two plants always have the same height.

We know that the height in inches for Kylie's plant is represented by the

equation y = 12x, where x is the time in months.

And the height of Glen's plant is represented by the equation 2y = 24x

Notice that if we take the second equation and we divide both sides by 2, we will get:

2y = 24x

2y/2 = 24x/2

y = 12x

This is the same equation than the one that represents the height of Kylie's plant.

Then the two plantes have the same height always.

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The correct answer is 5/2. The median trapezoid is the line segment that bisects the area of the trapezoid and has its end points on the 2 bases of the trapezoid.

The median length is √( (3/2)^2 + (4/2)^2 ) = √(9/4 + 16/4) = √(25/4) = 5/2. So, the length of the median of the trapezoid is 5/2.

Since the diagonals of a median trapezoid bisect each other, the median of the trapezoid is the line segment that connects the midpoints of the diagonals. To find the median length, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the 2 points. In this case, the median length is the square root of the sum of the squares of 1/2 length of the diagonals.

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The length of the median of the trapezoid will be 5/2 units.

Given that the median trapezoid is the line segment that divides the trapezoid's area and has its ends on its two bases,

The median length will be:

√( (3/2)^2 + (4/2)^2 )

= √(9/4 + 16/4)

= √(25/4)

= 5/ units

So, the length of the median of the trapezoid is 5/2.

The median of a median trapezoid is the line segment that links the midpoints of the diagonals since the diagonals of a median trapezoid bisect one another. We may use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and y-coordinates of the two points, to get the length of the median. The median length in this instance is equal to the square root of the sum of the squares of the diagonals' half-lengths.

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All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.

2n8, 5n10, n2, 4n-14

2n8 : This expression is even for all values of n because the coefficient of n is an even number (2).

5n10 : This expression is even for all values of n because the coefficient of n is an even number (5).

2n3 : This expression is even for all values of n because the coefficient of n is an even number (2).

n2 : This expression is even for all values of n because the coefficient of n is an even number (1).

4n-14 : This expression is even for all values of n because the coefficient of n is an even number (4).

All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.

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Answer: To find the price of the car in May, we can use the formula:

New price = Original price - (Original price x Discount rate)

In this case, the original price is $22,800, and the discount rate is 5%, which can be written as 0.05.

So, the new price in May is:

New price = 22700 - (22700 x 0.05)

New price = 22700 - 1135

New price = $21,565

So, the price of the car in May was $21,565.

To find the percentage of the price of the car in May as compared to the price of the car in April, we can use the formula:

(New price / Original price) x 100

In this case, the new price is $21,565 and the original price is $22,800

(21565 / 22700) x 100 = 0.95 x 100 = 95%

Therefore, in May, the price of the car was 95% as compared to the price of the car in April.

Step-by-step explanation:

Lela had the highest score.

Now, According to the question:

A skewed distribution is neither symmetric nor normal because the data values trail off more sharply on one side than on the other. In business, you often find skewness in data sets that represent sizes using positive numbers.

In a negatively skewed distribution, higher values are more frequent than lower values causing the distribution to present a longer left-tail. This implies in a median higher than the mean and in a mode higher than the median:

mean < median < mode.

Therefore, since Lela scored at the mode, Lela had the highest score.

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In order to replace the value in the explicit expression for h, one must evaluate a function h(x) for a particular value of the independent variable x.  h(-3)=30, h(0)=0, h(4)=-40

h(x)=-10x

Let's determine the values below:

h(0)= -10 * (0) = 0 and h(4)= -10 * (4) = -40, respectively.

h(-3)=30, h(0)=0, h(4)=-40.

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The true statements are:

A. KL=15

B. JL bisects IK

D. JL is the perpendicular bisector of IK

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign, ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

Given:

We have a triangle IJK.

m∠IJL=0.5 m∠JIK.

Side IJ ≅ side JK.

JL ⊥ IK.

It bisects the base.

That means,

JL bisects IK and JL is the perpendicular bisector of IK.

So, IL = LK.

3x = 2x + 5

x = 5

KL=15.

Therefore, A, B and D are the true statements.

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Step-by-step explanation:

always remember : the sum of all angles in a triangle is 180°.

so, one angle is 90° (it is a right triangle).

the second angle is 48°.

therefore,

180 = 90 + 48 + third angle

third angle = 180 - 90 - 48 = 42°

so, C is correct.

Answer:

  D.  0.391

Step-by-step explanation:

You want the approximate solution to f(x) = x² -3x +1 = 0 on the interval [0, 1] using 5 iterations of the Bisection Method.

The Bisection Method makes one iteration by finding the function value at the midpoint of the interval. The midpoint replaces the end of the interval whose function value has the same sign. At the end of one iteration, the midpoint of the halved interval is calculated.

Start:

  f(0) = 1, f(1) = -1. Interval: [0, 1]; midpoint: 1/2

First iteration:

  f(1/2) < 0. Interval: [0, 1/2]; midpoint: 1/4

Second iteration:

  f(1/4) > 0. Interval: [1/4, 1/2]; midpoint: 3/8

Third iteration:

  f(3/8) > 0. Interval: [3/8, 1/2]; midpoint: 7/16

Fourth iteration:

  f(7/16) < 0. Interval: [3/8, 7/16]; midpoint: 13/32

Fifth iteration:

  f(13/32) < 0. Interval: [3/8, 13/32]; midpoint: 25/64

The approximate solution after 5 iterations is x ≈ 25/64 ≈ 0.391.

__

Additional comments

The approximate solution in the interval to full calculator precision is 0.38196601125. The exact solution is 1.5-√1.25.

You will notice that the function values for the ends of the interval [0, 1] are [positive, negative]. So, when the function value at the midpoint is negative, that point replaces the right end of the interval.

Of course, the midpoint is the average of the interval end values.

On average, it takes about 3.3 iterations to improve the accuracy of the solution by 1 decimal place.

The 67th term of the arithmetic sequence -17,-23,-29 is -413.

What is the arithmetic sequence?

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same. This difference is called the common difference, and it can be represented by the variable d.

Given the sequence -17,-23,-29, we can see that the common difference is d = -23 - (-17) = -6

The nth term of an arithmetic sequence can be found using the formula:

a_n = a_1 + (n-1)d

where a_1 is the first term of the sequence, n is the term number and d is a common difference.

For the 67th term, a_1 = -17, n = 67 and d = -6

So the 67th term is:

a_67 = -17 + (67-1) * -6 = -17 + 66 * -6 = -17 - 396 = -413

Hence, the 67th term of the arithmetic sequence -17,-23,-29 is -413.

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Answer: -413

Step-by-step explanation:

a) Distance of Slide mountain in the Catskills is 6.2 miles

b) Distance of Gertrude's nose in the Shawangunk's = 6.65 miles

To find a distance on a map, you need to use a ruler or a measuring device such as a pair of compasses. Firstly, place the ruler on the two points you want to measure the distance between. If you are using a pair of compasses, adjust the legs so that the two points are inside the circle created by the compasses. Then, read the distance on the ruler or across the arc of the compasses.

If the distance is relatively short, you can also use the map scale located at the side or bottom of the map. To use the scale, line up the starting point with the scale and then measure the length of the line on the scale. This will give you the distance between the two points.

Finally, if the map has a grid system, you can count the number of squares between the two points and then refer to the grid scale to calculate the distance.

By using one of the methods described above, you should be able to easily measure distances on a map.

a) 2.325 inches * 4 miles/1.5 inches = 6.2 miles

b) 3.8 inches * 3.5 miles/2 inches = 6.65 miles

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