33. It's 2 years since I was last in Rome. ⇒ I haven't 34. I saw Tom last on his wedding day. ⇒ I haven't 35. I last ate raw fish when I was in Japan. ⇒ I haven't 36. It's years since Mary last spoke French. ⇒ Mary hasn't 37. It's ten weeks since since I last had a good night sleep. I haven't 38. He last paid taxes in 1970. He hasn't last taxes 39. I last ate meat 5 years ago. ⇒ I haven't since 1970 40. It's 3 months since since the windows were cleaned. The windows haven't 41. It's years since I took photographs.​

Answer:        -0.7

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

I don’t really have an explanation, it was all mental math

Answer:

Step-by-step explanation:

[tex]\sf 2(4-x)-3(x+3)=-11[/tex]

Expand:-

Now, add 1 to both sides:-

Divide both sides by -5:-

Therefore, the value of x is 2!

- - - - - - - - - - - - - - - - - - - - - -

Hope this helps!

Answer:

18+x = -40

Step-by-step explanation:

The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40

Answer:

y = -1/2x

Step-by-step explanation:

Currently, y = 2x - 5 is in slope-intercept form, whose general equation is y = mx + b, where

The slopes of perpendicular lines are negative reciprocals of each other.  We can show this with the following formula;

m2 = -1 / m1, where

Finding the slope of the other line:

Since 2 is the slope of y = 2x - 5, we can plug in 2 for m1 in perpendicular slope formula to find m2, the slope of the other line:

m2 = -1 / 2

m2 = -1/2

Thus, the slope of the other line is m = -1/2.

Finding the y-intercept of the other line:

We can find the y-intercept of the other line (i.e., b in the slope-intercept equation) by plugging in (-2, 1) for x and y and -1/2 for m in the slope-intercept form:

1 = -1/2(-2) + b

1 = 1 + b

0 = b

Thus, y = -1/2x is the line that passes through (-2, 1) and is perpendicular to y = 2x - 5.

Answer:  A    -6x² + 2x -4

Step-by-step explanation:

[tex]\frac{-12x^{3}+ 4x^{2} -8x}{2x}[/tex]                             >Divide each of the top terms by 2x[tex]=\frac{-12x^{3}}{2x} +\frac{4x^{2} }{2x} -\frac{8x}{2x}[/tex]

= -6x² + 2x -4

The value of the expression 226²⁸ ● (25)⁶ is approximately [tex]4.1406562 \times 10^{119.[/tex]

To evaluate the expression 226²⁸ ● (25)⁶, we can follow the order of operations (also known as PEMDAS/BODMAS) which states that we should perform any calculations inside parentheses, then evaluate any exponents, and finally perform any multiplications or divisions from left to right.

Let's break down the expression :

Evaluate the exponent (25)⁶

[tex](25)^{6} = 25^{(6\times 1)} = 25^6 = 244,140,625[/tex]

Substitute the value into the expression:

226²⁸ ● 244,140,25.

Evaluate the exponent 226²⁸

[tex]226^{28} = 226^{(2\times28) = 226^{56 \\[/tex]

Now, calculating [tex]226^{56}[/tex] might not be feasible manually due to the large exponent.

However, we can use a calculator or a computer program to obtain the result.

[tex]226^{56} \approx 1.6951718 \times 10^{112[/tex]

Substitute the value back into the expression:

[tex]1.6951718 \times 10^{112[/tex] ● 244,140,625

Perform the multiplication:

[tex]1.6951718 \times 10^{112}\times 244,140,625 \approx 4.1406562 \times 10^{119[/tex] .

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The value of the unknown side to the nearest hundredth is 6.78

Cosine rule states that; if a, b,c are the sides of a triangle and A,B,C are the opposite angles of the sides, then

c² = a² + b² -2ab CosC

Cosine rule is used when all the sides or two of the sides are given. The angle opposite to side c is angle C.

c² = 4² + 10² - 2(4)(10)cos 29

c² = 16 +100 - 80cos29

c² = 116 -69.97

c² = 46.03

c = √ 46.03

c = 6.78 ( nearest hundredth).

Therefore the value of c is 6.78

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The general form of the solutions of the recurrence relation is

[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]

We are given that;

Series=1, 1, 1, 1, -2, -2, -2, 3, 3, -4

Now,

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

If the characteristic equation has repeated roots, then the general solution is modified by multiplying each term by a polynomial in n whose degree is equal to the multiplicity of the root minus one. For example, if r is a root of multiplicity m, then the corresponding term in the general solution is

[tex]a_n = (A + B n + C n^2 + … + Z n^(m-1)) r^n,[/tex]

where A, B, C, …, Z are arbitrary constants.

In this question, the characteristic equation has roots 1, 1, 1, 1, -2, -2, -2, 3, 3, -4. The root 1 has multiplicity 4, the root -2 has multiplicity 3, and the roots 3 and -4 have multiplicity 2 each.

[tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]

where A, B, C, D, E, F, G, H, I, J and K are arbitrary constants.

Therefore, by the equation answer will be [tex]a_n = (A + B n + C n^2 + D n^3) 1^n + (E + F n + G n^2) (-2)^n + (H + I n) 3^n + (J + K n) (-4)^n,[/tex]

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Answer:

         m∠RQS = 102°

         m∠TQS = 78°

Step-by-step explanation:

    A straight angle is equal to 180 degrees. We will create an equation to solve for x.

         9x° + 3° + 7x° + 1° = 180°

         16x° + 4° = 180°

         16x° = 176°

         x = 11

    Next, we will substitute this value into the expressions representing the angles.

         m∠RQS = 9x° + 3° = 9(11)° + 3° = 102°

         m∠TQS = 7x° + 1° = 7(11)° + 1° = 78°

Given statement solution is :- The correct solutions to the quadratic equation  [tex]3(x-7)^2 = 27[/tex]  are x = 10 and x = 4.

Diego made an error in the step where he simplified [tex](x-7)^2 = 9 to x^2[/tex] - 72 = 9. The correct expansion of [tex](x-7)^2 is x^2 - 14x + 49[/tex], not [tex]x^2 - 72.[/tex]Therefore, his subsequent steps and solution are incorrect.

Mai made an error in the step where she simplified [tex](x-7)^2 = 9[/tex] to x - 7 = 9. The square root of 9 is ±3, so the correct equation should be x - 7 = ±3, not x - 7 = 9. Therefore, her solution is incorrect.

To solve the equation correctly, we start with the equation [tex]3(x-7)^2 = 27.[/tex]

Dividing both sides by 3, we have:

[tex](x-7)^2 = 9[/tex]

Taking the square root of both sides, we get:

x - 7 = ±3

Now, we need to solve for x by adding 7 to both sides:

x = 7 ± 3

This gives us two possible solutions:

x = 7 + 3 = 10

x = 7 - 3 = 4

So, the correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.

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The completely factorized forms are:

1.1) 2x + 4y - 6z (no further factorization)

[tex]1.2) 2pq(5p^5q - 2p^2 + 1)[/tex]

1.3) (m + n)(m + n - 5p)

1.4) 7c(4 - a) + d(-4 + a)

We have,

Let's factorize each expression completely:

1.1)

2x + 4y - 6z

There are no common factors among the terms, so we can't factorize it further.

1.2)

[tex]10p^6q^2 - 4p^3q^2 + 2pq[/tex]

The common factor among the terms is 2pq, so we can factor it out:

[tex]2pq (5p^5q - 2p^2 + 1)[/tex]

1.3)

(m + n)² - 5p(m + n)

Using the distributive property, we can expand the squared term:

(m + n)(m + n) - 5p(m + n)

Now we can factor out the common factor (m + n):

(m + n)(m + n - 5p)

1.4)

4(7c - d) + a(d - 7c)

Using the distributive property, we can expand the terms:

28c - 4d + ad - 7ac

Rearranging the terms:

(28c - 7ac) + (-4d + ad)

Factoring out common factors:

7c(4 - a) + d(-4 + a)

Thus,

The completely factorized forms are:

1.1) 2x + 4y - 6z (no further factorization)

[tex]1.2) 2pq(5p^5q - 2p^2 + 1)[/tex]

1.3) (m + n)(m + n - 5p)

1.4) 7c(4 - a) + d(-4 + a)

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We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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Answer:

A

Step-by-step explanation:

To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:

First, let's simplify the division 3 11 5 ÷ 3:

3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.

Next, let's subtract 9 5 from the result we obtained:

115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.

Therefore, the simplified expression is 70.

The correct answer is A. 70.

Answer:

60 degrees

Step-by-step explanation:

To convert radians to degrees, multiply by 180/pi

pi/3 * 180/pi = 180/3 = 60 degrees

Step-by-step explanation:

3 radians =

171.887 degrees

 AreaData Transfer RateDigital StorageEnergyFrequencyFuel EconomyLengthMassPlane AnglePressureSpeedTemperatureTimeVolume 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

Formula

3rad × 180/π = 171.887°

Answer:

5

She must therefore earn 5 points on the last test to achieve a mean score of 4.

Step-by-step explanation:

The sum of the data divided by the total number of data represents the mean, which is the average of a set of data.

The possible lengths of the tree lot are 25 + 5√5 yards and 25 - 5√5 yards.

Let's denote the length of the rectangular tree lot as "l" and the width as "w".

We know that the perimeter of a rectangle is given by the formula:

Perimeter = 2(l + w)

Given that the perimeter of the tree lot must be 100 yards, we can write the equation as:

2(l + w) = 100

Next, we know that the area of a rectangle is given by the formula:

Area = l × w

Given that the area of the tree lot must be at least 500 square yards, we can write the inequality as:

l × w ≥ 500

Now, let's solve the equations simultaneously to find the possible lengths of the tree lot.

Perimeter equation:

2(l + w) = 100

l + w = 50

w = 50 - l

Area inequality:

l × w ≥ 500

Substituting the value of w from the perimeter equation into the area inequality, we have:

l × (50 - l) ≥ 500

50l - l^2 ≥ 500

l^2 - 50l + 500 ≥ 0

Now, we need to find the values of l that satisfy the inequality. Since the coefficient of the squared term is positive, the graph of this quadratic opens upward. This means that the values of l that satisfy the inequality will be either the entire range of possible values or a portion of it.

To find the possible lengths, we can either factor the quadratic or use the quadratic formula. Let's use the quadratic formula:

l = (-(-50) ± √((-50)^2 - 4(1)(500))) / (2(1))

l = (50 ± √(2500 - 2000)) / 2

l = (50 ± √500) / 2

l = (50 ± 10√5) / 2

l = 25 ± 5√5

Therefore, the possible lengths of the tree lot are 25 + 5√5 yards and 25 - 5√5 yards.

In summary, the possible lengths of the rectangular tree lot are 25 + 5√5 yards and 25 - 5√5 yards, respectively.

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Subtraction and Division

Inverse operations help find the solution to equations.

Defining Inverse Operations

Firstly, let's define an operation. An operation in math is a function that can manipulate a value. Inverse operations are operations that are opposite operations that undo each other. For example, addition and subtraction are inverse operations because subtraction undoes addition. Multiplication and division are also inverse operations.

Solving the Equation

The equation 16 = 3x + 1 involves both addition and multiplication. So, to solve this, we can use the inverse operations of subtraction and division. First, subtract 1 from both sides.

Then, divide both sides by 3.

This shows that by using subtraction and division, we can undo the addition and multiplication used in the equation. This allows us to find the value of x.

Step-by-step explanation:

7! = 5040 ways

Given statement solution is :- On average, she spent approximately $115 per visit.

To calculate the total amount spent on the visits, we need to add up the co-payments and the cost of the shots.

Co-payments:

The co-pay for each visit is $25, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total co-payment is:

3 visits/week * $25/visit * 8 weeks = $600.

Shots:

You received the shot 2 times out of each visit, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total cost of the shots is:

2 shots/visit * $135/shot * 8 weeks = $2,160.

Total amount spent:

Co-payments + Shots = $600 + $2,160 = $2,760.

Therefore, the total amount spent for the visits and shots over 2 months is $2,760.

Trivia Answer:

To find out the average amount spent per visit, we can divide the total amount spent by the total number of visits. In this case, the total amount spent is $2,760, and the total number of visits is 3 visits/week * 8 weeks = 24 visits.

Average spent per visit = Total amount spent / Total number of visits

Average spent per visit = $2,760 / 24 visits

Average spent per visit ≈ $115.

Therefore, on average, you spent approximately $115 per visit.

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The cross-section that results from slicing a cube through the center vertically, perpendicular to the base, is both a rectangle and a square.

When a cube is sliced through the center vertically, perpendicular to the base, the resulting cross-section will be a rectangle and a square.

Let's consider the properties of a cube. A cube is a three-dimensional solid with six square faces. Each face of the cube is congruent and perpendicular to the adjacent faces. The edges of the cube are all equal in length, and the angles between the faces are all right angles (90 degrees).

When we slice the cube vertically through the center perpendicular to the base, we cut through the cube in such a way that the cross-section obtained is a plane figure. This cross-section will have the same shape as the face of the cube that was cut.

In this case, since the cube has square faces, the cross-section will also have the same shape. Therefore, a square is one of the shapes that apply to the resulting cross-section.

Additionally, since the slice is made through the centre of the cube, the resulting cross-section will pass through the midpoints of two opposite sides of the square face. As a result, the cross-section will have equal side lengths and parallel sides, making it a rectangle.

Final answer:

Therefore, the cross-section that results from slicing a cube through the center vertically, perpendicular to the base, is both a rectangle and a square. These shapes capture the properties of the cube's face and the nature of the cut.

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Answer:

x+4y=7

Step-by-step explanation:

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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The term 9b represents the cost to rent a bike.

We have,

               Rentals

Bike                            $9/h

Electric scooter          $10/h

Kayak                          $18/h

Canoe                         $20/h

Paddleboard               $22/h

Helmet                        Add $6

Here, the term 9b represents the cost to rent a bike.

In the provided rental options, the cost of renting a bike is $9 per hour.

The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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Answer:

correct answer is 650ml

The expression that shows the volume of the prism is x³ - x² - 6.

The prism above is a rectangular prism. The volume of the prism can be found as follows:

The volume of the prism can be found as follows:

volume of the rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = (x - 3)(x)(x + 2)

volume of the rectangular prism = (x² - 3x)(x + 2)

volume of the rectangular prism = x³ + 2x² - 3x² - 6

volume of the rectangular prism = x³ - x² - 6

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The number of students taking all three languages would be 1 student. The number of students taking none of the languages are 32.

The total number of students taking each language is given so the number of people taking these languages are:

15 + 14 - X + X = 30

X = 1

So, there is 1 student taking all three languages.

For the students taking none of these languages:

Total students - students taking at least one language = students taking none of these languages.

= 100 (total students) - (53 ( taking only one language ) + 14 ( taking Arabic and Bulgarian ) + X (taking all three languages))

= 100 - 53 - 14 - 1

= 32 students

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Given statement solution is :- The area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.

To calculate the area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.

Given that the radius (r) is 10 cm, the area of the base (ABase) can be calculated as follows:

ABase =[tex]πr^2[/tex]

ABase = 3.14 * [tex](10 cm)^2[/tex]

ABase = 3.14 * [tex]100 cm^2[/tex]

ABase = 314 [tex]cm^2[/tex]

The area of the base is [tex]314 cm^2.[/tex]

To calculate the volume (V) of the cylinder, you need to multiply the area of the base (ABase) by the height (h):

V = ABase * h

V = 314 [tex]cm^2[/tex] * 30 cm

V = 9420 [tex]cm^3[/tex]

The volume of the cylinder is 9420 [tex]cm^3.[/tex]

However, there seems to be some confusion in the provided information. The given values for the area of the base (ABase) and the volume (V) are not clear. The values "- 20 gm" and "cm cm?" are not meaningful units for area or volume.

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The discounted price of the item would be Rs. 23,940.

To calculate the discounted price of an item, you can use the following formula:

Discounted Price = Original Price - (Original Price * Discount Percentage)

Given that the original price (MP) is Rs. 26,600 and the discount is 10%, we can calculate the discounted price as follows:

Discounted Price = Rs. 26,600 - (Rs. 26,600 x 0.10)

Discounted Price = Rs. 26,600 - Rs. 2,660

Discounted Price = Rs. 23,940

Therefore, with a 10% discount, the discounted price of the item would be Rs. 23,940.

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