The vertices of a triangle are listed below. E(-1, 2), F(-5, -1), G(-1, -4) What is the area of the triangle? A. 24 square units B. 12 square units C. 16 square units D. 6 square units

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:

[tex]\frac{3x+11}{(x+3)(x+4)(x+5)}[/tex]

Step-by-step explanation:

Before adding we require the fractions to have a common denominator.

Multiplying the numerator/ denominator of the first fraction by (x + 5)

Multiplying the numerator/ denominator of the second fraction by (x + 3)

= [tex]\frac{x+5}{(x+3)(x+4)(x+5)}[/tex] + [tex]\frac{2(x+3)}{(x+3)(x+4)(x+5)}[/tex]

Now add the numerators leaving the common denominator

= [tex]\frac{x+5+2x+6}{(x+3)(x+4)(x+5)}[/tex]

= [tex]\frac{3x+11}{(x+3)(x+4)(x+5)}[/tex]

Answer:

  16x -2

Step-by-step explanation:

You know how to compute the perimeter of a rectangle of length L and width W:

  P = 2(L+W)

Here, you're asked to use the given algebraic expressions for length and width and simplify the result of putting those in the perimeter formula.

  P = 2((5x-2) +(3x+1))

  P = 2(8x -1)

  P = 16x -2 . . . the perimeter of the rectangle

Answer:

r < 3

Step-by-step explanation:

Step 1: Write out inequality

5r + 2 < 17

Step 2: Subtract 2 on both sides

5r + 2 - 2 < 17 - 2

5r < 15

Step 3: Divide both sides by 5

5r/5 < 15/5

r < 3

In this case, r has to be smaller than 3. So anything like -2, -15, or even -12413573875942 works as r, as long as it's smaller than 3.

Answer:

44

Step-by-step explanation:

180-48/3 to find the value of x

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

Step-by-step explanation:

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:

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:

x = 4

Step-by-step explanation:

[tex]x + 6 = 10 \\ x = 10 - 6 \\ x = 4[/tex]

Answer:

x=2

Step-by-step explanation:

to find x- intercept substitute y=0

move variable to the left hand side and change its sign -5x=-10

then divide both sides of the equation by -5

and the final answer is x=2

hope this helps!

Answer:

ummm

Step-by-step explanation:

Answer: miles

because hes measuring in miles and i answered this same question today

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:

it looks like you are trying to find x in this problem so x= -6

Answer:

Step-by-step explanation:

3 + 5x = 3x -9

-3  -3x   -3x  -3

2x = -12

2x/2 -12/2

X=     -6

Answer:

9/25

Step-by-step explanation:

I guess you mean 45/125

they are divisible by 5

45/5 = 9

125/5 =25

9/25

Answer:

5 hours

Step-by-step explanation:

49 - 14 = 35 and 35 ÷ 7 = 5

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)

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:

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:

23, 11, -13

Step-by-step explanation:

y+6(-2)=11

y-12=11

y=23

y+6(0)=11

y+0=11

y=11

y+6(4)=11

y+24=11

y=-13

Answer:

get it helps me with lI do not know the answer

Step-by-step explanation:

sorry

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 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:

(C) 50π

Step-by-step explanation:

For this problem, we need to find a way to relate the inner circle, to the square, to the outer circle.

Given that we know the area of a circle is πr^2, and our inner circle has a area of 25π, we can find the radius.

25π = πr^2

25 = r^2

5 = r

Note, that the diameter of the inner circle is parallel to the side of the square, meaning that the diameter of the inner circle is the length of the side of the square.

diameter = 2 * radius

d = 2 * 5 = 10.

Now that we know the value of the side of the square, we can find the length of the diagonal of the square, which is the diameter of the outer circle.

Using the properties of the 45-45-90 right triangle, we can say that the diagonal of the square is the length of the side times sqrt(2).

Outer_Diameter = 10 * sqrt(2)

Now to find the outer area, we need the formula for the area of a circle.  Note that the diameter is twice the radius, so we will simply divide by 2.

A = πr^2

A = π * [ ( 10 * sqrt(2) ) / 2 ]^2

A = π * [ 5 * sqrt(2) ] ^2

A = π * 25 * 2

A = 50π

So the area of the outer circle is 50π.

Cheers.

Step-by-step explanation:

(-3x-4) is -12. -12

(5-5x) is x. x

9-7 is 2. 2

+8. +8

-2+x

9+24x+4+ 40-40x

53-16x

Answer:

x= -2/9

Step-by-step explanation:

42-21x+12x=44

-21x+12x=44-42

-9x=2

x= -2/9

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

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