The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.

The missing parts of the proof of supplementary angles are:

Supplementary; ∠2 and ∠3; substitution; 2.

Supplementary angles are defined as angles whose measures sum to 180°.  Thus this is the first answer.  

Since we are told that ∠2 and ∠3 are supplementary, their measures sum to 180° and they are the second answer.

We know that m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.  We can substitute "m∠2 + m∠3" for 180° in the first equation; this is the substitution property.

To isolate m∠1 on the right, we will subtract m∠2 from each side, and get that m∠1 = m∠3 and the angles are congruent.

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Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer:

Step-by-step explanation:

First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03

That means that there was a gain of $7.03 per share for Archie.

That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:

(7.03x100)= 703

The answer then is:

Archie gained $703 from selling all of his shares.

Answer:

8

Step-by-step explanation:

let x be the number , then

[tex]\frac{3}{4}[/tex] x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

[tex]\frac{2}{9}[/tex] × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  [tex]\frac{3}{4}[/tex]  times of a number

Hence we will assume the number x ,

                     [tex]\frac{3}{4} of x = 27[/tex]

                     [tex]x = 27 X \frac{4}{3}[/tex]

                       [tex]x = 36[/tex]

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           [tex]y = 36 X \frac{2}{9}[/tex]

                               [tex]y = 8[/tex]

Thus, the two ninths of the number 36  is 8                            

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The dairy farmer should use 400 pounds of the 75% protein supplement and 800 pounds of the 30% protein ration to make 1200 pounds of a high-grade 45% protein ration.

To determine how many pounds of each protein supplement the dairy farmer should use, we can set up a system of equations based on the given information.

Let's denote the following:

x = pounds of the 75% protein supplement

y = pounds of the 30% protein ration

The total weight of the mixture is 1200 pounds, so we have the equation:

x + y = 1200

The protein content in the mixture should be 45% of the total weight, so we have the equation:

0.75x + 0.30y = 0.45 * 1200

Now we can solve this system of equations.

First, let's rewrite the second equation in decimal form:

0.75x + 0.30y = 540

To make it easier to work with, we can eliminate the decimals by multiplying both sides of the equation by 100:

75x + 30y = 54000

Now we have a system of equations:

x + y = 1200

75x + 30y = 54000

We can solve this system using any appropriate method, such as substitution or elimination. In this case, let's use the substitution method:

Solve the first equation for x:

x = 1200 - y

Substitute the value of x into the second equation:

75(1200 - y) + 30y = 54000

Simplify and solve for y:

90000 - 75y + 30y = 54000

-45y = -36000

y = 800

Now we can substitute the value of y back into the first equation to find x:

x + 800 = 1200

x = 1200 - 800

x = 400

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By using the given functions, each output value are as follows;

a. f(-5) = -13.

b. g(3) = -18.

c. 3g(1) - 4 = -10.

d. 2f(3) + g(2) = 14.

e. x = ±√8i or ±2√2i.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) under the given mathematical operation and independent variable.

Part a.

When x = -5, the output value for f(-5) is given by;

f(x) = 3x + 2

f(-5) = 3(-5) + 2

f(-5) = -13.

Part b.

When x = 3, the output value for g(3) is given by;

g(x) = -2x²

g(3) = -2(3)²

g(3) = -18.

Part c.

3g(1) - 4

3[-2(1)²] - 4

-6 - 4 = -10

Part d.

2f(3) + g(2)

2[3(3) + 2] + [-2(2)²]

22 - 8 = 14

Part e.

g(x) = 16

-2x² = 16

x² = -8

x = ±√8i or ±2√2i.

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According to the information, the number of the image would be 17/100 or 0.17

To express this number in fraction and decimal we must take into account different aspects. First of all we must consider the reference numbers that are on the number line.

On the other hand, we must count how many segments each unit of the line is divided into. In this case it is in 10. So to identify the number we can add a 0 to the denominator and take the numerator as an integer that would be 17. Then the fraction would remain:

In the case of the decimal we only have to carry out the division and we will obtain the decimal.

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The three true statements are:

Only f(x) and h(x) have y-intercepts.

Only f(x) and h(x) have x-intercepts.

The minimum of h(x) is less than the other minimums.

From the given table, we can compare the characteristics of the functions f(x), g(x), and h(x) to determine which statements are true.

Statement 1: Only f(x) and h(x) have y-intercepts.

Looking at the table, we can see that f(x) and h(x) have y-intercepts since they have values for f(0) and h(0), while g(x) does not have a y-intercept. Therefore, statement 1 is true.

Statement 2: Only f(x) and h(x) have x-intercepts.

To find x-intercepts, we look for values of x where the functions f(x), g(x), and h(x) equal zero. From the table, we can see that only f(x) and h(x) have x-intercepts, as they have values for x where f(x) and h(x) are equal to zero. Therefore, statement 2 is true.

Statement 3: The minimum of h(x) is less than the other minimums.

By comparing the values in the table, we can see that the minimum value of h(x) is -28, which is indeed less than the minimums of f(x) (-2) and g(x) (-7). Therefore, statement 3 is true.

Statement 4: The range of h(x) has more values than the other ranges.

The range of a function represents the set of all possible output values. From the table, we can observe that the range of h(x) has more values (-28, 0, 7, 14, 49) compared to the ranges of f(x) and g(x) (only two distinct values each). Therefore, statement 4 is true.

Statement 5: The maximum of g(x) is greater than the other maximums.

Looking at the values in the table, we can see that the maximum value of g(x) is 7, which is indeed greater than the maximums of f(x) (-2) and h(x) (14). Therefore, statement 5 is true.

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Answer: The sales tax rate is 14%.

To find the sales tax rate, we can use the formula:

Sales Tax Rate = (Sales Tax / Cost before Tax) * 100

Given that the item costs $350 before tax and the sales tax is 14%, we can substitute the values into the formula:

Sales Tax Rate = (14 / 350) * 100

Simplifying the expression inside the parentheses:

Sales Tax Rate = 0.04 * 100

Multiplying 0.04 by 100:

Sales Tax Rate = 4

Therefore, the sales tax rate is 4%, which means that the sales tax on the item is 4% of the cost before tax.

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

[tex]\bf{2y+4y=6-3y}[/tex]

[tex]\bf{6y=6-3y}[/tex]

Add 3y to each side

[tex]\bf{6y+3y=6}[/tex]

Combine like terms

[tex]\bf{9y=6}[/tex]

Divide each side by 9

[tex]\bf{y=\dfrac{6}{9}}[/tex]

[tex]\bf{y=\dfrac{2}{3}}[/tex]

Hence, the answer is 2/3.

The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

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Using angle rules, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

Angle 1 + 69 + 47 = 180 (sum of angles on a straight line)

Angle 1 = 180 - (69+47)

Angle 1 = 64°

Angle 2 + 64 + 63 = 180 (sum of angles in a triangle)

Angle 2 = 180 - (64+63)

Angle 2 = 53°

Angle 1 + Angle 3 = 180 (sum of angles in a triangle)

Angle 3 = 180 - 64

Angle 3 = 116°

Angle 6 + 136 = 180 (sum of angles on a straight line)

Angle 6 = 180 - 136

Angle 6 = 44°

Angle 5 + Angle 3 + 32 = 180 (sum of angles in a triangle)

Angle 5 + 116 + 32 = 180

Angle 5 = 180 - (116 + 32)

Angle 5 = 32°

47 + Angle 6 + Angle 4 = 180

47 + 44 + Angle 4 = 180

Angle 4 = 180 - 91

Angle 4 = 89°

Therefore, the values of angles 1 to 6 are 64, 53, 116, 89, 32 and 44 respectively.

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Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + [tex]\frac{r}{2}[/tex] - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.

Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.

66.67% of 45 cents is (66.67/100) * 45 = 30 cents.

So, Naruto spends 30 cents on ramen per day.

To find out how much he spends in 15 days, we multiply the daily cost by the number of days:

30 cents * 15 = 450 cents.

Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.

The lines passing through these pairs of points are parallel.The correct answer is option A.

To determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line.
For line a, the points are (-1, -2) and (3, -3).
Let's calculate the slope of line a:
m = (y2 - y1) / (x2 - x1)
m = (-3 - (-2)) / (3 - (-1))
m = (-3 + 2) / (3 + 1)
m = -1 / 4
Now, let's move on to line b. The points are (0,0) and (4, -1).
Again, calculate the slope of line b:
m = (y2 - y1) / (x2 - x1)
m = (-1 - 0) / (4 - 0)
m = -1 / 4
Comparing the slopes of line a and line b, we can see that they have the same value (-1/4). Therefore, the lines passing through these pairs of points are parallel.
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Based on the given information and adjustments, the adjusted bank balance for ABC Company on July 31 would be Br. 5,169.42.

Based on the provided information, let's analyze the various transactions and their impact on the bank reconciliation for ABC Company:

1. The deposit of Br. 410.90 made after banking hours: This deposit does not appear in the bank statement, so it should be added to the bank balance. After including this deposit, the adjusted bank balance would be Br. 5,375.37 (Br. 4,964.47 + Br. 410.90).

2. The erroneously charged check of Br. 79: This check should be deducted from the bank balance as it was charged in error by the bank. After deducting this amount, the adjusted bank balance would be Br. 5,296.37 (Br. 5,375.37 - Br. 79).

3. Outstanding checks: The outstanding checks that haven't been paid by the bank need to be deducted from the adjusted bank balance. The total amount of outstanding checks is Br. 610.75 (Br. 100 + Br. 10.25 + Br. 294.50 + Br. 205). After deducting this amount, the adjusted bank balance would be Br. 4,685.62 (Br. 5,296.37 - Br. 610.75).

4. Incorrectly charged check of Br. 210 as Br. 120: This error made by the bank needs to be corrected. The bank balance should be increased by the difference, which is Br. 90. Therefore, the adjusted bank balance would be Br. 4,775.62 (Br. 4,685.62 + Br. 90).

5. Proceeds from collection of an interest-bearing note receivable: The face amount of the note was Br. 500. Since the note was left with the bank's collection department, the amount collected should be added to the bank balance. Therefore, the adjusted bank balance would be Br. 5,275.62 (Br. 4,775.62 + Br. 500).

6. Interest earned on the average account balance: The interest earned of Br. 24.75 should be added to the bank balance. After including this amount, the adjusted bank balance would be Br. 5,300.37 (Br. 5,275.62 + Br. 24.75).

7. The returned check of Br. 10: This check was recorded in the check register as Br. 100 but was returned for Br. 10. The difference of Br. 90 should be deducted from the bank balance. Therefore, the adjusted bank balance would be Br. 5,210.37 (Br. 5,300.37 - Br. 90).

8. Fee charged by the bank for handling the collection of the note receivable: The fee of Br. 5.00 should be deducted from the bank balance. After deducting this fee, the adjusted bank balance would be Br. 5,205.37 (Br. 5,210.37 - Br. 5.00).

9. Check from customer John charged as Non-sufficient funds (NSF): The check of Br. 50.25 should be deducted from the bank balance. After deducting this amount, the adjusted bank balance would be Br. 5,155.12 (Br. 5,205.37 - Br. 50.25).

10. Service charge by the bank for the month of July: The service charge of Br. 12.70 should be deducted from the bank balance. After deducting this charge, the adjusted bank balance would be Br. 5,142.42 (Br. 5,155.12 - Br. 12.70).

11. Erroneously recorded check of Br. 85 as Br. 58: This error in the cash payment journal needs to be corrected. The bank balance should be increased by the difference, which is Br. 27. Therefore, the adjusted bank balance would be Br. 5,169.42 (Br. 5,142.42 + Br. 27).

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Answer:

a) All the students in Nadia's year are the population

b) All the students in Nadia's class are the sample

Step-by-step explanation:

She wants to find out if students in her year like the school lunches.

So, this is the population.

i.e All the students in Nadia's year

She asks her class to complete a survey,

So, this is the sample of the population (Her classmates are in the same year as her and so on)

i.e All the students in Nadia's class