3x + 13 = 37

solve two step equations

For given functions f and g, the sum of the areas of the enclosed regions is 2.004 sq. units. and the sum of the volumes of the enclosed regions is 1.283 cubic units

In this question we have been given two functions f and g defined by

f(x) = 1 + x + e^x^2 - 2x and g(x) = x^4 - 6.5x^2 + 6x + 2.

There are two regions on the interval 0 x 2 which are enclosed / and g. We need to find the sum of the areas of the enclosed regions and the sum of the volumes of the enclosed regions.

The graph of functions is as shown below.

We can observe that the graphs of y = f(x) and y = g(x) intersect in the first quadrant at the points (0, 2), (2, 4), and (A, B) = (1.032832, 2.401108).

The sum of the areas of the enclosed regions is given by

A = ∫[0-A] (g(x) - f(x)) dx + ∫[A - 2] (f(x) - g(x)) dx

A = 0.997427 +1.006919

A = 2.004

And the sum of the volumes of the enclosed regions is given by

Volume V =∫[0-4]  [[ƒ(x) − g(x)]² dx

V = ∫[0-4] [1 + x + e^x^2 - 2x - x^4 + 6.5x^2 - 6x - 2]^2 dx

V = 1.283

Therefore,  the sum of the areas of the enclosed regions is 2.004 sq. units. and the sum of the volumes of the enclosed regions is 1.283 cubic units

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The number of boxes Anica need to pack all the stuffed animals is 3.

Given that, Anica has 13 stuffed animals, and each box holds 5 animals.

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.

Here,

Number of boxes completely filled =13/5

5|13|2
  10
_____

   3

3 animals are left

Therefore, the number of boxes Anica need to pack all the stuffed animals is 3.

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Option D is correct that is BC = 2

A line is a perfectly straight, one-dimensional shape that is endlessly long and thin in both directions.

She tells us that AC is 15, and we may deduce that AC equals AB plus BC from the figure.

AC Equals AB plus BC.

AB=4X+1, BC=2X-4, and AC=15

15 = 4X +1 + 2X- 4

15 = 6X - 3

18 = 6X

X = 3

We now know that 2X - 4

2(3) - 4 = 2 since we have X = 3.

BC = 2.

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The cost of each shirt and pair of pants is $11 each.

Let us represent the shirt by x and pair of pants by y. So forming the equation based on the information. Equation for items bought by me -

x + 3y = 44 : Equation 1

Equation for items bought by my friend -

3x + y = 44 : Equation 2

Performing multiplication of equation 1 with 3

3x + 9y = 132 : Equation 3

Performing subtraction of equation 2 from equation 3

3x + 9y = 132

3x + y = 44

We get -

9y - y = 132 - 44

8y = 88

y = 88/8

Performing division

y = 11

Keep the value of y in equation 1

x + 3×11 = 44

x + 33 = 44

x = 44 - 33

x = 11

Hence, both of these items cost $11.

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Answer:

Step-by-step explanation:

Using PEMDAS order of operations:

ParnthesesExponentMultiplyDivideAddSubtract:

10 2 - 2 (8) + 11

(I am assuming that you mean 10 * 2):

10 * 2 - 2 (8) + 11

= 20 - 16 + 11

= 4 + 11

= 15.

A. The equation that can be used to represent the side a of the cube is a³ = 343.

B. The value of a is 7 units.

The diagram above is a cube . A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Therefore, the cube has a volume of 343 cm³.

Hence, the equation that can be used to represent the side a of the cube is as follows:

volume of a cube = l³

where

Therefore,

volume of the cube = a³

343 = a³

Let's solve the equation.

343 = a³

a³ = 343

cube root both sides

a = ∛343

a = 7 units

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At x = 4, the function f(x) = (x2 - 16)/(6x - 24) discontinues.

When a number is 0 in the numerator as well as the denominator, a point of discontinuous is reached. There's an point of disconnection there since both the exponent and the denominator are zeros. Plug into the last simplified equation to obtain the value, where is the region of discontinuous.

We are given the function as;

f(x) = (x² - 16)/(6x - 24)

We must find the function's discontinuities.

Now, when x = 4, the fraction 6x - 24 equals 0.

This means that the function is now incomplete when x = 4.

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The coordinate of the point N that divides the line segment MP will be (9, -5).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The coordinates of the endpoint are (-6, 5) and (21, -13). And the ratio is 5:4. Then the coordinate of the point N is given as,

x = (21 × 5 + (-6) × 4) / (5 + 4)

x = 81 / 9

x = 9

y = ((-13) × 5 + 5 × 4) / (5 + 4)

y = - 45 / 9

y = - 5

The coordinate of the point N that divides the line segment MP will be (9, -5).

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Answer:

Step-by-step explanation:

Answer:

x=25

Step-by-step explanation:

The price that is the Second standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18000.

The central tendency along the median and mode of a probability distribution is measured by the mean. It is also known as "expected value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the second standard deviation as shown below,

Second standard deviation  = mean + 2 × standard deviation

Second  standard deviation = 17000 + 2 × 500

Second  standard deviation = 17000 + 1000

Second  standard deviation = $18000

Therefore, the price that is the Second standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18000.

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The function f(x) = x + 5x + 1 has exactly one zero in the interval (-1, 0). To prove this, we can use the Intermediate Value Theorem.

This theorem states that if a function f(x) is continuous on an interval [a, b] and if its values at a and b have opposite signs, then there exists at least one root (zero) of the function in the interval (a, b). Therefore, since f(-1) = -6 and f(0) = 1, both of which have opposite signs, the Intermediate Value Theorem can be used to conclude that there exists at least one root of the function in the interval (-1, 0).

Furthermore, since the function is a quadratic function of the form f(x) = ax2 + bx + c, it is known that a quadratic equation can have at most two roots (zeros) (in a given interval). Therefore, since the Intermediate Value Theorem implies that the function f(x) has at least one zero in the interval (-1, 0), it follows that the function has exactly one zero in the interval (-1, 0).

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The statement describes the domain and range of the exponential function f(x) = – 4ˣ is

A.The domain and range are both the set of all real numbers.

The y-axis on a graph represents the possible output values, or range.

while the domain is the input values.

The domain of the exponential function f(x) = – 4ˣ is set of all real numbers

The range considering the domain is also set of all real numbers since it can be positive or negative depending on the value of the domain

It is worthy to note that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

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Angle F is correspond to angle S. Angle A is congruent to angle U

and Angle R is congruent to angle N.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion

Given that ΔFAR is similar to ΔSUN.

We need to find the corresponding sides.

Corresponding angles are the angles that are in the same position in any different 2-dimensional shapes.

For any two polygons to be congruent, they must have exactly the same shape and size.

This means that all their interior angles and their corresponding sides must be the same measure.

Angle F is correspond to angle S.

Angle A is congruent to angle U.

Angle R is correspond to angle N.

Hence, Angle F is congruent to angle S. Angle A is congruent to angle U

and Angle R is congruent to angle N.

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Math

-

Because point B is midpoint of AC , so AB = BC . Therefore :

8x + 4 = 10x - 6

10x - 8x = 4 + 6

2x = 10

x = 5 ✓

_____

Answer:

g = 68

Step-by-step explanation:

g/4 + 11 = 28

subtract 11 from both sides:

g/4 + 11 - 11 = 28 - 11

g/4 = 28 - 11

g/4 = 17

multiply both sides by 4:

4(g/4) = 4(17)

g = 68

Answer:

  20

Step-by-step explanation:

You want to know how many daily chores Haley has if 40% of them are 8 chores.

Let c represent the number of daily chores. The number of chores accomplished in the morning was ...

  0.40c = 8

Dividing by 0.40, we find ...

  c = 20

Haley has 20 daily chores.

a = 3 cm

b = 4 cm

c = ?

c = √{ a² + b² }

c = √{ 9 + 16 }

c = 5 cm

_____

Answer:

5cm

Step-by-step explanation:

You use the Pythagoras theorem

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {3}^{2} + {4}^{2} = {c}^{2} \\ 9 + 16 = {c}^{2} \\ 25 = {c}^{2} \\ \sqrt{25} = \sqrt{ {c}^{2} } \\ 5 = c \\ c = 5[/tex]

The linear function for D is defined as follows:

D(t) = -35t + 280.

The slope of 35 means that Nathan is traveling at a velocity of 35 miles/km per hour.

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

The coefficients of the function are given as follows:

From the table, two points are given as follows:

(3, 175) and (5,105).

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (105 - 175)/(5 - 3) = -35.

This slope represents that Nathan is traveling at a velocity of 35 miles/km per hour.

Hence:

D(t) = -35t + b

When x = 3, y = 175, hence the intercept b is obtained as follows:

175 = -35(3) + b

b = 280.

Thus the function is of:

D(t) = -35t + 280.

The table is given by the image shown at the end of the answer.

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the formula as one logarithm with a coefficient of 1 with a expression. assume all variables represent positive real numbers. 1/4logbx^5y^7-4/7logbx^4y is logbx^4y^11/28

Since the coefficients of the expression of two logs are not the same, we need to adjust the exponents in order to combine them into one logarithm. Since the first logarithm has a coefficient of 1/4, we multiply the exponent of the second logarithm by 4/7 to get 4/7*4 which is equal to 4. We then add 4 to the exponent of the first logarithm to get 11. This gives us a combined logarithm of logbx^4y^11/28.

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Answer: 17 - 9/7j

Step-by-step explanation:

Look, simplifying is really easy! Just go along and learn!

14 + (-4) - 6/7j - 3/7j + 7

The (+,-) rule, remember the minus always overides the plus no matter what.

6 + 3 = 9 So, -6 - 3 = -9

14 - 4 -9/7j + 7

14 - 4 = 10

10 + 7 - 9/7j

10 + 7 = 17

17 - 9/7j

This would be your simplified answer.

Answer:

The third one

Step-by-step explanation:

Answer:

The 2nd one

Step-by-step explanation:

So the absolute value of x is either -x or x, saying that we don't know if x is positive or negative,

so |x|+1<3 means that |x|<2, so I would say its the 2nd one.

The interest rate for Rebeka's account is 5%.

What is the meaning of interest rate?

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given that, Rebeka deposits $1500. She earn $131.25 as interest after 21 months.

The formula of simple interest is

I = PRT

I = interest

P = Principal

R = Rate of interest

T = time

In the given question,

P = $1500

I = $131.25

T = 21 months = 21/12 years.

Putting P = $1500, I = $131.25, T = 21/12 years in I = PRT:

131.25 = 1500 × R × (21/12)

Divide both sides by 1500 × (21/12):

R = 131.25 /[1500 × (21/12)]

R = [131.25 × 12] /[1500 × 21]

R = 0.05

R = 5%

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The evaluation of the function with which the number of players leading and informed can be found, is prevented as follows;

(a) The stage of the information

(d) The number of leaders and players informed

(c) The function using function notation is P(x) = 2 × 3⁽ˣ⁻¹⁾

(d) We can say that the number of players and leaders depend on the stage of the information

(e) The statement P(4) = 54 indicates that in stage 4, 54 people are informed

(f) Domain; [1 , ∞)

Range; [2, ∞)

(g) The shape of the graph is the curved shape of an exponential function un which the asymptote is an horizontal line

An exponential function is a function in which the argument is an index of a constant of the form f(x) = a·bˣ

(a) The independent variable is the input variable, which is the stage of the calling process

(b) Dependent variable is the output variable, which is the number of leaders and players who are informed

(c) The specified function that represents the number of players who are informed, is presented as follows;

P = 2 × 3ˣ⁻¹

Where;

P = The number of players informed

x = The of information of the players

Expressing the above function using function notation, we get;

P(x) = 2 × 3ˣ⁻¹

(d) We can say that the number of players and leaders informed is a function of the stage of the information

(e) The meaning of the equation P(4) = 54 is that at stage 4, the number of layers and leaders informed is 54

(f) The domain of the function P(x) = 2 × 3ˣ⁻¹ is the set of all positive integers equal to or larger than 1 or Z⁺ {1, 2, 3, ...}

The range of the function is the set of integers, such that 2 ≤ x ≤ ∞

(g) Please find attached the graph of the function created with MS Excel

The attached graph of the function indicates that the shape of the graph is the graph of an exponential function, which is non linear and has a horizontal asymptote , but does not have a vertical asymptote.

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Answer:

Step-by-step explanation:

To graph the points (0.5, 4.5) and (-0.5, -4.5) on a coordinate plane, you can use a ruler or a graph paper to plot the points.

To plot the point (0.5, 4.5), start by drawing the horizontal and vertical axes of the coordinate plane. The horizontal axis, or the x-axis, is the line that runs horizontally across the plane, and the vertical axis, or the y-axis, is the line that runs vertically. The intersection of the two axes is called the origin.

Next, locate the point (0.5, 4.5) on the coordinate plane. To do this, find the point that is 0.5 units to the right of the y-axis and 4.5 units above the x-axis. This point is the point (0.5, 4.5).

To plot the point (-0.5, -4.5), locate the point that is 0.5 units to the left of the y-axis and 4.5 units below the x-axis. This point is the point (-0.5, -4.5).

The resulting graph should look like this:

  |

4.5|       * (0.5, 4.5)

  |

  |

  |

  |

0.5|       * (-0.5, -4.5)

  |

  |

  |

 -4.5

 -4.5 -2.5 -0.5  0.5  2.5  4.5

         -0.5

The difference of 4h5k and -7hk5 Not possible.

Which of the following provides an example of to calculate the difference between 4h5k and -7h5k

Changing the situation 4h^5k - (-7hk^5)= 4h^5k +7hk^5

Making the distinction

4h^5k - (-7hk^5)

= 4h^5k +7hk^5

assemble similar phrases

Take note of similar phrases is  hk(4h^4+7k^5)

There can be no difference, therefore.

= hk(4h^4+7k^5)

As a result, the difference is Not possible.

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Answer:

Y-Intercept is equal to 100

Y-Intercept in Coordinate for is (0,100)

The value of b = 5 , h = -4 and k = -1 for the function f(x) = [tex]log_{5}[/tex](x - 4) - 1

What is a function ?

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

An input is connected to an output by a function. It resembles a device with an input and an output. In addition, the output is somehow connected to the input. The standard way to write a function is f(x) "f(x) =... "

Translated of logarithmic function:

f(x) =  [tex]log_{b}[/tex] (x + h) + k

where b is base, h - horizontal shift, k - vertical shift

According to given function the values are:

b = 5, h = - 4, k = - 1

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False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)

A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

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The Subtotal for 25 flash drives is $250.00. You can save $62.50. The new Subtotal becomes $187.50. Sales tax of 4% will equal $7.50. The Total for the 25 flash drives will be $187.50 + $7.50 which gives $195.00

To find the solution, we must solve for the questions individually;

The Subtotal is 25 x $10 = $250.00

You save = 25% of $250

which is 25/100 x 250 = $62.50

The new Subtotal = $187.50

Sales tax of 4% = 4% of $187.50

which gives 4/100 x 187.5 = $7.50

The Total for the 25 flash drives will be $187.50 + $7.50 = $195.00

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