Mathematics College

Hello, I need some assistance with this homework question please for precalculusHW Q44

Answers

Answer 1

SOLUTION:

Case: Logarithms

A logarithm is the opposite of power. In other words, if we take a logarithm of a number, we undo exponentiation.

We consider the log of power law below:

[tex]\begin{gathered} \log_aa^x=x\log_aa \\ =x \end{gathered}[/tex]

Given:

[tex]\log_33^{66}[/tex]

Required: Without using calculators, use log laws to answer

Method:

Applying the law above,

[tex]\begin{gathered} \log_33^{66} \\ =66\log_33 \\ =66\times1.(Remember\text{ same base law: }\log_33=1 \\ =66 \end{gathered}[/tex]

Final answer:

Related Questions

Between 9 pm and 6:36 am, the water level in a swimming pool decreased by 6/35 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?

Answers

First, we need to know the total hours from 9 pm to 6:36 am.

We have that from 9:00 pm to 6:00 am are 9 hours. We still have 36 minutes.

And

[tex]36\min \cdot\frac{1hour}{60\min }=0.6hour[/tex]

Then, the total hours are 9.6 hours.

The water level decreased by 6/35 in. Then:

[tex]d=\frac{\frac{6}{35}in}{9.6\text{hour}}\Rightarrow d=0.01786in/\text{hour}[/tex]

Then, the level decreased approximately 0.01786 in/hour at that period of time (the water level decreased at a constant rate).

can you show me the format to get the answer to m/3 +4=7

Answers

can you show me the format to get the answer to m/3 +4=7

we have

[tex]\frac{m}{3}+4=7[/tex]

solve for m

that means

isolate the variable m

step 1

subtract 4 both sides

[tex]\begin{gathered} \frac{m}{3}=7-4 \\ \frac{m}{3}=3 \end{gathered}[/tex]

step 2

multiply by 3 both sides

[tex]\begin{gathered} m=3\cdot3 \\ m=9 \\ \\ \\ \end{gathered}[/tex]

therefore

the answer is

m=9we have thatstep 1

is equal to

m/3 +4-4=7-4

step 2

is equal to

m/3=3

step 3

is given

step 4

is given

Part 2

Let

n------> number of hours

y -----> the total charge

Remember that

The linear equation in slope intercept form is equal to

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

y=mn+b

where

m=$25 per hour

b=$50

y=25n+50

For y=$125

Find out the number of hours

substitute the value of y in the equation and solve for n

125=25n+50

25n=125-50

25n=75

n=3 hours

therefore

the answers are

the total charge's equation is (25n+50)

the number of hours are 3

The value of a stock decreases by an average of 17 dollars each week. Which of the following represents the total average decrease in the stock after 6 weeks?

6|−17| = 102 dollars
|−17| − |6| = 11 dollars
|−17| − 6 = 11 dollars
−6|17| = 102 dollars

Answers

Answer: It is C.

i did the exam.

Step-by-step explanation: It is really about how it is set up so C is the right one.

a. If f(2)= 5, then the point __ is on the graph of f.

b. If (5,0) is on the graph of f, then f(5) =__

Answers

Answer:

a. (2, 5)

b. 0

Step-by-step explanation:

The function is y = f(x)

If we plug in a value for x, we should get a value for y and that (x, y) will be a point

a. We have x = 2 and y = f(2) = 5
So x = 2, y = 5 is a point otherwise written as (2, 5)

b. If y = 0, when x = 5 then f(5) = 0

state the possible rational zeros for each function. The find all zeros. Use the example in the picture to solve: f(x)=2x^3-23x^2-28x-8

Answers

We have to find the zeros of the polynomial f(x) = 2x^3-23x^2-28x-8.

The independent coefficient is -8, that has factors ±1,±2,±4 and ±8.

The leading coefficient is 2, and has factors ±1 and ±2.

The possible rational zeros (p/q) are: ±1/2, ±2/2=±1, ±4/2=±2 and ±8/2=±4.

The possible rational zeros are: ±1/2, ±1, ±2 and ±4.

A company sells equipment for $4,000. the original cost was $50,000.the accumulated depreciation is $45,000. the sale results in what?A. a loss of $4000B. a loss of $1000

Answers

ANSWER

Loss of $1000

EXPLANATION

Cost is $50000

The less accumulated depreciation is $45000

Hence, the book value on data on sale;

[tex]\begin{gathered} 50000-45000 \\ =5000 \end{gathered}[/tex]

Gain or loss on sale = Sale value - Book value;

[tex]\begin{gathered} 4000-5000 \\ =-1000 \end{gathered}[/tex]

Therefore a loss

Write an equation in slope-intercept form for the line with slope 4/3 and y-intercept 1.

Answers

Answer:

y = 4/3x + 1

Hope this helps :)

Step-by-step explanation:

The slope-intercept form is y = mx + b.

m = the slope which is 4/3

b = the y-intercept which is 1

So to substitute the numbers in, the final equation would be y = 4/3x + 1

HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST

Answers

Answer:

I'm not %100 sure this is correct but it seems like it wants a decimal

Step-by-step explanation:

D is 0.37

R is 0.34

That's the only thing that makes sense.

Please mark brainliest if correct!

Question is in the picture. No need for explanation. Just the answer is needed.

Answers

We have

[tex]\begin{gathered} y=7x+10 \\ y=-4x-23 \end{gathered}[/tex]

we make the next equality

[tex]7x+10=-4x-23[/tex]

then we sum like terms

[tex]7x+4x=-23-10[/tex][tex]\begin{gathered} 11x=-33 \\ x=\frac{-33}{11}=-3 \end{gathered}[/tex]

Then we substitute the value of x in the first equation

[tex]\begin{gathered} y=7(-3)+10 \\ y=-21+10 \\ y=-11 \end{gathered}[/tex]

ANSWER

x=-3

y=-11

your answer is
x=-3 or y=-11

What is the slope of line AB, where the points are A (-1,5) and B (3,-1)

Answers

[tex]-\frac{3}{2}[/tex]

Explanation

Step 1

when you have 2 points of a line P1 and P2, you can easily find the slope using:

[tex]\begin{gathered} \text{slope}=m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]

Let

P1=A=(-1,5)

P2=B=(3,-1)

Step 2

replace

[tex]\begin{gathered} \text{slope}=m=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=m=\frac{-1-5}{3-(-1)}=\frac{-6}{3+1}=\frac{-6}{4}=-\frac{3}{2} \end{gathered}[/tex]

I hope this helps you

determine x-axis and y-axis intercepts for -8x-6y=12

Answers

After determining the x and y axis, we get the x and y intercepts as 1.5 and -2.

Given the equation is -8x-6y=12

-6y=8x+12

y=-8x/6+12/6

y=-4x/3+2

To determine x intercept, set y=0

-4x/3+2=0

Multiply both sides of the equation by the common denominator.

-4x×3/3 + 2×3 = 0×3

Reduce the fraction.

-4x+6=0

Rearrange the variables to the left side of the equation.

-4x=-6

cancel - sign.

4x=6

x=6/4

x=3/2

Now, to determine y intercept, set x=0

-8x-6y=12

-8(0)-6y=12

-6y=12

y = -12/6

y = -2

Hence the x and y intercepts are 1.5 and -2 respectively.

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(4x + 8)° find the value of each variable

Answers

8x=80

so x=0

because then you have

80=80

x=10

A parabola is modeled with the equation x2 – 12x + 4y + 24 = 0. Which is the domain and range of the parabola?

D: (–∞, ∞); R: (–∞, 3]
D: (–∞, ∞); R: [3, ∞)
D: (–∞, 3]; R: (–∞, ∞)
D: [3, ∞); R: (–∞, ∞)

Answers

Answer:

first option

Step-by-step explanation:

[tex] {x}^{2} - 12x + 4y + 24 = 0[/tex]

[tex] {x}^{2} - 12x + 24 = - 4y[/tex]

[tex] - \frac{ {x}^{2} }{4} + 3x - 6 = y[/tex]

Now, we can find the domain and range, the easiest way first is to put this in vertex form

First, find the x coordinate of the vertex using

-b/2a,

[tex] \frac{ - 3}{2(( - 0.25))} = 6[/tex]

Now, plug in 6 into the original equation to obtain the y value of the vertex

[tex] - \frac{6 {}^{2} }{4} + 3(6) - 6 = - 9 + 18 - 6 = 3[/tex]

So our vertex is (6,3).

Next , we put this in vertex form.

[tex]a(x - h) {}^{2} + k[/tex]

where (h,k) is the vertex

and a is the leading coefficient

so our quadratic in vertex form is

[tex] - \frac{1}{4} (x - 6) {}^{2} + 3[/tex]

Part 3: Domain and Range.

The domain of any quadratic(unless we are doing a real world example with a variable that can not be negative like time, objects,etc) is always all real numbers.

So the domain is (-oo,oo)

Since our a is negative, the range of our parabola is (-oo,3]

The correct answer is the first option

what is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is sub divided into equal sections.

Answers

The length of the marked portion of line segment A is 25, B is 45 and C is 30.

What is line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The distance between two ends of a line segment is its length. Half-open line segments contain exactly one of the endpoints while other end point is open, while closed line segments have both the endpoints closed. Open line segments do not contain any of the endpoints.

Calculation of line segment A,

75 ÷ 3 = 25

25 × 1 = 25

Therefore, the length of the marked portion of line segment A is 25

Calculation of line segment B,

75 ÷ 5 = 15

15 × 3 = 45

Therefore, the length of the marked portion of line segment B is 45

Calculation of line segment C,

50 ÷ 5 = 10

10 × 3 = 30

Therefore, the length of the marked portion of line segment C is 30

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Required Question #7 7) 100^2 x 100^5 = 100^y y=?

Answers

Given the general rule for exponents:

[tex]a^n\cdot a^m=a^{n+m}[/tex]

then, in this case we have the following:

[tex]\begin{gathered} 100^2x100^5=100^y \\ \Rightarrow(100^2)\cdot(100^5)=100^{2+5}=100^7 \\ \Rightarrow y=7 \end{gathered}[/tex]

therefore, y=7

What is the value of x in the equation x-2/3 + 1/6 = 5/6

Answers

The value of x in the equation (x - 2)/3 + 1/6 = 5/6 is: x = 4

How to Solve an Equation?

To solve a given equation, find the value of the variable in the equation by isolating the variable to one side using the necessary properties of equality.

Given the equation, (x - 2)/3 + 1/6 = 5/6:

(x - 2)/3 + 1/6 = 5/6

Subtract both sides by 1/6:

(x - 2)/3 + 1/6 - 1/6 = 5/6 - 1/6 (subtraction property of equality)

(x - 2)/3 = 4/6

Multiply both sides by 3:

(x - 2)/3 × 3 = 4/6 × 3 (multiplication property of equality)

x - 2 = 2

Add both sides by 2:

x - 2 + 2 = 2 + 2 (addition property of equality)

x = 4

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Name two triangles that are congruent by ASA.Choose the correct answer below.(triangle)ABC = (triangle) hpw GHJ(triangle)ABC= (triangle)DEF(triangle)DEF= (triangle)GHJ

Answers

Congruence by ASA (Angle-Side-Angle): Triangles are congruent if any two angles and their included side are equal in the triangles.

For the given triangles:

[tex]\begin{gathered} \Delta ABC\cong\Delta\text{GHJ} \\ \\ \angle B=\angle H \\ \angle C=\angle J \\ BC=HJ \end{gathered}[/tex]

Give a test to a group of students the grades and gender are summarized below if one student is chosen at random find the property ability that the student was female or got AB round the solution of 3 decimal places

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Data Table

Step 02:

probability (female) or probability (B)

probability = favorable outcomes / total outcomes

probability (female) = 32 / 55

probability (B) = 8 / 55

probability (female) or probability (B) = (32 / 55) + (8 / 55) - (32/55)*(8/55) = 0.6426

The answer is:

probability (female) or probability (B) = 0.643

Find the area of the polygon. 2 m 19 m 2 m 17 m The area of the polygon is (Type a whole number.)

Answers

If the polygon is redrawn and completed as shown below

The area of the polygon = area of the rectangle ABCD - ( area of the rectangle AEFG + area of the rectangle HBJI)

Area of rectangle = L x B

For ABCD

L = 17 + 2= 19 m

B = 19 + 2 + 2 = 23 m

Area = 19 x 23 = 437 square metre

For AEFG

L= 2 m , B = 2 m

Area = 2 x 2 = 4 square m

For HBJI

L= 2 m , B = 2m

Area = 2 x 2 = 4 square m

[tex]\begin{gathered} Area\text{ of the polygon = 437 - ( 4+ 4)} \\ =\text{ 437 - 8} \\ =429m^2 \end{gathered}[/tex]

Robert rolled a die 30 times. Itlanded on four 7 times. What was theexperimental probability for landingon a four?AC11B

Answers

Probability= Number of required outcome / Number of possible outcomes

Number of possible outcomes= 30

Number of required outcome = 7

[tex]probability=\frac{7}{30}[/tex]

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Sam and his cousin Matt have the same birthday, but Sam is 5 years older than Matt. Let the variable x represent Sam’s age and y represent Matt’s age. Graph the relationship between Sam’s age and Matt’s age.

Answers

The relationship between Sam’s age and Matt’s age is given as x = y + 5

What is an equation?

An equation is an expression that can be used to show the relationship between numbers and variables.

The equation of a line in slope intercept form is:

y = mx + b

Where m is the slope and b is the y intercept

Let x represent Sam’s age and y represent Matt’s age. Sam is 5 years older than Matt, hence:

x = y + 5

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how do this problem and what would be the answer?

Answers

We will have the following:

[tex](g\circ f)(x)=2(4x+3)\Rightarrow(g\circ f)(x)=8x+6[/tex]

Find the 55 th term in the following sequence: -102, -98, -94, -90

Answers

Answer:

114

Step-by-step explanation:

Using the explicitly formula for an arithmetic sequence, the nth term is 4n-106.

Thus, the 55th term is 55(4)-106 = 114.

COULD REALLY USE HELP!only have a short amount of time!.Write the translated equation y = 1xl so that the vertex is at(-5, -3). You can use parenthesis instead of absolute valuebars for this answer.

Answers

With the function given as y = |x|, and the value of x on the graph is -5, when translated it becomes

[tex]y+3=|x+5|[/tex]

Because when x = -5, then y + 3 = 0 (that is, y = -3)

In a science project, the number of bacteria increases exponentially. Every hour, the number of bacteria triples. If the project starts with 100 bacteria, how many bacteria are present after 5 hours?

Answers

Consider that the exponential function can be written as follow:

f(x) = a

Bob's yard is in the shape of a semicircle with a diameter of 14 feet. Bobwants to buy grass to cover the area of his entire yard. How many squarefeet of grass does Bob need? Round to the nearest tenth.

Answers

EXPLANATION

The area of a semicircle is given by the following relationship:

[tex]\text{Area}_{\text{semicircle}}=\frac{1}{2}\cdot\pi\cdot r^2[/tex]

The radius of the semicircle is diameter/2=14/2 = 7 feet

Replacing terms:

[tex]\text{Area}=\frac{1}{2}\cdot\pi\cdot(7)^2[/tex]

Computing the power:

[tex]\text{Area}=\frac{1}{2}\pi\cdot49[/tex]

Simplifying numbers:

[tex]\text{Area}=24.5\cdot\pi=24.5\cdot3.14=76.93ft^2\approx77ft^2[/tex]

In conclusion, the answer is the option D.

x f(x)-2 -6-1-10 212 23-14 -6Which interval could contain a solution to f(x) = 0?A. -6

Answers

Notice that when x = -1, f(x) = -1, and if x = 0, then f(x) = 2.

As we can see, the values of f(x) change from negative to positive between -1 and 0. This means that between the interval -1 < x < 0, we can find f(x) = 0

Would you help me with 64 A, B , and C i

Answers

Given data:

Rate of decrease: 2.5 inches per hour

After 1.5 hours the candle is 11.5 in long

Let x be the number of hours

Let y be the length of the cangle remaining

Linear equation:

[tex]\begin{gathered} y=mx+b \\ \\ m=rate\text{ of change} \\ b=initial\text{ value} \\ \\ \\ y=-2.5x+b \end{gathered}[/tex]

Use given data to find b: After 1.5 hours the candle is 11.5 in long

x=1.5

y=11.5

[tex]\begin{gathered} 11.5=-2.5(1.5)+b \\ 11.5=-3.75+b \\ 11.5+3.75=b \\ b=15.25 \end{gathered}[/tex]

a. Formula:

[tex]y=-2.5x+15.25[/tex]

b. The formula describes the remaining length (y) using two terms:

-2.5x: first term, this term includes the slope or rate of change (-2.5) and the variable (x)

15.25: second term it the initial lengh of the candle

i. Evaluate the formula for x=3

[tex]\begin{gathered} y=-2.5(3)+15.25 \\ y=-7.5+15.25 \\ y=7.75 \end{gathered}[/tex]

After 3 hours burned the length of the candle is 7.75 inches

ii. Evaluate the formula for x=5

[tex]\begin{gathered} y=-2.5(5)+15.25 \\ y=-12.5+15.25 \\ y=2.75 \end{gathered}[/tex]

After 5 hours burned the length of the candle is 2.75inches

IncorrectYour answer Is Incorrect.Find the range of the quadratic function.y=3x2 - 30x + 77Write your answer as an inequality using x or y as appropriate.Or, you may instead click on "Empty set" or "All reals" as the answer.DSODO음EmptysetAll realsХ?

Answers

We are given the following quadratic function:

[tex]y=3x^2-30x+77[/tex]

To determine the range we need first to determine the vertex of the quadratic function. To do that, since we have an equation of the form:

[tex]y=ax^2+bx+c[/tex]

The x-coordinate of the vertex is given by:

[tex]x=-\frac{b}{2a}[/tex]

Replacing we get:

[tex]x=-\frac{-30}{2(3)}[/tex]

Solving we get:

[tex]x=\frac{10}{2}=5[/tex]

The y-coordinate of the vertex is found by replacing this value in the quadratic equation:

[tex]\begin{gathered} y=3(5)^2-30(5)+77 \\ y=3(25)-150+77 \\ y=2 \end{gathered}[/tex]

Now, since the term "a" is a positive number the parabola opens upwards, and the range is the values of "y" that are larger than the y-coordinate of the vertex, that is:

[tex]R=\mleft\lbrace y\in\R\parallel y\ge2\rbrace\mright?[/tex]

Julie can run 3 laps in 9 minutes. At this rate, how many laps can she run in 24 minutes?

Answers

In 24 minutes Julie can run 8 laps.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

Julie can run 3 laps in 9 minutes that is :

in 9 minutes = 3 laps

Now, to find the laps covered by Julie in 24 minutes we first find the laps rate per minutes by dividing 9 both the side :

in 9/9 minutes = 3/9 laps

in 1 minutes = 1/3 laps

Multiply 24 both the side :

in 24 minutes = 24/3 laps

in 24 minutes = 8 laps

Therefore, in 24 minutes Julie can run 8 laps.