What is the value of x in the equation 4x - 2(x + 3) = 8?
A x = 1
B. X = 2.5
C x = 3.5
D. x = 7

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π               → A = π - (B + C)

                                               → B = π - (A + C)

                                               → C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → RHS:

LHS:                        sin A - sin B + sin C

                             = (sin A - sin B) + sin C

[tex]\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex].\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark[/tex]

Answer:

slope: 1.5/3

y intercept: 3

Step-by-step explanation:

the line goes through the vertical line and meets at 3

from one point to the other it goes up 3 and over 1 and a half

if 1.5/3 doesn't work try 3/1.5

Answer:

-2[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The line passes through points (1,4) and (4,-4)

Slope (m) = change in y ÷ change in x

i.e m = [tex]\frac{-4 - 4}{4 - 1} = \frac{-8}{3} = -2\frac{2}{3}[/tex]

It is clear from the diagram that,

⇒ (2x - 5) + (x + 5) = 180

⇒ (2x + x) + (5 - 5) = 180

⇒ 3x + 0 = 180

⇒ x = 180/3

⇒ x = 60°

◈ From the geometry of figure,

⇒ ㄥ6 = (2x - 5)

⇒ ㄥ6 = (2×60 - 5)

⇒ ㄥ6 = 120 - 5

⇒ ㄥ6 = 115°

Answer:

5m•5m•5m

Step-by-step explanation:

You are multiply the factor by itself as many times as the exponent says. so if the factor is 5m, you would multiply it by itself by the exponent, which in our case is 3.

An expression is defined as a set of numbers, variables, and mathematical operations. The expression (5m)³ can be expressed as 5·5·5·m·m·m.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression (5m)³ can be expressed in the following manner,

[tex](5m)^3 = 5 \cdot 5 \cdot 5\cdot m\cdot m\cdot m[/tex]

Hence, the expression (5m)³ can be expressed as 5·5·5·m·m·m.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ2

Answer:

1:4

Step-by-step explanation:

Just because okay

Answer:

1) When we have a function y = f(x), evaluating this function in one given point (x0 for example ) is equivalent to changing the x inside the function by the value x0.

This will give us the point (x, f(x0)).

now, a graph is conformed by the set of all the points (x, f(x)).

2) The x and y-intercepts are the points where the graph intercepts the x-axis or the y-axis.

If you have a table with points (x, y), the y-intercept is the point (0, y') and the x-intercept is the point (x', 0)

Where x' and y' are known values.

If you have an equation:

y = f(x).

The x-intercept is the point (x', 0)

So you need to find the value x' such that f(x') = 0.

The y-intercept is the point (0, y')

So you need to evaluate the function in x = 0, and find the value of y.

y' = f(0).

3) The obvious answer is any science-related career, where graphs are used to transmit a lot of information with almost no words.

Another option can be an economist, where, for example, interpreting and comparing graphs can be useful to determine which option fits better the needs of a given company or what decision is better to be taken.

Answer:

19

Step-by-step explanation:

|-7| +|-5| + 7 = 7+5+7= 19

The length of ND = 3 units

The length of N'D' = 6

6 / 3 = 2

The scale factor is 2

Answer:  A) 2

Step-by-step explanation:

The shape has been enlarge which means B and D are  ruled out because if a shape gets enlarge its scale factor has to be greater than 1.

We will use the coordinate of the image of D  to find the scale factor.

Pre-image:  (2,2)   Enlarge or image: (4,4)    

So as we can see to get from 2 to 4 you will have to multiply by 2. So the scale factor is  2

Answer:

Ymani is 12 years old.

Step-by-step explanation:

Y + M = 54

M = 54 - Y

Y + 30 = M

Y + 30 = 54 - Y

2Y = 24

Y = 12

Ymani is 12 years old.

Answer:

She Ran 13,300 ft. hope this helps!

Step-by-step explanation:

Answer:

ANSWER ---> **15**

Step-by-step explanation:

If there are 120 calories in a single cup and 8 ounces in a cup, you would divide 120 by 8 to get your answer 15 for the single fluid ounce

The answer is 5 and 7 because the square root of 42 is 6.8

Answer:

Maggie is 14 years old.

Step-by-step explanation:

M + B = 36

B = 36 - M

2M - 6 = B

2M - 6 = 36 - M

3M = 42

M = 14

Maggie is 14 years old.

Answer:

10. 62 and 64

11. 27, 28, and 29

Step-by-step explanation:

Answer:

DF is congruent to ZX

Step-by-step explanation:

Pls make branliest.

Answer:

x=15

Step-by-step explanation:

Hope this helps.

Answer:

Eric's share is $1,800.

Step-by-step explanation:

You can write the following equations from the information given:

x+y+z=2,700 (1)

y=2z (2)

x=3y (3), where:

x=Eric's share

y= Jo's share

z=Richard's share

Now, you can replace (2) in (1) and (3) to have two equations:

x+2z+z=2,700

x+3z=2,700

x=3(2z)

x=6z

The two equations are:

x=6z (4)

x+3z=2,700 (5)

Then, you can replace (4) in (5) and solve for z:

6z+3z=2,700

9z=2,700

z=2,700/9

z=300

After this, you can replace the value of z in (4) to find x:

x=6*300

x=1800

Finally, you can replace the value of z in (2) to find the value of y:

y=2*300

y=600

According to this, the answer is that Eric's share is $1,800.

Answer:

The answers are A B D F

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

1. plug in 4 for F(x) making 4=x:

[tex]f(4)=4(4)+5[/tex]

2. multiply 4 and 4:

[tex]f(4)=4(4) +5[/tex]⇒[tex]f(4)=16+5[/tex]

3. Add 16 and 5 to get your answer:

[tex]f(4)= 16+5[/tex]⇒[tex]f(4)=21[/tex]

Answer: $120

Step-by-step explanation:

Given the following :

Initial deposit = $2000

Let fixed monthly deposit = d + $5 ; where d = monthly amount saved by grandparents and $5 = amount saved by you

Period of deposit = 36 months = 36 monthly deposits

Total amount required at the end of 36 months = $6500

Hence ;

$2000 + 36(d + $5) = $6500

$2000 + 36d + $180 = $6500

36d = $(6500 - 2180)

36d = $4320

d = $4320 / 36

d = $120

Monthly Amount contributed by grandparents = $120

Answer:

Two angles are Adjacent when they have a common side and a common vertex and don't overlap.

Step-by-step explanation:

Hope this helps, can't see your angles lol!

Answer:

  (i)  (x +4)^3 = x^3 +12x^2 +48x +64

  (ii)  (2m +1)^3 = 8m^3 +12m^2 +6m +1

  (iii)  (a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3

Step-by-step explanation:

Powers of a binomial have a pattern. The coefficients of the terms of the expanded product are the numbers in the corresponding row of Pascal's Triangle. Here, you want the 3rd power, so the coefficients of interest are ...

  1, 3, 3, 1

The pattern is ...

  (a +b)^2 = a^2 +2ab +b^2

  (a +b)^3 = a^3 +3a^2b +3ab^2 +b^3

The total of powers of the variable is equal to the exponent of the binomial. The powers of the first variable decrease to 0 while the powers of the second variable increase from zero.

When 'a' or 'b' is something with a coefficient, that whole term is raised to the appropriate power.

__

i) (x+4)^3 = x^3 +3·4x^2 +3·4^2x +4^3

  (x +4)^3 = x^3 +12x^2 +48x +64

__

ii) (2m +1)^3 = (2m)^3 +3·1·(2m)^2 +3·1^2·(2m) +1^3

  (2m +1)^3 = 8m^3 +12m^2 +6m +1

__

iii) (a -2b)^3 = a^3 +3·a^2·(-2b) +3·a·(-2b)^2 +(-2b)^3

  (a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3

_____

Additional comment on Pascal's triangle

The numbers in each row are the sums of the two numbers immediately above. For binomial expansion, you're only interested in the contents of a row. The "patterns" shown in the attachment are an extra added attraction, not particularly relevant to binomial expansion.

Answer:

Hence, the distance between (7,8) and (-8,0) is:

17

Step-by-step explanation:    (a,b)=(7,8) and (c,d)=(-8,0)

Hope this helps!!!!!!

The distance between the points (7, 8) and (–8, 0) = 17 units

The distance between two points is given by the formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]

For the line passing through the points (7, 8) and (–8, 0)

Substitute [tex]x_1=7, y_1=8, x_2=-8, y_2=0[/tex] into the equation above:

[tex]D=\sqrt{(-8-7)^2+(0-8)^2} [/tex]

This will be further simplified as shown below:

[tex]D=\sqrt{(-15)^2+(-8)^2} \\\\ D=\sqrt{225+64} \\\\ D=\sqrt{289} \\\\ D=17[/tex]

The distance between the points (7, 8) and (–8, 0) = 17 units

Learn more on distance between two points here: https://brainly.com/question/7243416

Answer:

A

Step-by-step explanation:

42+6=48

48/2=24

24-6=18

(2*24)-6=18

Answer:

c. 0.8 Hope this helps you!!!

Answer:

It Is C

Step-by-step explanation:

I got it wrong on my test, and it showed me the correct answer.

Don't mess up like me.

I got a 83.3.

WHY!

Answer:

5% were bad

Step-by-step explanation:

Multiply [tex]\frac{10}{100} with 200[/tex]

Then you get 5%

Answer:

16. a = 13

Step-by-step explanation:

Equation: y = -4(-2) + 5

1) Multiply -4 with -2. Whenever you multiply two negatives, the product turn into a positive number; therefore, -4(-2) = 8

2) Then, add 8 and 5 which is 13.

Hope this helps!