What is the reason for statement 7 in the given proof? A. definition of midpoint B. definition of slope C. Parallel lines have equal slopes. D. using point-slope formula

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Step-by-step explanation:

[tex] {x}^{3} + 3x + 1 = 1 = = = > \\ {x}^{3} + 3x = 0 = = = > \\ x({x}^{2} + 3) = 0 \\ x = 0 \: or \\ {x}^{2} + 3 = 0 = = = > \\ {x}^{2} = - 3 = = = > x 1= \sqrt{ - 3} \: or \: i \sqrt{3} \\ x2 = - \sqrt{ - 3} = = = > x2 = - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 5 = = = > \\ {x}^{3} + 3x - 4 = = = > \\ (x - 1)( {x}^{2} + x + 4) = 0 = = = > \\ x - 1 = 0 = = > x1 = 1 \\ {x}^{2} + x + 4 = 0 = = = > \\ x2 = - 1 + i \sqrt{3} \\ x3 = - 1 - i \sqrt{3} [/tex]

[tex] {x}^{3} + 3x + 1 = 3 = = = > \\{ x}^{3} + 3x - 2 = 0 = = = > x = 0.6[/tex]

The values of the inverse of the function, f(x) = x³ + 3·x + 1, obtained from  graphing of the function are;

a. f⁻¹(1) = 0

b. f⁻¹(5) = 1

c. f⁻¹(3) ≈ 0.59607

An inverse function is a function that reverses the action of another function, such that the inverse function maps the output of the function to the corresponding input.

The inverse of the function can be found by graphing the function, f(x) = x³ + 3·x + 1, using technology and then using inverse or table function to find the values of the inverse functions at the specified points

a. The value of the inverse function, f⁻¹(1), is the x-value, on the graph that corresponds to the point with a y-coordinate of 1.

The graph of the function indicates that at a y-value of 1, x = 0, therefore;

f⁻¹(1) = 0

b. Similarly, the graph indicates that a y-value of 5, x = 1, therefore;

f⁻¹(5) = 1

c. When the y-value = 3, we get;

x³ + 3·x + 1 = 3

x³ + 3·x - 2 = 0

Solving the above equation with an online tool, we get; x ≈ 0.59607

Therefore; f⁻¹(3) ≈ 0.59607

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Answer:

B.) 2x¹⁰y¹²

Step-by-step explanation:

To begin, because all of the terms in the top and bottom are combined (right next to each other being multiplied), the coefficients can be divided like any normal number. When you divide variables with powers, you need to subtract the denominator powers from the numerator powers.

Therefore,

60 / 30 = 2

x²⁰ / x¹⁰ = x²⁰ ⁻ ¹⁰ = x¹⁰

y²⁴ / y¹² = y²⁴ ⁻ ¹² = y¹²

Combined, the simplified expression is 2x¹⁰y¹².

The quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]

The expression is given as:

[tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]

Express x^2 - 49 as difference of two squares

[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]

Factorize other expressions

[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{(x -7)(x-7)}{3(x + 2)}[/tex]

Express as product

[tex]\frac{(x + 7)(x- 7)}{x + 2} \times\frac{3(x + 2)}{(x -7)(x-7)}[/tex]

Cancel the common factors

[tex]\frac{(x + 7)}{1} \times\frac{3}{(x -7)}[/tex]

Evaluate the product

[tex]\frac{3(x +7)}{(x -7)}[/tex]

Hence, the quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]

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The graph is attached with the answer.

When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.

The given Inequality is 2x + y ≤ 2

in slope intercept form can be written as

y ≤  -2x +2 , here slope is -2 and intercept is 2

As an equation it will be

y = -2x +2

x         y

0 ,       2

1 ,       0

2         -2

The graph is plotted

The area is shaded and the test for the origin is applied , and it lies in the shaded region.

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Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

[tex] 2x^2y^3 - 3x^2 = 149 - 4y^3 [/tex]

[tex] x^2(2y^3 - 3) = 149 - 4y^3 [/tex]

[tex] x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} [/tex]

[tex] x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} [/tex]

Try y = 1

[tex]x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}[/tex]

For y = 1, x is imaginary.

Try y = 2

[tex] x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3[/tex]

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5

The value of x + y is 5.

Polynomials are expressions which consist of variables, constants, coefficients and exponents.

We have the equation,

2x²y³ + 4y³ = 149 + 3x²

2x²y³ - 3x² = 149 - 4y³

x² (2y³ - 3) = 149 - 4y³

x² = (149 - 4y³) / (2y³ - 3)

x = √[(149 - 4y³) / (2y³ - 3)]

Now, we have to find two positive integers.

We can use trial and error method here.

Trial putting y = 1.

x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]

  = √[145 / (-1)]

  = √(-145)

There is no real root for √(-145). So y = 1 is not applicable.

Trial putting y = 2.

x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]

  = √[117 / 13]

  = √(9)

  = ± 3

But we need positive integers. So we ignore -3.

So x = 3 and y = 2 ⇒ x + y = 5

Hence x + y = 5.

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Answer:

a. When the time is greater than 0, but less than 345 minutes, the temperature of the turkey is increasing at roughly a linear rate.

b. When the time ranges from 345 to 360 minutes, the temperature of the turkey stays constant, at 165 degrees.

c. When the time is greater than 360 minutes, the temperature of the turkey decreases.

Answer:

(π2,15)(π2,15) is a local maximal

(3π2,9)(3π2,9) is a local minimal

Step-by-step explanation:

Answer:

answer D    ( if i interpreted your question correctly )

Step-by-step explanation:

Sqrt (c^2)  = √(c^2) = C

C is the right answer.

hope it helps...

Answer:

C.

Step-by-step explanation:

Calculating this in Desmos, the closest equation to the points on the graph will have to be c

Answer:

log x to the base 2 +log x to the base 4 =2

or log x/ log 2+ log x /lig 4 =2

or log x /log2 + log x /2.log 2 = 2

or log x/log 2(1+1/2)= 2

or log x/log 2 = 4/3

or 3.log x =4.log2

or logx^3=log 2^4

or x^3= 2^4

or x =(2)^4/3 or 2.(2)^1/3 ,Answer.

hope this helps

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

You solve this by factoring.

12140 = x^2-10x+65

0 = x^2-10x-12075

0=(x+105)(x-115)

The only positive solution is x=115

Answer:

The first graph

Step-by-step explanation:

The second graph does not have a point at (1, -2).

It looks like you're asking to solve for the coefficients [tex]a,b,c[/tex] such that

[tex]2x^2 - 5 = a(x+2)^2 - b(x+1) + c[/tex]

Expanding the right side gives

[tex]2x^2 - 5 = ax^2 + 4ax + 4a - bx - b + c[/tex]

[tex]2x^2 - 5 = ax^2 + (4a - b)x + (4a - b + c)[/tex]

The coefficients on both sides must be equal, so

[tex]\begin{cases}a = 2 \\ 4a-b = 0 \\ 4a - b + c = -5\end{cases}[/tex]

Solving the system yields [tex]\boxed{a=2 \implies b = 8 \implies c = -5}[/tex].

Answer:

The answer is 64

Step-by-step explanation:

If you find this answer helpful pls mark it the brainliest answer

it's easy 64 the key is in the pic.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The correct option is B.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

Since the graph of the equation is a line, therefore, it can be concluded that the relationship is linear as a result y varies directly with x.

Therefore we can write the relationship as,

y ∝ x

y = k x

The line goes through the point (-2,3), thus, substitute the points in the equation formed above,

3 = k × (-2)

k = -3/2

Now, substitute the value of k in the equation,

y = -(3/2)x

Hence, the correct option is B.

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Answer:

(-4,-3)

Step-by-step explanation:

The point where those 2 equations intersect is (-4,-3)

Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence

[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]

Differentiating [tex]f(x)[/tex] gives

[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]

Then

[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]

[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]

[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]

which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.

y=[tex]\frac{1}{2}[/tex]x+0.5

Hope it helps!

Answer:

512? xd

Step-by-step explanation:

Answer:

128

Step-1by-step explanation:

An easy way of solving these sort of problems is to set up an equation

Since we have a total, that being 512 burgers, we can set an equation equal to that number.

We can say that hamburgers is represented by x. Since we sold 3 times more cheeseburgers than the amount of hamburgers, we can represent this as 3x.

Since these totals are combined, we can represent this via an equation:

512 = x + 3x

Solve for x accordingly, and we are given 128, which is equal to the amount of hamburgers.

Answer:

C = 105°

Step-by-step explanation:

added in the picture

Answer:

325

Step-by-step explanation:

10 is 3^2 + 1

37 is 6^2 + 1

82 is 9^2 + 1

145 is 12^2 +  1

226 is 15^2 + 1

325 is 18^2 + 1

325 is the next number in the sequence and is also the answer.

Answer:

A = 13 degrees

B = 65.3 degrees

C = 180 - (13 + 65.3) = 101.7 degrees

Side a = 35 km

Side b = 141.4 km

Side c = 152.4 km

Answer:

yessss

Step-by-step explanation:

yessssssss

The condition that distinguishes organism from inorganic objects and dead organisms, being manifested by growth through metabolism, reproduction, and the power of adaptation to the environment through changes originating internally.

H(x) = 4(x - 7)^2 - 19

Hope you find it usefull

Answer:

A. -6

D. 3

Step-by-step explanation:

We conclude that 515 student tickets were sold, and 58 adult tickets.

Let's define the variables:

We can write the system of equations:

x = 9*y - 7

x*5 + y*8 = 3039

Now we can replace the first equation into the second one:

(9*y - 7)*5 + y*8 = 3039

45y + 8y  - 35 = 3039

53y = 3074

y = 3074/53 = 58

Now we can use:

x = 9y - 7 = 9*58 - 7 = 515

We conclude that 515 student tickets were sold, and 58 adult tickets.

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Answer: Two pounds of beef costs $7.38.

Step-by-step explanation:

Multiply the cost for one pound by the amount of pounds you need.

$3.69×2=$7.38

I hope this helps!!

Answer:

6.708.

Step-by-step explanation:

hope this helps

The graph of the inequality, x > 2 is the graph attached below.

Given the inequality as, x > 2, it means all possible values of x must be greater than 2.

Thus, the graph that will show all possible values of x that would be greater than 2 would be a vertical line indicating the values are over 2 and upwards.

Therefore, the graph that represents x > 2 is shown in the image attached below.

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