Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)

3(2x+4)=-6 6x+12=-6

- 12. -12

6x = -18

÷6. ÷6

x= -3

Answer:

-3

Step-by-step explanation:

3(2x+4)= -6

6x+12= -6

6x= -18

x= -3

Answer:

(0,12)

Step-by-step explanation:

To write the equation of a line, calculate the slope between points (-3,3) and (-5,-3). After, substitute the slope and a point into the point slope form. Then convert to the slope intercept form to identify the y-intercept.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{3--3}{-3--5}= \frac{6}{2}=3[/tex]

Substitute m = 3 and the point (-3,3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y -3 = 3(x--3)\\y-3 = 3(x +3)\\y-3=3x + 9\\ y = 3x + 12[/tex]

This means that it crosses at (0,12) since b - 12 for y=mx+b.

Answer:(0,12)

Step-by-step explanation:

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=28\pi \end{cases}\implies 28\pi =2\pi r\implies \cfrac{28\pi }{2\pi }=r\implies 14=r[/tex]

[tex]y = 0.392x + 638.118 \\ x = 2400 \\ y = (0.392 \times 2400) + 638.118 \\ y = 1578.92[/tex]

hope u understand

Answer:

[tex]f(-4)=1.3[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\frac{6}{-2+2e^{-0.3x}}[/tex]

we know that

f(-4)  is the value of the function for x=-4

substitute x=-4 in the function

[tex]f(-4)=\frac{6}{-2+2e^{-0.3(-4)}}[/tex]

[tex]f(-4)=\frac{6}{-2+2e^{1.2}}[/tex]

[tex]f(-4)=1.3[/tex]

Answer:

1.94

Step-by-step explanation:

We substitute -4 into as x in the equation, but first what is e?

e is a term that represents the base of a natural logarithm and is a irrational number, its called Euler's number. e is equivalent to:

[tex]e=2.718[/tex]

We can substitute -4 into the equation

[tex]=6/(-2+2*(2.718^(-0.3*-4)))[/tex]

[tex]=6/(-2+2*(2.718^(1.2)))[/tex]

[tex]=6/(-2+2*2.54)[/tex]

[tex]=6/(3.09)[/tex]

[tex]=1.94

Therefore f(-4)=1.94

the y intercept is -3 because its touching (0,-3).

The graph goes right one and down five so the slope is -5

y=mx + b

y= -5x -3

Answer:

k > 3

Option D

For any value of k greater than 3

Step-by-step explanation:

We ara dealing with an inequality

(k/3)*12 > 12

Dividing by 12 each side

(k/3)*12/12 > 12/12

(k/3) > 1

Multiplying by three

3*(k/3) > 3*1

k > 3

Answer:

k > 3

Option D

For any value of k greater than 3

Step-by-step explanation:

Answer:

156.7 miles.

Step-by-step explanation:

The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:

( 3959 + 3.1)^2 = x^2 + 3959^2

x^2 =  3962.1^2 - 3959^2

x^2 =  24555.41

x =  156.7 miles.

The solution is : 156.7 miles is the distance to the earth’s horizon from point P.

The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

here, we have,

from the given diagram, we get,

The radius and the tangent at the point of contact form a right angle so we can apply the Pythagoras theorem:

( 3959 + 3.1)^2 = x^2 + 3959^2

x^2 =  3962.1^2 - 3959^2

x^2 =  24555.41

x =  156.7 miles.

Hence, The solution is : 156.7 miles is the distance to the earth’s horizon from point P.

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{a(x)}{b(x)}[/tex]

= [tex]\frac{2x^2-5x+6}{x-3}[/tex]

= 2x + 1 + [tex]\frac{9}{x-3}[/tex]

quotient q(x) = 2x + 1 and remainder r(x) = 9

Answer:

(-7 , 3)

Step-by-step explanation:

3x^2 + 12x = 63 //Subtract 63 on both sides.

3x^2 + 12x - 63 = 0 //Common factor 3.

3(x^2 + 4x - 21) = 0 //Divide both sides by 3.

(x^2 + 7x - 3x - 21) = 0

x(x + 7) - 3(x + 7) = 0

(x + 7) (x - 3) = 0

x = -7 and 3

Solution: (-7, 3)

Answer:

whew chiile

Step-by-step explanation:

[tex]\huge\boxed{\text{The $5$ needs to be negative.}}[/tex]

Since the first binomial is [tex](x-5)[/tex], the [tex]5[/tex] is negative and must be that way when using the table.

Here's the corrected table:

[tex]\begin{array}{c|c|c|}\multicolumn{1}{c}{}&\multicolumn{1}{c}{3x}&\multicolumn{1}{c}{1}\\\cline{2-3}x&3x^2&x\\\cline{2-3}-5&-15x&-5\\\cline{2-3}\end{array}\\\\\\3x^2+x-15x-5\\3x^2-14x-5[/tex]

Answer:

Option A. [tex]0.42[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

[tex]BA^{2}=(1/2)^{2}+(1/3)^{2} -2(1/2)(1/3))cos(100)[/tex]

[tex]BA^{2}=0.1756[/tex]

[tex]BA=0.42[/tex]

➷ The period is the distance from one part of the function to the same part of it.

In this case, the period is 5

The amplitude is the half the distance from the largest and smallest value

3 + 6 = 9

9/2 = 4.5

In this case, the amplitude is 4.5

➶ Hope This Helps You!

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Answer:

210

Step-by-step explanation:

As there is one circle in first row, 2 circles in 2nd row and three in third row, which clearly implies that the number of circles in each row is equal to the row number. So, we have to calculate sum of first 20 numbers to calculate the total number of circles.

n=20

Total Circles=(n(n+1))/2

=(20 (20+1))/2

=(20(21))/2

=  420/2

=210

So the total number of circles will be 210.  

In general, you have that [tex](x-x_0)[/tex] is a factor of a polynomial [tex]p(x)[/tex] if and only if [tex]p(x_0)=0[/tex]

So, we want [tex]p(3)=0[/tex]. We have

[tex]p(3) = -3^3+ 9c -4\cdot 3 +3 = -27+9c-12+3 = 9c-36[/tex]

So, we have

[tex]p(3) = 0 \iff 9c-36 = 0 \iff x = \dfrac{36}{9} = 4[/tex]

Answer:

c = 4

Step-by-step explanation:

Given that (x - 3) is a factor of p(x) then x = 3 is a root and p(3) = 0

p(3) = - (3)³ + c(3)² - 4(3) + 3 = 0, hence

- 27 + 9c - 12 + 3 = 0

9c - 36 = 0 ( add 36 to both sides )

9c = 36 ( divide both sides by 9 )

c = 4

Answer:

Inverse = (arcos x) / 2.

Step-by-step explanation:

y = cos 2x

2x= arcos y

x = (arcos y) / 2.

Inverse = (arcos x) / 2.

The equation for the inverse of y = cos 2x is obtained by switching the x and y variables and solving for y, resulting in y = arccos (x) / 2.

The inverse of a function switches the roles of the x and y variables, so the first step to finding the inverse of y = cos 2x is to switch the x and y in the equation, giving us x = cos 2y. Now, we simply solve for y. The equation x = cos 2y is equivalent to 2y = arccos (x) where arccos is the inverse cosine function.  Therefore, the final answer is y = arccos (x) / 2. This is the equation for the inverse of y = cos 2x.

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If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:

7, 714/24 = 321.4167

This answer estimated can be 321. So yuh might need 321 panels.

ANSWER = 321 PANELS

Answer:300

Step-by-step explanation:

If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:

7, 714/24 = 321.4167

This answer estimated can be 321. So yuh might need 321 panels.

ANSWER = 321 PANELS

But the best estimate is 300 pannels

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=6^x\qquad \boxed{x=-3}\qquad \implies f(-3)=6^{-3}\implies f(-3)=\cfrac{1}{6^3} \\\\\\ f(-3)=\cfrac{1}{6\cdot 6\cdot 6}\implies f(-3)=\cfrac{1}{36\cdot 6}\implies f(-3)=\cfrac{1}{216}[/tex]

Answer: B on Edg

Step-by-step explanation:

Answer:

$24.15

Step-by-step explanation:

What you do is you take 15% and make it into a decimal which is .15.

Then you times it by $21. 21*.15=3.15.

You then take the $3.15 and add it to $21 to get

$24.15 as your answer.

Winona left a 15% tip for her $21 haircut, resulting in a tip of $3.15. When added to the cost of the haircut, it means she paid a total of $24.15.

The question is asking us to find out how much Winona paid in total for her haircut, including a 15% tip. To find the amount of the tip, we can multiply the cost of the haircut (which is $21) by 15% (or 0.15 in decimal form): $21 * 0.15 = $3.15. To find the total amount Winona paid, we simply add the cost of the haircut to the tip: $21 + $3.15 = $24.15. So, Winona paid a total of $24.15 for her haircut.

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Answer:

1.91° and -1.91°.

Step-by-step explanation:

2.8% of the thermometers are rejected on either end of the curve.  The bottom end, where the readings are too far below the mean, will have an area from this point to the left tail of the curve of 0.028.

The top end, where the readings are too far above the mean, will have an area from this point to the left tail of the curve of 1-0.028 = 0.972.

We look in a z table for these values.  We look within the cells of the table; the closest value to 0.028 is 0.0281, which corresponds with a z score of -1.91.  The closest value to 0.972 is 0.9719, which corresponds with a z score of 1.91.

We substitute these values into the z score formula, along with our values for the mean (0) and the standard deviation (1):

[tex]-1.91=\frac{X-0}{1}[/tex]

Simplifying the right hand side, X-0 = X; X/1 = X.  This means X = -1.91.

For the second value,

[tex]1.91=\frac{X-0}{1}[/tex]

Simplifying the right hand side, X-0 = X; X/1 = X.  This means X = 1.91.

This means the two values are 1.91° and -1.91°.

The cutoff values separating the rejected thermometers in a normally distributed thermometer reading with a mean of 0 and a standard deviation of 1°C are -1.88°C and +1.88°C. These values are determined using the z-scores that corresponds to the tail probabilities (2.8%) of the normal distribution.

The question involves determining the cutoff values that separate the rejected thermometers based on a normally distributed thermometer reading. We know that 2.8% of the thermometers are rejected for being too high, and another 2.8% for being too low. Here, this involves using the concept of the normal distribution and z-scores.

First, since each tail contains 2.8% of the data, the cumulative probability up to the cutoff point will be 100% - 2.8% = 97.2% for the higher cutoff and 2.8% for the lower cutoff. To find the z-scores that correspond to these areas, you can consult a standard normal distribution table or use an online tool. Typically, z-scores around ±1.88 correspond to a cumulative probability closest to 97.2% and -1.88 for 2.8%.

Since the mean (μ) is 0 and the standard deviation (σ) is 1°C, the thermometer readings the cutoff values or z-scores represent are given by z = (X - μ)/σ. Therefore, the thermometer readings for these z-scores are -1.88°C and +1.88°C. These are the cutoff values which separate the rejected thermometers.

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Answer:

If those are supposed to be exponents the answers are:

1.  1/36

2.  - 1/6

3.     1

4.  -6

5.  36

Step-by-step explanation:

The student is provided with the correct evaluations of five expressions given the value x = -6. Each expression is computed, and the correct numerical matches are presented.

The student is attempting to solve expressions given the value of x = -6. To find the correct matches, each expression must be computed separately. Let's start by calculating the given expressions:

x - 2: When x is -6, the expression becomes (-6) - 2 = -8.

x - 1: When x is -6, the expression becomes (-6) - 1 = -7.

x + 0: When x is -6, the expression is simply -6.

x + 1: When x is -6, the expression becomes (-6) + 1 = -5.

x + 2: When x is -6, the expression becomes (-6) + 2 = -4.

With these computations, the matches would be:

x - 2 matches with -8

x - 1 matches with -7

x + 0 matches with -6

x + 1 matches with -5

x + 2 matches with -4

Answer:

C. -2

Step-by-step explanation:

Since the leading coefficient is 1 and rational roots are of the form ...

±(divisor of the constant)/(divisor of the leading coefficient)

all of the possible rational roots must be whole number diviors of 12. The only one on the list is -2.

The Rational Root Theorem allows us to determine that -2 is a possible rational root for the polynomial p(x)=x2+3x+12.

According to the Rational Root Theorem, the possible rational roots of a polynomial equation can be found by taking all the factors of the constant term (in this case, 12) and dividing them by all the factors of the leading coefficient (in this case, 1 as the coefficient for x2 is 1). The factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12. As our leading coefficient is 1, our possible roots can include ±1, ±2, ±3, ±4, ±6, ±12.

Looking at the list of options provided: A. 24, B. -1/2, C. -2, D. 1/6, E. 1/2, we see that only -2 is a possible rational root for the polynomial p(x)=x2+3x+12 based on the Rational Root Theorem.

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Answer:

Part 3)

[tex]x=6\ units[/tex]

[tex]y=3\ units[/tex]

Part 4) [tex]x=18\sqrt{2}\ units[/tex]

Step-by-step explanation:

Part 3)

step 1

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

so

[tex]cos(30\°)=\frac{3\sqrt{3}}{x}[/tex]

and remember that

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}[/tex]

Simplify

[tex]x=(2*3)=6\ units[/tex]

step 2

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

so

[tex]sin(30\°)=\frac{y}{x}[/tex]

and remember that

[tex]sin(30\°)=\frac{1}{2}[/tex]

substitute

[tex]\frac{1}{2}=\frac{y}{6}[/tex]

[tex]y=6/2=3\ units[/tex]

Part 4) Find the value of x

Applying the Pythagoras Theorem

[tex]x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units[/tex]

Simplify

[tex]x=18\sqrt{2}\ units[/tex]

Answer:

[tex]5\sqrt{3}[/tex] OR [tex]8.69[/tex]

Step-by-step explanation:

Let's first simplify [tex]\sqrt{75}[/tex].

5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write [tex]\sqrt{75}[/tex] as:

[tex]5\sqrt{3}[/tex]

Now, let's find the answer in decimal form. We know that:

[tex]8^2=64[/tex] and [tex]9^2=81[/tex]

With that information, we know that the answer has to be between 8 and 9.

Divide 75 by 8: [tex]\frac{75}{8}=9.375[/tex]

Take the average of that answer and 8: [tex]\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875[/tex]

This answer we got is extremely close to the exact answer of [tex]\sqrt{75}[/tex], which is [tex]8.66025403...[/tex]. Since we are estimating, the answer above will do just fine.

Answer:

P(6 times in 9 selection) = 0.116

Step-by-step explanation:

There are 11 red checkers and 5 black checkers in a bag so

P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16

Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.

Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.

In this case, n = 9 and k = 6, P(red)=11/16 so

P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)

where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36

so  P(6 times in 9 selection)

= 36 * (11/16)^6 * (5/16)^3

= 0.116

The context is a binomial distribution where success is defined as drawing a red checker from the bag. With replacement, each draw is independent. Therefore, the formula for binomial probability can be used to calculate the probability of drawing a red checker exactly 6 times in 9 draws.

This is a problem of the binomial distribution. For a binomial distribution, each trial is independent, meaning the result of the previous trial does not affect the result of the next trial. This is satisfied since the question states that the checkers are selected with replacement.

'Success' in this context is defined as selecting a red checker which occurs with a probability of 11/16 (since there are 11 red checkers out of a total of 16). Failure is defined as selecting a black checker which occurs with a success probability of 5/16.

To find the probability of selecting a red checker exactly 6 times in 9 selections, we use the formula for binomial probability: P(k; n, p) = C(n, k) * (p^k) * (1 - p)^(n-k). Here, n=9 (number of trials), k=6 (desired 'successes') and p=11/16. When you substitute these values into the formula, you get the desired probability.

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When the dimensions of a two gallon container are tripled, the container can hold up to 54 gallons of liquid, since the volume will increase 27 times.

The question is about how a two gallon container can hold when all of its dimensions are tripled. In mathematics, when dimensions of a cube (or a rectangular prism, which the container can be assumed to be) are increased proportionally, the volume, which is proportional to the cube of the dimensions, increases by the cube of that same factor.

In this case, the dimensions of the container have all been tripled (a three-fold increase) which results in the volume of the space inside the container increasing by 3³ = 27 times. Therefore, the two gallon container, when its dimensions are tripled, can hold 2 gallons x 27 = 54 gallons. It's important to understand this is a principle of geometry and works irrespective of the units of measurement used (gallons, liters, cubic centimeters, etc.)

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Answer:

9 feet

Step-by-step explanation:

If each side is the equivalent, each side of the prism is the cube root of 729

Cube root of 729 is 9

Each side is 9 feet long

Answer:

176

Step-by-step explanation:

We see that it is an arithmetic sequence since we are subtracting the same number to a term to get the next term. So 876 - 7 = 869  &  869 - 7 = 862.

So the common difference d is -7

and the first term, a is 876

The nth term of an arithmetic sequence is given by  a + (n-1)d

where n would be 101, since we want to figure 101st term.

So:

[tex]a+(n-1)d\\876+(101-1)(-7)\\876+(100)(-7)\\=176[/tex]

Correct answer is the 2nd choice, 176

The 101st term in the sequence 876, 869, 862, ... is 176, found by using the formula for the nth term of an arithmetic sequence with a common difference of -7.

To find the 101st term in the sequence 876, 869, 862, ..., we first need to determine the common difference of the arithmetic sequence. Each term decreases by 7 (869 - 876 = -7 and 862 - 869 = -7), so the common difference is -7.

Now, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

The 101st term is calculated as follows:

Thus, the 101st term is 176.