Show that: (sec theta - cosec theta) (1 + tan theta + cot theta) = sec theta tan theta - cosec theta cot theta)

Answer:

8+8+55+55+88

Step-by-step explanation:

The surface area is the sum of all the sides

We have 5 sides

Top and bottom are the same

The area of the top is

1/2 bh = 1/2 (8)(2) = 8

The left and right sides are the same

The area of the left side is

5*11 = 55

The area of the front is

8*11 = 88

The sum of all the 5 sides are

top + bottom + left + right + front

8+8+55+55+88

Answer:

8 + 8 + 55 + 55 + 88

Step-by-step explanation:

Calculate area of base.

8 × 2 × 1/2 = 8

There are two triangles:

8 + 8

Calculate area of rectangle.

8 × 11 = 88

Calculate the areas of two rectangles.

5 × 11 = 55

55 + 55

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

17 feet

Step-by-step explanation:

[tex]15^{2}+8x^{2} = x^{2} \\225 + 64 = x^{2} \\289 = x^{2} \\17 = x[/tex]

Answer:

Step-by-step explanation: I hope it helps :)

1.

[tex]Surface\: area=\:2\pi rh+2\pi r^2\\h = 2ft\\diameter = 2ft\\Radius = d/2=2/2=1ft\\\\A=( 2\times 3.141\times1\times2)+(2\times 3.141 \times 1^2)\\A = (12.564)+(6.282)\\A = 18.846\\A = 18.85ft^2[/tex]

2.

[tex]Area \:of\: square = A=a^2\\A = 3^2\\A=9\\Area\:of \:one \:rectangle\: = (l\times b)\\ A = (8\times 3)\\A = 24cm^2\\\\A = 2(Area\: of\: square)+2(Area\: of \:rectangle)\\A = 2(9)+4(24)\\A = 18+96\\A =114cm^2[/tex]

3.

[tex]Area \: of\: base=?\\ r = 7\:in\\h = 12\:in\\A = \pi \times r^2\\A = 3.141 \times 7^2\\A = 153.909\\\\Height \: of \:the \:cylinder = 12\:inches\\Circumference = 2\pi \times r\\C= 2 \times 3.141 \times 7\\ C =43.98\\\\S.A= 2B+Ch\\S.A = 2(153.909)+43.98(12)\\S.A = 307.818+527.76\\S.A =835.578[/tex]

4.

[tex]Perimeter = a+b+c\\P = 10+8+6\\P = 24\\S.A =2B+Ph\\S.A = 2(24)+24(8)\\S.A =48+192\\S.A = 240\:yd^2[/tex]

Answer:

work is shown and pictured

Answer:

case 1

3x-7y=9

-4x+5y=1

using a graph tool

the solution is the point (-4,-3)------------------> one solution

case 2

y=6x-2

y=6x-4

two parallel lines

the system has no solution---------------> zero solution

case 3

-5x+y=10

-25x+5y=50

is the same line----------------> infinite solutions

Answer:

58 square units.

Step-by-step explanation:

From the graph attached,

Area of the figure = Area of the rectangle A + Area of two squares B and C

Area of rectangle A = Length × width

                                 = 10 × 5

                                 = 50 square units

Area of the square B = (Side)²

                                   = (2)²

                                   = 4 square units

Similarly area of the square C = 2² = 4 square units

Area of the total figure = 50 + 4 + 4

                                      = 58 square units

Therefore, 58 square units will be the answer.

Answer:

Proved.

Step-by-step explanation:

The functions are:

1.) f(x) = 3x - 27 (* I am giving an answer using this equation. Perhaps you did't copy the question well!)

2.) g(x) = [tex]\frac{1}{3} x[/tex] + 9

If two functions are inverses of each other, then:

f(g(x)) = x and g(f(x)) = x situation must be satisfied.

f(g(x)) = 3([tex]\frac{1}{3}x + 9[/tex]) + 27

We simply it to get;

f(g(x)) = x - 27 + 27 = x (*This is correct)

g(f(x)) = [tex]\frac{1}{3}[/tex](3x - 27) + 9 = x - 9 + 9 = x (* This is also correct!)

Step-by-step explanation:

You have to retain a certain amount of money

in that account forever. Say you need $50 to

start an account, you have $200 in that account.

You cannot take out more than $150 from that

account.

Answer:

A: If you do not keep at least that much money in the account, you will be assessed fees.

Step-by-step explanation:

Answer:

22.5 cm

Triangle area is (L x W) / 2

7.5 x 6 = 45

45 / 2 = 22.5

Step-by-step explanation:

brainlist plzzzz

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

Answer:

22

Step-by-step explanation:

Evaluate!

5(5)-3

25-3

22

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 10, thus

sum = 180° × 8 = 1440°

Each interior angle = 1440° ÷ 10 = 144°

Answer:

144 deg

Step-by-step explanation:

Sum of the measures of the angles of a polygon with n sides:

(n -2)180

For a 10-sided polygon, n = 10.

The sum of the measures is

(10 - 2)180 = (8)180 = 1440

Since the polygon is regular, all angles have the same measure, so the measure of 1 angle is

1440/10 = 144

Answer: 144 deg

Answer:

Plug in the x and y values into the equation

Step-by-step explanation:

Answer:

1360cm²

Step-by-step explanation:

Since the shape of the cake is in L shape, we can divide the cake in to rectangles..

The amount of space covered by the frosting = The sum of the areas of the sides that we can find in this L shaped cake diagram.

The sides of this cake, are shaped like a rectangle.

Hence, Area of a Rectangle = Length × Width

a) Side 1 = Rectangle on the left

Area of a Rectangle = Length × Breadth

Length = 30cm

Breadth =10cm

Area = 30 × 10 = 300cm²

Since we have another side with this measurement/ dimensions also,

Side 2 = 300cm²

Side 3 = The front face of the cube by the right

Area of a Rectangle = Length × Breadth

Length = 22cm - 10cm = 12cm

Breadth =10cm

Area = 12 × 10 = 120cm²

Likewise, we have the another side with the same dimensions as well

Hence, Side 4 = 120cm²

Side 5

30 × 5 = 150cm²

Side 6

10 × 5 = 50cm²

Side 7

20 × 5 = 100cm²

Side 8

22cm × 5 cm = 110cm²

Side 9

10cm × 5cm = 50cm²

Side 10

12cm × 5cm = 60cm²

The amount of space covered by the frosting = Area of Sides( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)

= (300 + 300 + 120 + 120 + 150 + 50 + 100 + 110 + 50 + 60) cm²

= 1360cm²

Answer:

1360

Step-by-step explanation:

it is correct on khan academy

Answer:

[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].

2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].

Hope this helped!

Answer:

A. g(x)=1/2x²

Step-by-step explanation:

Given:

f(x)=x²

We have to find g(x)

Since, we are given that g(2)=2

1. g(x)=1/2x²

x=2

g(x)=1/2(2)²

=1/2(4)

=4/2

=2

2. g(x)=1/4x²

x=2,

g(x)=1/4(2)²

=1/4(4)

=4/4

=1

3. g(x)= 2x²

at x=2,

g(x)=2(2)²

=2(4)

=8

4. g(x)=(1/2x)²

x=2

g(x)={1/2(2)}²

=(1/4)²

=1/16

A. g(x)=1/2x² is the answer

Answer: 0.00000565

Step-by-step explanation:

Required to win:

6 number match $10,000

5 number match $ 5,000

4 number match $ 1000

3 number match $ 5,00

2 number match $ 50

1 number match $ 10

Therefore, to win $10,000 ;

All 6 numbers must match

Number of right numbers = 6

Total numbers = 25

Since it is without replacement :

Probability = required outcomes / Total possible outcomes

P(First number match) = 6/25

P(second number match) = 5/24

P(third number match) = 4/23

P(fourth number match) = 3/22

P(fifth number match) = 2/21

P(sixth number match) = 1 / 20

Therefore, Probability of winning $10000 :

(6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (1/20) = 720 / 127512000 = 0.0000056465

= 0.00000565

Answer:

(1,-2)

Step-by-step explanation

y = -3x + 1

y = 2x - 4

-3x + 1 = 2x - 4

-5x + 1 = -4

-5x = -5

x = 1

y= 2(1) - 4

y = 2 - 4

y = -2

(1,-2)

Answer:

1/2

Step-by-step explanation:

Answer:

Exponential

Step-by-step explanation:

The liner function represents that there is a constant change in the original value of the asset

While on the other hand the ex[onential function refers to that function in which there is an increase or decreased in the value of the asset that contains the current value of the asset

Hence, the given situation denotes the exponential function

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Well to find n you gotta separate it.

3 1/5 + n = 9

-3 1/5

n = 5.8

Thus,

to seperate it you subtract 3 1/5 from both sides.

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Answer:

9 squares

Step-by-step explanation:

An equilateral has three equal sides.  You can have two squares on each side: AB, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  You can also have two squares on each side - BC, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  Again, you can have two squares on each side - CA, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  In addition, AB, BC and CA can be a diagonal of squares.  

TL;DR

In conclusion, you have 9 squares in all - 3 as diagonals of squares and 6 as sides of squares. Brainliest appreciated!

No square shares more than two vertices with the equilateral triangle, so we can find the number of squares having two of their vertices at two given points and triple the result. Given 2 points, 3 squares may be drawn having these points as vertices. The figure below shows a red equilateral triangle with the 3 squares that correspond to one of the sides of the triangle. Therefore, 9 squares share two vertices with the equilateral triangle.

Answer:

Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, both the base angles of that triangle measure a. We also know that a + b = 180 because of the definition of supplementary angles. So we have 2 equations from that info. First is the fact that

a + 7x = 180 and the second is

2x + a + a = 180 because of the Triangle Angle-Sum Theorem. If the left side of the first equation = 180 and the left side of the second equation also = 180, then by the transitive property of equality,

a + 7x = 2x + a + a and

a + 7x = 2x + 2a and

5x = a. Now that we know that a = 5x, we go back to our triangle and fill in 5x as a:

5x + 5x + 2x = 180 (the Triangle Angle-sum Theorem again) and

12x = 180 so

x = 15. If x = 15, then

a = 5(15) = 75,

b = 7(15) = 105, and

c = 2(15) = 30

Answer:

Step-by-step explanation:

The ceiling function is a python programming function that rounds a decimal point number to the nearest whole number.

Given the function expression  f(1.5), the ceiling function will round 1.5 to the nearest whole number which is 2

Answer:

  (x +1)^2 + (y +2)^2 = 25

Step-by-step explanation:

A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...

  (AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2

  (AC)^2 = 25

The center of the circle is at A(-1, -2), so the equation is ...

  (x -h)^2 +(y -k)^2 = r^2

for the circle centered at (h, k) with radius r.

We know that the square of the radius (r^2) is 25, so we can write the equation as ...

  (x +1)^2 +(y +2)^2 = 25

Answer:

(x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

Hope this helps :)

Answer:

V = 42 units ^3

Step-by-step explanation:

The volume of a rectangular prism is

V =Bh

V = 8*5 1/4

Changing to a mixed number

V = 8* ( 5*4+1) /4

   =8*21/4

    = 42 units^3

Answer:

[tex]\huge\boxed{V=42\ u^3}[/tex]

Step-by-step explanation:

Th formula of a volume of a prism:

[tex]V=BH[/tex]

B - base

H - height

We have

[tex]B=8;\ H=5\dfrac{1}{4}=\dfrac{5\cdot4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]

Substitute:

[tex]V=(8)\left(\dfrac{21}{4}\right)[/tex]    simplify 8 and 4

[tex]V=(8\!\!\!\!\diagup)\left(\dfrac{21}{4\!\!\!\!\diagup}\right)=(2)(21)=42[/tex]

Answer:

True.

Step-by-step explanation:

In t-test test the value of t can be either negative or positive.

If value of t is negative, then it lies to the left of the mean.

If value of t is Positive, then it lies to the right of the mean.

The given statement is "When you conduct a t test, the calculated value of t can be negative.".

Therefore, the given statement is true.

Answer:

h=3√3 cm

Step-by-step explanation:

An equilateral triangle has 3 Equal sides

The height of an equilateral triangle with side a =a√3/2

That is,

h=a√3/2

Where,

h=height of the equilateral triangle

a=side length

From the triangle given,

a=6cm

Therefore,

h=6√3/2

=3√3

h=3√3 cm