if f (x)=2x-4 if f(n+5)=

The greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.

The given logarithmic expression is log(1.3 x 10⁷)

Use the product rule of the logarithm logₐ(X.Y) = logₐ(X) + logₐ(Y), to get

log(1.3 x 10⁷)

= log(1.3) + log(10⁷)

= log(1.3) + 7 log(10) (Using the power rule of the logarithm logₐ(Xⁿ) = n logₐ(X))

= log(1.3) + 7            (Since log(10) = 1)

≈ 7.113 (approximate value)

We know that, log(1) = 0 and log(10) =1. And the logarithm is an increasing function.

So, log(1.3) is very close to 0 and strictly less than 1.

Therefore, the greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.

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The divisions problem are:

A decimal is a number that consists of a whole and a fractional part.

Given:

we have the condition as divisor in division are decimals

So, we know in division we have main two parts: Dividend and Divisor.

we have to take the divisor as decimals.

So let us take the example

4068 / 0.03

So, for solving it we can proceed as

4068 * 100 /3

= 1356 * 100

=135600

Similarly, there many like

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Answer:

[tex]\csc ^2(\theta)[/tex]

Step-by-step explanation:

Using Pythagorean identity,

[tex]\mathrm{1+\cot ^2(x)=\csc ^2(x)}\\\mathrm{=\csc ^2(\theta)}[/tex]

Answer:

1 + cot² θ = sec² θ

Step-by-step explanation:

1 + cot²θ =

I know this identity to be true:

sin² θ + cos² θ = 1

Divide both sides by sin² θ.

sin² θ / sin² θ + cos² θ / sin² θ = 1 / sin² θ

1 + cot² θ = sec² θ

Step-by-step explanation:

ATTACHED ARE THE SOLUTIONS !!!!

Step-by-step explanation:

a)=

y = 70 + 41 (exterior angle is equal to sum of its opposite interior angles)

so, y = 111°

Now,

y = x + 58° ((exterior angle is equal to sum of its opposite interior angles)

or. 111° - 58° = x

so, x = 53°

b)=

x = 180° - 127° (linear pair of x is corresponding to 127)

so, x = 53°

Now,

y = 83° (y is vertically opposite to angle that is corresponding to 83)

c)= x = 47° (alternate angles)

y = 47 + 32 (exterior angle is equal to sum of its opposite interior angles)

so, y = 79°

d)= other angle = 180-45-45 = 90

Using the formula:-

sinA/a = sinB/b = sinC/c

or, sin45/3 = sin45/y

or, 1/√2/3 = 1/√2/y

or, y = 3

Now,

sinC/c = sinA/a

or, sin90/x sin45/3

or, 1/x = 1/√2/3

or, 1/x = 1/3√2

so, x = 3/√2

6t ÷ 9

I hope this helps!

Answer: 6t

Step-by-step explanation:

there are 6 t's so yea it's  the 6th work for me -_-

Answer:

5

Step-by-step explanation:

5+5=2(5)

10=10

Answer:

X = 32

Step-by-step explanation:

X/4 = 8

To solve for x, multiply each side by 4

X/4*4 = 8*4

X = 32

Answer:

$58.32

Step-by-step explanation:

x = 1/3(79.26 + 95.70)

x = 1/3(147.96)  Divide 147.96 by 3

x = 58.32

The value of y when we make y the subject of the formula in 5x - 5y = 40 will be B. y = -3x - 8

It should be noted that an equation is simply used to show the relationship that exists between the variables that are given.

In this situation, the equation given s

is illustrated as:

-15x - 5y = 40

Divide through by -5

-3x - y = 8

Then make y the subject of the formula

y = -3x - 8

Therefore, value of y when we make y the subject of the formula in 5x - 5y = 40 will be y = -3x - 8.

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The coordinates of the midpoint are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

The midpoint is the middle point of a line segment and it is equidistant from both endpoints.

We have,

M_______X_______J

MX : XJ = 1 : 1

The formula for finding the coordinates of the midpoint is:

x = (a + c ) / 2

y = ( b + d ) / 2

(x, y) = coordinates of the midpoint.

Where (a, b) and (c, d) are the coordinates of the two endpoints.

We can consider,

M = (A, B)

J = (C, D)

X = (x, y)

Thus the coordinates of the midpoint X are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

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The value of logarithmic expression log 4 √47/5² is log (47/25)^1/4.

By considering the given  logarithmic expression

log 4 √47/5²

log  4 √47/25

log (47/25)^1/4

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer: rational

explain

Check the picture below.

keeping in mind that perpendicular lines have negative reciprocal slopes, and that we also know that the line is a perpendicular bisector, namely it cuts that segment into two equal halves as you can see in the picture, so it really passes through the midpoint of that segment, so let's get the slope of that green segment

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{7}}} \implies \cfrac{4}{-8}\implies -\cfrac{1}{2}[/tex]

so for the perpendicular bisector that'd be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1}\implies 2}}[/tex]

now let's check for the midpoint of the green segment

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +7}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (3~~,~~7)[/tex]

so we're really looking for the equation of a line whose slope is 2 and that it passes through (3 , 7)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 2}(x-\stackrel{x_1}{3}) \\\\\\ y-7=2x-6\implies {\LARGE \begin{array}{llll} y=2x+1 \end{array}}[/tex]

A potential exponential function (y = abˣ) that has a y-intercept of (0, 3) and passes through the point (2, 48) is equal to y = 3·4ˣ

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be represented by this standard formula:

y = abˣ

Next, we would solve for the value of "a" using y-intercept (0, 3):

y = abˣ

3 = ab⁰

3 = a(1)

a = 3.

Also, we would determine the value of "b" from point (2, 48):

y = abˣ

48 = 3b²

16 = b²

b = √16

b = 4.

Substituting the parameters into the standard formula, we have;

y = 3·4ˣ

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The better way for the customer to buy a sofa is to apply the Sale Tax after the discount.

Let us assume that the marked price of a sofa is $1000.

Now we will first take the sale tax and then the discount on the marked price.

Sale = 1000 × 5/100

= 50

So the price after the sale = 1000 + 50

= 1050

As the discount is $100

Therefore total is to be paid is

1050- 100

i.e., $950

Now we will calculate discount first then the sale tax.

As marked price is $1000 and discount is $100

So price after discount = $1000- $100

= $900

Now we will apply the sale tax on the discount price which is 5%

Sale price = 900 × 5/100

=45

Total price to be paid = 900 + 45

= $945

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x = 6 is the extraneous solution of the equation

The equation given is

[tex]\sqrt{3x + 7}[/tex] = x -1

To find the Extraneous solution we need to square on both sides of the equation

[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]

3x + 7 = [tex]x^{2}[/tex] --2x + 1

[tex]x^{2}[/tex] - 5x - 6 = 0

[tex]x^{2}[/tex] - 6x + x - 6 = 0

x(x - 6) +1(x -6) =0

(x-6)(x+1) = 0

x = -1, 6

Now we need to put the value of x in the equation

x = -1

[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1

[tex]\sqrt{4}[/tex] = -2

2≠ -2

Now put

x = 6

[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1

[tex]\sqrt{25}[/tex] = 5

5=5

Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation

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The two triangles are similar triangles and the graph of the triangles are attached

The complete question is added as an attachment

The coordinates of the triangle are given as

A (0, 3), B (3, 3) and C (3, -1)

So, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

Multiply each coordinate by a scale factor of 3 (k=3).

Here, we have

A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)

This gives

A' (0, 9), B' (9, 9) and C' (9, -3)

Next, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

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Answer:

1:12

Step-by-step explanation:

You have to convert both value to the same measurement, so you gonna find how many minutes is in 5 hours which is (300 minutes) then you put 25/300 then cancel out

The correct answer is 11.834.

Decimal Fraction Math refers to the mathematical expression of a fraction or mixed number where the denominator is a power of 10, such as 10, 100, or 1000, etc. Mathematical operations can be performed on fractions more easily when they are expressed in decimal form.

From 0 to 9, single-digit numerals are read exactly as they are written. However, when two numerals are involved, the left digit implies 10 times what the right digit indicates. In the number 24, that is, 4 is 4 and 2 is 20. Together, they make 24.

The rightmost digit of a three-digit number has the same meaning as the middle one, which is ten times the digit, and the leftmost digit, which is 100 times the digit.

√97.5 + 1.96

=  9.874 + 1.96

=  9874/1000 + 1960/1000

=  11834/1000

=  11.834

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The proof that is correct about vertical angles being congruent is; Joby's proof

Vertical angles are defined as the angles formed when two lines meet each other at a point. They are always equal to each other and as such they are congruent.

Now, from the given image, we see that four angles are formed which are; ∠1, ∠2, ∠3, ∠4

Now, according to vertical angle theorem, we can say that;

∠2 = ∠4 and ∠1 = ∠3

Thus, we can conclude that vertical angles are congruent by the vertical angle theorem

Thus, we conclude that Joby's proof is correct.

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Answer:transversal

Step-by-step explanation:

Answer:

I think the answer is 4 not sure though

Answer:

28 is the answer!

I got it right, look at the pic!!

The equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

Let the amounts of water that Sue's water bottle holds = x

According to the question,

given that,

Sue's water bottle holds the water = [tex]\frac{1}{2}x + \frac{1}{2}x[/tex] = [tex]\frac{2}{2}x[/tex] = x

Thus, assumption is true

Hence, the equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Different Types of Equations:

Some of the math equations used in algebra are:

Linear Equation

A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Quadratic Equation

This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.

Example:

[tex]a x^{2}[/tex] + b x + c = 0

Cubic Equation

This is a third-order equation. In cubic equations, at least one of the variables should be raised to exponent 3.

Example:

[tex]a x^{3}[/tex] + [tex]b x^{2}[/tex]+ cx + d = 0

[tex]a^{3}[/tex] – 27 = 0

Rational Equation

A rational equation is an equation that contains fractions with a variable in the numerator, denominator, or both.

Example:  

[tex]\frac{x}{2}[/tex] = [tex]\frac{x + c}{4}[/tex]

How to prove an equation

One way to prove that an equation is true is to start with one side (say, the left-hand side) and to convert it, by a sequence of equality-preserving transformations, into the other side. But remember that a proof must be easy to check, so each step deserves a justification. We keep the steps elementary, based on known facts of algebra. Also, a proof should always start with a statement of the claim that is being proved.

.

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The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x define expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to statement,

5⁻³ = 1/125

as, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex]

Here,

a= 5, x= -3, N = 1/125

therefore logarithmic form is :  [tex]log_5(\frac{1}{125} ) =-3[/tex]

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Answer:  Robbie pay in twelve months $1080 .

$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.

Step-by-step explanation:

As given

Robbie Morse has a $47,500 insurance policy.

The annual premium is $987.53.

Robbie pays $90.00 monthly.

First find out the Robbie pay in twelve months .

Robbie pay in twelve months = 12 × 90

                                                 = $ 1080

Second find out how much more does Robbie pay .

Robbie pay extra = Robbie pay in twelve months -  annual premium

                            = $ 1080 - $987.53

                            = $92.47

Therefore the $92.47 more Robbie pay .

Third find out the what percentage does Robbie pay .

Formula

Robbies pay more = $92.47

Annual premium = $987.53

Put in the above

Percentage = 9.36 % (Approx)

9.36 %(Approx) Robbie pay.