Use less than, equal to, or greater than to complete this statement: The measure of each exterior angle of a regular 10-gon is the measure of each exterior angle of a regular 7-gon.

a. equal to
b. greater than
c. less than
d. cannot tell

Answer:

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The height of the trapezoid has a length of 4 units

From the question, we are to determine the height of the trapezoid

The area of a trapezoid can be calculated by the formula,

\(A = \frac{1}{2}(a+b) h\)

Where A is the area

a and b are the bases

and h is the height

The median of a trapezium is given by

\(\frac{1}{2} (a+b)\)

From the given information,

A = 96 square units

\(\frac{1}{2}(a+b) = 24 \ units\)

Putting the parameters into the formula,

96 = 24 × h

h = 96 ÷ 24

h = 4 units

Hence, the height of the trapezoid has a length of 4 units

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Answer:

Step-by-step explanation:

(1/2)(1/2)=1/4

1 can only be divided by one other integer except1, hence it is not a prime number.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.

Given this definition, 1 is not a prime number because it can only be divided by one other integer, which is 1 itself.

Based on the explanation above, we can then conclude that 1 is not a prime number.

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Answer:

1 is True 2 is False 3 is False 4 is True 5 is False

Step-by-step explanation:

In the quadrilateral WXYZ, the value for area and perimeter is obtained as 289 square units and 63 units respectively.

What is a quadrilateral?

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are ∠A, ∠B, ∠C, and ∠D. A quadrilateral has the following sides: AB, BC, CD, and DA.

To find the perimeter and area of the quadrilateral with vertices W(-12, -2), X(-12,12), Y(5,13), Z(5,-2), we can use the distance formula to find the length of each side and the formula for the area of a quadrilateral.

Distance formula: The distance between two points (x1, y1) and (x2, y2) is given by -

d = √((x2 - x1)² + (y2 - y1)²)

Using this formula, we can find the lengths of the sides of the quadrilateral -

WX = √((-12 - (-12))² + (12 - (-2))²)

WX = 14

XY = √((5 - (-12))² + (13 - 12)²)

XY = √(289)

XY = 17

YZ = √((5 - 5)² + ((-2) - 13)²)

YZ = 15

ZW = √((-12 - 5)² + ((-2) - (-2))²)

ZW = 17

Perimeter: The perimeter of the quadrilateral is the sum of the lengths of its sides.

P = WX + XY + YZ + ZW = 14 + 17 + 15 + 17 = 63

Therefore, the perimeter of the quadrilateral is 63 units.

Area of a quadrilateral: The area of a quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) is given by -

A = (1/2) |x1y2 + x2y3 + x3y4 + x4y1 - y1x2 - y2x3 - y3x4 - y4x1|

Using this formula, we can find the area of the quadrilateral -

A = (1/2) |(-12 x 12) + (5 x 13) + (5 x (-2)) + (-12 x (-2)) - (-2 x 12) - (5 x 12) - (5 x (-12)) - (13 x (-12))| = 289

Therefore, the area of the quadrilateral is 289 square units.

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The cost of installing a typical septic system without any special features can vary depending on various factors, such as the size of the property, soil type, and location. On average, a septic system installation can cost anywhere from $3,000 to $7,000.

The cost of installing a septic system can depend on various factors, such as the size of the property, soil type, location, and regulations in the area. The installation process typically involves excavating the area, installing the septic tank and leach field, and connecting the plumbing to the septic system. The cost of the septic tank itself can range from $500 to $2,000, and the leach field can cost around $2,000 to $4,000. In addition, there may be additional costs associated with obtaining permits and hiring contractors.

Therefore, the cost of installing a typical septic system without any special features can range from $3,000 to $7,000, depending on various factors.

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Answer: the answer to this is true

We have proved that the in radius of a right triangle with legs a and b and hypotenuse c is equal to a/(2+sqrt(a^2+b^2)).

Let ABC be a right triangle with legs a and b and hypotenuse c, and let r be the radius of the inscribed circle. Draw the perpendicular from the center of the inscribed circle to the hypotenuse c, and let the length of this segment be h. Then we have:

r = (a + b - c)/2 (since the inradius is half the perimeter minus the semiperimeter)

h = (a*b)/c (since the area of the triangle is (1/2)ab and also (1/2)ch)

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Multiplying both sides by r and substituting for r and h, we get:

r(a^2 + b^2) = rc^2

r(a + b - c)(a + b + c) = 2ab

r = 2a*b/(a + b + c)(a + b - c)

Substituting the expressions for a, b, and c in terms of sin and cos, we get:

r = 2sin(theta)cos(theta)/(2cos(theta) + 2sin(theta))(2cos(theta) - 2sin(theta))

r = sin(theta)*cos(theta)/(cos(theta) - sin(theta))^2

Simplifying using the identity (cos(theta) - sin(theta))^2 = cos^2(theta) - 2*cos(theta)sin(theta) + sin^2(theta) = 1 - sin(2theta), we get:

r = sin(theta)cos(theta)/(1 - sin(2theta))

r = (1/2)sin(2theta)/(1 - sin(2theta))

r = (1/2)(1 + sin(2theta))/(1 - sin^2(2theta))

r = (1/2)(1 + sin(2theta))/cos^2(2*theta)

Using the double angle identities, we get:

r = (1/2)(1 + 2sin(theta)cos(theta))/(2cos^2(theta) - 1)^2

r = (1/2)(1 + 2(ab/c^2))/(1 - (a^2 + b^2)/c^2)^2

r = (1/2)(c^2/(a^2 + b^2 - c^2))

r = (1/2)(c^2/b^2)

r = c/(2*b)

Substituting for c and b, we get:

r = (a/(2*sqrt(a^2 + b^2)))

Therefore, we have proved that the inradius of a right triangle with legs a and b and hypotenuse c is equal to a/(2+sqrt(a^2+b^2)).

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Answer:

624

Step-by-step explanation:

Answer:

A: Isosceles (two sides the same)

B: Equilateral (all sides the same)

C: Scalene (all sides different)

Step-by-step explanation:

Step-by-step explanation:

Sum of arithmetic terms = n/2 × [2a + (n - 1)×d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.

this is the same as n/2 × (a1 + an), because

an = a1 + (n-1)×d

so, for the series above :

a or a1 = 2

d = 7, as every new term is the previous term plus 7.

for n

37 = a1 + (n-1)×d = 2 + (n-1)×7

and now solve for n

35 = 7n - 7

42 = 7n

n = 6

so, the sum of all terms is

6/2 × (2+37) = 3×39 = 117

Answer:

c

Step-by-step explanation:

Answer:

Pam laid 60 tiles on Saturday and 20 on Sunday.

Step-by-step explanation:

Given that Pam laid three times as many tiles on Saturday as she laid on Sunday, if Pam laid 80 tiles over the weekend altogether, to determine how many tiles did she lay on Saturday the following calculation must be performed:

3X + X = 80

4X = 80

X = 80/4

X = 20

Therefore, Pam laid 60 tiles on Saturday and 20 on Sunday.

Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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Answer:

number of cans Raina will be needed in court floor is 14 cans

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

Raina is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood stain covers 115 square feet. How many cans will she need to cover the court?

CALCULATION;

Given:

length of the rectangular shape =46 feet

width of the the rectangular shape = 35 feet.

The floor of the court room is having a rectangular shape, then we need to calculate the surface Area of the rectangular shape first in order to know the number of cans that Raina will be needed

Surface Area= Length × Width

= 46feet × 35 feet

=1610 square ft

Then to get the number of cans , we need to divide the surface Area by each can of wood stain covers which is 115 square feet,

number of cans Raina will be needed in court = 1610 square ft / 115 square ft = 14

number of cans Raina will be needed in court floor is 14cans

The value of x and y from the figure is 55/3 and 16 respectively

A line is the shortest distance between two points. An angle is the point where two lines meet.

From the given figure, the following are true

2y + 3 + x = 90

Determine the base angle "x"

x + x + 70 = 180

2x + 70 = 180

2x= 180 - 70

2x = 110

x = 55

Substitute

2y + 3 + 55 = 90

2y + 58 = 90
2y = 90 - 58
2y = 32

y = 16

Also

3x +2y + 3 = 90

3x + 32. = 87

3x = 87 - 32

3x= 55

x = 55/3

Hence the value of x and y from the figure is 55/3 and 16 respectively

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the range of the graph is simply the region that it covers vertically, well, from the picture we can see the graph goes down down down to -2 vertically, makes an U-turn and goes back up, the arrowheads mean it keeps on going to infinity, so vertically the graph never goes below -2, so its range is just from -2 up to infinity, or in interval notation [ -2 , +∞ ).

the formula for dy/dx in terms of x and y is:

dy/dx = -3/(x) * y

the value of dy/dx at the point (81, 16) is - 16/27

To find the formula for dy/dx in terms of x and y, we'll differentiate the given equation with respect to x:

\((90x^{(3/4)})(y^{(1/4)})\) = 4860

Differentiating both sides with respect to x:

d/dx [\((90x^{(3/4)})(y^{(1/4)})\)] = d/dx [4860]

Using the product rule for differentiation:

(3/4)(90)\((x^{(-1/4)})(y^{(1/4)})\) + (90\(x^{(3/4)\))(1/4)(\(y^{(-3/4)\))(dy/dx) = 0

Simplifying:

(3/4)(90)\((x^{(-1/4)})(y^{(1/4)})\)  + (90\(x^{(3/4)\))(1/4)(\(y^{(-3/4)\))(dy/dx) = 0

Rearranging terms and isolating dy/dx:

(dy/dx) = -[(3/4)(90)\((x^{(-1/4)})(y^{(1/4)})\)] / [(90\(x^{(3/4)}\))(1/4)(\(y^{(-3/4)\))]

Simplifying further:

(dy/dx) = -3/(x) * y

Therefore, the formula for dy/dx in terms of x and y is:

dy/dx = -3/(x) * y

Now let's find the value of dy/dx at the point (81, 16):

Substituting x = 81 and y = 16 into the formula:

dy/dx = -3/(81) * 16

      = -3/81 * 16

      = - 16/27

Therefore, the value of dy/dx at the point (81, 16) is - 16/27

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4x (4x+3)(4x-3) is the given expression. Here we can use the formula of special products to multiply the given expression.The formula for special product is (a+b)(a-b)=a²-b² .

Consider a=4x and b=3. Substituting the values in the formula, we get

(a+b)(a-b)=a²-b² (4x+3)(4x-3) = (4x)² - (3)²  = 16x² - 9

The given expression 4x (4x+3)(4x-3) can be simplified as 4x(16x² - 9).The next step is to simplify the given expression. Multiply 4x by 16x² and 4x by -9. We get, 4x(16x²) + 4x(-9) = 64x³ - 36x.

Therefore, 4x (4x+3)(4x-3) simplified is 64x³ - 36x.The expression to be solved is (6x + 7)(x+6). Multiplying the given expression (6x + 7)(x+6), using special product method, we get

(6x + 7)(x+6)=6x(x+6) + 7(x+6)= 6x² + 36x + 7x + 42= 6x² + 43x + 42.

Therefore, (6x + 7)(x+6) = 6x² + 43x + 42.

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Answer:

h=9

r=3

and im not so sure about the other 2

Answer:

h = 81

r = N/A

a = 36\pi ^2\\

b = N/A

Step-by-step explanation:

Answer:

826131672772214031100614219154556952747400487828020192584

this is the exact answer. thanks for the points!

Answer:

3x^2(3+x)

Step-by-step explanation:

Answer: 3x^2(3+1)

Because it is divisible by 3 and x^2

Answer:

Step-by-step explanation:

32350*3%= $970.50

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The lengths of the legs of a right triangle, where one acute angle measures 65 degrees and the hypotenuse measures 12, are approximately 10.88 and 5.07.

To find the lengths of the legs of a right triangle, we can use the trigonometric functions sine and cosine. Since we know one acute angle and the hypotenuse, we can use the following formulas:

sin(65) = opposite/hypotenuse

cos(65) = adjacent/hypotenuse

Plugging in the known values and solving for the unknowns, we get:

sin (65) = opposite/12

opposite = 12sin (65) ≈ 10.88

cos (65) = adjacent/12

adjacent = 12cos (65) ≈ 5.07

Therefore, the lengths of the legs of the right triangle are approximately 10.88 and 5.07.

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Answer:

vertex = (1, - 9 )

Step-by-step explanation:

The x- coordinate of the vertex is at the midpoint of the zeros.

Given

f(x) = (x - 4)(x + 2)

Find the zeros by letting f(x) = 0 , that is

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 4 = 0 ⇒ x = 4

Then

\(x_{vertex}\) = \(\frac{-2+4}{2}\) = \(\frac{2}{2}\) = 1

Substitute x = 1 into f(x) for corresponding y- coordinate

f(1) = (1 - 4)(1 + 2) = (- 3)(3) = - 9

Vertex = (1, - 9 )

Answer:

I dont now what is that?????