Perform long division on the following, please show work:
a) 33.143 / 100
b) 175.876 / 0.01

Step-by-step explanation:

these 2 parallel lines create similar triangles.

that mags they're is one common scaling factor for the side lengths bergen the 2 triangles.

and that means they must have the same ratio.

the large triangle has the side lengths

24 + 9 = 33

32 + x

the smaller triangle has the corresponding side lengths

24

32

so, the equal ratios are

24/33 = 32/(32+x)

24(32 + x) = 32×33

32 + x = 32×33/24 = 4×11 = 44

x = 44 - 32 = 12

Answer:

Yes, they are equal.

Step-by-step explanation:

Because these are both right triangles, we know that one angle is similar. And seeing that side MO is the hypotenuse of both triangles, by the SA theorem we know that the two are equal. Or because we know that this is a reactangle or square by the four equal angles, we know that because this triangle is split in half, the triangle have to be equal.

-Hope this

According to the information, the mathematical expression with which the problem is solved is 8x < 672.

To find the expression that solves this problem we must take into account that it is an inequality. So we must use the symbols greater than > or less than <. Additionally, we must read the information in the statement to identify how it goes to the inequality.

According to the above, there are less than 84 students who answered that they had never bought online (x). Then the expression would start like this:

Subsequently, they do not say that x equals one eighth of the total number of students. Then the expression would be modified like this:

Finally, if we simplify this expression, it would look like this:

So, that would be the expression of this inequality.

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Answer:

k = .5 inches

Step-by-step explanation:

In total, they have 6000 grams of sand.

What are basic arithmetic operations?

The basic arithmetic operations are the four fundamental mathematical operations used to manipulate numerical values. They are addition, subtraction, multiplication, and division.

To solve the problem, we need to know the conversion factor between kilograms and grams, which is 1 kilogram = 1000 grams.

First, we can find out how many grams of sand Lucas has in his bucket. We are given that he has 2 kilograms of sand, so we can use the conversion factor to convert kilograms to grams:

2 kilograms x 1000 grams/kilogram = 2000 grams

Therefore, Lucas has 2000 grams of sand in his bucket.

Next, we can find out how many grams of sand Mac has in his bucket. We are given that he has 4 kilograms of sand, so we can use the conversion factor again:

4 kilograms x 1000 grams/kilogram = 4000 grams

Therefore, Mac has 4000 grams of sand in his bucket.

To find out the total amount of sand they have in grams, we can add the amount of sand each of them has:

2000 grams + 4000 grams = 6000 grams

Therefore, in total, they have 6000 grams of sand.

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The solution to the equation is x=3, which means that when x is equal to 3, the equation is true.

The solution of an equation is the value of the variable that satisfies the equation.

In this case, the solution is x=3, which means that when x is substituted with 3, the equation is true.

We can say that the solution is unique, as there is only one value of x that satisfies the equation. It is also a real solution, as the value of x is a real number.

Additionally, we can say that the solution is finite, as there is a specific value for x that satisfies the equation.

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Answer:

please give brainliest

Step-by-step explanation:

396.253521127

Answer:

I CAN NOT SEE THAT OML

Step-by-step explanation:

25-9x² can be expressed in factor form as (5+3x)(5-3x)

An expression is combination of variables, numbers and operators.

The given expression is 25-9x²

We have to factor it completely

We have an identity that a²-b²=(a+b)(a-b)

25-9x² can be written as 5²-(3x)²

Now apply the identity

(5+3x)(5-3x)

Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)

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[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ x^3+\cfrac{1}{8}\implies x^3+\cfrac{1^3}{2^3}\implies x^3+\left( \cfrac{1}{2} \right)^3~\hfill \stackrel{\textit{let's just for a second make}}{\cfrac{1}{2}=a} \\\\\\ x^3+a^3\implies (x+a)(x^2-ax+a^2)\implies \left( x+\frac{1}{2} \right)\left( x^2-\frac{x}{2}+\frac{1}{4} \right)[/tex]

The amount after 3 years with an interest rate of 7.5% will be $1,242.3.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Assume the yearly interest rate is 7.5% and the interest is compounded once a year.

If the amount of investment is $1,000 and the amount after 3 years is given as,

A = P(1 + r)ⁿ

A = $1,000 × (1 + 0.075)³

A = $1,000 × (1.075)³

A = $1,000 × 1.24229

A = $1,242.3

The amount after 3 years with an interest rate of 7.5% will be $1,242.3.

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Answer:

Triangle A is not a scale drawing

Triangle B is a scale drawing

Triangle C is not a scale drawing

As a result, the length of the second rectangle is 22.5 inches.

Every square is also a rectangle because a square is a parallelogram with all particular corners at right angles. Yet not all rectangles are squares; for a rectangle to be a square, all of its sides must be the same length.

We can infer that the two rectangles may have a similar shape but differ in size because we can see how similar they are to one another.

By using the fact that the ratio of the adjacent angles of two comparable rectangles is the same, we can determine the length of the following rectangle.

Let x be the second rectangle's length. Then we can establish a ratio:

9/6 = x/15

We can cross-multiply to find x:

9 x 15 = 6 × x

135 = 6x

x = 22.5

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Answer:

Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).

Step-by-step explanation:

Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).

Answer:15 because it is connected to the line

Step-by-step explanation:

Answer: 56 inches

Step-by-step explanation:

To find the length of each side, use Pythagorean's Theorem, a² + b² = c²

Note the bottom sides are the same length and the top two are the same length.

Bottom sides:

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

Top sides:

9² + 12² = c²

81 + 144 = c²

225 = c²

15 = c

Add it all together

13 + 13 + 15 + 15 = 56

The perimeter is 56 inches.

Hope this helps!

Answer:

8.50667 or approximately 8.51 feet per second

Step-by-step explanation:

The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.

The missing degrees in the circle are 260 degrees.

What is circle ?

A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.

To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.

In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.

Therefore, we can set up the following equation:

100 + x = 360

To solve for x, we can subtract 100 from both sides:

x = 260

Therefore, the missing degrees in the circle are 260 degrees.

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They are relatively prime.

Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,

they must have no common factors other than 1,

so they are relatively prime.

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True,  39.0625 is the value of First division .

What is division, and how does it work?

Multiplication is the opposite of division. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.

                                    In mathematics, division is the process of dividing a number into equal parts and determining how many of those parts there are in total. For instance, breaking 15 into 3 equal groups of 5 is equivalent to dividing 15 by 3.

= 97.65625 / 2.5

 =  39.0625

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The volume of the composite figure is 301 cm³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given is shape of ice creme we need to find the shapes in it and the volume.

1) The figure is a composite figure of a hemisphere and a cone.

2) Volume of hemisphere = 2/3 π × radius³, here radius is 4 cm

Volume = 2/3 π × 4³

= 2/3 × 3.14 × 64

= 134 cm³

Volume of a cone  = 1/3 π × radius² × height, here height is 10 cm

Volume = 1/3 × 3.14 × 16 × 10

= 167 cm³

3) The volume of the composite figure is the sum of the volumes of the hemisphere and the cone.

= 134 + 167 = 301 cm³

Hence, the volume of the composite figure is 301 cm³

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The region that contains the solution to the system is region B

Given the following system of inequalities

y ≤ x - 2

y ≥ 1/4x - 4

Next, we analyze each of the inequalities expressions

Inequality 1: y ≤ x - 2

Inequality 2: y ≥ 1/4x - 4

Using the above as a guide, we have the following:

This means that the intersection regionn contains the solution

This is represented by the region (b)

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The value of the angles of the parallelogram are 72 degree and 108 degree.

A quadrilateral with the opposing sides parallel is known as a parallelogram. It has numerous crucial traits, including:

A parallelogram has equal-length opposite sides. A parallelogram has opposite angles that are equally sized. A parallelogram's diagonals cut each other in half. A parallelogram is divided into four equal-sized triangles by its diagonals. A parallelogram's internal angles add up to 360 degrees. A parallelogram is classified as a rectangle if it also contains four right angles, making it a rectangle-shaped parallelogram.

Let us suppose the smaller angle = x.

The other angle is thus x + 36.

In a parallelogram the opposite angles are equal thus:

x + x + x + 36 + x + 36 = 360

4x + 72 = 360

4x = 288

x = 72

The value of x + 36 = 72 + 36 = 108

Hence, the value of the angles of the parallelogram are 72 degree and 108 degree.

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The distance between Seaside and Samuel's house is approximately 77.8 kilometers.

To find the distance between Seaside and Samuel's house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the distance between Seaside and Samuel's house, and the other two sides are the distances from Stafford to Samuel's house and from Stafford to Seaside.

1. Let x be the distance between Seaside and Samuel's house.

2. According to the Pythagorean theorem, x^2 = 24^2 + 74^2

3. Simplifying the equation gives us x^2 = 576 + 5476

4. Further simplifying gives us x^2 = 6052

5. Taking the square root of both sides gives us x = 77.8

Therefore, the distance between Seaside and Samuel's house is approximately 77.8 kilometers

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For the arithmetic sequence:

f(n) = f(1) + (n - 1)*4

Where the first term of the sequence is f(1) = 2

are:

f(1) = 2

f(2) =  6

f(3) = 10

f(4) =  14

f(5) =  18

We want to write the first five terms of a sequence, so first let's define the sequence.

We can define an arithmetic sequence with the recursive formula:

f(n) = f(n) + 4

And the explicit formula.

f(n) = f(1) + (n - 1)*4

Where we can define the first term of the sequence as f(1) = 2

Then the first five terms are:

f(1) = 2

f(2) = 2 + 4 = 6

f(3) = 6 + 4 = 10

f(4) = 10 + 4 = 14

f(5) = 14 + 4 = 18

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The normalized orthogonal distance between the robot and the reference trajectory line is approximately 4.16.

The normalized orthogonal distance is the distance between the robot and the reference trajectory line. We can use the following formula to calculate the normalized orthogonal distance:

normalized orthogonal distance = |(y2 - y1)x0 - (x2 - x1)y0 + x2y1 - y2x1| / √((y2 - y1)^2 + (x2 - x1)^2)

Where (x0, y0) is the position of the robot, and (x1, y1) and (x2, y2) are the positions of the two points on the reference trajectory line.

Plugging in the values given in the question, we get:

normalized orthogonal distance = |(7 - 3)5 - (8 - 2)0 + 8*3 - 7*2| / √((7 - 3)^2 + (8 - 2)^2)

Simplifying the equation, we get:

normalized orthogonal distance = |20 - 0 + 24 - 14| / √(16 + 36)

normalized orthogonal distance = |30| / √(52)

normalized orthogonal distance = 30 / √(52)

normalized orthogonal distance ≈ 4.16

Therefore, the normalized orthogonal distance between the robot and the reference trajectory line is approximately 4.16.

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The time is takes to manufacture the piece after two improvements is 28 minutes

From the question, we are to calculate how long it takes to manufacture a metal piece

First, we need to find the new time taken to manufacture the metal piece after the two improvements.

The first improvement reduces the time by 8%. This means that the new time is:

32 - (8% of 32)

= 32 - 2.56

= 29.44 minutes

The second improvement reduces the time by 5%. This means that the new time is:

29.44 - (5% of 29)

= 29.44 - 1.45

= 27.99 minutes

We can round this to the nearest minute, which gives us 28 minutes.

Hence, it takes 28 minutes to manufacture the metal piece.

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The radian measure of 180 degrees is [tex]\pi \\[/tex] radians.

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

We are given that;

Radius=5units

Radian=180 degrees

Now,

The arc length of a circle is given by the formula:

arc length = (r * theta)

where r is the radius of the circle and theta is the angle in radians subtended by the arc at the center of the circle.

We know that the radius of the circle is 5 units, and we want to find the radian measure of an arc that subtends an angle of 180 degrees.

Since 180 degrees is half of a full circle, the arc length of this arc will be half of the circumference of the circle:

arc length = (1/2) * 2 * pi * r

          = pi * r

Plugging in r = 5, we get:

arc length = pi * 5 = 5pi

Now we can use the formula for arc length to find the radian measure of the arc:

arc length = r * theta

5pi = 5 * theta

theta = pi

Therefore, by the arc length the answer will be [tex]\pi[/tex] radians.

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The surface area of the prism is 224 ft².

Having identical endpoints in three dimensions, a prism is a solid object. This combination consists of flat faces, identical bases, and equal cross-sections.

We are given a figure of a prism having a square base.

We know that

Surface Area of Prism (A) = 2a² + 4ah

We are given the following information:

a = 4 ft

h = 12 ft

On substituting these values in the formula, we get

⇒A = 2(4)² + 4(4)(12)

⇒A = 2(16) + (16)(12)

⇒A = 32 + 192

⇒A = 224 ft²

Hence, the surface area of the prism is 224 ft².

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Since there are multiple questions so the question answered above is attached below

The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).

To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).

Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.

(-(5)/(2)) | 20  44  -17  -5
         |______________

Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.

(-(5)/(2)) | 20  44  -17  -5
         |     -50
         |______________
         | 20

Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.

(-(5)/(2)) | 20  44  -17  -5
         |     -50   3   10
         |______________
         | 20  -6  -14   5

Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).

Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).

f(x) = 20x^(3)+44x^(2)-17x-5

= (4x+1)(5x-1)(x+5)

Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).

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