Evaluate the function f(x)=−4x−3 f(x)=−4x−3 for x=−6x=−6.

Answer:

B. -20

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

q, and p

The mathemtical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The  word expression is:

5 less than twice x

Twice the x  = 2x

5 less than twice the x:

= 2x - 5

Thus, the mathematical expression for the word expression  5 less than twice x "  is 2x - 5 option (A) 2x -5 is correct.

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8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.

Given is a tour group of 22 people. The group is looking for rooms in a motel to stay in for the night and no more than 3 people can stay in each room.

The number of people who can live in 1 room = 3

This means, we have 3 people for 1 room.

For 1 people, we will have - (1/3) room

For 22 people, we will need -

(22/3)

7.3 rooms

Approximately, 8 rooms will be needed and the last room will have only one member of the group.

Therefore,  8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.

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Answer:   -1.9

Step-by-step explanation:just add up the values for the weight change

(-1.8)+(0.9)+(-1.4)+(0.4)

-1.9

The length of AD is [tex]\dfrac{8}{3}[/tex].

Given:

BD is the angle bisector of the triangle ABC.

The figure of the triangle ABC.

To find:

The length of AD.

Explanation:

According to the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the same proportion of the other two sides.

Let [tex]x[/tex] be the length of AD. Then, the length of DC is [tex]6-x[/tex].

Using the Angle Bisector Theorem, we get

[tex]\dfrac{8}{10}=\dfrac{x}{6-x}[/tex]

[tex]\dfrac{4}{5}=\dfrac{x}{6-x}[/tex]

[tex]4(6-x)=5(x)[/tex]

[tex]24-4x=5x[/tex]

[tex]24=5x+4x[/tex]

[tex]24=9x[/tex]

[tex]\dfrac{24}{9}=x[/tex]

[tex]\dfrac{8}{3}=x[/tex]

Therefore, the length of AD is [tex]\dfrac{8}{3}[/tex].

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Answer:  The required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]

Step-by-step explanation:  We are given two functions as follows :

[tex]f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.[/tex]

We are to find f of g, i.e., f(g(x)).

To find the required value, first we have to find the f value of the function g(x).

We have

[tex]f(g(x))=f(x^2)=\dfrac{2}{x^2}.[/tex]

Thus, the required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]

original height was 5" and it was enlarged to 30"

 find the ratio by dividing 30 by 5

30 / 5 = 6

 so ratio would be 1/6 meaning for every 1 inch of the original the new one is 6 inches

now you need to multiply the original width by 6 to find the new width

7" x 6 = 42"

 new width = 42"

      49 is the number to be added to both the sides of the equation to complete the square.

   The equation given in the question is

Which can be written as  [tex]x^{2} +2\times (7x)=-32[/tex]

We have to convert it into square form.

  Since the standard form of the equation in square form is

(a + b)² = a² + 2ab + b²

By comparing this standard equation with the given equation,

a = x

&

b = 7

By substituting the values of 'a' and 'x' in the standard square form,

x² + 14x + 7² = -(32) + 7²

x² + 14x + 49 = -32 + 49

(x + 7)² = 17

     Therefore, 49 should be added in both the sides of the equation in order to complete the square.

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Answer:  [tex]\frac{1}{3}[/tex]

Explanation:

let y = [tex]log_{8} (2)[/tex]

whenever we transfer base from  log from one side to other it will remain be base after shifting to the other side.

Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]

here we have n = y, m=2, x=8    by substituting the values

we will get

[tex]8^{y} = 2[/tex]          (1)

we can write 8 in power of 2 that is [tex]2^{3}[/tex]

we will rewrite the above equation (1) as

[tex]2^{3y} = 2[/tex]

we can equate the power when base is same then we will get

3y = 1

then

[tex]y=\frac{1}{3}[/tex]

The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

Let the given logarithmic function be x to have:

[tex]log _82=x[/tex]

This can be transformed into indices to have:

[tex]8^x = 2[/tex]

Solve the resulting indices for "x" a shown:

[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]

Cancel the base and equate the power to have:

[tex]3x = 1\\x = \frac{1}{3}[/tex]

Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3

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Answer:

y − 100 = -12.5 (x − 4)

Step-by-step explanation:

Pick two points on the line to calculate the slope:

m = (y₂ − y₁) / (x₂ − x₁)

m = (100 − 125) / (4 − 2)

m = -12.5

Next, use point-slope form to write the line equation.

y − y₁ = m (x − x₁)

y − 100 = -12.5 (x − 4)

The correct answer is:

The domain contains only natural numbers.

The graphs of geometric sequences are a series of unconnected points rather than a smooth curve because:

The domain contains only natural numbers.

As the geometric sequence us given as:

[tex]a_1=a,a_2=ar,a_3=ar^2,....[/tex]

where a is the first term of the sequence and r is the common ratio of the geometric sequence.

Also [tex]a_n[/tex] denotes the nth term of the sequence where n belongs to natural numbers that is the domain of the function is natural numbers.

The reason why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve is because: B. The domain contains only natural numbers.

A geometric sequence is typically a series of real and natural numbers that are calculated by multiplying the next number by the same number each time.

Mathematically, a geometric sequence is given by the expression:

[tex]a, \;ar, \; ar^{2} ....a_n[/tex]

Where:

In a geometric sequence, the graphs of geometric sequences comprises a series of unconnected points rather than a smooth curve is because the domain is made up of only natural numbers.

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To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.

The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.

Let's define the larger number as x and the smaller number as y. According to the problem:

Substitute Equation 2 into Equation 1:

x + (x - 9) = 67

2x - 9 = 67

2x = 67 + 9

2x = 76

x = 38

Now, we can find y using Equation 2:

y = x - 9

y = 38 - 9

y = 29

Therefore, the larger number is 38 and the smaller number is 29.

The suitable way to use the numbers 8, 6, and 2 to create an expression with an exponent that results in the value of 8 is by utilizing the equation 2^3. This equation means 'two raised to the power of three', meaning 2 multiplied by itself thrice, giving us the desired result, 8.

To solve this question, we need to consider the mathematical operation of exponentiation, which involves a base number and an exponent. The exponent represents the number of times the base number is to be multiplied by itself.

Given the numbers 8, 6, and 2, we aim to use each number only once to create an expression that includes an exponent and yields a value of 8. The suitable way to do this is by following the equation 2^3 (where 2 is the base number and 3 is the exponent).

To explain further, an exponent is the number of times a number, known as the base, is multiplied by itself. For instance, 2^3 should be read as 'two raised to the power of three', essentially depicting 2 * 2 * 2, resulting in 8. This follows the standard rules of Exponential Arithmetic.

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