Simplify the expression
(
7
a
5
b
6
)
4
.

The complete table of values of the absolute value function is

x     g(x)

-3      22

-2      13

0        5

1        14

3       32

The equation of the function is given as

g(x) = |9x + 5|

Next, we set the values of x in the table to the above equation

So, we have

g(-3) = |9(-3) + 5| = 22

g(-2) = |9(-2) + 5| = 13

g(0) = |9(0) + 5| = 5

g(1) = |9(1) + 5| = 14

g(3) = |9(3) + 5| = 32

So, the complete table of values of the absolute value function is

x     g(x)

-3      22

-2      13

0        5

1        14

3       32

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18+7(n-3)

=======================================================

Explanation:

We can rewrite the right hand side of choice C like so

18+7(n-3)

18+7(n-1-2)

18+7(n-1)+7(-2)

18+7(n-1)-14

4+7(n-1)

Which is now in the form a+d(n-1)

This confirms choice C to be arithmetic. The other choices cannot be written in the format of a+d(n-1). Choices A and B are quadratic sequences while choice D is exponential.

The first few terms of choice C are: 4, 11, 18, 25, 32, ...

To get new terms, add 7 to the previous one.

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

Notice how if n = 5 for instance, then,

[tex]a_n = 4+7(n-1)\\\\a_5 = 4+7(5-1)\\\\a_5 = 32\\\\[/tex]

and

[tex]b_n = 18+7(n-3)\\\\b_5 = 18+7(5-3)\\\\b_5 = 32\\\\[/tex]

This confirms that [tex]a_n = b_n[/tex] when n = 5. I'll let you check other positive integer values for n.

Answer:

[tex]\textsf{c)} \quad s_n=18+7(n-3)[/tex]

Step-by-step explanation:

An arithmetic sequence has a constant difference between each term.

General formula of an arithmetic sequence

[tex]\boxed{s_n=a+(n-1)d}[/tex]

where:

When expanded, the formulas for answer options a and b will both contain an n² term, so we can immediately discount them since an arithmetic sequence is linear.

Similarly, we can also discount option d since this formula includes an exponential term and is therefore not linear.

Therefore, the only valid answer is option c.

To confirm, rewrite the formula for c in the general form for an arithmetic sequence:

[tex]\begin{aligned}\implies s_n&=18+7(n-3)\\s_n&=18+7n-21\\s_n&=7n-3\\s_n&=7n-7+4\\s_n&=7(n-1)+4\\s_n&=4+(n-1)7\end{aligned}[/tex]

Therefore, formula that defines an arithmetic sequence is:

[tex]\boxed{s_n=18+7(n-3)}[/tex]

The linear expressions are subtracted to:

-2x + 17. Option A

-4x - 2. Option B

 2x + 6. Option B

Algebraic expressions are expressions made up of variables, terms, factors, coefficients, and constants.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc.

Given the expression:

A. (4x + 8) - (6x - 9)

expand the bracket

4x + 8 - 6x + 9

collect like terms

-2x + 17

B. (3x - 4) - (7x - 2)

expand the bracket

3x - 4 - 7x + 2

collect like terms

-4x - 2

C. (10x + 2) - (8x - 4)

expand the bracket

10x + 2 - 8x + 4

collect like terms

2x + 6

Thus, the linear expressions are subtracted to -2x + 17, -4x - 2,  2x + 6

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Answer:

x=-13

Step-by-step explanation:

-7x-46=45

+46. +46

-6×=91

÷ ÷

6. 6

x=-13

Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B

A ratio can be defined as the comparison of two or more number indicating their sizes in relation to each other.

It also explains how any times a number contains another.

From the information given, we have;

To determine the distance Neptune is from the sum than Mercury, we divide the distance for Neptune by that of Mercury

= 4.5 x 10^10/  5.8 x 10^7

= 776. 86

Turn into scientific notation

= 7. 76 × 10^2

Thus, Neptune is 7. 76 × 10^2 times farther than Mercury from the sun. Option B

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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The statement as an inequality expression is 739214 < x < 740000

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The statement is given as

"The number on Riben's ticket has a value between the values 739214 and 740000”

Let the value on the ticket be x

So, the statement can be represented as

"x has a value between the values 739214 and 740000”

"Between" means the values are exclusive

So, the statement can be represented as

739214 < x < 740000

Hence, the statement as an inequality expression is 739214 < x < 740000

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Possible question

Represent the following statement as an inequality

"The number on Riben's ticket has a value between the values 739214 and 740000”

Starting with the volume of a cube with side length [tex]x[/tex],

[tex]V(x) = x^3[/tex]

differentiate both sides with respect to time [tex]t[/tex]. By the chain rule,

[tex]\dfrac{dV}{dt} = 3x^2 \dfrac{dx}{dt}[/tex]

We're given that [tex]\frac{dx}{dt} = 2\frac{\rm in}{\rm min}[/tex].

39. At the moment [tex]x=8\,\rm in[/tex], solve for [tex]\frac{dV}{dt}[/tex].

[tex]\dfrac{dV}{dt} = 3 (8\,\mathrm{in})^2 \left(2\dfrac{\rm in}{\rm min}\right) = 384 \dfrac{\rm in^3}{\rm min}[/tex]

41. Find [tex]x[/tex] when [tex]V = 55\,\rm in^3[/tex].

[tex]55\,\mathrm{in}^3 = x^3 \implies x = 55^{1/3} \,\rm in[/tex]

Solve for [tex]\frac{dV}{dt}[/tex].

[tex]\dfrac{dV}{dt} = 3 \left(55^{1/3} \,\mathrm{in}\right)^2 \left(2\dfrac{\rm in}{\rm min}\right) = 6\cdot55^{2/3}\dfrac{\rm in^3}{\rm min}[/tex]

we get the value of expression | a³ - b³ | as 35 when a = 2 and b = -3.

We are given an expression:

a³ - b³

The absolute value of the expression will be:

| a³ - b³ |

Now, we have a = 2 and b = - 3

So, substituting the values in the expression, we get that:

| a³ - b³ |

| ( 2 ) ³ - ( - 3 )³ |

| 8 - ( - 27 ) |

| 8 + 27 |

= | 35 |

= 35

Therefore, we get the value of expression | a³ - b³ | as 35 when a = 2 and b = -3.

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the height of the aquarium is 2.5ft

The aquarium is filled with water that weights 15,680 pounds in total, and we know that the density of water is 62.42 lb/ft^3, then the volume of water is:

V = 15,680/62.42 = 251.20 ft^3

Now, this is the volume of the cylinder will be 251.20 ft^3, and if the diameter is 8ft (the radius is 4ft) then the height H will be such that the volume:

V = 2*3.14*R^2*H

Is:

251.20 ft^3 = 2*3.14*(4ft)^2*H

251.20ft = 100.48ft^2*H

251.20ft/100.48ft^2 = H = 2.5ft

So the height of the aquarium is 2.5ft

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Answer:

x = -1

y = -5

(x,y) = (-1,-5)

x = 0

y = 0

(x,y) = (0,0)

x = 1

y = 5

(x,y) = (1,5)

Step-by-step explanation:

y = 5(-1)

y = 5*-1

y = -5

y = 5(0)

y = 5*0

y = 0

y = 5(1)

y = 5*1

y = 5

Answer: 11

Step-by-step explanation:

If you use 0 dimes, you can use 11 nickels.

If you use 1 dime, you can use 9 nickels.

A chart develops:

0 11

1 9

2 7

3 5

4 3

5 1

So there are 6 ways to make 55 cents with nickels and dimes alone.

Now for the situation with 1 quarter:

We can have 0 dimes and 6 nickels.

We can have 1 dime and 4 nickels.

A chart follows:

0 6

1 4

2 2

3 0

So there are 4 ways to make change with nickels and dimes and 1 quarter.

Finally, if we use 2 quarters, we have 5 cents left over which must be a nickel adding 1 more way.

So there are 6 + 4 + 1 ways = 11 total ways to make 55 cents with nickels dimes and quarters.

Answer:1 quarter 1 dime 4 nickels=55¢

Step-by-step explanation:

a quarter is 25¢ a dime is 10¢ and a nickel is 5¢ so i have 25¢+10¢ thats 35¢                      so i added 4 more 5¢ and i got 55

The probability the first roll is a 2 and the second roll is an odd number is 1/12

When we are unsure of the outcomes or simply want to know how probable something is to happen, we talk about probabilities. A random event is mathematically represented by probability. The collection of all potential outcomes is the sample space S for a probability model.

When we roll a dice there are 6 possible outcomes S={1, 2, 3, 4, 5, 6}.

The probability of showing a 5 is

Probability of showing 2 = 1/6

And the probability of showing an odd number is

Probability of showing an odd number = 3/6

Rolls are independent of one another, so there is a chance that the first roll will show a 5 and the second roll will reveal an even number.

( Probability of showing 2) ( Probability of showing an odd number) = 1/6 × 3/6 = 1/12.

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Based on the angles given of 1 and 5, the type of angles that they are is B. Corresponding angles.

Corresponding angles are angles that form as a result of a parallel line, or parallel lines being intersected by transverse lines. As a result, the same angles are created in certain instances.

When the angles given appear in the same position on the different transverse and parallel lines, then they are corresponding.

This means that angles 1 and 5 are corresponding angles because they appear in the same position.

In conclusion, the angles are corresponding.

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The graph of the equation y = (s + 2)(s - 3) is plotted and it cuts the x - axis at the points -2 and 3.

Parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

Given is a function as -

y = (s + 2)(s - 3)

We have -

(s + 2)(s - 3)

s(s - 3) + 2(s - 3)

s² - 3s + 2s - 6

s² - s - 6

Replace 's' with 'x'. Now, you will get a quadratic equation as follows -

x² - x - 6

The graph of a quadratic equation represents a parabola. The parabola will cut the x - axis at the points -

(x - 2)(x - 3) = 0

x = -2 and x = 3

Therefore, the graph of the equation y = (s + 2)(s - 3) is plotted and it cuts the x - axis at the points -2 and 3.

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Answer:

58.1

Step-by-step explanation:

8.6 is your diameter. You need to find the radius first which is always half of you diameter. Knowing that your radius is 4.3.

The formula you use for area is:

a = [tex]\pi[/tex]r²

a = [tex]\pi[/tex]4.3²

a = 58.08805

Rounded to the nearest tenth is:

58.1

we get the same result if we multiply an number by 3 or if we multiply the numbers by 5 and then add 2.

Given that

To find

So, according to the question

we have,

Let's assume that number is x,

So, from question we can say that

                             = (3 × x) + 2

                   result = 3x + 2

and

                             = (5 × x) + 2

                   result = 5x + 2

Now, from question we know that the results are same

So,

                  3x+ 2  = 5x+ 2    

Now, simplify this        

                   5x - 3x = 2 - 2  

                          2x = 0

                            x = 0/2

                            x = 0

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Answer:

5

Step-by-step explanation:

[tex]\frac{3^8}{3^3}=3^{8-3}=3^{\boxed{5}}[/tex]

Answer:

3⁸

3³

(since they have the same numbers , you subtract → divide means subtract → law of indices)

Answer = 3⁸ - 3³

= 3⁵

The trigonometric functions is y = 5/12.

The trigonometric functions sine, cosine, tangent, cosecant, secant, and cotangent really execute the opposite operation, which is what the inverse trigonometric functions do. We are aware that the right angle triangle is particularly amenable to trig functions. When two sides of a right triangle's measure are known, these six crucial functions are employed to determine the angle's measurement.

The convention symbol uses arc-prefixes such as arcsin(x), arccos(x), arctan(x), arccsc(x), arcsec(x), and arccot to denote the inverse trigonometric function (x).

arc sin(x) = arc tan (x/√1-x^2), x ∈ (0,1)

let,

y = tan (arc sin(5/13)) _____(1)

y = tan (arc tan ( 5/13/√1-(5/13)^2))

y = tan ( arc tan ( 5/ √13^2 - 5^2))

y = tan (arc tan (5/12))

y = 5/12

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Answer:

no bc the answer to the problem would be 341300

Answer:

A

Step-by-step explanation:

The rays that form the angles can extend for infinite length.

Answer:

x = 9

Step-by-step explanation:

Add 15 on both sides

[tex]x - 15 + 15 = -6 + 15[/tex]

Simplify it

[tex]-6 + 15 = 15 - 6 = 9\\x = 9[/tex]

Answer: 70 cats

Step-by-step explanation:

add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.

The simplified form is  18 + 7 / 10 -16 +26 /6 is  mathematically given as

-9/2

This is further explained below.

Generally, the equation for the expression is  mathematically given as

[tex]\frac{ 18 + 7}{ 10} -\frac{16 +26}{6}[/tex]

Therefore

Add 18 and 7.

[tex]\frac{25}{10}-\frac{16+26}{6}[/tex]

[tex]$\frac{5}{2}-7$[/tex]

To write -7 as a fraction with a common denominator, multiply by 2/2.

[tex]\frac{5}{2}-7 \cdot \frac{2}{2}[/tex]

Combine -7 and 2/2

[tex]\frac{5}{2}+\frac{-7 \cdot 2}{2}[/tex]

Combine the numerators over the common denominator.

[tex]\frac{5-7 \cdot 2}{2}[/tex]

Simplify the numerator.

-9/2

Move the negative in front of the fraction.

Decimal Form:

-4.5

In conclusion, The simplified for is  18 + 7 / 10 -16 +26 /6

-9/2

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The amount of force on the grain of rice is 23.52 × 10⁻⁵ newtons.

The right format for scientific notation is a × 10ᵇ, where an is an integer or decimal number with an absolute value more than or equal to one and less than ten, or 1 < |a| < 10. For the scientific notation to be mathematically equivalent to the original value, b must be a power of 10.

The Force of a particle is given as:

F = ma, where m is the mass and a is the acceleration.

Now, the mass of a grain of rice is 2.4 × 10⁻⁵ kg.

The acceleration due to gravity is 9.8 m/s².

Therefore, the force on the grain of rice is :

F = ma

F = 2.4 × 10⁻⁵ kg × 9.8 m/s²

F = 23.52 × 10⁻⁵ newtons

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Answer:

1.2 miles.

Step-by-step explanation:

because her weight is similar to that of a teenaged girl, she wouldn't be able to pedal very hard, or for long periods of time- she doesn't have the stamina for a cross-country ride. Therefore, using various statistics on house location in relation to park location, we can assume that the distance is about 1.2 miles.

Answer:

The outliers affect the mean, median, and other percentiles

Step-by-step explanation:

Because extreme points are highlighted in a box plot, it is simple to identify data points for further investigation. You may discover that the outliers are errors in your data or that they are unusual for another reason.

Step-by-step explanation:

6⅓ + 4¾ + 3 7/12

Convert to improper fraction

= 19/3 + 19/4 + 43/12

LCM= 12

= 76 + 57 + 43

12

= 176/12

= 44/3

Answer