A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoes is -4.8 meters. The equation 12+d=-4.8 represents the situation.

The result of the given expression is-

[tex]2^3\left(x-\frac{3}{2}\right)^6[/tex]

The amount of times a quantity is multiplied is referred to as its exponent. Power is defined as a number multiplied by itself a certain number of times.

The number that a number is raised in order to define its power as an entire expression is known as its exponent.

Now, consider the following exponent rule;

[tex](x y)^m=x^m y^n, x^{m+n}=x^m x^n, \text { and } \frac{1}{x^n}=x^{-n}[/tex]

Now, according to the question, the given expression is;

[tex]\frac{(2 x-3)^6}{8}[/tex]

Taking 2 common from the numerator;

[tex]\frac{\left[2\left(x-\frac{3}{2}\right)\right]^6}{8}[/tex]

Now, apply the given exponent rule [tex](a b)^m=a^m b^m[/tex] in the above equation.

[tex]\frac{\left[2\left(x-\frac{3}{2}\right)\right]^6}{8}=\frac{2^6\left(x-\frac{3}{2}\right)^6}{8}[/tex]

Apply [tex]a^{m+n}=a^m a^n[/tex] in the above result.

[tex]\begin{aligned}\frac{2^6\left(x-\frac{3}{2}\right)^6}{8} &=\frac{2^{(3+3)}\left(x-\frac{3}{2}\right)^6}{8} \\&=\frac{2^3 \cdot 2^3\left(x-\frac{3}{2}\right)^6}{8} \\&=\frac{8 \cdot 2^3\left(x-\frac{3}{2}\right)^6}{8} \\&=2^3\left(x-\frac{3}{2}\right)^6\end{aligned}[/tex]

Therefore, the simplified form of the given expression is [tex]2^3\left(x-\frac{3}{2}\right)^6[/tex].

To know more about the exponent rule, here

https://brainly.com/question/11975096

#SPJ4

-

The complete question is-

Separate the coefficient from the variable in each expression and write the variable with a negative exponent if it was originally in the denominator.

[tex]\frac{(2 x-3)^6}{8}[/tex]

Answer: 1/3

Step-by-step explanation:

It is

Answer:

Explicação passo-a-passo:

Podemos atribuir a incógnita x ao número de objetos que há na caixa. Assim, teremos as seguintes relações:

Metade dos objetos da caixa = 1/2x

Terça parte dos objetos da caixa = 1/3x

Portanto, o número de objetos que há na caixa será dado resolvendo a equação:

1/2x + 1/3x = 25

3/6x + 2/6x = 25

5/6x = 25

x = 25/(5/6)

x = 25 . (6/5)

x = 150/5

x = 30

Novas perguntas de Matemática

1.Na portaria de um prédio chegaram, certo dia, 65 cartas. Desse total,1/5 foi entregue no 1°andar. Qual é o número de cartas distribuídas nos outros …

Faça um grafico da função f(x)= -x² +2x -1 Pfv!!

4. Em cada figura, AB é um diâmetro. Determine a medida x

O gráfico a seguir representa a função f(x)=a^x-1 em que a é positivo. Nessas condições, qual é o valor de A?

Maria começou a trabalhar numa loja de venda de sapato e receberá mensalmente um salário de r$ 1000 nós vamos comissão de 3

Um numero somado com

Brainly.com.br

Pesquise a resposta para qualquer pergunta...

ytzinhawww

ytzinhawww

há 5 minutos

Matemática

Ensino fundamental (básico)

1.Na portaria de um prédio chegaram, certo dia, 65 cartas. Desse total,1/5 foi entregue no 1°andar. Qual é o número de cartas distribuídas nos outros andares? (tem que fazer a conta)

a. 20

b. 35

C. 48

d. 52

2.foram entrevistados 420 candidatos a determinada vaga de um emprego. sabe-se que 5/7 desse número de candidatos foram rejeitados. Então, foram aceitos:

a. 300 candidatos

b. 210 candidatos

C. 380 candidatos

d. 120 candidatos

3.a figura está dividida em cinco partes iguais. a parte pintada representa:

⬜⬜⬜⬜

a. 10%

b. 12%

C. 20%

d. 25%

4.numa caixa 100 bolas, 45 são vermelhas, 20 são azuis, e o restantes são amarelas. em relação ao total a porcentagem de bolas amarelas é:

a. 55/100

b. 25/100

c. 45/100

d. 35/100

5.um dia tem 24 horas, uma hora tem 60 minutos e 1 minuto tem 60 segundos. a fração da hora que corresponde a 35 minutos é:

a. 7/4

b. 7/12

C.35/24

d. 60/35

6.dois terços da população de um município correspondem a 36000 habitantes. pode-se afirmar que esse município tem:

a) 18000 habitantes

b) 36000 habitantes

C) 48000 habitantes

d) 54000 habitantes

7.uma plantação foi feita de modo a ocupar 2/5

da terça parte da área de um sítio, como mostra a figura em relação à área total do sítio, a fraçao que representa a área ocupa por essa plantação é:

⬜⬜

⬜⬜

⬜⬜

⬜⬜

⬜⬜

bem por favor alguém me ajude preciso até amanhã pq é muito importante e se for me ajuda n esquece a conta pq a prof é bem exigente.tchau

All the given options are correct

The variation expression is given as

(2x + 3y) ∝ (x + 5y)

Rewrite as an equation

So, we have

(2x + 3y) = k(x + 5y)

Remove the brackets

So, we have

2x + 3y = kx + 5ky

Collect the like terms

So, we have

kx - 2x = 3y - 5ky

This gives

x(k - 2) = y(3 - 5k)

Divide by both sides by y(k - 2)

x/y = (5k - 3)/(2 - k) --- option (a)

Multiply both sides by y

x = y(5k - 3)/(2 - k) --- option (b)

Express x/y = (5k - 3)/(2 - k) as ratio

x : y = (5k - 3) : (2 - k) --- option (c)

Hence, all the given options are correct

Read more about variation at

https://brainly.com/question/6499629

#SPJ1

The distance between the two points as depicted on the graph is:

√5.

Given, the points are:

(1,2) = (x₁,y₁) and

(3,1) = (x₂,y₂)

We know that distance between two points is:

d = √(x₂-x₁)²+(y₂-y₁)²

d = √(3-1)²+(1-2)²

d = √(2)²+(-1)²

d = √4+1

d = √5

Hence we get the distance between two given points as √5

Learn more about Coordinate geometry here:

https://brainly.com/question/7243416

#SPJ9

Answer:

pamachino ala iscola iyo kapito binisimo bambena ilina

Answer:

the 2 nd and 5 th box contain irrational number

Step-by-step explanation:

1 St and 3 Rd are clearly rational and 4 th can be converted into rational like root 25 is 5.

Answer: (-3,2)

Step-by-step explanation:

Answer:

(-3, 2)

Step-by-step explanation:

There are two methods on finding the vertex. The one I will be using is the faster version.

y=2x^{2}+12x+20

a=2   b=12   c=20

First use the formula -b/2a.

-(12)/2(2)=

=-12/4=-3

-3 is the x-coordinate.

Plug in -3 into the equation for x.

y=2(-3)^{2}+12(-3)+20

y=2(9)+12(-3)+20

y=18-36+20

y=2

The y-coordinate is 2

Use (x, y) for the vertex.

x=-3

y=2

The vertex is (-3, 2)

Hope this helps!

Please mark as brainliest if correct!

The absolute value of the given integer(i.e. -7) is  7

Absolute value:

The absolute value (or modulus) | x | of a real number x is its non-negative value regardless of its sign.

A number's absolute value can be assumed as its distance from the origin along the real number line. Furthermore, the distance between two real numbers is the absolute value of their difference.

Let's assume the given integer=-7 and need to find the absolute value of the  given integer.

Then the absolute value of the given integer(i.e. -7) is  7

Therefore, The absolute value of the given integer(i.e. -7) is  7

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ9

The function rule for g(x) is (x₊6)² ₋ 5. According to the given data we apply the translations onto the graph and from the graph we determine the function of g(x).

Given, the function of f(x)  = x²

The base graph is moved up or down in the y-axis direction when a graph is vertically translated. Each point on a graph is moved k units up the graph to translate it vertically. Shifting the f (x) k units vertically will allow you to sketch the equation g (x) = f (x) + k.

The graph of g(x) is f(x) translated to 6 units left and down 5 unit.

Draw the translations onto the graph. In the given graph provided, the yellow curve indicates the function g(x).

therefore g(x) = (x₊6)² ₋ 5 is the function from the graph.

Learn more about Graphical problems here

brainly.com/question/4025726

#SPJ9

Number of gallons of gas would need to travel 874.35 miles 174.034

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given:

Gallons Used             Miles Driven

 3333                                663.3

 4444                                 884.4

 4646                                 924.6

From table we can write

3333/663.3 = 5.024

4444/884.4= 5.024

4646/ 924.6 = 5.024

So,  number of gallons of gas would need to travel 874.35 miles

=874.35/5.024

=174.034

Learn more about ratio here:

https://brainly.com/question/23499990

#SPJ1

Answer:

x = 22 y = 113

Step-by-step explanation:

3x-15 = 2x+7

-2x         -2x

x-15 = 7

+15     +15

x = 22

180-51 = 129

y+16 = 129

-16       -16

y = 113

Answer:

x = 22

y = 113

Step-by-step explanation:

The angles marked as (2x+7) and (3x-15) are vertical angles, and therefore are equal to each other.

2x + 7 = 3x - 15 simplifying:

7 = x - 15

22 = x

Angles marked as (3x-15) and (y+16) form a linear pair and are therefore supplimetery. Now that we know the value of x, we can set up the following equation.

3(22) - 15 + y + 16 = 180 simplifying:

66 - 15 + y + 16 = 180

66 + y + 16 = 195

y = 113

Answer:that  a accute angle

Step-by-step explanation:

5/9x -11 = -51

5/9x = 11 - 51

5/9x = -40

5x = -360

x = -72

The solution of the equation given as g = 4a +4/5 for a is a = 1/20(5g - 4)

The equation is given as

g = 4a +4/5

Multiply through the equation by 5

So, we have

5 * (g = 4a +4/5)

Evaluate the products

So, we have

5g = 20a + 4

Subtract 4 from both sides of the equation

So, we have

20a = 5g - 4

Divide through the equation by 20

So, we have

a = 1/20(5g - 4)

Hence, the solution of the equation given as g = 4a +4/5 for a is a = 1/20(5g - 4)

Read more about equations at

https://brainly.com/question/2972832

#SPJ1

Answer:

 A.

The system has infinitely many solutions of the form y = -3x - 6 where x is any real number.

Step-by-step explanation:

Answer:

1. [tex] \frac{39}{59} = 39:59[/tex]

2. [tex]\frac{52}{120} = 13:30[/tex]

Answer:

r=2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

68=3(6r−1)−7(1−3r)

68=(3)(6r)+(3)(−1)+(−7)(1)+(−7)(−3r)(Distribute)

68=18r+−3+−7+21r

68=(18r+21r)+(−3+−7)(Combine Like Terms)

68=39r+−10

68=39r−10

Step 2: Flip the equation.

39r−10=68

Step 3: Add 10 to both sides.

39r−10+10=68+10

39r=78

Step 4: Divide both sides by 39.

39r/39=78/39

r=2

Answer:

put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges

Step-by-step explanation:

Answer: y=-4/5x-1.5

Step-by-step explanation: Both values are negative because your line is angled downwards from left to right and your y-intercept is below the x-intercept line.

Your 'b' or y-int is a little wonky, but I'm confident with what answer I'm handing to you.

Answer:

calculate the number of terms of the series 5;8;11;...173

Answer: x=5.5

Step-by-step explanation:

First you need to find the slope using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. Thankfully, we have (0, 0) and (1, 8) as points, which makes it easy to find that the slope is 8.

Once we have the slope, we divide 44 by 8 to get 5.5

The two triangles are congruent because each transformation is a rigid motion. Therefore, option B is the correct answer.

Given that, triangle ABC is reflected in the x-axis, rotated 180°, and translated 2 units to the right and 4 units down to form triangle XYZ.

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape. The translation is sliding a figure in any direction without changing its size, shape or orientation.

We know that reflection, rotation and translation in the vertical or horizontal direction are rigid motions.

Rigid motions do not change the size of a polygon so that the two polygons are congruent.

The two triangles are congruent because each transformation is a rigid motion. Therefore, option B is the correct answer.

To learn more about the transformation visit:

https://brainly.com/question/11709244.

#SPJ1

351.7 ft is the length of the street

City workers are using a snowplow to clear a street. A tire on the snowplow is 3.2 ft in diameter and has to turn 35 times in traveling the length of the street.

The total distance of the street is the number of times the wheel turns multiplied by its circumference. Thus:

C = πD

L = nπD

L = 35 x 3.14 x 3.2

Use the value 3.14 for pi. Round your answer to the nearest tenth. Do not round any Intermediate steps

L = 351.7 ft

Hence 351.7 ft is the length of the street

learn more about of length here

https://brainly.com/question/2806054

#SPJ9

The domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

The graph represents the given parameters

On the graph, we have the following endpoints

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

The domain

The definition of the domain implies that the domain of a function is the set of x values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the maximum

Closed circle at (-2, -1)

Open circle at (-5, -2)

Remove the y coordinates

So, we have

Closed circle at (-2)

Open circle at (-5)

Combine the x values

-2 ≤ x < -5

The range

The definition of the range implies that the range of a function is the set of y values of the graph.

Recall that

Closed circle at (-2, -1)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the smaller larger y value of the endpoints)

Open circle at (-5, -2)

Maximum = (0, 1)

Remove the x coordinates

So, we have

Open circle at (-2)

Maximum = (1)

Combine the y values

-2 < y < 1

Hence, the domain of the function is -2 ≤ x < -5 and the range is -2 < y < 1

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

16,384,000 more people resided in Tokyo

Tokyo population = 34,450,000

Mexico Population = 18,066,000

To find how many more people resided in Tokyo, we subtract =

34,450,000 - 18,066,000 = 16,384,000

What is a good budget for an apartment?

One popular rule of thumb is the 30% rule, which says to spend around 30% of your gross income on rent. So if you earn $2,800 per month before taxes, you should spend about $840 per month on rent.

To learn more about rent visit: https://brainly.com/question/15386402

#SPJ4

The width is 53 yards and the length is 108 yards.

To find the dimensions:

Now, solve as follows:

The width measures 53 yards.

To calculate the length, multiply 53 by two and add two.

Therefore, the width is 53 yards and the length is 108 yards.

Know more about perimeter here:

https://brainly.com/question/19819849

#SPJ4

The correct question is given below:
The length of a new rectangular playing field is 2 yards longer then double the width. If the perimeter of the rectangular playing field is 322 yards, what are its dimensions?

Answer:

Without being able to measure it, it looks like the first on is 45 degrees and the second one is 90 degrees.

Step-by-step explanation:

Do you have a protractor that you can measure them with?

The scale of the drawing by using proportion is 3 : 5.

According to the given question.

Melissa drew a scale drawing of a city.

The width of the park in the drawing is 36 inches.

And the actual width of the park is 60 yards.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Therefore, the scale of the drawing by using proportion

= 36iches/ 60 yards

= 3/5

= 3 : 5

Hence, the scale of the drawing by using proportion is 3 : 5.

Find out more information about scale here:

https://brainly.com/question/28060140

#SPJ4

Answer:

(0,-2)?

Step-by-step explanation: