(-2a²) (36³)

What’s do I simply using the properties of exponents

Answer:

They are all true except for D

Step-by-step explanation:

What they are asking you to do, is take your rectangle and flip it over the top.  QR would stay right where it is and line ST would now be on top and line QR would be the bottom.  If you can picture that, you can see that all the statements would be true but D.

The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.

Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:

P = (√2 + 1) / (√2 - 1)

P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]

P = (√2 + 1)² / (2 - 1)

P = (√2 + 1)²

P = 2 + 2√2 + 1

P = 3 + 2√2

Q = (√2 - 1) / (√2 + 1)

Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]

Q = (√2 - 1)²

Q = 2 - 2√2 + 1

Q = 3 - 2√2

Then, the value of P² + Q² + P · Q is:

M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)

M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8

M = 9 + 8 + 9 - 8 + 3 - 8

M = 21 - 8

M = 13

The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.

The statement is poorly formatted and reports typing mistakes, correct form is presented below:

If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.

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Answer:

[tex]h^7-6[/tex]

Step-by-step explanation:

1) Regroup terms.

[tex]h^4h^3-6[/tex]

2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]h^{4+3}-6[/tex]

3) Simplify 4 + 3 to 7.

[tex]h^7-6[/tex]

Step-by-step explanation:

The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters

Answer:

3024

Step-by-step explanation:

Each chosen member (out of 9 members) will occupy a different position

out of these four (president , vice-president , secretary , treasurer).

So, here we have to calculate the Number of Permutations of 9 members Taken 4 at a Time :

= 9P4

= 9 × 8 × 7 × 6

= 3024

Answer:

x^2/ 16 + y^2/4 = 1

Step-by-step explanation:

The major axis is 4 and that goes with the x variable.  It is the major axis because 4 is a larger value than 2.

4 x 4 = 16

2 x 2 = 4

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:

(x - h)² / a² + (y - k)² / b² = 1     (1)

Where:

The major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:

x² / 16 + y² / 4 = 1

The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.

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Answer: it’s 128 (also what you did on my question was not cool, do better)

Step-by-step explanation:

We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128

The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.

Given:

Square base edge  lenght 2 cm than the height of the pyramid.

Height of the pyramid is 6 cm.

Square base edge length = Height of pyramid + 2cm

= 8 cm.

Base area:

Area of the square is calculated as side².

Area of square = 8*8

= 64 cm²

Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]

[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]

The volume of the pyramid is [tex]128[/tex] cm³.

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Answer:

22°

Step-by-step explanation:

Since IJ is a diameter, arc LJ measures 68 degrees.

Therefore, the measure of angle JKL is (112-68)/2=22°

Step-by-step explanation:

180(n-2)/n=90 ( this is the solution for the 90)

cross multiplying

180n-360=90n

180n-90n=360

90n=360

90n/90=360/90

n=4, the number of sides for the polygon with 90° is 4 sides

Solution for 100°

180(n-2)/n=100

180n-360=100n

180n-100n=360

80n=360

80n/80=360/80

n=4.5

Same applies to the rest 110°,125° ,150°,175°

The rate of  VAT is 10%.

In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.

We assume the rate of discount and the rate of VAT to be r%.

Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.

Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)

Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).

Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).

The price after VAT is given to be Rs. 9900.

Thus, (100 + r)(100 - r) = 9900,

or, 100² - r² = 9900,

or, r² = 100² - 9900,

or, r² = 10000 - 9900 = 100,

or, r = ±√100 = ±10.

Since r is the rate of VAT, it cannot be negative, making r = 10.

Thus, the rate of  VAT is 10%.

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The scale factor from Figure A to Figure B is 4

From the question, we have the following statement:

Figure B is a scaled copy of Figure A.

The corresponding side lengths of figure A and figure B are:

Figure A = 10

Figure B = 40

The scale factor from Figure A to Figure B is then calculated as:

Scale factor = Figure B/Figure A

Substitute the known values in the above equation

Scale factor = 40/10

Evaluate the quotient

Scale factor = 4

Hence, the scale factor from Figure A to Figure B is 4

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The area of the plastic used to form the lampshade is 2021.25 square centimeters

The given parameters in the question are:

Outer radius, R = 28 cm

Inner radius, r = 7 cm

Angle, ∅ = 315

The area of the plastic used to form the lampshade is calculated using the following area  of sector formula

A = ∅/360 * π(R² - r²)

Substitute the known values in the above equation

A = 315/360 * 22/7 * (28² - 7²)

Evaluate the exponents

A = 315/360 * 22/7 * (784 - 49)

Evaluate the difference

A = 315/360 * 22/7 * 735

Evaluate the product

A = 2021.25

Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters

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Answer:

Ben was standing in the

Step-by-step explanation:

84 000 000

+ 00 530 000

+ 00 000 216

_________________

84 530 216

From this u can see that the 3 is in the ten thousands place

Based on the sequence of numbers given, the number that is represented by the question mark is 2679 = 2.

The sequence requires that you count the number of circles that a group of number has. For instance 9 has one circle and 8 has two circles because of the way they are drawn.

The numbers 111, 3213, and 1234 will therefore be equal to 0 because there is no number that has a circle in it.

The number 8096 however, will be equal to 5 because there are 5 circles. Two in 8. 1 in 0. 1 in 9. 1 in 6.

This means that the last number of 2679 will therefore be equal to 2 because there are two circles. One circle is in 6, and the other circle is in  9.

In conclusion, the number represented by the question mark is 2.

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Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 95000, r = 0.06, n = 12.

Hence the value of the loan after t years is:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]

[tex]A(t) = 95000(1.005)^{12t}[/tex]

You have monthly payments of $1,200, hence the amount paid after t years is:

P(t) = 12 x 1,200t = 14400t

Then we have to solve for:

A(t) = P(t)

[tex]14400t = 95000(1.005)^{12t}[/tex]

Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.

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The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16

Rational expressions are written in the form a/b where a and b are integers.

According to the question, we need to determine the expression that is equal to x-4/2(x+4)

From the fourth option;

x²-16/2x+8 * x+4/x²+8x+16

Factorize the quadratic part to have;

x²-16/2x+8 * x²+8x+16/x+4

(x+4)(x-4)/2(x+4) * x+4/(x+4)^2

Cancel out the common expression to have;

x-4 * 1/2(x+4)

x-4/2(x+4)

Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16

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The approximate area of the hexagon  = 672 cm²

What is hexagon ?

apothem of the hexagon = 14 cm

perimeter of the hexagon = 96 cm

Area of the hexagon = [(3√3) / 2] a²     ; where a is the measure of the side

hexagon has 6 sides.

Perimeter = 6a

96 cm = 6a

96 cm / 6 = a

16 = a

There are 6 triangles in the hexagon .

Area of a triangle = (height * base) / 2

A = (14 cm * 16 cm) / 2

A = 224 / 2

A = 112 cm²

The approximate area of the hexagon = 112 cm²  * 6 triangles = 672 cm²

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Answer: D). 672 cm2

Step-by-step explanation:

Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

Given: 4x - 8y = 9 ............(1)

8x - 7y = 9 ............(2)

To be the same line, the equations have to be multiples of each other.

Multiplying (1) by 2, we get

2(4x - 8y = 9) = 8x - 16y = 18

From (1) solve the value of y, we get

4x - 8y = 9 ............(1)

-8y = -4x + 9

The value of y = (1/2)x - 9/8

From (2),

8x - 7y = 9

solve the value of y, we get

-7y = -8x + 9

The value of y = (8/7)x - 9/7

To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

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[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{3V}{\pi h} } .[/tex]

Step-by-step explanation:

[tex]\displaystyle\\V=\frac{1}{3} \pi r^2h.\\[/tex]

Multiply both sides of the equation by 3:

[tex]3V=\pi r^2h.[/tex]

Divide both sides of the equation by πh:

[tex]\displaystyle\\\frac{3V}{\pi h} =\frac{\pi r^2h}{\pi h} \\\frac{3V}{\pi h}=r^2\\ r^2=\frac{3V}{\pi h} .\\r*r=\sqrt\frac{3V}{\pi h} *\sqrt{\frac{3V}{\pi h} } \\r=\sqrt{\frac{3V}{\pi h} } .\\[/tex]

Answer:

Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32

Answer:  slope=-1

Step-by-step explanation:

9-13     -4

------   ---------    -4/4=-1

4-0       4

Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.

A fraction is not defined when the denominator is zero.

In this problem, the expression is given by:

cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.

The denominators are zero in two cases:

Hence the equation is not defined for an angle of 90º.

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Answer:

y = 5x - 7

Step-by-step explanation:

y = mx + c

y = 5x + c

to find c, input given coordinates

8 = 5 x 3 + c

8 = 15 + c

-c = 15 - 8

-c = 7

c = -7

put that all together and you get:

y = 5x - 7

The equation of the line with a slope of 5 that contains the point (3,8) is

The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Given that the slope is 5 and the line contains the point (3,8), we can substitute these values into the equation and solve for the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

We have:

y - 8 = 5(x - 3)

Expanding and simplifying:

y - 8 = 5x - 15

Now, let's isolate y:

y = 5x - 15 + 8

y = 5x - 7

Therefore, the equation of the line with a slope of 5 that contains the point (3,8) is y = 5x - 7.

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The length of the line segment of octagon which is AB equal to 3.4 cm.

Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.

We are required to find the length of the line segment AB.

A regular octagon has eight equal sides.

Area of regular octagon=Perimeter*apothem/2-----------1

We have to put the value of area and apothem in equation 1.

54=perimeter*4/2

Perimeter=(54*2)/4

=27 cm

Perimeter=27 cm.

Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,

Perimeter=8*side

27=8*AB

AB=27/8

=3.375 cm

After rounding off it will be equal to 3.4 cm.

Hence the length of line segment is equal to 3.4 cm.

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Answer:

A

Step-by-step explanation:

The annual rate of inflation is 35560.86%.

To find the annual rate of inflation:

Now, sub in 4 and 0.099

Therefore, the annual rate of inflation is 35560.86%.

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The correct question is given below:

The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?

The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.

Set 1: 12, 8, 10, 50

Set 2: 13, 9,8

To determine the mean for each set

Mean = totality of elements/number of elements

Mean of Set 1:

[tex]$=\frac{12+8+10+50}{4}[/tex]

[tex]$=\frac{80}{4}=20$[/tex]

Mean of Set 2:

[tex]$=\frac{13+9+8}{3}[/tex]

[tex]$=\frac{30}{3}=10$[/tex]

To determine the mean absolute deviation (MAD) of the data in each set.

M.A.D of Set 1:

[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]

[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]

M.A.D of Set 2:

[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]

[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]

The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.

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688,747,536 ways in which the people can take the seats.

There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.

When the whistle blows, each person needs to change to an orthogonally adjacent seat.

(This means that the person can go to the seat in front, or the seats in the sides).

This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.

Now, if we take the options that each seat has, and we take the product, we will get:

P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.

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The value of x if a, b, and c are collinear points and b is between a and c : 7

Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.

According to the given information:

if A, B, and C are col-linear points and B is between A and C

then

AB+BC=AC

AB=x+6

BC=3x-5

AC=36-x

(x+6)+(3x-5)=36-x

(x+3x)+(6-5)=36-x

4x+1=36-x

4x+x=36-1

5x=35

x=35/5

x=7

The value of x is 7

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The inequality that describes the number of stars S that Kwame must earn per day to get a prize from the classroom treasure box is: S > 16.

The number of stars that he earns is represented by the variable S. He must earn more than 16 stars to earn a prize from the classroom treasure box, hence the inequality that represents the desired amount is given as follows:

S > 16.

Which is read as:

S is greater than 16, which is derived from the Fact that Kwame must earn more than 16 stars per day to get a prize, as stated in the problem.

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Answer:

- 7

Step-by-step explanation:

note that

+ (- ) = - ( adding a negative is equivalent to subtraction )

- (- ) = + ( subtracting a negative is equivalent to addition )

then

7 + (- 14) = 7 - 14 = - 7

Answer: 4

Step-by-step explanation:

[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]