Write a formula for each rule, and graph the formula for each one.

1.The perimeter P of an equilateral tri-angle equals three times the length of a side s.

2.The number of tablespoons T is equal to the number of teaspoons x divided by 3.

The expression for the side length of the bulletin board is √n (option B).

A square is an object with four sides that are of equal length. The sum of angles in a square is 360 degrees. A square has two diagonals that are of equal length that bisect each other at a right angle.

The area of a square can be determined by calculating the square of a side length.

The area of a square = length x length

= length²

If the area of a square is given, to determine its side length, find the square root of the area.

Length of a side = √area

√n

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Hey you man what are you doing here go to there

Answer:

[tex]tan(x)=\frac{44\sqrt{89}}{89}[/tex]

Step-by-step explanation:

tan is defined as: [tex]tan(x)=\frac{opposite}{adjacent}[/tex]

sin is defined as: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]

cos is defined as: [tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]

We can also define tan as: [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

because plugging in the definitions of sin and cos in we get: [tex]tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}[/tex]

which you'll notice is the original definition of tan(x)

So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

[tex]sin(x)=\frac{44}{45}\\\\cos(x)=\frac{\sqrt{89}}{45}\\\\tan(x)=\frac{sin(x)}{cos(x)}[/tex]

plugging in sin(x) and cos(x) we get:

[tex]tan(x)=\frac{\frac{44}{45}}{\frac{\sqrt{89}}{45}}\\\\tan(x)=\frac{44}{45}*\frac{45}{\sqrt{89}}\\\\tan(x)=\frac{44}{\sqrt{89}}[/tex]

We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: [tex]\frac{\sqrt{89}}{\sqrt{89}}[/tex] which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

[tex]tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}[/tex]

The supergym sold 15,826.24 membership last year

This year it's employees sold 10,412

This number is 52% more that they sold last year

The first step is to calculate 52% of 10,412

52/100 × 10,412

= 0.52 × 10412

= 5,414.24

The number of membership sold this year can be calculated as follows

= 5414.24 + 10,412

= 15,826.24

Hence the number of membership they sold last year is  15,826.24

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Answer:

Step-by-step explanation:

[tex]f(x)=x^2-12x^2+27\\f(x)=x^2-2(x)(6)+6^2-6^2+27\\f(x)=x^2-2(x)(6)+6^2-36+27\\f(x)=(x-6)^2-9[/tex]

This is the graph of the function f(x)=x² shifted right about the x-axis

by 6 units and dropped down about the y-axis by 9 units

Answer:

25/6

Step-by-step explanation:

We determine the scale factor by comparing the lengths of corresponding sides of the square. 
The length of O’N’=15 and the length of ¯¯¯¯¯¯¯¯¯¯¯ON=9

The equation for the scale factor, k is then given by:

O’N’=kON

15=9k

K= 15/9= 5/3.

The scale factor is k= 5/3

The other side of the fence based on the information illustrated is 6.5 feet.

It should be noted that the perimeter of a rectangle is illustrated as:

= 2(length + width)

In this case, the width is given as 7/2 = 3.5 feet.

It should be noted that the perimeter is given as 20 feet.

Therefore, the length will be:

2(length + width) = 30

2(length + 3.5) = 20

2Length + 7 = 20

2L = 20 - 7

2L = 13

L = 13/2

L = 6.5

Therefore, the length is 6.5 feet.

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Answer:

Step-by-step explanation:

450 * 99.40 =  44730

The dimensions of the rectangular prisms are:

Prism M: l=4 cm , w=1 cm and h=6 cm

Prism W: l=2 cm , w=2 cm and h=6 cm

Prism Z: l=6 cm , w=1 cm and h=4 cm

Prism J: l=2 cm , w=4 cm and h=3 cm

Prism R: l=2 cm , w=3 cm and h=4 cm

Prism F: l=1 cm , w=8 cm and h=3 cm

Given, a rectangular prism with a volume of 24 cm³

Dimensions of the prism if the volume is 24 cm³.

Prism M:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×4×1=24

4h=24

h=24/4

h=6 cm

Prism W:

l=4 cm and w=2 cm

we know that volume = h×l×w

h×2×2=24

4h=24

h=24/4

h=6 cm

Prism Z:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×6×1=24

6h=24

h=24/6

h=4 cm

Prism J:

l=2 cm and w=4 cm

we know that volume = h×l×w

h×2×4=24

8h=24

h=24/8

h=3 cm

Prism R:

l=2 cm and w=3 cm

we know that volume = h×l×w

h×2×3=24

6h=24

h=24/6

h=4 cm

Prism F:

l=1 cm and w=8 cm

we know that volume = h×l×w

h×1×8=24

8h=24

h=24/8

h=3 cm

hence we get the required dimensions.

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The average number of viewers over the two week is D. 4.85 x 10^5.

It should be noted that the scientific notation simply has to do with writing of numbers that are either too large or too small. This will be illustrated thus:

In this case, the TV show had 5.6 x 10^5 viewers in the first week and 4.1 x 10^5 viewers in the second week.

Therefore, the average number of viewers over the two weeks will be:

= (5.6 × 10^5) + (4.1 × 10^5) / 2

= 4.85 × 10^5

Note that we had to divide by 2 since it's average.

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Answer:

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

PEMDAS

multiplication and division are on the same level, when you see both work from left to right

addition and subtraction are also on the same leve, work from left to Right

P > E > M = D > A = S

Answer:

p e m d a s

Step-by-step explanation:

I hope it's helpful for you

Answer:

Midpoint formula is given as [(x1+x2)÷2, (y1+y2)÷2], where x and y are coordinates of the points.

Midpoint = [(19+17)÷2, (6+(-3))÷2]

= (36÷2, 3÷2)

= (18, 1.5)

The value of the area are;

Rectangle A = 54 square units

Triangle B = 2 square units

Rectangle C = 6 square units

Whole figure = 62 square units

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

From the figure shown, we have two rectangles

Area of the bigger rectangle;

Length = 9

Width = 6

Now, substitute the value

Area = 9(6)

Multiply through

Area = 54 square units

Area of the smaller rectangle

Length = 9 - 7 = 2

Width = 9 - 6 = 3

Substitute the values

Area = 2(3)

Multiply through

Area = 6square units

The formula for area of a triangle is expressed as;

Area = 1/2 base× height

Base = 9 - 6 = 3

Height = 9 - 2 = 3

Substitute the value

Area = 1/ 2 ×2(3)

Area = 6/ 3

Area = 2

The total area = Rectangle A + rectangle B + Triangle

Total area = 54 + 6 + 2

Total area = 62 square units

Hence, the area is 62square units

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Answer:

A=54 B=3 Whole=73

Step-by-step explanation:

I know this because i did this aswell

Answer:

9.88x

Step-by-step explanation:

multiply both numbers together

It should be noted that 10^-3 × 10^6 in scientific notation is 10³.

It should be noted that scientific notation is simply used in Mathematics to express the numbers that are either too small or too large.

This will be illustrated based on the information given. In this case, we want to multiply 10^-3 × 10^6. This will be illustrated thus:

= 10^-3 × 10^6.

It should be noted that since the question is about multiplication, the powers will be added.

= 10^-3 × 10^6.

= 10³

The answer is 10³.

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Answer: 345.79 - The value of the digit 7 is 7 thousandths, or 0.007.

sorry if this doesn't help..

The equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8) is y = - 1 / 2 x + 6(y equals negative one-half times x plus 6)

The equation of the line is perpendicular to y = 2x + 3 and passes through the point (−4, 8).

Therefore, perpendicular lines follows the rule:

m₁m₂ = -1

Hence,

2m₂= -1

m₂ = - 1 / 2

Therefore, let's find the slope of the line using (-4, 8)

8 = - 1 / 2 (-4) + b

b = 8 - 2

b = 6

Therefore, the equation of the line is y = - 1 / 2 x + 6

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Answer: The answer is D- y= -1/2x+6

Answer: 4/5

Step-by-step explanation:

y = mx + b

m represents the slope in this line.

Answer:

4/5

Step-by-step explanation:

Equation is in slope intercept form:

[tex]y = mx + b[/tex]

where m is the slope and b us the y-intercept

so, slope is 4/5

The given expressions have been evaluated to be equivalent or not equivalent as follows:

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

Next, we would determine whether or not the given expressions are equivalent:

3x + 12 and 3(4 + x):

Opening the bracket, we have:

3(4 + x) = 3x + 12 (Equivalent).

2(3x - 30) and 6 - 30;

Opening the bracket, we have:

2(3x - 30) = 6x - 60

2(3x - 30) = 6 - 30 (Not equivalent).

4(5 - 4x) and 20x - 16;

Opening the bracket, we have:

4(5 - 4x) = 20 - 16x

4(5 - 4x) = 20x - 16 (Not equivalent).

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========================================================

Explanation:

I'll use the substitution method to solve this system of equations.

Solve the third equation for z

2x+z = 5

z = 5-2x

Then solve the second equation for y

x+2y = 5

2y = 5-x

y = (5-x)/2

y = -0.5x+2.5

Plug each of these into the first equation so we can solve for x.

x+y+z = 6

x+(-0.5x+2.5)+(5-2x) = 6

-1.5x+7.5 = 6

-1.5x = 6-7.5

-1.5x = -1.5

x = (-1.5)/(-1.5)

x = 1

Let's use this to find y and z

y = -0.5x+2.5 = -0.5*1+2.5 = 2

z = 5-2x = 5-2*1 = 3

Therefore,

x = 1

y = 2

z = 3

Or we can write it like this:  (x,y,z) = (1,2,3)

-------------------

Check:

Plug these values into equation 1 and simplify

x+y+z = 6

1+2+3 = 6

6 = 6

We get the same thing on both sides.

This confirms equation 1.

Repeat for equation 2.

x+2y = 5

1+2*2 = 5

1+4 = 5

5 = 5

This confirms equation 2.

Lastly, plug those values into equation 3

2x+z = 5

2*1+3 = 5

2+3 = 5

5 = 5

Equation 3 is confirmed.

All three equations are true when (x,y,z) = (1,2,3). The solution is fully confirmed.

We will compute the volume of each figure.

1) Figure A

We have a cone with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the cone is:

2) Figure B

We have a cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 6 cm.

The volume of the cylinder is:

3) Figure C

We have an inclined cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the inclined cylinder is:

4) Figure D

We have a parallelepiped with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the parallelepiped is:

5) Figure E

We have an inclined square pyramid with:

• Ab = base area = 20 cm²,

• h = heigh = 10 cm.

The volume of the square pyramid is:

Answer

Among these figures, figure C and figure D have the same volume.

Answer:

125.

Step-by-step explanation:

5^3

= 5 * 5 * 5

= 25 * 5

= 125.

The probability of rolling exactly  one six = 0.04

what is probability ?

Probability is a branch of mathematics that deals with the occurrence from of a random event . the value is expressed from zero to one .Probability has been introduced in mathematics  to predict how likely events are to happen .

So , acc the question "exactly one six " means  that one roll so that probability must be doubled the probability of " not six " is 4/5 . the probability of a 6 on the roll and not on the second is 1/5 x 4/5 =4/ 25 .

The six could come on the second roll so thst probability must be doubled .

the overall probability of exactly one six 8/25 or 0.32

completing toatl probability -no sixes =4/25 x 4/25 =16/25 =0.04

two sixes =1/5x 1/5 =1/25= 0.04

Hence , the probability of rolling exactly one six = 0.04

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Answer:

10.8

Step-by-step explanation:

30% of 36

= 30/100 * 36

= 3/10 * 36

= 108/10

= 54/5

= 10.8

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