The segment below is dilated by a scale factor of 22 to form I ′J ′ What is the measure of I ′J ′ ?

The period of this Ferris wheel can be calculated as 30 seconds. The amplitude is 25

a. We have 60 seconds in a minute

In a minute it makes 2 rotations. The period = 60 secs / 2 rotations

= 30 seconds

b. We have h = 25 - 25cos [tex]\frac{25}{30} t[/tex]

25 - 25cos[tex]\frac{25}{15} t[/tex]

We would have the table in the attachment

d. Amplitude

= max - min / 2

= 50 - 0 / 2

= 25

The perimeter of the decking area is 800cm.

It is important to note that the decking area takes the shape of a rectangle

The formula for determining the perimeter of the decking area is given as;

Perimeter = 2 multiplied by the sum of the length and width of the rectangle

It is mathematically written as;

Perimeter = 2 ( length + width)

Where;

Now, let's substitute the values into the formula

Perimeter = 2 ( 150 + 250)

Sum the bracket

Perimeter = 2 ( 400 )

Perimeter = 2 × 400

Perimeter = 800 cm

Thus, the perimeter of the decking area is 800cm

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Answer:

325 adult tickets

Step-by-step explanation:

Let adult tickets be x, student tickets are 75 less than adult tickets, so let student tickets be x-75

The total is 575

x+x-75 = 575

2x = 650

x = 325 adult tickets

The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

It is important to note that the maximum height is the peak altitude the balloon reached

To find the difference, we use the formula

Change = Maximum height - recovery height

Maximum height = 5000 meters

Recovery height = 3700 meters

Substitute the values

Change = 5000 - 3700

Change = 1300 meters

Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

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A quadratic equation that models something from one's daily life is when calculating areas, and determining a product's profit.

It should be noted that a quadratic equation means an algebraic equation of the second degree in x.

The quadratic equation in its standard form is ax² + bx + c = 0. Here, a and b are the coefficients, x is the variable, while c is the constant term.

Quadratic equations are used in everyday life, as when calculating areas, and the determination of a product's profit and formulating the speed of an object.

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Answer:

361

Step-by-step explanation:

discriminant = b² - 4ac

= (21)² - 4(1)(20)

= 441 - 80

= 361

Levada borrows $30,900 from her bank to open a florist shop at rate of 0.98% per month.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

It is given that Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.

P = $30,900

T = 18 months

Interest  = 5.5%

Interest rate =  P×R×T

5.5 = 30,900 × R × 18

R = 0.000988

Or, R = 0.98% per month.

The complete question is

"a) How much must she pay the bank in 18 months?"

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Answer:

  A, D

Step-by-step explanation:

Lines are parallel if consecutive interior angles at a transversal are supplementary.

In the given figure, angles EAH and AED are consecutive interior angles associated with transversal AE. If they total 180°, then AC║EF.

Similarly, angles FCI and CFG are consecutive interior angles associated with transversal CF. If they total 180°, then AC║EF.

Either of these will prove AC║EF:

Answer:

7

Step-by-step explanation:

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7 answer

Answer:

the answer is -2/729

Step-by-step explanation:

When you're given the first term and the common ratio, you just need to multiply the first term by the common ratio and then raise to the power of the nth term minus 1.

In this case, 6(-1/3)^7

The size of the corner you need to cut in order for your box to have this area is 0.5 inches

The base length is given as:

Length = 7

When the edges are removed, the new length becomes

New length = 7 - x - x

Evaluate

New length = 7 - 2x

The base width is given as:

Width = 4

When the edges are removed, the new length becomes

New width = 4 - x - x

Evaluate

New width = 4 - 2x

The area of the bottom of the box is calculated as:

Area = New length * New width

This gives

Area = (7 - 2x) * (4 - 2x)

Rewrite as:

A(x) = (7 - 2x) * (4 - 2x)

The area is given as:

Area = 16

So, we have:

(7 - 2x) * (4 - 2x) = 16

Expand

28 - 14x - 8x + 4x^2 = 16

Rewrite as

4x^2 - 14x - 8x + 28 - 16 = 0

Evaluate the like terms

4x^2 - 22x + 12= 0

We have:

4x^2 - 22x + 12= 0

Expand the equation

4x^2 - 24x - 2x + 12 = 0

Factorize the equation

4x(x - 6) - 2(x - 6) = 0

Factor out x - 6

(4x - 2)(x - 6) = 0

Solve for x

x = 0.5 or x = 6

The value of x = 6 is too big for the dimensions of the box.

So, x = 6 is an extraneous solution for the equation

Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches

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2|48,64,72,96,108

2|24,32,36,48,54

2|12,16,18,24,27

2|6,8,9,12,27

2|3,4,9,6,27

2|3,2,9,3,27

3|3,1,9,3,27

3|1,1,3,1,9

3|1,1,1,1,3

LCM

The two bottom graphs demonstrate translations.

We will have a translation only if:

The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.

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The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:

B = 180° - A - C

B = 180° - 25° - 90°

B = 65°

a = 16 × (sin 25°/sin 65°)

a ≈ 7.461

c = 16 × (sin 25°/sin 90°)

c ≈ 6.762

The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

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Answer:

18564 ways

Step-by-step explanation:

The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :

then

This can be done in [tex]C^{6}_{18}[/tex]  ways.

[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]

The blank space in the task content should be filled with; Wages.

A wage by it's primitive definition is a fixed regular payment usually paid on a daily or weekly basis by the employer to an employee which could be skilled or unskilled.

Commission, and salary which is a monthly analogue of wages is another form of employee compensation.

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Answer:

60 cubic inches

Step-by-step explanation:

You multiply 3 and 4 to get 12, then 12 and 5 to get 60

3 x 4 x 5 = 60

The volume of a solid exists the measurement of how much area an object brings up. It exists measured by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

Volume exists as a three-dimensional measurement; that exists, it measures the collective length, width, and height of a figure. Because planes, polygons, and other two-dimensional figures don't contain height, they contain no volume. Only solids and figures with dimensions more significant than or equivalent to three have volume.

The volume of a solid exists as the measurement of how much space an object brings up. It exists estimated by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

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Answer:

11.863 g

Step-by-step explanation:

5.623 g + 6.24 g = 11.863 g

Answer:

19.50

Step-by-step explanation:

32m = 624

m = 19.50

need more words

Fractions are mathematical expressions that relate two numbers as a quotient. Thus the answer to this question is:  [tex]\frac{3d + b}{d}[/tex]

Fractions are expressions in a form of a quotient that relates one number to another number. The two numbers can be classified as either the numerator or the denominator. The number above the division line is the numerator, while that below the line is the denominator. Some types of fractions are proper fractions, improper fractions, and mixed fractions.

A given fraction can undergo basic arithmetic operations when two or more are involved. Also, a fraction can be added to one another, or subtracted from a whole number.

The given expression in the question involves the addition of a whole number (3), to a fraction (b/d).

Given: 3 + b/d

The LCM is d, thus;

3 + b/d = [tex]\frac{3d + b}{d}[/tex]

Therefore, the required answer is: [tex]\frac{3d + b}{d}[/tex]

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See below for the examples of sectors and arcs of a circle

The area of a sector is calculated as:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees

[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

Using the above formulas, the sector areas are:

1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]

2.  [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]

3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]

4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]

5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]

The length of an arc is calculated as:

[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees

[tex]L = r\theta[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

Using the above formulas, the arc lengths are:

1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]

2.  [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]

3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]

4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]

5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]

The examples include:

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The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let x represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, V, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]

Which gives;

[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]

6•x² - 106•x + 315 = 0

[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

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Hope that helps...........................

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of magic steel and y represent the amount of alloy #33, hence:

(0 * x) + (y * 0.28) = 700(1 - 0.86)   (1)

Also:

x + (1 - 0.28)y = 0.86(700)    (2)

From both equations:

x = 350, y = 350

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

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None of the three points (A, B, C) lies on the circumference of the unit circle.

Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:

Point A

[tex]d = \sqrt{4^{2}+3^{2}}[/tex]

d = 5

Point B

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }[/tex]

d = √29 /10

d ≈ 0.539

Point C

[tex]d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}[/tex]

d = √58 /4

d ≈ 1.904

None of the three points (A, B, C) lies on the circumference of the unit circle.

The statement presents a typing mistake, correct form is shown below:

A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?

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hi,

the function is given with it's canonic form.  

canonic form is  :  f(x) = a ( x-α)² + β

α  and β are the value of the coordonnates of the vertex.

so here we  have : ƒ(x) = 2(x−1)² +3

with α = 1  and β = 3

so vertex is  V (1;3)

So yes, answer is   A.

Answer:

y = 3x + 1

Step-by-step explanation:

The formula for equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

Now, since we have coordinates, we will get the equation as;

(y - y1)/(x - x1) = m

(y - 1)/(x - 0) = 3

y - 1 = 3x

y = 3x + 1