Write a rule to describe each transformation.
J(2, 2), (3, 4), H(4,3), G(3,0)
to
J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)

Answer:

55 miles per hour

Step-by-step explanation:

The equation is:

R = d / s

We know

d = 495 miles

s = 9 hours

Let's solve

R = 495 / 9

R = 55 miles per hour

So, their driving rate is 55 miles per hour

Answer:

4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.

The area of the base of the bin is 9 ft^2.

The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.

Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.

We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.

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Answer:

41,500 people

Step-by-step explanation:

First you find 3% of 36,000= 1,080

Then you do 1080 x 5= 4,500

Then finally do 36,000 + 4,500= 41,500

The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

Given that,

We have to find the total surface area of the triangular prism in the given picture.

We know that,

First, we need to calculate the area of ​​the triangle

a = area of triangle

a = 1/2 ×15 cm × 8 cm

a = 60 cm²

Now,

We must determine the three rectangles' areas.

a₁ = 2cm × 17cm

a₁ = 34cm²

a₂ = 2cm × 15cm

a₂ = 30cm²

a₃ = 2cm ×8cm

a₃ = 16cm²

Now, we must multiply the triangle by two and sum all the estimated areas.

a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²

Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

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Answer: No

Step-by-step explanation:

Look at the 3 numbers in the sequence,

Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)

However, for the sequence listed above

Looking at 1st and 2nd term,

Ratio = 110/120 = 11/12

Looking at 2nd and 3rd term,

Ratio = 105/110 = 21/22 which is not the same as 11/12.

Hence, since the ratio is not the same, this sequence is not a geometric sequence.

As per the power rule of exponents, the solution of 3 to the power of 3 is 27.

The term exponent in math is defined as a number shows how many times the number is multiplied by itself.

Here we have to solve 3 to the power of 3.

Here according to the Power Rule of Exponents then we have the rule as

=> aⁿ = a × a × a... (n times)

Therefore, the given expression is written as

=> 3³

Now, based on the power of exponent rule it can be rewritten as,

=>  3 × 3 × 3

Then we have to multiply the values then we get

=> 27

Therefore, the value of 3 raised to 3rd power is 27.

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Answer:

Below

Step-by-step explanation:

Formula for sum of interior angles of a   n - gon

(n-2) * 180

for this 12 sided 'gon

  (12-2) * 180 = 1800°        

            ( and for a 'regular' dodecagon each would be 1800/12 = 150°

Answer:

Option C) 1,800°

Step-by-step explanation:

To Find : Interior Angles of a Decagon

In order to find interior angles of any polygon we usually use the formula

(n-2)x180

Over Here it is a 12 sided polygon

So,

(12-2)x180

10x180

1800

Hence the interior angles of a decagon is 1800°

Answer:

2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8)  When you are multiplying powers that have the same bases, you add the exponents.

When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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Answer: 1/7

Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.

The Africa region saw the largest increase in the proportion of households with computers between 2008 and 2018.

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The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.

If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now

Using midpoint formula

[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2

Find common denominator and write the numerators above common denominator

-5+2/12 =-3/12

            =-1/4

Hence we find midpoint between numbers.

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The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.

Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.

Given:

Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.

He used the same amount of concrete to construct a spherical barrier.

According to the information  given in the exercise, the height and the radius of the pylons are the following:

Height h = 2 ft

Radius r = 1 ft

So, the volume of the cone,

= (1/3)πr²h

= (1/3)π(1)²(2)

= (2/3)π cubic feet.

And the volume of the sphere is twice the volume of the cone.

So, the volume of the sphere,

4πr³/3 = 2π/3

2r³ = 1

r³ = 1/2 = 0.5

r = ∛0.5 = 0.8 ft.

Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.

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The cartoonist's purpose of the given cartoon is C: "to make people laugh at a play on the words".

Though the cartoon in the picture is designed based on the concept that fungal bands are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a music band called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.

Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.

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The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .

What is an Acute Angle ?

The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).

From the figure ,

we can see that the measure of the sides are given as a = 9 , b = 8 and

the measure of angle A is 79° .

By Applying the Law Of Sines ;

we get ,

[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]

Substituting the values in the above equation ,

we get ;

[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]

Simplifying further ,

we get ;

[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]

substituting the value of Sin79° as 0.9816 ;

we get ;

[tex]SinB = \frac{0.9816}{9} \times 8[/tex]

[tex]SinB=0.8725[/tex]

So , B ≈ 61° .

Therefore , the measure of angle B is 61° .

The given question is incomplete , the complete question is

Find the measure of Angle B in the given figure .

Note that the angle B is acute . Round to the nearest degree .

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Saad's income tax will be N.I.L.

Here, saad's yearly income is Rs 2,36,000.

The rate of income tax on his income will be nil because,

    INCOME                                TAX RATE

0-2,50,000                                    NIL

2,50,000-5,00,000                       5%

5,00,001-10,00,000                       20%

More than 10,00,000                      30%

                          Computation of tax liability of Saad

Tax on 1st 2,36,000 = N.I.L

As his income is less than 2,50,000 no income tax shall be charged to saad's income.

Therefore, the tax liability of saad would be 0.

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Answer:

the percentage is 62%

Step-by-step explanation:

The graph of equation is in image.

When a linear equation is graphed, it always results in a straight line because each term has an exponent of 1. This is why it is referred to as a "linear equation."

There are linear equations with one and two variables, respectively.

Given equations

2x + 3y = 5

4x - 5y = -1

For equation 1

2x + 3y = 5

The table of values appears as follows

x    1     -2    4

y    1      3    -1

Coordinates for equation 2

4x - 5y = -1

The table of values as thus

x    1     2    -4

y    1     1.8   -3

And the intersection point of equation is (1, 1)

Hence the graph of equation is intersecting at (1, 1).

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The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

The sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].

What is sine function?

The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.

The general sine function is

[tex]y = Asin(b(x+c)+D[/tex]

Where

Amplitude = A

Period = [tex]\frac{2\pi }{B}[/tex]

Phase shift = c

Vertical shift = D

Given:

A = 4 (amplitude)

[tex]\frac{2\pi }{B} = 4[/tex]  (period)

[tex]B = \frac{\pi }{2}[/tex]

Since midline: y = 1

And we know that graph of [tex]4sin(\frac{\pi }{2}x)[/tex], midline to be y = 1.

It must have vertical shift D = 1.

Since, y - intercept (0, 1)

⇒ x = 0, y = 1

⇒ It has no phase shift  ⇒ c = 0

Since it satisfy [tex]y = 4sin(\frac{\pi }{2}(x+c))+D[/tex]

The graph of the sine function is attached below.

Hence, the sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].

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Answer:

1/6

Step-by-step explanation:

There are 6 letters and the spinner lands on one at a time

1. The quotients of the following division operations are as follows:

a) 126 ÷ 12 is 10.5.

b) 217 ÷ 4 is 54.25.

c) 75 ÷ 6 is 12.5.

d) 11 ÷ 9 is 1.2222.

e) 200 ÷ 35 is 5.7143.

2a) The quotient of 7 ÷ 2.2 is a nonterminating or repeating decimal.

2b) The quotient of 0.5 ÷ 0.12 is a nonterminating or repeating decimal.

2c) The division operation with a quotient that is nonterminating or repeating decimal is 2 ÷ 2.7.

3) The identification of each resulting quotient as a terminating or nonterminating, repeating decimal is as follows:

4) The quantity of meat in one piece of hamburger, if they are evenly shared or divided, is 41.67 g.

The quotient is the result of the division operation.

Every division operation involves the dividend (the numerator), the divisor (the denominator), the division operand (÷), and the equal sign (=).

2)

a) 7 ÷ 2.2 = 3.181818

b) 0.5 ÷ 0.12 = 4.16667

c) 3 ÷ 0.8 = 3.75

9 ÷ 0.16 = 56.25

2 ÷ 2.7 = 0.740740

3)

a. 2 ÷ 3 = 0.6667

b. 5 ÷ 1.2 = 4.16667

c. 0.3 ÷ 0.9 = 0.3333

d. 2.4 ÷ 1.8 = 1.3333

4) Total weight of ground pork = 1.25 kilograms

1 kg = 1,000 g

1.25 kg = 1,250 g

The pieces of patties = 30

The weight of each piece = 41.67 g (1,250/30)

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Answer:

Step-by-step explanation:

(9a⁴b⁷) x (6a³b⁸)

(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)

54 x a⁷ x b¹⁵ = 54a⁷b¹⁵

Answer:

(9a⁴b⁷).(6a³b⁸)

=54a⁷b¹⁵

The fans at the semi final is less than the fans at the final .

The implementation of the away goals rule makes any goals scored away from home effectively count twice when the scores are tied, as is customary in matches with home and away legs, such as the knockout stage of the Champions League.

Champions League and Europa League, two of its premier club championships, starting in the 2021–22 season.

Semi final : 250*4/6+4 = 100

Final : 400*3/7+3= 120

Hence, The fans at the semi final is less than the fans at the final .

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Answer:The student needs to score 20 points

Step-by-step explanation:

? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20

Based on the description above, the individuals in this setting is option A: homes.

The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.

In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.

Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.

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Answer:

Roots:  -7, 2

Step-by-step explanation:

-x² = 5x - 14

-x² -5x +14 = 0

x² + 5x - 14 = 0

(x + 7)(x -2) = 0

x = -7 or x = 2