Solve each equation. Check your answers.
log 6 x-3=-4

ln (t) = [tex]log_e(t)[/tex] is always true, by the definition of logarithm.

Now,

Hence, ln (t) = [tex]log_e(t)[/tex] is always true, by the definition of logarithm.

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Answer:C

Step-by-step explanation:

its  because the formula gives away the answer in a impecable way

The quotient of √x ³ / √5 x ² is √ ( x / 5 )

To find : the product of √x ³ / √5 x ²

By checking the power of roots for each term

The terms which are given are √x ³ and √5 x ²

Since both the numbers have the same root power they can be combined under the same square root for further operation

Dividing the terms

=> √ ( x ³ / 5 x ² )

=> √ ( x / 5 )

Therefore, we get the quotient of √x ³ / √5 x ² as √ ( x / 5 ).

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After factorizing the expression we get: (2x ₋ 1) (2x ₋ 3) as factors of the expression.

Given the expression is 4x² ₋ 8x ₊ 3 = 0

factorize the expression.

The word "factor" is used to describe a number as the result of any two other numbers. Any mathematical object, including numbers, polynomials, and algebraic expressions, can have factors by using the factorization method. Finding the factors of a given algebraic expression is referred to as factorization of an algebraic expression.

4x² ₋ 8x ₊ 3 = 0

4x² ₋ 2x ₋ 6x ₊ 3 = 0

2x(2x ₋ 1) ₋ 3(2x ₋ 1) = 0

(2x ₋ 1) (2x ₋ 3)

Hence we get the factors of the expression as (2x ₋ 1) (2x ₋ 3)

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Answer:

line segment

Step-by-step explanation:

I'm no Einstein, but that looks like a line segement

ngl

Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 3x}{log \\4}[/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_ax=N[/tex]

where, a is the base of function or equation

           x define expression

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

The given expression is,

log₄3 x

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

log₄3 x =  [tex]\frac{log \ 3x}{log \ 4}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 3x}{log \\4}[/tex]

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The statement that is true about the graphed function f(x) is that D. F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).

The intersection of the x-axis, the horizontal line, and the y-axis, the vertical line, creates a coordinate plane, which is a two-dimensional plane. The origin is the point at which these parallel lines cross one another.

In this case, the statement that is true about the graphed function f(x) is that F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).

The appropriate graph is attached.

In conclusion, the correct option is D.

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Answer:

43.09

Step-by-step explanation:

Jordin after working for 23 hours and 15 minutes would be paid $302. 25

From the information given, we have that;

Let's convert the minutes to hour

60 minutes is equivalent to 1 hour

Then 15 minutes is equivalent = x hour

cross multiply

x = 15/ 60

x= 0. 25 hour

He worked = 23 + 0. 25 = 23.25 hours

Then,

$13. 00 = 1 hour

$x = 23. 25

cross multiply

x = 13 × 23. 25

x = $302. 25

Thus, Jordin after working for 23 hours and 15 minutes would be paid $302. 25

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The total number of occasions the dice would land on 1 or 3 is 98.

The probability space associated with a randomly chosen experiment is established by three components: the result space, whose element is an experiment outcome, a collection of events F whose elements represent subsets of, and a probability measure IP assigned towards the elements in F.

As a result, for problems like Cards, Coins, and Dices, it is preferable to record the potential scenarios and determine the individual probabilities of each case before ORing/ANDing them in accordance with the problem demand. If done correctly, this will provide a great solution that will never fail you.

All of the probability will add upto 1.

this give us the equation:

P(1)+0.17 + 0.18 + 0.09 + 0.15 + 0.1 = 1

P(1) + 0.69 = 1

P(1) = 1 - 0.69

   P(1)  = 0.31

We now need to find the probability of 1 or 3

P(1 or 3) = P(1) + P(3)

             = 0.31 + 0.18

             = 0.49

We now use the predicting outcomes formula.

expected = P(1 or 3) x no. of times.

                = 0.49 x 200

                = 98

the total number of times the dice will land on 1 or on 3 = 98.

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a. The type of sequence we have here is a Geometric Progression.

b. The common ratio of the sequence is 7/10.

c. iPhone 10 will cost $83 in 2025.

Given sequence is:  

$1000, $700, $490, $343, $240

a. To determine the type of sequence we find the common ratio between terms:

   700/1000 = 7/10

   490/700 = 7/10

All terms differ by a common ratio hence it is a geometric progression.

b. From above,          

 1000 × 7/10 = 700

 700 × 7/10 = 490

 490 × 7/10 = 343

 343 × 7/10 = 240

Hence, the common ratio of G.P is 7/10.

c. The next terms in the given G.P is:

240 × 7/10 = 168

So, iPhone 10 will cost $168 in 2023.

168 × 7/10 = 118

So, iPhone 10 will cost $118 in 2024.

118 × 7/10 = 83

So, iPhone 10 will cost $83 in 2025.

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Solution :

base 10

A number base (or base for short) of a numeral system tells us about the unique or different symbols and notations it uses to represent a value. For example, the number base 2 tells us that there are only two unique notations 0 and 1. The most common number base is decimal, also known as base 10.

Step1:

Converting 1120 to base 10.

1*103=1000

1*102=100

2*101=20

0*100=0

Adding all to get Ans=1120 based 10

Step2

Converting 1120 based 10 to 5

The equation calculation formula for 1120 based 10 numbers to 5 is like this below.

5|1120

5|224|0

5|44|4

5|8|4

5|1|3

5|1|1

Ans:13440 based 5

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The expression is simplified to 10x² + 48x + 3 =0

Given the expression as;

[tex]5^(^4^x^+^1^)^(^x^+^2^) + 4. 5^x^(^x^+^1^5^) = 5^-^2^x^2+^2^1^x^-^1[/tex]

We take the numerators have the same base, then we have;

(4x+1)(x+2) + 4(x(x+ 15) = -2x² + 21x - 1

expand the bracket

4x² + 8x + x + 2 + 4(x² + 15x) =  -2x² + 21x - 1

4x² + 8x + x + 2 + 4x² + 60x =  -2x² + 21x - 1

collect like terms

4x² + 4x² + 2x² + 8x + x + 60x - 21x = - 1 - 2

Add or subtract like terms

10x² + 48x = -3

Make into a quadratic equation

10x² + 48x + 3 =0

Thus, the expression is simplified to 10x² + 48x + 3 =0

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The thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

It should be noted that the given measures are ABC = 70° and DEF = 110°

it should be noted that supplementary angles are the angles that have the addition as 180°.

In this case,

ABC + DEF

= 70° + 110°

= 180°

Therefore, the thing that intuition says about the degree measures of these angles is that ABC and DEF are supplementary angles.

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The inverse function is given by f⁻¹(x)=∛x+2 and the inverse is a function.

The opposite function is referred to as the inverse of a function. To map the dependent variable y based on the independent variable x, we should ideally utilize a function. The relationship that determines the value of x based on a certain value of y is known as an inverse function.

The domain of a function shifts to the range for an inverse function, and vice versa.

For a function that is mathematically denoted by the formula y=g(x), where g(x) is a polynomial of x. We use y to solve the equation for x.

Given function is in the form  f(x)=(x-2)³

It can be written as

y=(x-2)³

Then we take the cube root on either sides of the equation.

∛y=x-2

or, x=∛y+2

So the inverse function is:

f⁻¹(x)=∛x+2

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Answer:

Step-by-step explanation:

Formula: Amount of taxes part time x 1+(amount jumped)

Therefore just do : 765 x 7.12 = $5446.80

sa paanong paraan nagiging instrumento

Answer:

Steps below

Step-by-step explanation:

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Answer:

-16x+4

Step-by-step explanation:

4 is the only constant term there dont have to change

-4x-12x =-16x

so you get -16x+4

Hey there!

-4x + 4 - 12x

COMBINE the LIKE TERMS

= (-4x - 12x) + (4)

= -4x - 12x + 4

= -16x + 4

Therefore, your answer should be:

-16x + 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A is uniquely associated with an object f(a) in B. A function is therefore a many-to-one (or sometimes one-to-one) relation. The set A of values at which a function is defined is called its domain, while the set f(A) subset B of values that the function can produce is called its range. Here, the set B is called the codomain off.

A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function.

A function, its domain, and its co-domain are declared by the notation f: X→Y, and the value of a function f at an element x of X, denoted by f(x), is called the image of x under f, or the value of f applied to the argument x.

Functions are also called maps or mappings, though some authors make some distinction between "maps" and "functions"

f(x) = x - 2

X=0

f(0) = 0-2

f(0) = -2 ...(1)

f(1) = 1-2

f(1) = - 1 .....(2)

f(2) = x-2

f(2)= 2-2

f(2)= 0....(3)

Answer = Straight line figure

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The equation of the graph that is obtained by translating the parent function is as follows:

g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

The following is a translation of the parent function f(x), which may be derived from the graph as follows:

2 units left translation

1 unit up translation

The translation of the sequence mentioned above is expressed as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Therefore, the equation of the graph that has been translated is g(x) = |x + 2| + 1

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Answer: Solution is where the x intercepts on the graph

Step-by-step explanation:

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{9}}} \implies \cfrac{ -5 }{ -10 }\implies \cfrac{1}{2}[/tex]

[tex]\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}{4}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{9}) \\\\\\ y-4=\cfrac{1}{2}x-\cfrac{9}{2}\implies y=\cfrac{1}{2}x-\cfrac{9}{2}+4\implies y=\cfrac{1}{2}x-\cfrac{1}{2}[/tex]

Answer:

[tex]4\frac{1}{2} [/tex]

Step-by-step explanation:

To make the division easier, we will convert them to improper fraction first.

[tex]12 \frac{3}{8} \div 2 \frac{3}{4} \\ = \frac{99}{8} \div \frac{11}{4} [/tex]

Now we will change the sign to multiply and swap the numerator and denominator of the divisor fraction.

[tex] \frac{99}{8} \div \frac{11}{4} \\ = \frac{99}{8} \times \frac{4}{11} \\ = \frac{396}{88} \\ = \frac{9}{2} = 4 \frac{1}{2} [/tex]

Answer:

-2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

For a given atom, net charge can be determined by looking at how many protons the atom has in its nucleus and how many electrons it has surrounding its nucleus.

More specifically, the atom will have

a positive net charge if it has more protons in its nucleus than electrons surrounding its nucleus

a negative net charge if it has more electrons surrounding its nucleus than protons in its nucleus

no net charge if it has equal numbers of protons and electrons

When an atom carries a positive net charge, it forms a cation, or positively charged ion. Likewise, when an atom carries a negative net charge, it forms an anion, or negatively charged ion.

In your case, the atom is said to contain

eight protons

nine neutrons → they do not influence the net charge of the atom

ten electrons

Now, electrons and protons carry opposite charges. A proton is said to carry a 1+ charge, while an electron is said to carry a 1−.

In your case, you have 8 protons and 10 electrons. This means that the atom will carry a total

2×(1−)=2−

net charge.

Therefore, you are dealing with an anion that carries a 2− net charge, i.e. it has two more electrons than it does protons.

The rationalization of the  denominator is  4√3 / 6 .

We have given a fraction √8/√6 .          ...(1)

The denominator of the fraction is √6.

Multiplying and dividing by √6 in equation (1), we get

√8/√6 = √8 × √6 /√6 × √6

           = √48 /6

          = 4√3 / 6

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Yes , the given function is an inverse function which is given by  [tex]f^{-1}(y)=\frac{y-2}{\sqrt{2} }[/tex] .

We have given a function [tex]f(x)=x\sqrt{2} -1+3[/tex] .        ....(1)

On simplifying the equation we, get

     [tex]f(x)=x\sqrt{2} +2[/tex]

Let y = f(x)

      [tex]y=x\sqrt{2} +2\\\\y-2=x\sqrt{2}\\\\x=\frac{y-2}{\sqrt{2} }[/tex]           ......(2)

Swap the values of x and y, then the inverse is then

     [tex]x=f^{-1}(y)[/tex]     ...(3)

Comparing equation (2) and (3) , we get

  [tex]f^{-1}(y)=\frac{y-2}{\sqrt{2} }[/tex]

We can check that this is really an inverse function or not

Putting [tex]x=f^{-1}[/tex] in equation (1) , we get

   [tex]f(f^{-1}(y))=\frac{y-2}{\sqrt{2} } \sqrt{2} -1+3\\\\y=y-2+2\\\\y=y[/tex]

 As LHS = RHS  which means inverse function is correct .

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Answer:

(-2, -2)

Step-by-step explanation:

The point U, when rotated 270 degrees, will end up at the point (-2, -2) on the graph.

Answer:

x = -4

Step-by-step explanation:

x - 16 = -20

16 is being subtracted from x. To get x alone, you need to add 16 to x - 16.

We must do the same to both sides of an equation, so we add 16 to both sides of the equation.

x - 16 + 16 = -20 + 16

x = -4

Answer:

2.5

Step-by-step explanation:

15/6 (3p + 3s) = 2.5
18/7 (4p + 3s) = 2.5