4. Function f is defined by f(x) = 2x - 7 and g is defined by g(x) = 5*.
a. Find f(3), f(2), f(1), f(0), and f(-1).
1325104
b. Find g(3), g(2), g(1), g(0), and g(-1).

Answer:

Step-by-step explanation:

half hisage. Then subtract

Answer: 12 years old

Step-by-step explanation:

You should use variables:

Set x as tyler's age.

32 = 2x + 8

32 - 8 = 2x

24 = 2x

12 = x

Therefore, Tyler is 12 years old.

Answer:

b = 10

Step-by-step explanation:

You take the decimal, divide it by the addend and then you take the fraction and subtract that by the sum and then multiply your answer by 5.

Solution of exponential equation 27³x=81 is , [tex]x = \frac{1}{243}[/tex]

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

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

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

According to given statement,

27³ x = 81

divide both side by 27³ , the equation becomes :

[tex]= > x = \frac{81}{27^3} \\\\= > x = \frac{3^4}{(3^3)^3}\\\\= > x = \frac{3^4}{3^9}\\\\= > x = \frac{1}{3^5} = \frac{1}{243}[/tex]

Thus solution for this equation is  [tex]x = \frac{1}{243}[/tex]  

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Answer:

The answer is 2.4lbs

Step-by-step explanation:

1.32 divided by .55 is 2.4, meaning the bag weighed 2.4lbs :)

The solution to the system of linear equations is x=3 and y= -4.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

For solving this question, you should apply the addition method. Thus, you should sum the equations 1 and 2.

6x + y = 14  (1)

−2x −y =−2 (2)

6x-2x+y-y=14-2

4x=12

x=3

From equation 2, you can find y for x=3

−2x −y =−2 (2)

-2*3-y=-2

-6-y=-2

-y=-2+6

-y=4

y= -4

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The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

The features of the log are used to increase a single logarithm into numerous logarithms (or) compression multiple logarithms together into a single logarithm. A logarithm is simply another way of writing exponents. Thus, logarithm properties are obtained from exponent properties.

log (4 s⁴ t)

can be written as log (4 s⁴ t):

Property used in the solving (log b*c = log b  + log c) and (log ₐᵇ = b log a)

log (4 s⁴) + log( t)

log (4 ) + log(s⁴) + log( t)

Expand log (s⁴) by moving 4 outside the log.

log (4 ) + log(s) + log( t)

The expression also can be written as :

2log(2) + 4log(s)  + log(t)

The expanded form of the given logarithms ( log 4 s⁴ t) is =  2log(2) + 4log(s)  + log(t).

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The value of x for log (7 x+1)=log (x-2)+1 is 7.

Due of their connection to exponential functions, logarithmic functions are crucial. Exponential equations and the characteristics of exponential functions may both be investigated using logarithms. Additionally, they will be of great service in calculus, where they will be used to determine the slope of specific functions and the region enclosed by particular curves. They also have useful uses in economics.

Given,

log (7 x+1)=log (x-2)+1

log(7x + 1) - log(x - 2) = 1

using log (m/n) = log m - log n

log (7x+1 / x-2) = 1

It can be expressed as -

7x + 1 / x - 2 = 10 ¹

7x + 1 = 10x - 20

3x = 21

x = 7

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Answer:

your equation is Y = 6

Step-by-step explanation:

Use Midpoint Formula to find the slope M first

Name the coordinates of both points x1 = -2, y1 = -6, x2 = 4,  y2 = 6

Plug them in the formula

M = y2 - y1/ x2 - x1

M =( 6 - 6)/( 4 - (-2))

M = 0/6

M = 0

Then use point slope formula

Plugin the slope M = 0 in the formula and pick one of the points above. Name the coordinates of  the point X1 = 4 and y1 = 6

y - y1 = m(x - x1)

y - 6 = 0(x - 4)

y - 6 = 0

y = 6

your equation is Y = 0x  + 6 but keep in this form y = b

This is a horizontal Line

Answer:

Step-by-step explanation:

Let n represent the unknown number-

[tex]\frac{3}{4}n-3=-9\\ \\ \frac{3}{4} n-3+3=-9+3\\ \\ \frac{3}{4} n=-6\\\\ \frac{4}{3}(\frac{3}{4}n)=\frac{4}{3}(-6)\\ \\ n=-8[/tex]

Unknown number = -8

Saying it in digits = [tex]\frac{3}{4}n-3=9[/tex]

For any function, we call x the "numerator" value and y is the "denominator" value.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. Which ultimately implies that, a function is used for mapping an input variable to an output variable.

We know that fraction represents a part of a number or any number of equal parts.

The parts of a fraction are;

In Mathematics, a fraction comprises two main parts and include the following:

Numerator

Denominator

For any function in the Mathematics, we call variable x the numerator value while y is the denominator value.

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Answer:

B.

Step-by-step explanation:

The Pythagorean theorem only works with right triangles. a and b are the lengths of the legs. c is the length of the hypotenuse. The hypotenuse is the longest side of a right triangle.

Answer: B.

We have been given that -

scale = 1:75000.

we have to find out

(a) scale expressed as 1 cm represents n km.

Map scale refers to the ratio between distance on a map and the corresponding distance on the ground. For example, on a 1:100000 scale map, 1cm on the map equals 1km on the ground

so 1,00,000 cm = 1 km.

(b) given -

distance between two towns on the map is 25 cm.

Find the actual distance, in kilometres, between the two towns.

Scale is given as 1:75000

for 25 cm distance = 25×75000 cm

                              = 18,75,000 cm

therefore 1875000 cm = 18.75 km.

the real distance between two points is 18.75 km.

(c) . The area of the lake in the real world is 3.5 square kilometers.

1 square kilometer is equal to 1 kilometers squared.

since 1 kilometer is equal to 100,000 centimeters, then 1 square kilometer is equal to 100,000^2 centimeters which is equal to 1 * 10^10 square centimeters.

3.5 square kilometers on the map is therefore equal to 3.5 * 10^10 square centimeters.

1 centimeter on the map is equal to 75000 centimeters in the real world.

1 square centimeter on the map is equal to 75000^2 centimeters in the real world which is equal to5625 * 10^6 square centimeters in the real world.

take 3.5 * 10^10 square centimeters in the real world and divide it by 5625 * 10^6 square centimeters and you get .0006 * 10^4 square centimeters which is equal to 6 square centimeters on the map.

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Answer:

x = 6

Step-by-step explanation:

The 'ZERO" of the function is the 'x' value(s) where it crosses the x-axis (and

'y' = ZERO)

Answer:

x = 6

Step-by-step explanation:

the zero of the function is the value of x on the x- axis where the graph crosses.

the graph crosses the x- axis at 6

then the zero is x = 6

The solution for the value of x for the Logarithmic expression 2㏑x + 3㏑2 = 5 is

4.30716.

A logarithmic equation is one that includes the logarithm of a variable-containing expression. To address exponential equations, first determine whether both sides of the equation can be written as powers of the exact number.

Some properties of ㏑ function are-

Now, as per the given expression;

2㏑x + 3㏑2 = 5

Use the Power Rule: n㏑A = ㏑Aⁿ

㏑x² + ㏑2³ = 5

Now, apply the Product Rule : ㏑A + ㏑B = ㏑(AB)

㏑(x² ×2³) = 5

㏑(x² ×8) = 5

Raise the formation to exponential form, using e as the base.

e∧㏑(x² ×8) = e⁵

Comparing the base of both sides;

x² ×8 = 5

x² = 5/8

x = ±√5/8

x = ±4.30716

Due to domain restrictions, the argument of any logarithm is always positive & greater than zero.

Therefore, the value of x is estimates as x = 4.30716.

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Answer:

LCD= 24

Step-by-step explanation:

[tex]\frac{5}{8}=\frac{15}{24}\\ \\\frac{11}{12}=\frac{22}{24}[/tex]

Answer:

18213

Step-by-step explanation:

Given equation,

→ 467 × 39

Let's solve the problem,

→ 467 × 39

→ 18213

Thus, the answer is 18213.

Taking into account the definition of a system of linear equations, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

[tex]\left \{ {{A=7B} \atop {A+B=144}} \right.[/tex]

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the first equation in the second one you get:

7B + B= 144

Solving:

8B= 144

B= 144÷8

B= 18 tons

Remembering that A= 7B, the value of A is calculated as:

A= 7×18

A= 126 tons

Finally, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.

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The Inverse of given function F(x) = 1 / 4x is F⁻¹(x) = 1 / 4 x

F(x) = 1 / 4x is a function of x.

Changing F(x) to the variable y

This means that F(x) = 1/4x becomes y = 1/4x.

Changing the variables x and y in the previously obtained equation

This means that we can deduce x = 1 / 4y from the equation y = 1 / 4x.

Solving the newly discovered equation for y

This means that we must simplify the equation by rearranging the terms in order to obtain the equation in terms of the variable x.

x =  1 / 4y

=> 4 y = 1 / x

=> y = 1 / 4 x

As a result, we obtain the required equation.

Switching the variable y with F⁻¹(x)

This assumes, y = 1 / 4 x becomes F⁻¹(x) = 1 / 4 x

Hence, the value of the given function F⁻¹(x) = 1 / 4 x

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Logarithmic form: logₓ y = 4

A logarithmic form is a method to write equations when solving for a variable in an exponent. Any exponential equation can be written as a logarithm. The logarithmic form is used to calculate an exponent of an equation.

The logarithmic form is a rearrangement of the exponential form.

Exponential form: aᵇ = c

Logarithmic form: logₐ c = b

Comparing this with our equation, a=x, b=4, c=y

Therefore, we get the logarithmic form as logₓ y = 4

Conversion from exponential to logarithmic form gives the final answer as logₓ y = 4

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Answer:

y equals negative one-sixth times x plus 5

This is correct, it's not plus 3, it's plus 5!

Decimal should the digital scale show is 0.2

The grocery store asked me to buy 3 [tex]\frac{1}{5}[/tex] pounds of ham. You will be asked to find the number of decimal places displayed by the digital scale.

3 [tex]\frac{1}{5\\}[/tex] lbs = 3 lbs + [tex]\frac{1}{5}[/tex] lbs

[tex]\frac{1}{5}[/tex] = 0.2

3 [tex]\frac{1}{5}[/tex] = 3.2

Therefore, the digital scale is displayed in decimal.

Real numbers, natural numbers, whole numbers, rational numbers, and other sorts of numbers can all be categorized in mathematics. There are decimal numerals among them. Integer and non-integer numbers are represented using this format as a standard.

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

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Answer: 176cm

Step-by-step explanation:  To find the circumference of the circle, we will use the circumference formula: 2πr = 2 × 22/7 × 28

The equation of the line that passes through  ​(-3​,2​), and is perpendicular to 3x - 5y = -2 is:

y - 2 = -5/3(x + 3), or

y = -5/3x - 3

The equations of two lines that are perpendicular to each other will always have a slope (m) that are negative reciprocals to each other.

Thus, given the equation of a line as, 3x - 5y = -2, rewrite in slope-intercept form (y = mx + b) to easily determine its slope (m):

3x - 5y = -2

- 5y = -3x - 2

y = 3/5x + 2/5

The slope (m) = 3/5.

The negative reciprocal of 3/5 is -5/3.

Hence, the slope (m) of the line that is perpendicular to 3x - 5y = -2 would be -5/3.

Substitute (a, b) = (-3, 2) and m = -5/3 into y - b = m(x - a):

y - 2 = -5/3(x - (-3))

y - 2 = -5/3(x + 3) [point-slope form]

Rewrite the equation in slope-intercept form:

y - 2 = -5/3(x + 3)

y - 2 = -5/3x - 5

y = -5/3x - 5 + 2

y = -5/3x - 3 [slope-intercept form]

In summary, the equation of the line that passes through  ​(-3​,2​), and is perpendicular to 3x - 5y = -2 is:

y - 2 = -5/3(x + 3) [point-slope form], or

y = -5/3x - 3 [slope-intercept form].

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The value of the expression log₅62 by using the change of base theorem is 2.5644.

Given that the expression is log₅62.

We are required to find the value of the expression by using the change of base formula.

The change of base formula is basically used to find the base of the log value is different from 10. It says that [tex]log_{a}b[/tex]=log b/log a.

Expression is log₅62.

log₅62=log 62/log 5

Now we have to use the value of log 62=1.7923 and log 5=0.6989 in the above expression.

=1.7923/0.6989

=2.5644

Hence the value of the expression log₅62 is 2.5644.

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