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Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

An equation is an expression that shows the relationship between two or more numbers and variables.

Medical practitioners recommend losing around 1–2 pounds (0.5–0.9 kg) per week.

Hence for a year:

Amount of weight loss = (1 * 365) or (2 * 365)

Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

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Step-by-step explanation:

a) 14w + 21

- Factor out 7 from the expression

7 (2w + 3)

b) 27x + 18

- Factor out 9 from the expression

9 (3x + 2)

Hi!

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[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

#1 7(2w+3)

#2 9(3x+2)

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

We need to factor these two expressions.

[tex]\twoheadrightarrow\sf 14w+21[/tex] and [tex]\twoheadrightarrow\sf 27x+18[/tex]

For now let's focus on the first expression.

Note that both terms, 14w and 21, have something in common.

In fact, they have 7 in common. So we factor it out by dividing 14w and 21 by 7.

[tex]\twoheadrightarrow\sf14w\div7=2x\\\twoheadrightarrow\sf21\div7=3[/tex]

[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they are positive

[tex]\twoheadrightarrow\sf 2w+3[/tex]

[tex]\bullet[/tex] Put parentheses around 2w+3

[tex]\twoheadrightarrow\sf (2w+3)[/tex]

[tex]\bullet[/tex] Put7 outside the parentheses

[tex]\twoheadrightarrow\sf7(2w+3)[/tex]

[tex]\bullet[/tex] Great job! We factored the expression

__________________________________________________________

This problem can be solved the same way!

This time, both terms have a 9 in common.

[tex]\twoheadrightarrow\sf 27x+18[/tex]

So we divide both terms by 9.

[tex]\twoheadrightarrow\sf 27x\div9=3x\\\twoheadrightarrow\sf18\div9=2[/tex]

[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they're positive

[tex]\twoheadrightarrow\sf 3x+2[/tex]

[tex]\bullet[/tex] Next, put parentheses around 3x+2 and put 9 outside the parentheses

[tex]\twoheadrightarrow\sf 9(3x+2)[/tex]

[tex]\bullet[/tex] Great job! We factored both expressions

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

What must have motivated the behavior of the Investor to commit to such a large stock is; Option C: High Total Earnings

A) Low real returns; This cannot be his motivation to buy large shares because real return is what is earned on an investment after accounting for taxes and inflation. Thus, the lower, the less encouraging to investors.

B) Higher shares costs; This only means that the share cost is currently high which indicates strength of the company but it does not guarantee that it will scale up at a very fast rate again.

C) High total earnings; Thus would be an encouragement to the investor because the higher the total earning potential of an investment, the more the profitability and the more attractive to others.

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The surface area of the figure is approximately: 178 units².

The surface area of any figure is the area of all its faces.

Find the area of each face as shown below:

Area of base = w² = 6² = 36 units²

Area of the 4 rectangular faces = 4(6)(3) = 72 units²

Area of the 4 triangular faces = 4[1/2bh]

b = w = 6 units

h = √(y² + (w/2)²) = √(5² + (6/2)²) = 5.8 units

Area of the 4 triangular faces = 4[1/2(6)(5.8)] = 69.6 units²

Surface area = 36 + 72 + 69.6 ≈ 178 units²

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Step-by-step explanation:

[tex] = 0,43[/tex]

[tex] = \frac{0,43}{1} [/tex]

[tex] = \frac{0,43}{1} \times \frac{100}{100} [/tex]

[tex] = \frac{43}{100} [/tex]

The diagram that shows all the lines of symmetry is diagram B.

We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).

With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.

So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.

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Answer:

6x-4

Step-by-step explanation:

3x•2= 6x

-2•2=-4

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Answer:  [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]

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Given:  [tex]\textsf{(3x - 2)}^2[/tex]

Find: [tex]\textsf{Simplify the expression}[/tex]

Solution:  It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number.  If so the following steps would be followed.

Expand

Simplify

Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.

Answer:

Step-by-step explanation:

1) y = [tex]\frac{1}{3}[/tex]

2) x = [tex]\frac{1}{3}[/tex]

3) y = -3

4) x = [tex]\frac{-1}{-12}[/tex]

Answer:

11,3,3,12

Step-by-step explanation:

1st y= 11 because -2/3(-6)=4 4+7=11

1st x= 3 because -2/3(3)=-2 and -2+7 is 5

2nd y=-3  because -2/3(15)=-10 -10 +7=-3

2nd x=-12 because -2/3(-12)=8 8+7=15

Answer:

(1) 85×9=765 (2) 127×3=381

Answer:

The slope of line p is 3 and the slope of line q is -3

Answer:

It's the first option: -5, 1 and 4

A rise of 8 and a run of 6. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space.

On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).

The distance between AB will be

AB² = (-5 + 5)² + (-2 + 4)²

AB² = 4²

AB = 4

The distance between BC will be

BC² = (-2 + 5)² + (-2 + 2)²

BC² = 3²

 BC = 3

Then the rise and run will be

rise / run = 4 / 3

Then this can be written as

rise / run = 8 / 6

Then the correct option is B.

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Answer:

[tex]0.07[/tex]

Step-by-step explanation:

FORMULA :

[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]

……………………………

then

[tex]p\left( \text{drive to school} |sophomore\right) =\frac{p\left( \text{drive to school} \cap \text{sophomore} \right) }{p\left( \text{sophomore} \right) }[/tex]

                                [tex]= \frac{2}{2+25+3}[/tex]

                                [tex]=\frac{2}{30}[/tex]

                                [tex]=\frac{1}{15}[/tex]

                                [tex]=0.066666666667[/tex]

Answer:

79°

Step-by-step explanation:

An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.

If the angle is 281° it can go 79° more degrees before getting back to the start.

360° - 281° = 79°

3(x-4) ≥ 5x +2

3*x - 3*4 ≥ 5x +2

3x - 12≥ 5x - 2

-12 + 2 ≥ 5x- 3x

-10 ≥ 2x

2x ≤ -10

x ≤ -5

Answer:

335.16 ft

Step-by-step explanation:

The number of people who can go to the amusement park is 8.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given: the group of friends had $280.

For parking=  $19.50

Remaining will be,

=$(280-19.50)

= $ 260.5

Cost of ticket per person = $33.75

Thus, number of tickets they can buy

=260.5 / 33.75

=7.718 = 8 peoples

Hence, number of people who can go to the amusement park is 8.

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If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get

[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]

Integrate both sides:

[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]

Use the initial condition to solve for [tex]C[/tex] :

[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]

Then the particular solution to the initial value problem is

[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]

(A)

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Work Shown:

x = number of quarters

3x = number of dimes

0.25x = value of just the quarters, in dollars

0.10(3x) = 0.30x = value of just the dimes, in dollars

0.25x+0.30x = 0.55x = total value in dollars

0.55x = 9.35

x = (9.35)/(0.55)

x = 17

Alison has 17 quarters and 3x = 3*17 = 51 dimes

17 quarters = 17*0.25 = $4.25

51 dimes = 51*0.10 = $5.10

17 quarters + 51 dimes = $4.25 + $5.10 = $9.35

The answers are confirmed.

The function g(x) gets shifted toward right by 6 units. Then the correct option is C.

The complete question is attached below.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

The function f(x) is given below.

f(x) = 10ˣ

And the function g(x) is given as

g(x) = f(x – 6)

Then the function can be written as

[tex]\rm g(x) = 10^{x - 6}[/tex]

The function g(x) gets shifted toward right by 6 units.

Then the correct option is C.

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Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.

The difference between Palomas and Antons' points on the English test is of 14 points.

When two numbers can be written in the form as p:q , they are said to be in Ratio.

It is given that

The ratio of Michaels point to Paloma point is 12 :11

The ratio of Michaels point to Anton's Point is 4:3

Let Paloma's point be x

then Michaels point will be 12x/11

and Anton's points will be

(12x/11 ) / Anton's points = 4 /3

Anton's points = 9x/11

It is given that the sum of the points of the three students is 224

so

x + (12x/11)+ (9x/11) = 224

32x /11 = 224

x = 77

Paloma's points = 77

Anton's Points = 9x/11 = 63

The difference between Palomas and Antons' points on the English test

=77 -63

= 14 points.

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Answer:

1/2, -1/8, 1/32

Step-by-step explanation:

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

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

[tex] - \frac{1}{8} ( - \frac{1}{4}) = \frac{1}{32} [/tex]

Answer:

A = -1

B = -3

C = -7

Step-by-step explanation:

See attached image.

The given quadratic equation is

[tex]2 {x}^{2} - x - 3 = 0[/tex]

comparing with

[tex] {ax}^{2} + bx + c = 0[/tex]

We get ,

[tex]a = 2 \\ b = - 1 \\ c = - 3[/tex]

formula :

[tex]D = {b}^{2} - 4ac \\ \\ D = {( - 1)}^{2} - 4 \times 2 \times ( - 3) \\ \\ D = 1 - ( - 24) \\ \\D = 1 + 24 \\ \\D = 25.[/tex]

Discriminant of given quadratic equation is 25 .

option (B) 25 ✔

Answer:

12 :D

Step-by-step explanation:

First we substitute all x's for -2 :)

f(-2)=−-2^3−3(-2)^2+8

Now we solve :)

f(-2)=−-2^3−3(-2)^2+8

f(-2)=− -8 −3(-2)^2 + 8

f(-2) = -8 - 3(-4) + 8

f(-2) = - 8 + 12 + 8

f(-2) = 4 + 8

f(-2) = 12 :)

f will equal 12 :)

Have an amazing day!!

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The expression that has a value of 16 when n = 5 is  [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.

An expression is mathematical statement consisting of variables , constant and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]

On solving it can be seen that

The value of 16 when n= 5 is given by

7 +45/5 = 7+9 = 16

Therefore Option C is the right answer.

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Answer:

A resposta certa é:

[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]

Step-by-step explanation:

1° equação:

Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)

2° equação:

Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.

3° equação:

As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.

4° equação:

Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.

5° equação:

Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação

Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)

Answer:

90

Step-by-step explanation:

Add up all the numbers in the data set and divide that number by the amount of numbers in the data set

85 + 97 + 84 + 88 + 95 + 100 + 81 = 630

630/7 = 90