2x+(y+x)=4 write in standard form

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = [tex]5x^5[/tex]

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After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

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Answer

the question is not correct

Answer:

d = 8 cm

Step-by-step explanation:

We want to find the length of segment d.

We are given a circle, with two segments that intersect the circle. We also know that a = 4 cm, b = 12 cm, c = 6 cm.

We are also given that if two segments intersect inside or outside a circle, ab = cd. Because the two segments do intersect the circle, we can use the equation that was given.

We can plug the values that we know into the equation.

ab = cd

4 * 12 = 6 * d

Now, divide both sides by 6.

[tex]\frac{4 * 12}{6} = d[/tex]

8 = d

So, d is 8 cm.

Please find attached the drawing showing the two prisms that make up the composite figures, created with MS Word

Composite figures are geometric figures that comprises of two or more regular figures.

a) The geometric figure in figure a indicates that the figure is a composite figure consisting of two geometric figures which are cuboids, with dimensions;

Cuboid on the left; Width = 4 cm, breadth = 2 cm, height = 7 cm

Cuboid on the right; Width = 5 cm, breadth = 2 cm, height = 3 cm

b) The figure is a composite figure, which consist of a cuboid and a hollow triangular prism opening at its center.

The dimensions of the cuboid are; Width = 10 cm, thickness = 14 cm, height = 10 cm

The dimensions of the hollow triangular prism are; Base length = 6 cm, height = 4 cm

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The vertices of the polygon are : A'(-3.2, 4.8), B'(-1.6, 1.6), C'(3.2, -1.6), D'(3.2, 3.2).

To dilate a polygon centered at the origin, we multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is four fifths.

Let's calculate the coordinates of each vertex of the dilated polygon:

Vertex A' (x, y):

[tex]x = (-4) \times (4/5) = -3.2\\y = 6 \times (4/5) = 4.8[/tex]

Vertex B' (x, y):

[tex]x = (-2) \times (4/5) = -1.6\\y = 2 \times (4/5) = 1.6[/tex]

Vertex C' (x, y):

[tex]x = 4 \times (4/5) = 3.2\\y = (-2) \times (4/5) = -1.6[/tex]

Vertex D' (x, y):

[tex]x = 4 \times (4/5) = 3.2\\y = 4 \times (4/5) = 3.2[/tex]

Therefore, the vertices of the dilated polygon A'B'C'D' are:

A'(-3.2, 4.8)

B'(-1.6, 1.6)

C'(3.2, -1.6)

D'(3.2, 3.2)

So the correct answer is: A'(-3.2, 4.8), B'(-1.6, 1.6), C'(3.2, -1.6), D'(3.2, 3.2).

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Answer:

B) [tex]4i\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}[/tex]

An expression which the model represent include the following: A. [tex]\frac{7}{8} \div \frac{1}{8}[/tex].

In Mathematics and Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

By critically observing the model shown in the image attached below, we can reasonably infer and logically deduce that each interval represents the numerical value, 1/8.

Since the arrow increased from 0 to 7/8, it implies that an expression which the model represent can be written as follows;

[tex]\frac{7}{8} \div \frac{1}{8}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

False

Step-by-step explanation:

Since a triangle must contain 3 interior angles all adding to 180°, then there can't be more than one right angle since 2 right angles would add up to 180°.

Answer:

Step-by-step explanation:

Answer:

30 paperclips were still on the floor.

Step-by-step explanation:

First, we need to make sure that both of the fractions have the same denominator so that they will be measured on the same scale. 2/5 -> will be 4/10 when multiplied by 2. Now we calculate how many paperclips were picked up. 4/10 + 3/10 = 7/10 which means that 70 paperclips were picked up because 7/10's of a 100 is 70. Next we find the paperclips on the floor 10/10-7/10 = 3/10 or 30 paperclips.

Answer:

To find the rectangular coordinates of the polar coordinates (3, -2), we can use the following formulas:

x = r cos(theta)

y = r sin(theta)

where r is the distance from the origin to the point, and theta is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.

In this case, r = 3 and theta = -2. To convert the angle to radians, we can add 2 pi to it, since negative angles represent angles measured clockwise from the positive x-axis in polar coordinates. So, theta = -2 + 2 pi = 4.283 radians.

Using the formulas, we get:

x = 3 cos(4.283) ≈ -1.008

y = 3 sin(4.283) ≈ -2.573

Therefore, the rectangular coordinates of the polar coordinates (3, -2) are approximately (-1.008, -2.573).

To find the polar coordinates of the rectangular coordinates (2, 5pi/4), we can use the following formulas:

r = sqrt(x^2 + y^2)

theta = atan2(y, x)

where x and y are the rectangular coordinates of the point.

In this case, x = 2 and y = 0. To find the angle, we can use the fact that the point is in the fourth quadrant, where x is positive and y is negative. Therefore, the angle is pi + 5pi/4 = 9pi/4 radians.

Using the formulas, we get:

r = sqrt(2^2 + 0^2) = 2

theta = atan2(0, 2) = 0

Therefore, the polar coordinates of the rectangular coordinates (2, 5pi/4) are (2, 9pi/4).

Answer:

C:0.24

Step-by-step explanation:

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

The height of the stone projected upward is given by h(t) = -16t² + 122t + 15

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

Let h represent the height of the stone above the ground after t seconds. Given that:

h(t) = -16t² + v₀t + h₀

Given that the platform is 15 ft high, hence h₀ = 15 ft. Also, the rate is 122 ft/s, hence, v₀ = 122 ft/sec.

The equation becomes:

h(t) = -16t² + 122t + 15

The height of the stone is h(t) = -16t² + 122t + 15

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The solutions to the given exponential inequalities are provided below.

To solve exponential inequalities in R, we need to follow certain steps. Let's solve each of the given exponential inequalities one by one:

[tex]25^(5x) = 3^(-s):[/tex]

First, let's take the logarithm on both sides to eliminate the exponentials:

[tex]log(25^(5x)) = log(3^(-s))[/tex]

Using the logarithmic property, we can bring down the exponents:

(5x)log(25) = (-s)log(3)

Since log(25) = 2 and log(3) is a constant, we can simplify the equation:

10x = -slog(3)

Dividing both sides by 10, we get:

x = (-slog(3))/10

[tex]9^(x+3) - 3^(*-440):[/tex]

We can rewrite [tex]3^(-440) as 1/(3^440):\\9^(x+3) - 1/(3^440)[/tex]

Combining the terms with a common base:

[tex](3^2)^(x+3) - 1/(3^440)[/tex]

Using the exponent rule, (a^m)^n = a^(mn):

[tex]3^(2x+6) - 1/(3^440)\\3^(x-3) - 9x - 1 = 1/27:[/tex]

We can rewrite 1/27 as [tex]3^(-3):[/tex]

[tex]3^(x-3) - 9x - 1 = 3^(-3)[/tex]

Moving the terms to one side:

[tex]3^(x-3) - 9x - 1 - 3^(-3) = 0[/tex]

4^(37·2x+8):

Using the exponent rule[tex], (a^m)^n = a^(mn):[/tex]

4^((37·2)x+8)

Simplifying the exponent:

[tex]4^(74x+8)[/tex]

Note that without specific values for variables or more specific instructions, it is not possible to provide numerical solutions.

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After analyzing various transactions and discrepancies, the adjusted bank balance can be obtained by adding or subtracting the corresponding amounts from the ledger balance of Br. 4,173.83 as of July 31.

The given information describes various transactions and discrepancies between the bank statement balance and the ledger balance of ABC Company as of July 31. To determine the adjusted balance, we need to analyze each item:

The deposit of Br. 410.90 made after banking hours will not appear in the bank statement until the next statement is issued. Therefore, it does not affect the July 31 balance.

The check drawn for Br. 79 was erroneously charged by the bank for Br. 973. This means the bank deducted an incorrect amount from ABC's account. The adjustment will increase the bank balance by Br. 894.

The outstanding checks, totaling Br. 610.75, have not been paid by the bank yet. These checks need to be subtracted from the bank balance.

The check written for Br. 210 was incorrectly charged as Br. 120 by the bank. This error results in an adjustment of Br. 90, increasing the bank balance.

The proceeds from the collection of the interest-bearing note receivable from David, amounting to Br. 500, should be added to the bank balance.

The interest earned on the average account balance during July, Br. 24.75, should be added to the bank balance.

The check for Br. 10, returned with the statement, had been recorded as Br. 100 in the check register. This discrepancy results in an adjustment of Br. 90, decreasing the bank balance.

The bank charged a fee of Br. 5.00 for handling the collection of the note receivable. This fee should be subtracted from the bank balance.

The check from customer John, amounting to Br. 50.25, was charged as Non-Sufficient Funds (NSF) by the bank. This adjustment decreases the bank balance.

The bank service charge for the month of July, Br. 12.70, should be subtracted from the bank balance.

The incorrect recording of check number 875, which was issued for Br. 85 but recorded as Br. 58, results in an adjustment of Br. 27, decreasing the bank balance.

By considering all these adjustments, we can calculate the adjusted bank balance by adding or subtracting the respective amounts from the ledger balance of Br. 4,173.83

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The input value that produces the same output value for the two functions on the graph is x = 0.

To determine the input value that produces the same output value for the two functions, we need to find the x-coordinate at which the lines f(x) and g(x) intersect on the graph.

The line labeled f(x) passes through the points (-3, 3), (0, 3), and (4, 3). Since all these points have the same y-coordinate of 3, we can conclude that f(x) is a horizontal line.

The line labeled g(x) passes through the points (-4, -3), (0, 0), and (4, 3). By connecting these points, we can observe that g(x) is not a horizontal line and has a positive slope.

Since the lines f(x) and g(x) intersect at a single point, we need to determine the x-coordinate of this point to find the input value that produces the same output value for both functions.

By examining the graph, we can see that the lines f(x) and g(x) intersect at the point (0, 3).

This means that when x = 0, both f(x) and g(x) have an output value of 3.

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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The value of x is 1

An arc of a circle is a section of the circumference of the circle between two radii.

Part of the theorem that deals with this relationship are;

The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Also there is a theorem that states the angle at the centre is twice the angle at the circumference.

Therefore;

165x - 1 = 82 × 2

165x - 1 = 164

165x = 164+1

165x = 165

x = 165/165

x = 1

Therefore the value of x is 1

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Answer:

Distance between opposite corners = 95 meters

Step-by-step explanation:

Because this is a rectangle, the distance between opposite corners of the field is essentially the length of the diagonal.

The diagonals of rectangles are congruent, so we only have to find the length of one diagonal.

Remember that rectangles have four right angles in their corners

The diagonal, the length, and width of a rectangle make a right triangle, where the diagonal is the hypotenuse (i.e., side opposite the right angle).

Thus, we can find the length of the diagonal using the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

Step 1:  Plug in 57 and 76 for a and b in the Pythagorean theorem and simplify on the left-hand side of the equation:

57^2 + 76^2 = c^2

3249 + 5776 = c^2

9025 = c^2

Step 2:  Take the square root of both sides to find c, the length of the hypotenuse (aka the distance between opposite corners of the farmer's field):

√(9025) = √(c^2)

95 = c

Thus, the distance between opposite corners of the farmer's field is 95 meters.

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

14 is an integer

-32.62 is not

-13/4 is not

15/3 = 5 is an integer

51 is an integer

The vertex of f(x) = -5 - x² - 3x is (-3/2, -17/4).

Here's how to find it:First, we need to know that the vertex of a parabola is (-b/2a, f(-b/2a)), where f(x) is the function in standard form, ax² + bx + c.So, in this case, a = -1, b = -3, and c = -5. Thus,-b/2a = -(-3)/2(-1) = 3/2f(-b/2a) = -5 - (3/2)² - 3(3/2) = -5 - 9/4 - 9/2 = -17/4.

Therefore, the vertex of f(x) = -5 - x² - 3x is (-3/2, -17/4). Note that the minus sign in front of x² means the parabola opens downwards, so the vertex is the highest point of the graph.

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Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

The expression is factored to give;

(x + 4) = 0 , (x + 10) = 0. Step 2

From the information given, we have that the quadratic equation is expressed as;

x² + 14x + 40 =0

Now, find the product of 40 and the coefficient of x squared

The product is 40

Find the pair factors of 40 that adds up to 14, we have;

x² + 10x + 4x + 40 = 0

Group the expression in pairs, we get;

(x² + 10x) + (4x + 10)

factor the common terms, we have;

x(x + 10) + 4(x + 10)

Then, we have;

(x + 4) = 0

(x + 10) = 0

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Answer:

here are 117,600 ways the runners can finish first, second, and third in the race.

Step-by-step explanation:

The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.

The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.

For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.

Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.

To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.

Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.

[tex]\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168[/tex]

Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2