Question 3 of 10
Which of the following must be true for an expression to be a difference of
two squares?
a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients
OA. a, b, and c
B. a and b
OC. a and c
D. b and c

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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Answer: 4

Step-by-step explanation:

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

Expected value of playing the game  = $0.8

What is cost ?

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

25% chance to win back $2 = $2  25% = $0.5

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing game = $2.8 - $2 = $0.8

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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 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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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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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.

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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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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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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The name of the polygon is (B) hexagon.

To find the name of the polygon:

Therefore, the name of the polygon is (B) hexagon.

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The complete question is given below:

A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?

A) Octagon

B) Hexagon

C) Heptagon

D) Quadrilateral

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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The midpoint between A and E is (0,1)

The coordinates of the cities are given as:

A(-2,3), B(2,7), C(7,8), D(6,3) and E(2,-1).

From the above, we have:

A = (-2,3)

E = (2,-1)

The midpoint between A and E is calculated using

Midpoint = 1/2 * (x1 + x2, y1 + y2)

Substitute the known values in the above equation

Midpoint = 1/2 * (-2 + 2, 3 - 1)

This gives

Midpoint = 1/2 * (0, 2)

Evaluate the product

Midpoint = (0, 1)

Hence, the midpoint between A and E is (0,1)

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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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[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:

- 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

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 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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Step-by-step explanation:

3×5×2 = 30 lorry trips to deliver 2,500 crates.

3 lorries, 5 trips per day, 2 days

that means that one lorry trip transports

2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.

now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.

that looks like

x × 6 × 83.33333... = 10,000

x × 6 × 83 1/3 = 10,000

x × (6×83 + 6 × 1/3) = 10,000

x × (498 + 2) = 10,000

500x = 10,000

x = 20

so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.

these are altogether 20×6 = 120 lorry trips.

that is 4 times the number of the original scenario (30 trips).

and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).

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:

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°

Answer:

Step-by-step explanation:

13

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 area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

For given question,

We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]

The region bounded by given curves is as shown below.

The area of this region would be,

[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]

Now we evaluate above integral.

[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]

[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]

Therefore, the area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

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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

Answer:

14

Step-by-step explanation:

Subtract 3 from both sides to isolate g / make g the subject :

g + 3( -3 ) = 17 (-3)

g = 17-3

g = 14

Substituting this into the equation gives us :

14 + 3  = 17

17 = 17

So our final answer is 14

Hope this helped and have a good day

Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

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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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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?