state whether -4^{2} and (-4)^{-2} represent the same quantity. Explain.

the answer is 20 hope it helped :)

Answer:

I think the answer is H

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Answer:H=191.2

Step-by-step explanation:

H=2.9(39)+78.1

H=113.1+78.1

H=191.2 cm

The simplest form of the square root of \(243x^7\) is \(9x^3\sqrt{3x}\).

We know that, we can write the number and expression as,

243 = 3*3*3*3*3 = \(3^5=3^4*3^1\)

\(x^7=x^6*x^1\)

Hence,

Square root of 243 is \(\sqrt{3^4*3^1}=3^2*\sqrt{3}=9\sqrt{3}\).

Square root of \(x^7\) is \(\sqrt{x^6*x^1}=x^3\sqrt{x}\)

Hence,

Simplest form of square root of \(243x^7\) is \(9\sqrt{3}*x^3\sqrt{x} = 9x^3\sqrt{3x}\).

Square root

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number.

The square root symbol is usually denoted as ‘√’. It is called a radical symbol. To represent a number ‘x’ as a square root using this symbol can be written as: \(\sqrt{x}\).

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Answer:

\(\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}\)

\(\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10\)

\(\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10\)

\(\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}\)

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The mean scores are the same.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more spread out that Lisa's, which means Lisa's test scores are more consistent.

The particular solution to the following system is x(t) = C₁\(e^{5t}\) + C₂\(e^{t}\) + (5/2) \(e^{t}\)/D

x' = 3x + 2y + 3\(e^{t}\)

y' = 2x + 3y - 2\(e^{t}\)

The first equation can be written as

(D-3)x - 2y = 3\(e^{t}\)

The second equation can be written as

-2x + (D-3)y = - 2\(e^{t}\)

(D-3)²x - 4x = (D-3)3\(e^{t}\) - 4\(e^{t}\)

(D²+9-6D-4)x = 3\(e^{t}\) - 9\(e^{t}\) - 4\(e^{t}\)

(D²-6D+5)x = - 10\(e^{t}\)

Auxiliary Equation

m²-6m+5=0

(m-5)(m-1)=0

CF = C₁\(e^{5t}\) + C₂\(e^{t}\)

Particular Integral

PI = -10\(e^{t}\)/(D²-6D+5)

= -10\(e^{t}\)/(D-5)(D-1)

= (5/2) \(e^{t}\)/D

x(t) = C₁\(e^{5t}\) + C₂\(e^{t}\) + (5/2) \(e^{t}\)/D

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Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Answer:

\( \dfrac{28}{81} \)

Step-by-step explanation:

\(-\dfrac{4}{9}(-\dfrac{7}{9}) =\)

\( = \dfrac{4 \times 7}{9 \times 9} \)

\( = \dfrac{28}{81} \)

Answer:

x = 4

Step-by-step explanation:

Given: 190x + 700 = 1,460

1. Subtract 700 from both sides:

190x + 700 - 700 = 1,460 - 700

190x = 760

2. Divide both sides by 190 to isolate x:

190x ÷ 190 = 760 ÷ 190

x = 4

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Answer:

$450

Step-by-step explanation:

The TV is on sale for 20% off.

The original price is $90 more than the sale price.

Discount on TV = 20% of total.

\(.2x = 90\)

Divide both sides by .2 to solve for x.

\(\frac{0.2x}{.2} = \frac{90}{.2}\)

\(x = $450\)

Answer:

try this

Step-by-step explanation:

Make a straight cut through the center, cutting the cake in half.

Stack the two halves, one on top of the other and then cut them all in half #2. stack these 4 pieces of cake on top of each other and make your third cut, cutting them all in half for 8 equal, but messy, pieces of cake with 3 cuts.

Answer:

It's friday for me so here u go

Step-by-step explanation:

Answer:The answer is in the attached file

Step-by-step explanation:

Answer:

No solution:  \(4(0.6x-0.9)=2.4x-2.8\)

One solution:  \(0.5(3x-8)=0.8x+0.9\)

Many solutions:  \(4.2x-3.8=7(0.6x-0.7)+1.1\)

Step-by-step explanation:

\(4.2x-3.8=7(0.6x-0.7)+1.1\)

\(\implies 4.2x-3.8=4.2x-3.8\)

Therefore, true for all \(x\) so many solutions

\(4(0.6x-0.9)=2.4x-2.8\)

\(\implies 2.4x-3.6=2.4x-2.8\)

\(\implies -3.6=-2.8\)

Therefore, no solution

\(0.5(3x-8)=0.8x+0.9\)

\(\implies 1.5x-4=0.8x+0.9\)

\(\implies 0.7x=4.9\)

\(\implies x=7\)

Therefore, one solution

Answer:

208/8=26

Step-by-step explanation:

Each friend would get 26 beads.

The statement makes sense and is clearly true. When graphing linear functions, the rate of change is represented by the slope of the line.

The rate of change of a linear function is equal to its slope, which means that the steeper the slope, the greater the rate of change.

Therefore, if two linear functions are graphed and one has a greater slope than the other, it also has a greater rate of change. This can be explained by the fact that the slope represents the change in the dependent variable for every unit change in the independent variable, so a larger slope indicates a greater amount of change per unit.

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Answer:

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3) For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4) For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

Step-by-step explanation:

This can be done using the completing the square method.

The standard equation of a circle is given by \((x - a)^2 + (y-b)^2 = r^2\)

1) For \(x^2 + y^2 - 4x + 12y - 20 = 0\)

\(x^2 - 4x + y^2 + 12y = 20\\x^2 - 4x + 2^2 + y^2 + 12y + 6^2 = 20 + 4 + 36\\(x-2)^2 + (y+6)^2 = 60\\\)

Therefore, for \(x^2 + y^2 - 4x + 12y - 20 = 0\), the standard form is \((x-2)^2 + (y+6)^2 = 60\\\)

2) For \(x^2 + y^2 + 6x - 8y - 10 = 0\)

\(x^2 + 6x + y^2 - 8y = 10\\x^2 + 6x + 3^2 + y^2 - 8y + 4^2 = 10 + 9 + 16\\(x + 3)^2 + (y- 4)^2 = 35\\\)

Therefore, for \(x^2 + y^2 + 6x - 8y - 10 = 0\), the standard form is \((x + 3)^2 + (y - 4)^2 = 35\\\)

3)  For \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\)

Divide through by 3

\(x^2 + y^2 + 4x + 6y = 5\)

\(x^2 + y^2 + 4x + 6y = 5\\x^2 + 4x + 2^2 + y^2 + 6y + 3^2 = 5 + 4 + 9\\(x + 2)^2 + (y+ 3)^2 = 18\\\)

Therefore, for \(3x^2 + 3y^2 + 12x + 18y - 15 = 0\),  the standard form is \((x + 2)^2 + (y+ 3)^2 = 18\\\)

4)  For \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\)

Divide through by 5

\(x^2 + y^2 - 2x + 4y = 6\)

\(x^2 + y^2 -2x + 4y = 6\\x^2 - 2x + 1^2 + y^2 + 4y + 2^2 = 6 + 1 + 4\\(x - 1)^2 + (y+ 2)^2 = 11\\\)

Therefore, for \(5x^2 + 5y^2 - 10x + 20y - 30 = 0\),  the standard form is \((x - 1)^2 + (y+ 2)^2 = 11\\\)

5) For \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\)

Divide through by 2

\(x^2 + y^2 - 12x - 8y = 4\)

\(x^2 + y^2 - 12x - 8y = 4\\x^2 - 12x + 6^2 + y^2 - 8y + 4^2 = 4 + 36 + 16\\(x - 6)^2 + (y+ 4)^2 = 56\\\)

Therefore, for \(2x^2 + 2y^2 - 24x - 16y - 8 = 0\),  the standard form is \((x - 6)^2 + (y+ 4)^2 = 56\\\)

6) For \(x^2 + y^2 + 2x - 12y - 9 = 0\)

\(x^2 + 2x + y^2 - 12y = 9\\x^2 + 2x + 1^2 + y^2 - 12y + 6^2 = 9 + 1 + 36\\(x+1)^2 + (y-6)^2 = 46\\\)

Therefore, for\(x^2 + y^2 + 2x - 12y - 9 = 0\), the standard form is \((x+1)^2 + (y-6)^2 = 46\\\\\)

For Plato / Edmentum

Just to the test and got it right ✅

9514 1404 393

Answer:

  $105

Step-by-step explanation:

The thicker wall takes 345 -205 = 140 more blocks. Each of those costs $0.75, so the added blocks will cost ...

  140 × $0.75 = $105

The thicker wall will cost $105 more.

We want to see which statements are true about the functions f(x) and g(x). The true statements are:

Let's read each statement and then let's see why is true or why is not true.

1) "The graphs share the same axis of symmetry"

We define the axis of symmetry as a vertical line that divides the graph in two halves, in the case of parabolas, the axis of symmetry always passes through the vertex.

So with this in mind,  you can clearly see that both functions have the same axis of symmetry, so this first statement is true.

2) "The y-intercept for f(x) is greater than the y-intercept for g(x)."

The y-intercept of a function is the value of y at which the graph intercepts the y-axis.

By looking at the graph, you can see that f(x) will intersect the y-axis way above than g(x), this implies that the statement is correct.

3) "f(2) + g(4) = 0"

By looking at the graph we can see that:

f(2) + g(4) = 2 + (-3) = -1

So the statement is false.

4) "The domain of f(x) has more elements than the domain of g(x)."

The domain is the set of values of x that the functions allow, because both are quadratic functions, both have the same domain, which is the set of all real numbers.

5) "The graphs share the same relative maximum."

Relative maximums are values of the function that are larger than the surrounding values in a given interval, here you can see that g(x) and f(x) don't have the same curvature (g(x) actually has a universal maximum) thus this is false.

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Answer:

The farm would need 235.2 liters daily for 4 horses, 8 sheep and 16 chickens.

Step-by-step explanation:

The daily consumption of water in the farm must be:

\(x = (4\,horses)\times \left(50\,\frac{L}{horse} \right) + (8\,sheep)\times \left(4\,\frac{L}{sheep} \right) + (16\,chickens)\times \left(0.2\,\frac{L}{chicken} \right)\)

\(x = 235.2\,L\)

The farm would need 235.2 liters daily for 4 horses, 8 sheep and 16 chickens.

To identify which of the following options are true:

Option 1: Yes, the domains of g(X) and h(x) include all real numbers but since it says h(x) is restricted, Option 1 is not true.

Option 2: The function i(x) and h(x) are not inverse function because the inverse of log₃ (x + 1) is 3^x - 1. Option 2 is not true as well.

Option 3: Out of the 4 functions, i(x) is not the function that increases most rapidly. Hence, Option 3 is not true as well.

Option 4: The range of f(x) is y ≥ 0. The range of g(x) is y ≥ - 14. The range of h(x) is y > 1. The range of i(x) is all real numbers. Hence, the range of i(x) includes more negative y-values than the ranges of f(x), g(x), or h(x). Option 4 is true.

Appraisal is defined as the process by which people evaluate the events, situations, or occurrences that lead to their having emotions.

Appraisal refers to the cognitive process through which individuals assess and evaluate the various events, situations, or occurrences that trigger emotional responses within them. It involves the interpretation and analysis of the meaning and significance of these events, which ultimately influences the emotional experience and response. During the appraisal process, individuals assess several key factors, such as the relevance of the event to their goals, the implications and consequences of the event, and the personal significance it holds for them. They also evaluate their ability to cope with or manage the event and consider the potential for future similar events. The appraisal process is subjective and influenced by individual beliefs, values, and previous experiences. Different people may appraise the same event differently, leading to variations in emotional responses.

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When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.

To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.

If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.

Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.

In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.

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Answer:

  1.5 < x < 34.7

Step-by-step explanation:

You want a compound inequality describing possible lengths (x) for the third side of a triangle with sides 18.1 and 16.6.

The shortest side cannot be any shorter than the difference of the two known sides:

  18.1 -16.6 = 1.5

The longest side cannot be any longer than the sum of the two known sides:

  18.1 +16.6 = 34.7

The possible lengths of the third side are given by ...

  1.5 < x < 34.7

__

Additional comment

If the third side is exactly equal to the sum or the difference, then the "triangle" looks like a line segment. It has zero area. That possibility is usually disallowed. If you want to allow it, then change < to ≤ in the inequality.

Answer:

Step-by-step explanation:

Opposite angles of a rhombus are congruent, and adjacent angles of a rhombus are supplementary.

The Standard from of \(\sqrt{7} n^{2}\) is \((\sqrt{7} n^{2}+ (0*n) + (c*0) = \sqrt{7} n^{2}\), degree is 2, leading co-efficient is \(\sqrt{7\\}\) and the polynomial is a monomial when classified on the basis of number of terms.

To solve this question, we need to have a proper understanding of the standard form, degree and leading coefficient of the polynomial.

A polynomial is expressed in its standard form by writing the variable with the highest power along with its co-efficient first, then the next degree and so on. The standard form of polynomial, \(f(x) = a_{n} x^{n}+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+...+a_{2} x^{2}+a_{1} x^{1}+a_{0} x^{0}\\ or, f(x) = a_{n} x^{n}+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+...+a_{2} x^{2}+a_{1} x+a_{0}\)

where "x" is the variable and "a" are the coefficients.

In our case, the variable is "n" and its power is 2, and there are no other terms in this polynomial, i.e., comparing with the above mentioned standard form of f(x), we can derive that \((a_{1}=0), (a_{0}=0)\).

Hence, the Standard from of \(\sqrt{7} n^{2}\) is \([(\sqrt{7} *n^{2})+ (0*n) + (c*0)] = \sqrt{7} n^{2}\).

Now, degree of a polynomial is the highest power of the variable, present in the polynomial. Here, since there is only one valid term, it is the highest power in itself and hence, degree is 2.

Leading coefficient of a polynomial is the co-efficient of the term having the highest power at the variable. Here, since the polynomial has only one term, the leading co-efficient is \(\sqrt{7\\}\).

Finally, since the polynomial has only one term, it is classified as a "Monomial".

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Answer:

Step-by-step explanation:

10+banna x orange

Answer:

Apple=10. Banana=6. Orange=6.

Step-by-step explanation:

Answer:

1) at the highest Point

KE= 0  PE=2116.8 N

2) 3 m above the ground

PE= 529.2 N KE=1587.6 N

3) at the ground

KE= 2116.8 N and PE=0

Step-by-step explanation:

The potential energy is given by

PE= mgh   where m is the mass , g is the acceleration due to gravity which is equal to 9.8 m/s² and h is the height.

The kinetic energy is given by KE= 1/2 mv² where m is the mass of the body and v is the velocity.

1) at the highest Point

Now at the highest point the  velocity is zero

KE= 1/2 mv²

KE= 0

PE = mgh

PE= 18 *9.8* 12= 2116.8 N

Total Energy = KE + PE= 0 + 2116.8 N= 2116.8 N

2) 3 m above the ground

At 3 m above the ground

PE= mgh

PE= 18 *9.8* 3= 529.2 N

According to law of conservation of energy the total energy ( sum of KE and PE)  remains the same at every point.

Total Energy = KE + PE

2116.8 N-529.2N= 1587.6N

KE=1587.6 N

3) at the ground

at the ground the height will be zero

PE= mgh

PE= 18 *9.8* 0= 0 N

According to law of conservation of energy the total energy ( sum of KE and PE)  remains the same at every point.

Total Energy = KE + PE

2116.8 N=2116.8 N + 0

KE= 2116.8 N

or

KE= 1/2 mv²

KE = 1/2* 18 *(15.36)²= 2116.8

The critical point is x=1, additionally, f'(x) does not exist at x = 0 and x = 3, which are also critical points. The maximum value of f(x) over the interval [0,3] is 11/3, which occurs at x = 3.  If g(x) = 3x²– x + 2 over [1, 3] then c = 11/12 satisfies the MVT

a. i. To find the critical points of f(x), we need to find where its derivative equals zero or does not exist. Taking the derivative of f(x) with respect to x, we get f'(x) = 4x - 4. Setting this equal to zero, we get x = 1, which is a critical point. Additionally, f'(x) does not exist at x = 0 and x = 3, which are also critical points.

ii. To find the extrema of f(x) over the interval [0,3], we need to evaluate f(x) at the critical points and endpoints of the interval. We have f(0) = -8, f(1) = -9/3, f(3) = 11/3, and f'(x) = 0 at x = 1. Therefore, the minimum value of f(x) over the interval [0,3] is -3, which occurs at x = 1. The maximum value of f(x) over the interval [0,3] is 11/3, which occurs at x = 3.

b. The Mean Value Theorem (MVT) states that for a continuous and differentiable function f(x) over the interval [a, b], there exists at least one value c in (a, b) such that  \(f'(c) = (f(b) - f(a))/(b - a)\)

In this case, g(x) = 3x² - x + 2 is continuous and differentiable over [1, 3]. Therefore, there exists at least one value c in (1, 3) such that g'(c) = (g(3) - g(1))/(3 - 1). Simplifying this equation, we get 6c - 1 = 19/2, which means c = 11/12 satisfies the MVT.

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Complete Question:

Find the following, show all work.

\(f (x) = \frac{2x^{2}}{3} + x^{2} - 4x -8\)

Find:

i. Critical Points. Explain in 50 words.

ii. Extrema for f(x) over the interval [0,3]. Explain in 50 words.

b. g(x) = 3x²– x + 2 over [1, 3], what value satisfies the MVT? Explain in 50 words.