from a square cadrboard sheet, a 5cm wide strip was cut away. the area of the remaining rectangle is 266 cm. find the original dimensions of the square cardboard sheet.

Answer:  D. 58 degree

Step-by-step explanation:

A triangle has a total of 180 degrees

92 + 30 = 122 degree

180 - 122 = 58 degree

So, the answer is D. 58 degree

The value of x for the given figure will be equal to √212.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Apply the Pythagorean theorem for the first triangle,

H² = x² - 6²

Apply the Pythagorean theorem for the second triangle,

B² = 27² - x²

Apply the Pythagorean theorem to the third triangle,

H² = 27² - x² - 21²

H² = -x² + 288

x² - 6² = -x² + 288

2x² = 424

x² = 212

x=√212

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Answer:

1,500,000

Step-by-step explanation:

Let's assume the value of sales that the salesman made during the year to be x.

The bonus that he received at the end of the year is 7% of the value of the sales he made. So, his bonus would be 0.07x.

Therefore, his total income for the year is his basic monthly salary plus the bonus he received. We know that his total income was Rs 441,000. Hence, we can write:

28,000 * 12 + 0.07x = 441,000

Simplifying this equation:

336,000 + 0.07x = 441,000

0.07x = 105,000

x = 1,500,000

Therefore, the value of the sales that the salesman made during the year was Rs 1,500,000.

let x as the total sales

441 000 = 12(28 000) + 0.07x

441 000 = 336 000 + 0.07x

441 000 - 336 000 = 336 000 - 336 000 + 0.07x

105 000 = .07x

x = 1 500 000

12 * 28 000 = 336 000   (12 months salary)

0.07(1 500 000) = 105 000 (total sales)

336 000 + 105 000 = 441 000

Therefore, salesman total sales for the whole year is RS 1 500 000.

Step-by-step explanation:

To calculate the change in temperature from 8 a. m. to 4 p. m., time we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. 7.22°C - 3.3°C = 4.92°C Therefore, the change in temperature from 8 a. m. to 4 p. m. is 4.92°C.

To calculate the change in temperature from 8 a. m. to 4 p. m., we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. The temperature at 8 a. m. was 3.3°C, and the temperature at 4 p. m. was 7.22°C. Subtracting 3.3°C from 7.22°C gives the change in temperature of 4.92°C. To calculate the change in temperature from 8 a. m. to 4 p. m., we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. 7.22°C - 3.3°C = 4.92°C This means that the temperature increased by 4.92°C from 8 a. m. to 4 p. m. by time . The answer to the question is 4.92°C.

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Answer:

You buy the following from Best Buy:

1 new Chromebook for $550, 1 wireless mouse for $20, 1 wireless keyboard for $20

What is the Subtotal:

You use your Elite Members Best Buy credit card to save 6%, how much do you save:

What is the new Subtotal: $

Sales tax is 5%: $

What is the total: $

Step-by-step explanation:

[tex]34\times3333333=n[/tex]

[tex]34\times3333333=113333322(n)[/tex]

[tex]n\times454=x[/tex]

[tex]113333322(n)\times454=x[/tex]

[tex]113333322(n)\times454=51453328188(x)[/tex]

[tex]\fbox{x = 51453328188}[/tex]

The equation to represent this scenario is  2x+4y = 100

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The worth of x  number of multiple-choice questions = 2x

The worth of y  number of short-response questions = 4y

Assessment is worth 100 total points.

So,  the equation to represent this scenario is  2x+4y = 100

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Answer: 176.79

Step-by-step explanation:

15 (165) / 14

15 times 165 = 2475

2475 / 14 = 176.785

Round up to 176.79

Answer:

The three integers are 30, 180, and 540.

Step-by-step explanation:

The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without a remainder. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

In this case, we are given that the GCD and LCM of three integers are 6 and 1080, respectively. This means that the three integers must have a GCD of 6 and an LCM of 1080.

We are also given that the first two numbers are 60 and 72. The GCD of 60 and 72 is 12, which is not equal to 6. Therefore, these two numbers cannot be the first two integers.

To find the three integers, we need to find two numbers with a GCD of 6 and an LCM of 1080. One possible pair of numbers is 30 and 180, which have a GCD of 6 and an LCM of 180.

The third number must be a multiple of 6 and a factor of 1080. A possible value for the third number is 540, which is a multiple of 6 and a factor of 1080.

The three integers are 30, 180, and 540.

Answer: 1/2

Step-by-step explanation:

:D

The missing number is equal to 42

Let the missing number be 'x'

Therefore, we have the equation as

[tex]\frac{2}{35} = \frac{1}{30} + \frac{1}{x}[/tex]

Solving this equation further, we have

[tex]\frac{1}{x} = \frac{2}{35} - \frac{1}{30}[/tex]

Taking L.C.M. on R.H.S. side, we have

[tex]\frac{1}{x} = \frac{(2)(30) - (1)(35)}{(30)(35)}[/tex]

[tex]\frac{1}{x} = \frac{60 - 35}{1050}[/tex]

[tex]\frac{1}{x} = \frac{25}{1050}[/tex]

[tex]\frac{1}{x} = \frac{1}{42}[/tex]

On cross multiplying this equation, we get
[tex]x = 42[/tex]

Therefore, we can say that the missing number is equal to 42.

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Answer:

B (7,-1)

Step-by-step explanation:

(7,-1) is 2 points away from (7,1).

(4,1) and (7,4) are both 3 points away. (11,1) is 4 points away.

That makes B (7,-1) the closest to (7,1)

Answer:

11$

Step-by-step explanation:

We will use simultaneous equation

X = hostas

Y = geraniums

6X + 6Y = 138 ----> (first equation)

6X + 4Y = 116 -----> (second equation)

(Substract)

6X + 6Y = 138

6X + 4Y = 116

2Y = 22

Y = 22/2

Y = 11$  

I hope my answer helps you.

The 20 ft/sec is the timing of the string when 500 ft of string has been let out for the kite at a height of 300 ft, the wind carrying the kite horizontally away from her at a rate of 25 ft/sec.

Let dd be the real distance among the kite and the female, vv be the vertical distance among the female and the kite, and hh horizontal distance. Since the vertical distance is a constant (v = 300v=300) we understand that:

v^2 + h^2 = d^2 quad Rightarrow quad 300^2 + h^2 = d^2v 2 +h 2 =d 2 ⇒300 2 +h 2 =d 2

wherein dd and hh are capabilities of time tt, this means that that:

2hdfrac = 2ddfrac2h dtdh =2d dtdd

Since the vertical distance is v=300v=300, and the real distance is d = 500d=500, we understand that:

300^2 + h^2 = 500^2 quad h = sqrt = 400300 2 +h 2 =500 2 ⇒h= 500 2 −300 2 =four hundred

We're inquisitive about the price of extrade of the real distance dd so we have:

begin color dfrac &= dfrac cdot h cdot dfrac = dfrac cdot four hundred cdot 25 = color 20 text enddtdd = d1 ⋅h⋅ dtdh = 5001 ⋅four hundred⋅25=20 ft/sec

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Answer: The differential equations is

y3 3x3logx = 8x3.

Step-by-step explanation:

break the given original- value problem. The DE is homogeneous. xy2dy/ dx = y3- x3; y( 1) = 2.

result

Given a homogenous discriminational equation, xy2 dy/ dx = y3- x3

xy2dy/ dx = y3- x3

dy/ dx = ( y3- x3)/ xy2

dy/ dx = (( y/ x) 3- 1)/( y2/ x2)---( 1)

Put y/ x = v ⇒ y = xv

separatew.r.t x

dy/ dx = x.dv/ dx v

Equation( 1) becomes,

⇒ dv/ dx v = ( v3- 1)/ v2

⇒ dv/ dx = (( v3- 1)/ v2)- v

⇒ dv/ dx = ( v3- 1- v3)/ v2

v2. dv = -1/x.dx

Integrate on both sides, we get

∫ v2. dv = ∫- 1/x.dx

v3/ 3 = - logx C

1/3( y3/ x3)) log x = C( 2)

Now, given that y( 1) = 2

Substituting y = 2 and x = 1 in equation( 2)

(1/3) ×(23/13)) log 1 = C

C = 8/3

From equation( 2), we get

⇒( y3/ 3x3) logx = 8/3

thus, the needed differential equation is y3 3x3logx = 8x3.

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The solution to the expression a⁴ + b⁴ is 641 when a = 2 and b = 5

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

a = 2

b = 5

Also, from the question, we have

a^4 + b^4

Express the exponents in the above expression properly

So, we have the following representation

a⁴ + b⁴

Substitute the known values in the above equation, so, we have the following representation

a⁴ + b⁴ = 2⁴ + 5⁴

Evaluate the exponents

'This gives

a⁴ + b⁴ = 16 +625

Evaluate the sum

'This gives

a⁴ + b⁴ = 641

Hence, the solution is 641

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Complete question

Given that a = 2 and b = 5

WHAT IS a^4 + b^4

Answer:

2nd option, [ An expected height of 150 centimeters when the femur has a length of 37.7 ]

Step-by-step explanation:

y is a scale for height

x is a scale for femur length

BUT, the difference between the 2nd and 4th answer is in the words "expected" and "actual."

The reason the correct answer includes the word "expected" is because we are looking at THE LINE OF BEST FIT that is plotted on the graph. This line represents what we expect based on the relationship between the two variables

The dots represent REAL DATA that has been recorded.

Recursion uses more memory compared to iteration because every time the recursive function is called the function call is stored in stack, The correct option is B

Recursion is the process of defining a problem or the solution to a problem in terms of a simpler version of itself. There two types of recursion the first one is called direct recursion when the second is called indirect recursion.

Therefore recursion is a method of solving problem where the solution depends on solutions to smaller instances of the same problem.

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Answer:

22

Step-by-step explanation:

Knowledge Needed

| | (absolute value) = Makes anything inside positive after solving.

A negative number multiplied or divided by another negative number is positive.

Question

Set up the equation

| -(-22) |

| 22 |

Stays positive.

22

Answer:

6

Step-by-step explanation:

Examine this sequence. What are the relations of these values?

Every time you increase 1 term in the sequence, divide by 2.

768/2 = 384

384/2 = 192

etc.

Write a geometric sequence formula.

[tex]a_n = a*r^(^n^-^1^)[/tex]

A is the starting value (768), and r is the common ratio, or what the value is being multiplied by to get the next term. N is the term, where you can plug it in. For the eighth value, plug in 8 for n.

768 * ? = 384

1/2

r = 1/2

[tex]a_n = 768 * 1/2^(^n^-^1^)[/tex]

For finding the eighth value, plug in 8 for n.'

[tex]768 * 1/2^(^8^-^1^)[/tex]

[tex]768 * 1/2^7[/tex]

768 * 0.0078125

6

The equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

Point (6,-4),

2x - y = 5,

Calculate the slope as the line is perpendicular to line 2x - y = 5

m = 2

The slope of the line perpendicular, m = - 1 / 5

Calculate the equation of the line as shown below,

[tex]y - (-4) = - 1 / 5 (x - 6)[/tex]

5 (y + 4) = -x + 6

5y + 20 = -x + 6

5y + x = -14

Therefore, the equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5 is 5y + x = -14.

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The complete question is:

What is an equation of the line that passes through the point (6,-4) and is perpendicular to the line 2x - y = 5?

Answer:

Step-by-step explanation:

This has some significance in logic because if two propositions have the same truth table they are in a logical sense equal to each other – and we say that they are logically equivalent. So: ¬p∨(p∧q)≡p→q, or "Not p or (p and q) is equivalent to if p then q."

...

Logically Equivalent Statements.

p q p→q

F F T

The z score of a dog of this breed weighs 52 pounds is 0.571. The weight of the dog if z is -0.35 is 45.55 kg. The weight of the dog if z is 0.35 is 50.45 kg.

A z score refers to a numerical measurement that defines a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

The z score is given by:

z = (x - µ)/σ

where x is the raw score, µ is the mean, and σ is the standard deviation.

In the given case,

x = 52 pounds

µ = 48 pounds

σ = 7 pounds

Hence,

z = (52 - 48)/7 = 0.571

If z = -0.35

Then

-0.35 = (x - 48)/7

x - 48 = -2.45

x = 45.55 kg

Hence, the weight of the dog if z is -0.35 is 45.55 kg.

If z = 0.35

Then

0.35 = (x - 48)/7

x - 48 = 2.45

x = 50.45 kg

Hence, the weight of the dog if z is 0.35 is 50.45 kg.

Note: The question is incomplete. The complete question probably is: The weights of a certain dog breed are approximately normally distributed with a mean of 48 pounds, and a standard deviation of 7 pounds. A dog of this breed weighs 52 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. A dog has a z-score of -0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds

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The equation of a parabola with vertex at (0, 0) and axis of symmetry along the y-axis is of the form y = ax^2. The parabola passes through the point (-1, 1), so we can set up the following equation:

y = a * x^2

1 = a * (-1)^2

Solving for a, we get a = 1. Therefore, the equation of the parabola is y = x^2.

Answer:

X=4 Y=28

Step-by-step explanation:

We have our two equations, 2x+4=12 and Y=4x+12
Solve for x of one of the equations so that the repeating (common) variable can be cancelled out.

Using 2x+4=12, we can solve for the x-value and replace it back into y.

2x+4=12
2x=8
x=4

We can replace our new x-value into the other equation, y=4x+12

y=4(4)+12
y=16+12
y=28

So x=4, and y=28

The function in this problem is defined as follows:

f(x) = 6x - 1.

Giving how many points a player is awarded when a dice of x is rolled.

The possible values at which the dice can land is up:

1,2,3,4,5,6.

Then the numeric values of the function are calculated replacing x by their values.

The only inputs that make sense are 1,2,3,4,5,6, as they are the values at which the dice can land. For example, a dice cannot land on neither 5.5 nor 10.

The function in this problem is defined as follows:

f(x) = 6x - 1.

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Answer:

  b = -2.875

Step-by-step explanation:

You want the value of b such that (-2, 10) is a point on the graph of g(x)= 5/x −bx²+1.

Fill in the given values and solve for b.

  g(-2) = 10

  5/(-2) -b(-2)² +1 = 10

  -2.5 -4b +1 = 10

  -4b = 11.5

  b = -11.5/4

  b = -2.875

Answer: 0.6 hours

Step-by-step explanation:

      We will set up a proportion to help us solve.

[tex]\displaystyle \frac{1,500\; \;miles}{4.5\;\;hours} =\frac{200\;\;miles}{x\;\;hours}[/tex]

      Next, we will cross-multiply and solve by multiplying and using inverse operations.

1,500 * x = 200 * 4.5

1,500x = 900

x = 0.6 hours

Answer:

i think the answer is 2/5

Step-by-step explanation: