2. Given that (ab - c) + d = e
Solve for a

Answer:  see proof below

Step-by-step explanation:

Use the following Power Reducing Identities:

[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]

Use the following Product to Sum Identity:

[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]

[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

Answer:

Ten billion

Step-by-step explanation:

There would around 16×10⁻¹⁰ ants to wrap around the earth.

Circumference is the distance around a circle., basically it is the perimeter of the circle.

Given that, an average sized ant is about 4×10⁻³ meter long the circumference of the earth is about 4×10⁻⁷ meters, we are asked to find the number of ants that would it take to wrap around earth,

To find the same, we will multiply the size of ants to the circumference of the earth,

So, 4×10⁻³ × 4×10⁻⁷

= 16×10⁻¹⁰

Hence, there would around 16×10⁻¹⁰ ants to wrap around the earth.

Learn more about circumference, click;

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Answer:

3.14 is the simplified version (approximate) to π

Answer: You write the latitude first, followed by a comma, and then the longitude.

Step-by-step explanation:

Answer:

x= -2/9

Step-by-step explanation:

42-21x+12x=44

-21x+12x=44-42

-9x=2

x= -2/9

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π    and         cos A = cos B · cos C

scratchwork:

  A + B + C = π

               A = π - (B + C)

         cos A = cos [π - (B + C)]                              Apply cos

                    = - cos (B + C)                                    Simplify

                    = -(cos B · cos C - sin B · sin C)          Sum Identity

                    = sin B · sin C - cos B · cos C               Simplify

cos B · cos C = sin B · sin C - cos B · cos C               Substitution

2cos B · cos C = sin B · sin C                                        Addition

                     [tex]2=\dfrac{\sin B\cdot \sin C}{\cos B \cdot \cos C}[/tex]                                     Division

                     2 = tan B · tan C

[tex]\text{Use the Sum Identity:}\quad \tan(B+C)=\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}[/tex]

Proof LHS → RHS

Given:                              A + B + C = π

Subtraction:                     A = π - (B + C)

Apply tan:                  tan A = tan(π - (B + C))

Simplify:                               = - tan (B + C)

[tex]\text{Sum Identity:}\qquad \qquad \qquad =-\bigg(\dfrac{\tan B+\tan C}{1-\tan B\cdot \tan C}\bigg)[/tex]

Substitution:                        = -(tan B + tan C)/(1 - 2)

Simplify:                               = -(tan B + tan C)/-1

                                            = tan B + tan C

LHS = RHS:   tan B + tan C = tan B + tan C  [tex]\checkmark[/tex]

Answer:

Exact form: [tex]-11.06[/tex]

Decimal form: [tex]-11.066667[/tex]

Step-by-step explanation:

[tex]-8+9.2[/tex] ÷ [tex]-3[/tex]

Let's simplify. We will have to change [tex]9.2[/tex] and [tex]-3[/tex] a draction

[tex]-8+\frac{9.2}{-3}[/tex]

This equals

Exact form: [tex]-11.06[/tex]

Decimal form: [tex]-11.066667[/tex]

Hope this helps!

Answer:

7 science teachers

Step-by-step explanation:

42 and 14 in a ratio 3:1

if 42/2 =21 maths teachers then 7 science teachers

Answer:

25/35

Step-by-step explanation:

5 times 7 equals 35 and that means that this is the denominator because that is our total amount.

5 times 5 equals 25 and that makes it the numerator because that is what is being taken out of 5 jars

Hopefully this helps you :)

Answer:

x = 5

Step-by-step explanation:

We are given the function;

f(x) = 5(x-3) + 17

And f(x) = 12

Thus;

5(x-3) + 17 = 12

Expanding the bracket gives;

5x - 15 + 17 = 12

5x + 2 = 12

5x = 12 - 2

5x = 10

x = 10/2

x = 5

Thus,for f(x) = 12, x has to be 5

Answer:

Step-by-step explanation:

1. isolate the variable   subtract both sides by 8                   (12x+8-8<116-8)  

2. Divide both sides by twelve                                               (12x/12<116-8/12)                                            

3. Simplify                                                                                 (x<108/12)      

=12x+8−8<116−8

=12x<108

[tex] \frac{12x}{12} < \frac{108}{12} [/tex]

x<9

First off, we need the slope

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{8-(-4)}{1-(-2)}[/tex]

That leaves you with

12/3 = 4

point-slope form: y-y1 = m ( x - x1)

So...

y - (-4) = 4 ( x - (-2))

y + 4 = 4 (x + 2)

y + 4 = 4x + 8

Now subtract 4 from both sides of the equation

y = 4x +4

Answer:

The answer is 4r² – 9

Denise answer is correct.

Step-by-step explanation:

One of the methods of solving the given equation [(2r – 3)(2r + 3)] is the FOIL method

Using the FOIL method (Used for multiplying binomials)

F stands for first

O stands for outer

I stands for inner

L stands for last

In this method, it means we will first multiply the first terms followed by multiplying the outer term, then multiplying the inner terms and finally, the last terms.

So, for the equation  (2r – 3)(2r + 3)

First : (2r)(2r) = 4r²

Outer : (2r)(+3) = 6r

Inner : (–3)(2r) =  – 6r

Last :  (–3)(+3) =  – 9

Adding the results we get

4r² + 6r – 6r – 9 (+6r and – 6r cancels out)

= 4r² – 9

∴ (2r – 3)(2r + 3) = 4r² – 9

Hence, Denise answer is correct

Answer:

2.4 miles.

Step-by-step explanation:

10sec = 4 miles.......what abt.....

6 sec =  ??

cross multiply:

6sec × 4miles ÷ 10 sec= 2.4miles

Answer:

24 cubic feet

Step-by-step explanation:

3 × 4 × 2 = 24

Step-by-step explanation:

The formula for volume is l×w×h, a d the ending unit will be cubed/to the third power.

So you would do 4ft×3ft×2ft, which equals 24ft³

Answer:

unit rate is 2

Step-by-step explanation:

Notice that if we multiply both '1' and '3' in 1/3 by 2, we get:

4/6 : 2/6,

which reduces to 4/2, or 2, which is the desired unit rate.

Answer:

The answer is 2:1

Step-by-step explanation:

what is a unit rate?

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

When writing a unit rate the denominator is always 1

If you want to obtain a unit rate you divide both quantities by the second one.

Answer:

length = 20 m

width = 16m

Step-by-step explanation:

Answer:

261

I hope this helps!

Answer:

333.15 Kelvin (K)

Step-by-step explanation:

When you convert from Celsius to Kelvin, you add 273.15

60 C + 273.15 = 333.15 K

So, that is the answer. Hope this helps!

Answer:

333.15 Kelvin (333 rounded)

Step-by-step explanation:

You must add 273.15.

60 + 273.15 = 333.15.

The answer is 333.15 (333 rounded.)

Answer:

d = 4

Step-by-step explanation:

6-3d=10-d

-2d=4

divide d by -2

the answer is 4.

Answer:

6-3d=10-5d...Multiplying 5 with (2-d)

5d-3d=10-6....Taking - 5d to left and writing it +5d and Taking +6 to right and making it - 6

2d=4...Subtracting as required

d=4/2

d=2....Normal division

Answer:

Step-by-step explanation:

Area of a triangle is given by

[tex] A = \frac{1}{2} bh[/tex]

where b is the base

h is the height

From the question

A = 48 sq. in

h = 16 in.

Substitute the values into the above formula and solve for the base

That's

[tex]48 = \frac{1}{2} 16b \\ 48 = 8b \\ \frac{8b}{8} = \frac{48}{8} [/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

given the expression (3³)² = n⁶, we are to find the value of n.

To do that we will apply one of the laws of indices shown

[tex](a^m)^n = a^{mn}[/tex]

Applying the law to the question

(3³)² = n⁶

[tex]3^{3*2} = n^6\\\\[/tex]

[tex]3^6 = n^6\\\\[/tex]

Since the power of both values at both sides are equal, they will cancel out to give;

[tex]3 = n[/tex]

Hence the value of n is 3

its 2

N=2

and i know this since i got it wrong and it showed me the correct answer :)

Answer:

get it helps me with lI do not know the answer

Step-by-step explanation:

sorry

Answer:

Five days

Step-by-step explanation:

First, we have to find out how much food they ate:

240 - 180 = 60

Now, we have to find out the number of days they would take to eat 60 pounds of food. We can do that by dividing:

60/12 = 5

They took five days to have 180 pounds leftover.

Answer:

No, it is not a magic square.

Step-by-step explanation:

A magic square is when whatever way you add it from, it is always the same answer (the magic sum). As you can clearly tell, it doesn't add up to the same number.

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

The blueprints say that 1 inch represents 10 feet. This means we can form the equation below

1 inch = 10 feet

Of course 10 feet is much larger than 1 inch, so they cannot be actually equal to one another, but it helps tie together the two quantities. And it also allows us to multiply both sides by 3 to get

3 inches = 30 feet

So 3 inches on paper means we have 30 feet in real life.

Similarly,

1 inch = 10 feet

5.5 inches = 55 feet (multiply both sides by 5.5)

The 3 inch by 5.5 inch rectangle on paper corresponds to a 30 feet by 55 feet rectangle in real life.

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

In short, you multiply each given dimension by 10

3 inches goes to 3*30 = 30 feet

5.5 inches goes to 5.5*10 = 55 feet

Answer:

Step-by-step explanation:

Perimeter of a polygon = Sum of all sides of the polygon

Perimeter of the given rectangle = 2[(5x - 2) + (3x - 0.5)]

                                                      = 2[8x - 2.5]

                                                      = (16x - 5)

Perimeter of the given triangle = (2x + 3) + (2x + 3) + (10x - 5)

                                                   = 14x + 1

Since perimeter of the rectangle and triangle are same, equation will be

(16x - 5) = (14x + 1)

16x - 14x = 5 + 1

2x = 6

x = 3

Perimeter = (16x - 5)

                 = 48 - 5

                 = 43 units

Answer:

The student can used

297+613 = x

Step-by-step explanation:

It is because the sum is unknown , and we can imagine it as "x". This, we formed a equation.

Answer:

The amount of D's there were is 275.4

Step-by-step explanation:

D : A

6 : 19

D : 872

Cross multiply 872 and 6

6*872 = 5232

Then divide the total by 19

5232/19 = 275.4 (simplified)