Let g(x)=3 x+2 and f(x)= x-2 / 3 . Find each value.
g(f(-4))

Step-by-step explanation:

4×10^1= 40

4×10^2=400

4×10^3=4000

4×10^4=40000

Answer:

"㏑ 4-14, find each product."

Step-by-step explanation:

[tex]4 \times 10^1(10 \times 1) = 40\\4 \times 10^2(10 \times 10) = 400\\4 \times 10^3(10 \times 10 \times 10) = 4,000\\4 \times 10^4(10 \times 10 \times 10 \times 10) = 40,000[/tex]

The distance between points A and B is 9.22units, approximately.

This is further explained below.

Generally, In the image attached, you can observe a representation of the problem.

We have to find the distance between points A and B, which have coordinates (7,0) and (0,6), respectively.

The definition of distance between two given points is

[tex]d=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]

Using points A and B, the distance between us

[tex]&d_{A B}=\sqrt{(7-0)^2+(0-6)^2}\\\\d_{A B}=\sqrt{49+36}\\\\\ d_{A B}=\sqrt{85} \\\\&d_{A B} \approx 9.22[/tex]

In conclusion, the distance between points A and Ais 9.22 units, approximately.

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Answer:

The answer is 34.2L

Step-by-step explanation:

5buc x 1.8gal = 9gal

9gal x 3.8L = 34.2L

The sum of all exterior angles in any n-sided polygon is 360 degrees, so:

[tex]72 + 63 + 75 + x + 34 + 74 = 360 \\ x + 318 = 360 \\ x = 360 - 318 \\ x = 42[/tex]

The height of the rectangular prism is 3 units.

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges.

Given:

Length(L)= 4 units

width(w)= 3 units

Diagonal(D) = [tex]\sqrt{34}[/tex] units

According to given question we have

The formula for rectangular prism  is

[tex]L^{2} +w^{2} + h^{2} = D^{2} \\\\4^{2} +3^{2} +h^{2} =(\sqrt{34} )^{2} \\\\16+9+h^{2}=34\\\\25+h^{2}=34\\\\h^{2}=34-25\\\\h=\sqrt{9} \\\\h=3 units[/tex]

Therefore, the height of the rectangular prism is 3 units.

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Answer: x2 . f(x) - 2x . f (x) + 6 . f(x)

Step-by-step explanation:

The average speed of car is 14.4 m/s.

We can see that from Photo 1 to Photo 2, the car covers 9 times the 0.8 meter distance. So, calculating the total distance traveled between the time span second photo was clicked.

Total distance traveled = 0.8×9

Performing multiplication

Total distance traveled = 7.2 meters

Now, the time is given as 0.5 seconds.

Finding the average speed using formula -

Average speed = total distance traveled ÷ total time taken

Keep the given values in formula to find the average speed.

Average speed = 7.2 ÷ 0.5

Performing division

Average speed = 14.4 m/s

Hence, the average speed of the car is 14.4 m/s

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The complete question is attached in figure.

The complete representation of the expression is 7/ 10^-1 = 7 x 10^1

Index forms are simply defined as the exponent or power of a number raised to a variable or number.

It is known as the standard form of a number.

It is also known as the exponential representation of an expression or number .

Example;

The index form of 200 is 2 × 10^2

The index form of 40 is 4 × 10 ^1

Given the expression;

7/10-  = 7x10^

We have;

7/ 10^-1 = 7 x 10^1

Thus, the complete representation of the expression is 7/ 10^-1 = 7 x 10^1

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It should be noted that the square root and the cube root of the number has been attached.

It should be here that the cube root of a number is the factor that we multiply by itself three times in order to get the original number.

It should be noted that thee symbol for cube root is 3✓ . Finding the cube root of a number is the opposite of cubing a number.

On the other hand, the square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

It shouod be noted that for example, 4 and −4 are square roots of 16, because 4² = ² = 16.

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The solution for the x for the inequality ||3x −1|+5| <1 is x<7/3

In the given problem basically, ||3x −1|+5| <1, we are dealing with the absolute value, which for real numbers is referred to as the non-negative value of that number without regard for consideration to its sign. Denoted by the symbol "| |', it is also known as the modulus of the number, and also with the inequality, which is a non-equal comparison between two numbers, additional mathematical expressions.

the inequality equation we got is ||3x-1|+5|<1

now we are taking the absolute value of it, we get

=>3x + 1 + 5 < 1

subtracting 1, and 5 from both sides, we get

=>3x < 1 + 5 + 1

=>3x < 7

=>x < 7/ 3

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Answer:

E) None of the above

Step-by-step explanation:

If Larry drives to work in the morning, he will hit traffic. Therefore:

A) If Larry hits traffic, it must be morning.

B) If Larry drives to work in the afternoon, he will not hit traffic.

C) If Larry doesn't hit traffic, it must not be morning.

D) If Larry drives to work in the afternoon, he will hit traffic.

E) None of the above.

To be the solution of all real numbers the left side expression must be the same as the right side so option (D) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the equation,

3x+6=2x+10+x-4

3x + 6 = 2x + x + 10 - 4

3x + 6 = 3x + 6

For every real number will satisfy the equation.

But the left-hand side is equal to the right-hand side.

Now,

Let's consider an equation,

2x + 3 + 4x = 6x + 2 + 4

2x + 4x + 3 = 6x + 6

6x + 3 = 6x + 6

3 = 6 since it is false it means it will not have any real solution.

Hence "To be the solution of all real numbers the left side expression must be the same as the right side".

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Answer: -9,0

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

In math, mode is the number which appears most in the data set. When dealing with this, first put all of the numbers in numerical order, least to greatest.

19, 28, 31, 36, 44, 48, 55, 59, 68, 75, 75, 82, 93

Notice how 75 appear twice and all the other numbers appear once. Therefore the mode is 75.

When the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set.

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

From the number line in the question, we can see that:

As a general rule, open circles implies that the number at that endpoint is not included part of the solution set.

Hence, the complete statement is "when the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set."

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The number of bowling games played for $34 is 8

The  mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by linear equation y = 3.50x + 6.00

We are given that total money spent is $34

The number of bowling  games played is assumed to be x

Now, we have substitute the value of y in the linear equation to get number of bowling  games played

34 = 3.50x +6.00

34 - 6 = 3.50 x

28 = 3.5x

x = 28/ 3.5

x = 8

So, the number of bowling games played for $34 is 8

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The function represents an exponential growth and the y-intercept is (0,0.2)

How can you tell whether an exponential function is growing or deteriorating?

Given - y=0.2(3.8) x

For a. function, [tex]y = ab^{x}[/tex]

the function represents exponential growth if a > 0  and b > 1 .

the function represents exponential decay if a > 0 and 0> b > 1.

In either case, the y-intercept is (0,a).

From the given, a = 0.2 and b = 3.8 because 2> 0 and  b > 1 .

then the function represents an exponential growth and the y-intercept is (0,0.2)

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Answer:

no

Step-by-step explanation:

half of 250k would be 125k and if you add that to 250k that would be 375k

The translated figure, 1 unit left and 6 units up, is given at the end of the answer.

The original figure is missing, and is given at the end of the answer.

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The rule for a shift of 1 unit left and 6 units up is given as follows:

(x,y) -> (x - 1, y + 6).

The coordinates of the vertices of the original figure are given by:

(-7, -3), (-2,-4), (-7,-9), (-1,-9).

Hence the coordinates of the vertices of the translated figure are given by:

(-8, 3), (-3,2), (-8,-3), (0,-3).

The translated figure, 1 unit left and 6 units up, is given by the second graph at the end of the answer.

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Answer:

at least one mile for sure

Express 7 and 21 as a product of their prime factors and write in index form.

The power rule states (a^m)^n = a^mn

7= 7^1

21 = 7x7x7 = 7^3 = 7^2 x7^1

(7^1)1/2 x (7^2x7^1)^1/2 = 7^1/2 x 7^2/2x7^1/2

7^1/2 x 7x7^1/2 = 7 x (7^1/2)^2

7x7 = 49

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The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The mass of the sun = 2 x 10³⁰ kilograms.

The mass of golf ball = 0.05 kilogram = 5 x 10⁻² kilograms

Now, Calculate the mass of the sun about the mass of the golf ball as;

The mass of the sun/the mass of a golf ball = 2 x 10³⁰/ 5 x 10⁻²

                                                                   =  4 x 10³¹

So, The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

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Yes, ln 5+ log₂10 can be written as a single logarithm.

Single logarithm expression for ln 5+ log₂10 is 2.60943791243.

  ln 5+ log₂10

=1.60943791243 +1

= 2.60943791243

The logarithm is exponentiation's opposite function in mathematics.

The power to which a number must be increased in order to obtain another number is known as a logarithm. This shows that the logarithm of a fixed integer base b represents the exponent to which that number must be raised in order to reach a specific number x.

The logarithm with a base of 10 is the common logarithm, commonly referred to as the value of log base 10. The common logarithm of 10 has a value of 1, or 1.

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The value of k that makes the equation 0.000342891 = 3.42891 × [tex]10^k[/tex]  true when k = -4.

Scientific notation is a form of writing large numbers with a base that is greater than or equal to 1 and less than 10 and multiplying this base with powers of 10 in the way we can write large numbers in compact form.

Here in the given question, the actual value is 0.000342891 and we need to write it n the form of scientific notation.

We know in scientific notation base should be greater than or equal to 1 and less than 10.

∴  0.000342891 in scientific notation can be written as 3.42891×10⁻⁴ as we have moved the decimal 4 digits to the right of the actual value.

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The 5th term in the sequence is 1/9

The sequence is defined by

g subscript n equals 9 times open parentheses 1 third close parentheses to the power of n minus 1 end exponent.

Rewrite properly as

g(n) = 9 * (1/3)^n - 1

For the 5th term, the value of n is 5

So, we have

g(5) = 9 * (1/3)^5- 1

Evaluate the difference

g(5) = 9 * (1/3)^4

Evaluate the exponent

g(5) = 9 * 1/81

Evaluate the product

g(5) = 1/9

Hence, the 5th term in the sequence is 1/9

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The exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ

We have that:

The saving account has initially = $ 14

After 1 year, the balance became = $ 16.24

After 2 years, the balance became = $ 18.84
Difference in the initial amount and amount after 1 year = $ 16.24 - $ 14 = $ 2.24

Difference in the amount after 1 year and amount after 2 years = $ 18.84 - $ 16.24 = $ 2.60.

An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.

Here, the exponential function will be:

y = 14 ( 1.16) ˣ where x is the time period

Money after 20 years = 14 ( 1.16)²⁰ = $ 272.45

Therefore, we get that, the exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ

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The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

Transformation is the movement of a plane figure from one point to another. Transformation may also be an increase / decrease in the size of the figure. Examples of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in size of a figure by a scale factor.

The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

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