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3 years ago

Select all equations which are equivalent to 2(x +3) =20

Mathematics

2 answers:

OleMash [197]3 years ago

8 0

2x + 3 = 20
Subtract 2 from both sides
2x= 27
X= 13.5

notka56 [123]3 years ago

8 0

1 and 5.. because on 1 you decide by 2 by everything...and on 5 you distribute

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I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

4 0

3 years ago

−7x−6y=2<br> 7x+4y=−6<br> solve for x and y

ikadub [295]

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:x=-2,\:y=2}$

Step-by-step explanation:

$\begin{bmatrix}-7x-6y=2\\ 7x+4y=-6\end{bmatrix}$

$\mathrm{Substitute\:}x=-\frac{2+6y}{7}$

$\begin{bmatrix}7\left(-\frac{2+6y}{7}\right)+4y=-6\end{bmatrix}$

$\begin{bmatrix}-2-2y=-6\end{bmatrix}$

$\mathrm{For\:}x=-\frac{2+6y}{7}$

$\mathrm{Substitute\:}y=2$

$x=-\frac{2+6\cdot \:2}{7}\\\\x=-2$

5 0

2 years ago

What is the area of a parallelogram?

denis23 [38]

D is the correct answer

the area of a parallelogram is equal to: base x height

$18 \times 7 = 126$

good luck

3 0

2 years ago

Read 2 more answers

A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it

makvit [3.9K]

Answer:

The length of the hallway is 10 m.

Step-by-step explanation:

Given:

Time taken to cover 1 km = 2.5 hours

Distance covered in 2.5 hours = 1 km

Therefore, speed of robot = $\frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h$

Now, speed is constant.

Now, time taken to cover the length of hallway = 90 s

Speed of the robot = 0.4 km/h

Converting 0.4 km/h to m/s, we multiply by the factor $\frac{5}{18}$ . This gives,

$0.4\times \frac{5}{18}=\frac{1}{9}\ m/s$

Now, distance of the hallway is equal to the product of speed and time. So,

Distance of hallway = Speed $\times$ Time

Distance of hallway = $\frac{1}{9}\times 90=\frac{90}{9}=10\ m$

Therefore, the length of the hallway is 10 m.

5 0

2 years ago

Madison created two functions.

Degger [83]

Madison created two functions.For Function A, the value of y is two less than four times the value of x.

The table below represents Function B.
-3,-9
-1,5
1,-1
3,3

In comparing the rates of change, which statement about Function A and Function B is true?

A.

Function A and Function B have the same rate of change.
B.

Function A has a greater rate of change than Function B has.
C.

Function A and Function B both have negative rates of change.
D.

Function A has a negative rate of change and Function B has a positive rate of change.

C is correct

3 0

2 years ago

Read 2 more answers