(1+y)^2-y^2=-11x+10 write in standard form

Adjusted bank statement balance: Br. 4,317. We need to deduct this fee from the adjusted bank statement balance.

To reconcile the bank statement balance with the company's ledger balance, we need to account for the various transactions and adjustments. Let's go through each item one by one:

1. A deposit of Br. 410.90 made after banking hours and doesn't appear in the bank statement:

Since the deposit was made after banking hours, it is understandable that it doesn't appear on the bank statement. We need to add this deposit to the bank statement balance.

Bank statement balance: Br. 4,964.47

+ Deposit not appearing on the bank statement: Br. 410.90

Adjusted bank statement balance: Br. 5,375.37

2. A check drawn for Br. 79 had been erroneously charged by the bank Br. 973:

The bank erroneously charged Br. 973 for a check of Br. 79. We need to deduct this amount from the bank statement balance.

Adjusted bank statement balance: Br. 5,375.37

- Erroneous bank charge: Br. 973

Adjusted bank statement balance: Br. 4,402.37

3. Outstanding checks:

We need to deduct the amounts of the outstanding checks from the adjusted bank statement balance.

Adjusted bank statement balance: Br. 4,402.37

- 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

Adjusted bank statement balance: Br. 3,792.62

4. A check written for Br. 210 had been incorrectly charged by the bank as Br. 120:

The bank incorrectly charged Br. 120 instead of Br. 210 for a check. We need to add the difference to the adjusted bank statement balance.

Adjusted bank statement balance: Br. 3,792.62

+ Incorrect bank charge adjustment: Br. (210 - 120) = Br. 90.00

Adjusted bank statement balance: Br. 3,882.62

5. Proceeds from the collection of an interest-bearing note receivable from David:

The collection of the note receivable adds to the company's bank balance. We need to add the face amount of the note to the adjusted bank statement balance.

Adjusted bank statement balance: Br. 3,882.62

+ Proceeds from note collection: Br. 500.00

Adjusted bank statement balance: Br. 4,382.62

6. Br. 24.75 interest earned on the average account balance during July:

The interest earned increases the company's bank balance. We need to add this interest amount to the adjusted bank statement balance.

Adjusted bank statement balance: Br. 4,382.62

+ Interest earned: Br. 24.75

Adjusted bank statement balance: Br. 4,407.37

7. A check for Br. 10 returned with the statement had been recorded as Br. 100:

The check was incorrectly recorded in the company's ledger. We need to deduct the difference from the adjusted bank statement balance.

Adjusted bank statement balance: Br. 4,407.37

- Incorrectly recorded check adjustment: Br. (100 - 10) = Br. 90.00

Adjusted bank statement balance: Br. 4,317.37

8. Br. 5.00 fee charged by the bank for handling collection of the note receivable:

The bank fee reduces the company's bank balance. We need to deduct this fee from the adjusted bank statement balance.

Adjusted bank statement balance: Br. 4,317

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To compare the values of the numbers 5.04 and 5.40, we can use the symbols > (greater than), < (less than), and = (equal to). In this case, 5.04 is less than 5.40.

Therefore, we can write:5.04 < 5.40 Alternatively, we can say that 5.40 is greater than 5.04.

Therefore: 5.40 > 5.04 Lastly, we can say that the numbers are not equal, since 5.04 is not the same as 5.40.

Therefore: 5.04 ≠ 5.40 In conclusion, we can compare the values of the numbers 5.04 and 5.40 and find that 5.04 is less than 5.40, which we can express as 5.04 < 5.40.

Alternatively, we can say that 5.40 is greater than 5.04, which we can express as 5.40 > 5.04.

Finally, we can say that the numbers are not equal, since 5.04 is not the same as 5.40, which we can express as 5.04 ≠ 5.40.

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The equation that can be used to find the value of x is 2x + 2.1 = 7.5.

An isosceles triangle is a triangle that has two sides equal to each other and the base angles congruent to each other.

Therefore, the isosceles triangle has a perimeter of 7.5 m. The shortest side of the isosceles triangle is 2.1 m.

Let's find the value of x.

Therefore,

2x + 2.1 = 7.5

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The answer is $(x-7)(x-3)$.

Given expression is $x^2-10x+21=-10x+21$We can factor this expression by splitting the middle term. That means we have to find two numbers which, when multiplied, will give us $21$ and when added will give us $-10$.That means we have to find two numbers $a$ and $b$ such that $ab=21$ and $a+b=-10$.The numbers are $-3$ and $-7$.Now, let's write $-10x$ as $-3x-7x$.$$x^2-3x-7x+21$$$$x(x-3)-7(x-3)$$$$(x-7)(x-3)$$Thus, the given expression can be factorised as $$(x-7)(x-3)$$

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To ensure 4 ounces of 3/4 strength isomil, we would add approximately 118.28 milliliters of water to 3 ounces of isomil powder.

To ensure 4 ounces of 3/4 strength isomil, we need to calculate the amount of isomil powder and water needed.

First, we need to determine the amount of isomil powder required. Since the strength is 3/4, we only need 3/4 of the total volume to be isomil. In this case, the total volume is 4 ounces, so 3/4 of 4 ounces is [tex](3/4) \times 4 = 3[/tex]ounces of isomil powder.

Next, we need to determine the amount of water needed. Since the total volume is 4 ounces and we already have 3 ounces of isomil powder, the remaining 1 ounce needs to be water.

To convert ounces to milliliters, we need to know the conversion rate. In general, 1 ounce is approximately equal to 29.57 milliliters. Therefore, 4 ounces is approximately equal to [tex]4 \times 29.57 = 118.28 milliliters.[/tex]

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Given statement solution is :- The actual length of the part is 3751/64 inches.

To find the length of the actual part, you can use the scale factor and the length of the part on the drawing. The formula for finding the actual length is:

Actual Length = Length on Drawing × Scale Factor

In this case, the length on the drawing is given as 3 7/8 inches, and the scale factor is given as 15 ¹/8. Let's calculate the actual length:

Length on Drawing = 3 7/8 inches = (3 × 8 + 7) / 8 = 31/8 inches

Scale Factor = 15 ¹/8

Now we can substitute the values into the formula:

Actual Length = (31/8 inches) × (15 ¹/8)

To perform the multiplication, we can convert the mixed fraction into an improper fraction:

15 ¹/8 = (15 × 8 + 1) / 8 = 121/8

Now we can multiply the fractions:

Actual Length = (31/8) × (121/8)

To multiply fractions, we multiply the numerators together and the denominators together:

Actual Length = (31 × 121) / (8 × 8)

Actual Length = 3751 / 64

Therefore, the actual length of the part is 3751/64 inches.

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The expression cos x/cot x simplifies to sin x by utilizing trigonometric identities and canceling out the common cosine terms in the numerator and denominator.

To simplify the expression cos x/cot x, we need to utilize trigonometric identities. Cotangent (cot x) is the reciprocal of the tangent function, so we can rewrite cot x as 1/tan x.

Now, substituting 1/tan x for cot x in the expression cos x/cot x, we have:

cos x / (1/tan x)

To divide by a fraction, we multiply by its reciprocal. Therefore, multiplying cos x by tan x, we get:

(cos x)(tan x)

Using the identity tan x = sin x / cos x, we can substitute sin x / cos x for tan x:

(cos x)(sin x / cos x)

The cos x term in the numerator and denominator cancels out, leaving us with:

sin x

Therefore, the simplified expression for cos x / cot x is sin x.

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Answer:

28°C

Step-by-step explanation:

If the temperature started at 22°C and increased to a higher temperature of 50°C, then the increase would be 28°C.

We can write an equation:

50-22=28

Hope this helps! :)

Step-by-step explanation:

The increase in temperature was 28°C.

To find the increase in temperature, we subtract the initial temperature from the final temperature:

Final temperature - Initial temperature = Increase in temperature

50°C - 22°C = 28°C

Therefore, the increase in temperature was 28°C.

i believe its 8 inches

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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To find the particular solution of the differential equation y''' - 4y' = t + 3cos(t) + e^(-2t), we assume a general form for the solution. After solving, we obtain y(t) = -1/2t^2 + (1/2)sin(t) - (1/8)e^(-2t) + (1/16)te^(-2t) + C1 + C2t + C3e^(-2t), where C1, C2, and C3 are arbitrary constants.

To find the particular solution of the given differential equation y''' - 4y' = t + 3cos(t) + e^(-2t), we will use the method of undetermined coefficients.

Guess the form of the particular solution.

Since the right-hand side of the equation consists of a polynomial term (t) and trigonometric terms (cos(t)), as well as an exponential term (e^(-2t)), we will guess a particular solution of the form:

y_p(t) = At^2 + Bt + Ccos(t) + De^(-2t)

Calculate the derivatives of the guessed solution.

y'_p(t) = 2At + B - Csin(t) - 2De^(-2t)

y''_p(t) = 2A - Ccos(t) + 4De^(-2t)

y'''_p(t) = Csin(t) + 8De^(-2t)

Substitute the guessed solution and its derivatives into the original differential equation.

Substituting into the equation:

(Csin(t) + 8De^(-2t)) - 4(2A - Ccos(t) + 4De^(-2t)) = t + 3cos(t) + e^(-2t)

Simplifying the equation, we get:

Csin(t) + 8De^(-2t) - 8A + 4Ccos(t) - 16De^(-2t) = t + 3cos(t) + e^(-2t)

Collect like terms and solve for the coefficients.

Matching the coefficients of the terms on both sides, we have:

Csin(t) + 8De^(-2t) = 0 (1)

-8A + 4Ccos(t) - 16De^(-2t) = 3cos(t) (2)

0t + 0 + 0 - 8A + 0 - 16De^(-2t) = t + e^(-2t) (3)

From equation (1), we have C = 0, and from equation (2), we get C = 3/4.

Equating the exponential terms in equation (3), we have -16De^(-2t) = e^(-2t), which gives D = -1/16.

Finally, from equation (3), we find -8A = t, which implies A = -t/8.

Therefore, the particular solution is:

y_p(t) = (-t/8)t^2 + Bt + (3/4)cos(t) - (1/16)e^(-2t)

where B is an arbitrary constant.

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Answer:

The given differential equation is a third-order, non-homogeneous, linear differential equation. To find its particular solution, we can use the method of undetermined coefficients. This method involves assuming a form for the particular solution based on the form of the non-homogeneous term, and then determining the values of the coefficients by substituting the assumed form into the differential equation.

In this case, the non-homogeneous term is `t + 3cos t + e^-2t`. Since this term contains a polynomial of degree 1, a cosine function, and an exponential function, we can assume that the particular solution will have the form `y_p = At + B + Ccos t + Dsin t + Ee^-2t`, where `A`, `B`, `C`, `D`, and `E` are constants to be determined.

To determine the values of these constants, we can substitute the assumed form for `y_p` into the given differential equation and equate coefficients. This will result in a system of linear equations that can be solved for `A`, `B`, `C`, `D`, and `E`. Once these values are determined, we can write down the particular solution as `y_p = At + B + Ccos t + Dsin t + Ee^-2t`.

Elsa is approximately 65.0 inches tall.

To find Elsa's height, we need to determine the z-score corresponding to the 75th percentile. The 75th percentile is the value below which 75% of the population falls.

Using the z-score formula: z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation, we can rearrange the formula to solve for x.

Plugging in the given values, we have z = (x - 63.5) / 2.5. To find the z-score corresponding to the 75th percentile, we need to find the z-score associated with the area of 0.75 under the standard normal distribution curve.

Using a standard normal distribution table or a calculator, we find that the z-score is approximately 0.6745.

Substituting the z-score into the formula, we have 0.6745 = (x - 63.5) / 2.5. Solving for x, we find x ≈ 65.0 inches. Therefore, Elsa is approximately 65.0 inches tall.

In a normally distributed population, we can use z-scores to find percentiles and vice versa. By finding the z-score corresponding to the 75th percentile (which is 0.75), we can determine the height value associated with that percentile.

The z-score represents the number of standard deviations an observation is away from the mean. In this case, Elsa's height is taller than 75% of the population, so her height corresponds to the 75th percentile.

By rearranging the z-score formula and substituting the given values, we can solve for Elsa's height. In this case, the resulting value is approximately 65.0 inches. This means that Elsa's height is greater than the height of 75% of adult women in the United States.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Both figures have an area of 4 units squared, so yea, the area is the same.

The area of a square of side length S is equal to S squared, for the square, we can see that:

S = 2 units.

Then the area is:

A = (2 units)² = 4 square units.

For the triangle, we know that the area is equal to:

A = B*H/2

Where B = base, H = height.

We can see that:

B = 2 units.

H = 4 units.

Then:

A = (2 units)*(4 units)/2= 4 square units.

So yea, both have the same area.

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Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

The total cost of wallpaper for the rectangular room is $1105

The area of her bedroom can be calculated thus :

Area of bedroom = 17 * 13 = 221 ft²

Cost per square feet = $5

Cost of wallpaper = Area of bedroom * cost per square feet

221 * $5 = $1105

Therefore, the cost of wallpaper would be $1105

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The ends of the points of the latus rectum of the parabola are (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, - 3), respectively.

In this question we find the equation of a parabola, whose axis of symmetry is parallel with the x-axis. From which we need to determine the points of the latus rectum, that is, the ends of the line that contains the focus of the parabola. First, write the entire equation of the parabola:

(y + 1)² = 4 · (x + 1)

Second, find the y-coordinates of the ends of the latus rectum:

(y + 1)² = 4 · (x + 1)

(y + 1)² = 4 · (0 + 1)

(y + 1)² = 4

y + 1 = ± 2

y = - 1 ± 2

y = 1 or y = - 3

Third, write the coordinates of the ends of the latus rectum:

(x₁, y₁) = (0, 1) and (x₂, y₂) = (0, - 3)

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The equation of the ellipse is (x + 4)²/6.25 + (y + 3)²/2.75 = 1

From the question, we have the following parameters that can be used in our computation:

Vertices =  (-9, - 3) and (1, -3)

Focus = (-1, - 3)

The standard equation of an ellipse is represented as

(x - h)²/a² + (y - k)²/b² = 1

Calculating h and k, we have

(h, k) = 1/2 * (-9 + 1, - 3 - 3)

(h, k) = (-4, -3)

So, we have

(x + 4)²/a² + (y + 3)²/b² = 1

Recall that

Focus = (-1, -3)

So, we have

c = |-4 - (-1)| = 3

Also, we have

a = 1/2 * |-9 - (-4)|

a = 2.5

Lastly, we have

b² = c² - a²

This gives

b² = 3² - 2.5²

b² = 2.75

So, we have

(x + 4)²/2.5² + (y + 3)²/2.75 = 1

(x + 4)²/6.25 + (y + 3)²/2.75 = 1

Hence, the equation is (x + 4)²/6.25 + (y + 3)²/2.75 = 1

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The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:d

Step-by-step explanation:

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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On the interval 3 ≤ x ≤ ∞, function g has a greater rate of growth.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In this context, we can reasonably infer and logically deduce that the graph of function g(x) would be steeper than the graph of function f(x) because a slope of 3 is greater than a slope of -2.

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Answer:

60

Step-by-step explanation:

[tex]a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60[/tex]

Therefore, the value of a is 60 degrees

Answer:

Adding +6 in turn

Step-by-step explanation:

-13+6=(-7)

(-7)+6=(-1)

(-1)+6=5

5+6=11

11+6=17

17+6=23

23+6=29

29+6=35

........... And so on

Answer:

72

Step-by-step explanation:

17+1²=18

18+2²=22

22+3²=31

31+4²=47

47+5²=72

To solve the equation (17-3x)/(x-3)(x-4) = (x+1)/(x-4), we need to first simplify both sides of the equation and then find the values of x that satisfy the equation.

Let's start by simplifying the equation. We notice that both sides have a common denominator of (x-4), so we can eliminate it by multiplying both sides of the equation by (x-4):

[tex](x-4) * (17-3x) = (x-4) * (x+1)[/tex]

Expanding the equation, we get:

[tex]17x - 4x - 3x^2 + 12 = x^2 - 3x + x - 4[/tex]

Simplifying further, we have:

[tex]-3x^2 + 13x + 12 = x^2 - 2x - 4[/tex]

Bringing all terms to one side, we get:

[tex]-3x^2 - x^2 + 13x + 2x + 12 + 4 = 0[/tex]

Combining like terms, we have:

[tex]-4x^2 + 15x + 16 = 0[/tex]

Now, we have a quadratic equation. To solve it, we can either factor it, complete the square, or use the quadratic formula. However, the given equation is not easily factored.

Using the quadratic formula, x = [tex](-b ± \sqrt(b^2 - 4ac)) / (2a),[/tex] where a = -4, b = 15, and c = 16, we can calculate the solutions for x.

x = (-15 ± √(15^2 - 4 * -4 * 16)) / (2 * -4)

x = (-15 ± √(225 + 256)) / -8

x = (-15 ± √481) / -8

Therefore, the solutions for x are:

x ≈ 4.28 and x ≈ -0.53

These are the values of x that satisfy the given equation (17-3x)/(x-3)(x-4) = (x+1)/(x-4).

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Answer:

b > -3, so 6b > -18 is the correct answer.

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.