Given a circle of radius 21cm correct to the nearest cm. What is the possible maximum error when calculating its area?

Answer:

24m

Step-by-step explanation:

If we imagine this situation as a right angled triangle, 25m is the hypotenuse, 7m is the height and we need the base length

so by Pythagoras thorium we can say that [tex]\sqrt[2]{25^2 -7^2}[/tex]= base length

which is= 24

Assuming that you want this to be expanded, simply multiply each term in the first set of parentheses with each term in the second parentheses:

(-2x + 10) (-9x + 5)

18x^2 - 10x - 90x + 15

18x^2 - 100x + 15

If the question, instead, is asking you to find the x-intercepts, set the expression to zero and solve:

0 = (-2x + 10) (-9x + 5)

0 = -9x + 5 <- divide -2x+10 on all sides

5/9 = x

OR

0 = -2x + 10

5 = x

Answer:

(-2x + 10) (-9x + 5) is a polynomial expression that represents the product of two binomials. To solve this expression, you can use the FOIL method, which stands for First, Outer, Inner, Last.

FOIL method:

First: multiply the first terms of each binomial (-2x and -9x) to get 18x^2

Outer: multiply the outer terms of each binomial (-2x and 5) to get -10x

Inner: multiply the inner terms of each binomial (10 and -9x) to get -90x

Last: multiply the last terms of each binomial (10 and 5) to get 50

Then, combine like terms to get the final expression:

(-2x + 10) (-9x + 5) = 18x^2 - 100x - 90x + 50 = 18x^2 - 190x + 50

Step-by-step explanation:

Brainliest Plss

Answer:

-6

Step-by-step explanation:

Simply substitute x = 2 & y = -1 into the function:

[tex]f(2,-1) =[/tex] [tex]\\\sf{3x + 4y - 8[/tex]

               [tex]3(2) + 4(-1) - 8[/tex]

                [tex]6 - 4 - 8[/tex] = -6

Therefore, the value of f(2, -1) for the function f(x, y) = 3x + 4y - 8 is -6.

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Note tha the   surface area of the toy box is 390cm².

To find the surface area of the toy box, we need to calculate the areas of all the faces and then sum them up.

The toy box is in the shape of a rectangular prism with dimensions:

Length = 15 cm

Width = 5 cm

Height = 6 cm

The surface area of a rectangular prism can be found using the formula  

Surface Area = 2(LW + LH + WH)

Substituting the values we have  -

Surface Area = 2(15 * 5 + 15 * 6 + 5 * 6)

= 2(75 + 90 + 30)

= 2(195)

= 390 cm²

Hence, the surface area of the toy box is 390 square centimeters.

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Answer:

C

Step-by-step explanation:

x + [tex]\frac{3}{4}[/tex] y = 5 ( multiply through by 4 to clear the fraction )

4x + 3y = 20 → (1)

x - [tex]\frac{1}{2}[/tex] y = 0 ( multiply through by 2 to clear the fraction )

2x - y = 0 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

6x - 3y = 0 → (3)

add (1) and (3) term by term to eliminate y

(4x + 6x) + (3y - 3y) = 20 + 0

10x + 0 = 20

10x = 20 ( divide both sides by 10 )

x = 2

The measure of angle D of the given Kite is: 127°

From the diagram, the figure represents a kite.

Properties of a kite are:

- Two pairs of adjacent sides are equal.

- Two diagonals intersect each other at right angles.

- The longer diagonal bisects the shorter diagonal.

- The angles opposite to the main diagonal are equal.

Thus:

The angle B = the angle D

The sum of all angles of a quadrilateral = 360

Given: ∠A = 36 and ∠C = 70

Thus:

2∠D = 360 - (36 + 70)

2∠D = 254

∠D = 127°

So, the measure of angle D = 127°

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Answer: it stand for 3 million or 3,000,000

Step-by-step explanation:

Answer:

million

Step-by-step explanation:

millions always have six 0's behind it

The temperature drops by [tex]31\°C[/tex] from day to night in this city.

To calculate the temperature drop from day to night in [tex]\°C[/tex], we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: [tex]-40\°C[/tex]

Average daily high temperature: [tex]-9\°C[/tex]

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = [tex]-9\°C - (-40\°C)[/tex]

Simplifying the equation:

Temperature drop = [tex]-9\°C + 40\°C[/tex]

Temperature drop = [tex]31\°C[/tex]

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by [tex]31\°C[/tex] from day to night in this city.

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Hello!

So the 2 angles of the base are equal, so:

(180 - 74)/2 = 53° one of the 2 angles

          74°

          /\
        /    \
      /        \
    /            \

53°             53°

180 - 74*2 = 32°

          32°

          /\
        /    \
      /        \
    /            \

74°             74°

So the others angles can be:

- 74° and 53°

- 74° and 32°

The steps that should be followed in order to solve the inequality statement -3t + 7 ≥ 9 include the following: B. subtract 7, divide by -3, and flip the inequality symbol.

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-3t + 7 ≥ 9

By subtracting 7 from both sides of the equation (inequality), we have;

-3t + 7 - 7 ≥ 9 - 7

-3t ≥ 2

By dividing both sides of the equation (inequality) by -3, we have;

t ≥ 2/-3

t ≤ 2/3 (flip the inequality symbol).

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a.

The estimated total cost of the grocery items is $36.

b.

The actual total cost of the grocery items is $35.82.

for part a.

We will round each price to the nearest dollar:

$5.12 =  $5

$3.07 = $3

$7.11 = $7

$1.67 = $2

$13.18=  $13

$5.67 = $6

Summing them up, we have:

$5 + $3 + $7 + $2 + $13 + $6 = $36

the estimated total cost of the grocery items is $36.

for part b.

We will calculate the actual total cost of the grocery items by using a calculator:

$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82

In conclusion, we will find the  actual total cost of the grocery items as $35.82.

The complete question is added as an image

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For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA

For question 3.)

To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;

Sine rule:

a/sinA = b/sinB = c/sinC

where;

a = 8

A = sinA

b = 5

B = SinB

c = 9.45

C = Sin 90°

The three ratios;

= 9.45:sin90°; 5:sinB; 8:sinA

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The solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].

To solve the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] , we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. Here's a step-by-step explanation:

Case 1: |[tex]2x+1[/tex]| ≥ [tex]3[/tex]

Subtract 1 from both sides of the inequality:

[tex]2x + 1 - 1[/tex] ≥ [tex]3 - 1[/tex]

2x ≥ 2

Divide both sides of the inequality by 2:

[tex]$\frac{2x}{2} ≥ \frac{2}{2}$[/tex]

x ≥ 1

Case 2: -([tex]2x+1[/tex]) ≥ [tex]3[/tex]

Multiply both sides of the inequality by -1 (to reverse the inequality):

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

-2x - 1 ≤ -3

Add 1 to both sides of the inequality:

[tex]-2x - 1 + 1[/tex] ≤ [tex]-3 + 1[/tex]

-2x ≤ -2

Divide both sides of the inequality by -2 (note that we need to reverse the inequality sign when dividing by a negative number):

[tex]$\frac{-2x}{-2} ≥ \frac{-2}{-2}$[/tex]

x ≥ 1

Combining the solutions from both cases, we have x ≥ 1.

Therefore, the solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].

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Answer: 1/ 3 ^9

Step-by-step explanation:

Answer:

1/39

Step-by-step explanation:

3-9=1/39

The answer is 0ne over three exponent nine

Answer:

12 km (565m)

Step-by-step explanation:

Hello!

[tex]\sf 89x - 135 = 24\\\\89x = 24 + 135\\\\89x = 159\\\\\boxed{\sf x = \dfrac{159}{89}} \\\\[/tex]

Using cosine Rule, the value of the requested angle is 33.12°

Since the three sides are given, we use the Cosine rule :

Hence,

CosA = (10²+4²-7²) / (2 × 10 × 4)

Cos A = 67/80

Cos A = 0.8375

A = [tex] {cos}^{ - 1} (0.8375)[/tex]

A = 33.12

Therefore, the value of the missing angle is 33.12

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Answer:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

The measure of the angle B is 32. 0 degrees

To solve the given triangle, we need to know the different trigonometric identities and their ratios.

We have that these identities are;

From the information given, we have that;

Opposite side of angle B = 5

Hypotenuse side = 9.43

Using the sine identity, we get that;

sin B = 5/9.43

Divide the values, we have;

sin B= 0.5302

Find the inverse value of the sine identity and then substitute

B = 32. 0 degrees

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The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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Answer:

To find the sum of x₁ and x₂, we need to solve the system of equations:

y = x² ...(1)

y = 1,002x - 2,000 ...(2)

Since both equations are equal to y, we can set them equal to each other:

x² = 1,002x - 2,000

To solve this quadratic equation, we can rearrange it into standard form:

x² - 1,002x + 2,000 = 0

Now, we can factorize the equation:

(x - 2)(x - 1,000) = 0

Setting each factor equal to zero, we get two solutions:

x - 2 = 0 => x = 2

x - 1,000 = 0 => x = 1,000

The sum of distinct solutions x₁ and x₂ to the system of equations y = x² and y = 1,002x - 2,000 is 1,002.

The problem here involves finding the solutions to the system of equations. Those equations are y = x² and y = 1,002x - 2,000. To solve this system of equations, we can set the two equations equal to each other, because they both equal y.

So, we have: x² = 1,002x - 2,000. Rearranging, we get x² - 1,002x + 2,000 = 0. This is a quadratic equation, and we can solve for x using the quadratic formula: x = [1,002 ± sqrt((1,002)² - 4*1*2,000)] / (2*1). This will yield 2 solutions for x, let's call them x₁ and x₂.

The question asks for the sum of x₁ and x₂. In a quadratic equation ax² + bx + c = 0, the sum of solutions is given by -b/a. Here, a = 1 and b = -1,002, so the sum of solutions x₁ and x₂ is -(-1,002)/1 = 1,002.

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Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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The student in the video is trying to determine if the number of sides of a regular polygon has a relationship to the sum of its interior angles.

They are specifically interested in finding a formula that can be used to calculate the sum of the interior angles of any regular polygon, given the number of sides.

The student's conjecture is that the sum of the interior angles of a regular polygon is equal to (n-2)*180, where n is the number of sides.

In order to test their conjecture, the student drew a regular polygon with 3 sides, 4 sides, 5 sides, and so on, up to a regular polygon with 100 sides. They then calculated the sum of the interior angles of each polygon and compared their results to their conjecture.

The student's results showed that the sum of the interior angles of each regular polygon was equal to (n-2)*180, as they had conjectured. This suggests that their conjecture is correct.

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Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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The simplified expression is m^1 or simply m.

To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.

First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.

Now, we can simplify the expression further: 1/m^8 * m^9.

When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.

Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.

Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.

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The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

Assuming that a movie has strong marketing and positive reviews, it is reasonable to expect that it could earn $16 million in its opening weekend.

Step-by-step explanation:

The question of when a movie will earn $16 million is a complex one that depends on a variety of factors. The success of a film is influenced by its marketing, critical reception, and competition from other movies in the marketplace. However, there are some general trends that can be observed when it comes to box office performance.

Typically, the first week of a movie's release is the most important for earning revenue. This is because theaters often give priority to new releases and allocate more screens to them.

Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas.  A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.

To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.

Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.

Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.

Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:

Rectangle: Area = length × width

Triangle: Area = (base × height) / 2

Circle: Area = π × radius²

Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.

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