Which of these expressions is equivalent to log(4^6)?

Answer:

x = 6

Step-by-step explanation:

Equation: x² - 12x + 36 = 0

Quadratic formula: ax² + bx + c = 0 --> x = (-b ± √(b² - 4ac))/2a

Substitute: x = (12 ± √(12² - 4 * 36))/2

Multiply: x = (12 ± √(144 - 144))/2

Subtract: x = (12 ± 0)/2

Solve: x = 6

Answer:

The value of x = 6

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given that,

x² -12x + 36 = 0

To find the solution of given equation

Here a = 1, b = -12 and c = 36

x = [-b ± √(b² - 4ac)]/2a

 =  [--12 ± √((-12)² - 4*1*36)]/2*1

 = [12 ± √(144 - 144)]/2

 = 12/2 = 6

The value of x = 6

Answer:

The way that you would be able to show -63 is 126/-2

The decimal 2.63 is not recurring. However, 2.63 can be expressed as the fraction 263/100 but it cannot be simplified further.

To express the repeating decimal number 2.63 as a quotient of two integers, we can use a straightforward method. First, let's identify the repeating part, which is the "63" after the decimal point. This part repeats infinitely. To convert this into a fraction, we need to set up an equation where x is the repeating decimal:

x = 2.63

Now, we'll subtract the non-repeating part to isolate the repeating part:

100x = 263 (multiplied both sides by 100 to eliminate the decimal)

Now, we'll subtract x from 100x:

100x - x = 263 - 2.63

99x = 260.37

To isolate x, we divide both sides by 99:

x = 260.37 / 99

Now, we can simplify the fraction:

x = 26037 / 9900

To express 2.63 as a quotient of two integers, it is equal to 26037/9900. This fraction can be simplified further if needed, but it is already in the form of two integers.

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Answer:

Step-by-step explanation:

The line is tangent. Therefore, the angle between the tangent and the radius is the right angle.

We know: the sum of the angles measures in a triangle is 180°.

Therefore we have the equation:

[tex]x+36+90=180[/tex]          combine like terms

[tex]x+126=180[/tex]            subtract 126 from both sides

[tex]x=54[/tex]

The value of x is [tex]54^{0}[/tex].

A line that touches the circle at a single point is known as a tangent to a circle.

As by theorem:

The tangent is always perpendicular to the radius of the circle.

Also, The sum of the angles measures in a triangle is 180°.

By, Using Angle Sum property, we have

90 + x + 36 = 180

x+ 126= 180

x= 180-126

x= 54[tex]^{0}[/tex]

Hence, the value of x is [tex]54^{0}[/tex].

Learn more about tangent here:

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Answer:

The total liters of oil in the first container originally was 32 liters

total liters of oil in the second container originally was 64 liters

Step-by-step explanation:

Let

x----> total liters of oil in the first container originally

y----> total liters of oil in the second container originally

we know that

y=2x ----> equation A

(y-7)=3(x-13) ----> equation B

substitute equation A in equation B

(2x-7)=3(x-13)

2x-7=3x-39

3x-2x=39-7

x=32 liters

Find the value of y

y=2(32)=64 liters

Answer:

there are 100 centimeters in a meter

Step-by-step explanation:

you can remember this by the prefix centi which means 100.

The answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

20/25 x 100 —> 2000/25 = 80%

Answer:

80%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the slope-intercept form y = mx + b to find the slope m and y intercept 'b'

Y - Intercept: 5

(Slope:) -3/4

To find the y intercept you must make x zero and solve for y:

3(0) + 4y = 20

0 + 4y = 20

4y/4 = 20/4

y = 5

This means that the y intercept is:

(0, 5)

Hope this helped!

The portion of the trip through the mountains was 112.5 miles.

To find this, first, let's denote the time spent in the plains as [tex]\( t_1 \)[/tex] and the time spent in the mountains as [tex]\( t_2 \)[/tex]. Since the total trip took 3 hours and 48 minutes (which is[tex]\( \frac{3}{4} \) hours[/tex]), we have:

[tex]\[ t_1 + t_2 = 3.75 \][/tex]

The distance traveled in the plains is [tex]\( d_1 = 90t_1 \)[/tex] and in the mountains is[tex]\( d_2 = 37.5t_2 \)[/tex]. The total distance traveled is 300 miles, so:

[tex]\[ d_1 + d_2 = 300 \][/tex]

Substituting the expressions for [tex]\( d_1 \)[/tex] and [tex]\( d_2 \):[/tex]

[tex]\[ 90t_1 + 37.5t_2 = 300 \][/tex]

We can rearrange the first equation to express [tex]\( t_1 \)[/tex] in terms of [tex]\( t_2 \)[/tex]:

[tex]\[ t_1 = 3.75 - t_2 \][/tex]

Substituting this into the second equation:

[tex]\[ 90(3.75 - t_2) + 37.5t_2 = 300 \][/tex]

[tex]\[ 337.5 - 90t_2 + 37.5t_2 = 300 \][/tex]

[tex]\[ 337.5 - 52.5t_2 = 300 \][/tex]

[tex]\[ 52.5t_2 = 37.5 \][/tex]

[tex]\[ t_2 = \frac{37.5}{52.5} \][/tex]

[tex]\[ t_2 = \frac{5}{7} \] hours[/tex]

Now, to find the distance traveled in the mountains:

[tex]\[ d_2 = 37.5 \times \frac{5}{7} \][/tex]

[tex]\[ d_2 = 112.5 \] miles[/tex]

So, the portion of the trip through the mountains was 112.5 miles.

Complete question

A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains. If a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?

Answer:

B

Step-by-step explanation:

The volume of a rectangular prism is the length times width times height.

V = LWH

V = (4√3)(3√6)W

V = 12√18 W

V = 36√2 W

If the volume is irrational, then W cannot have a radical that is half of a perfect square, because when multiplied by √2, that would yield a rational volume.  For example, √18 × √2 = √36 = 6.

Therefore, the answer must be B, because 12 is not half of a perfect square.

V = 36√2 (4√12)

V = 144√24

V = 288√6

Answer:

choice A is correct

Step-by-step explanation:

For a fair coin, the theoretical probability of obtaining heads or tails is 50%

Increasing the number of trials has the effect of making the experimental probability and theoretical probability equal

Answer:

It's the first option.

Step-by-step explanation:

Assuming it is a fair coin you would expect the experimental probability to get closer to 50%.  

50% is the theoretical probability  for a fair coin because there are 2 equally possible outcomes ,heads or tails.

Step-by-step explanation:

It is solved above

no of children and adult are let as x and y respectively

Galen sold 195 adult tickets and 645 children's tickets at the church carnival.

Let's assume that the number of adult tickets sold is x.

The number of children's tickets sold is 30 more than 3 times the number of adult tickets sold. So, the number of children's tickets sold would be 3x + 30.

The total amount earned from selling adult tickets would be 5x, and the total amount earned from selling children's tickets would be 3(3x + 30) = 9x + 90.

Since the total amount earned from selling all the tickets is $2820, we can set up the equation:

5x + 9x + 90 = 2820

Simplifying the equation,

14x + 90 = 2820

Subtracting 90 from both sides,

14x = 2730

Dividing both sides by 14,

x = 195

Therefore, Galen sold 195 adult tickets. And the number of children's tickets sold would be 3(195) + 30 = 615 + 30 = 645.

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Answer:

Room and board

30%

Step-by-step explanation:

If you look at the numbers in the table, you can easily see Room and board is the largest expense, with $127.50, three times more than the second place.

Now, to find the percent of that expense vs her income we just have to divide this big expense ($127.50) by the total income she has ($425).

% = $127.50 / $425 = 30%

So, that expense is 30% of her income, that's a big chunk, but it's normal for lodging expenses.

Answer:

3,150.

Step-by-step explanation:

These are all of the steps to completely and correctly solve this question.

Hope this helps.

Kyle.

Answer:

the cost increased the most in 2006 - 2012

The cost increase at the greatest average rate in the time interval from 2006 to 2012 will be 1.833.

The average rapid change describes how quickly one quantity changes in comparison to another.

The table is shown.

It is clear that in six years, the rate of the cost of mailing a postcard will be 11. Then the average rate will be

Average rate = 11/ 6

Average rate = 1.833

Thus, the cost increase at the greatest average rate in the time interval from 2006 to 2012 will be 1.833.

More about the average rate link is given below.

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The expression (5y+4)*(-2y+6) simplifies to -10y² + 22y + 24 when multiplied out using the distribution method. Note, it's very important to use the correct syntax when writing mathematical expressions, clarity helps avoid mistakes.

Your question appears to be asking for the result of multiplying two polynomial expressions. However, your question contains a syntax error. It should properly be written as '(5y+4)*(-2y+6)'.

To find the result, you can use the distribution method also known as the FOIL method(First, Outer, Inner, Last). Let's walk through this step by step.

First: Multiply the first terms in each binomial: 5y*-2y=-10y²

Outer: Multiply the outer terms: 5y*6=30y

Inner: Multiply the inner terms: 4*-2y=-8y

Last: Multiply the last terms: 4*6=24

So we have -10y² + 30y - 8y + 24. Combine like terms to get the final answer: -10y² + 22y + 24.

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To build a scale model, the student's school height is first converted to centimeters using the scale factor (50.4 cm), then divided by the length of a toothpick and a cotton swab respectively to determine how many of each would be needed to reach the scaled height. The model will be 8 toothpicks tall and approximately 7 cotton swabs tall.

To solve the problem of building a scale model of the student's school, we need to apply the scale factor provided and the measurements of the materials at hand. The school is 30 feet tall, and the scale is 1 ft:1.68 cm.

To calculate the height of the model in toothpicks, we'll convert the height of the school from feet to centimeters, and then divide by the length of a toothpick:

For the model in cotton swabs, we'll also convert the height to centimeters and then divide by the length of a cotton swab:

Complete Question is :

"You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.68 cm. If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be? The model will be toothpicks tall. Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.2 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number. The model will be approximately cotton swabs tall."

Answer:

I did this question just the other day. The answer you are looking for is B or the second one.

Step-by-step explanation:

Answer:

The correct answer option is B. [tex] a _ 1 = -4[/tex], [tex] r = \frac{1}{2} [/tex], [tex] n = 6 [/tex], [tex] S_n = -\frac{63}{8} [/tex].

Step-by-step explanation:

We are given the following:

[tex]6_\sum_{n=1}[/tex] [tex]-4(\frac{1}{2} )^{n-1}[/tex]

and we are to identify the first term ( [tex] a _ 1 [/tex] ), common ratio ( [tex] r [/tex] ), number of terms ( [tex] n [/tex] ) and the sum of n terms ( [tex] S_n [/tex] ).

Here, [tex] a _ 1 = -4[/tex],

[tex] r = \frac{1}{2} [/tex],

[tex] n = 6 [/tex]; and

[tex]S_n = \frac{a_1(1-r^n)}{(1-r)} = \frac{-4(1-0.5^6)}{(1-0.5)} = -\frac{63}{8}[/tex]

ANSWER

[tex]f(x) = x - 12[/tex]

EXPLANATION

The first x-value is 32.

When we subtract 12 from 32, we get:

[tex]32 - 12 =2 0[/tex]

The next y-value is 14.

When we subtract 12 from 14, we get:

[tex]14 - 12 = 2[/tex]

Also when we subtract 12 from -2, we get,

[tex] - 2 - 12 = - 14[/tex]

Let m be the missing x-value,then

[tex]m - 12 = - 6[/tex]

This implies that,

[tex]m = - 6 + 12[/tex]

[tex]m = 6[/tex]

Let n be the missing y-value, then

[tex] - 10 - 12 = n[/tex]

[tex]n = - 22[/tex]

Therefore we can generalize and write the function rule,

[tex]f(x) = x - 12[/tex]

Answer:

The correct answer option is 0.8.

Step-by-step explanation:

We are given the results of spinning a four colored spinner 50 times and we are to find the experimental probability of not getting a blue (in decimal).

Number of times blue spinner is spun = 10

Total number of times spinner is spun = 50

P (not blue) = [tex] 1 - \frac { 1 0 } { 5  0 } = 1 - \frac { 1 } { 5 } =\frac{4}{5}[/tex] = 0.8

The answer above is right

k=hj

do u mean to make subject of k

The formula after substitution of indicated variable, k is k = h*j .

The given formula in the question is h = k/j .

We have to substitute the formula to find the required parameter variable k .

Thus we have ,

⇒ h = k/j

∴  k = h*j .

Therefore, the formula after substitution of indicated variable, k is k = h*j .

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Answer:

42 1/2>42.500

Step-by-step explanation:

the answer would be D

The number of ways to choose 2 pairs of jeans from 5 is calculated using combinations, resulting in 10 different ways, corresponding to option A.

To determine the number of ways to choose 2 pairs of jeans from 5, we need to use the combination formula, which is defined as C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, and '!' denotes factorial.

In this case, n = 5 and k = 2. Therefore, the calculation becomes:

C(5, 2) = 5! / (2! * (5 - 2)!)
= (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1))
= (5 * 4) / (2 * 1)
= 20 / 2
= 10 ways.

So, there are 10 ways to choose 2 pairs of jeans from 5 pairs, which corresponds to option A.

You are right, it is in fact 8(15-m)

:D

Answer:

8(15 - m)

Step-by-step explanation:

Answer:

both sets have the same number of points

Answer:

It is d.

Step-by-step explanation:

They have different medians and modes.  The 7th grade results , as you would expect, show better results than the 5th grade data.

Answer:

(17 × 2) ÷ ( 5x × y )

Step-by-step explanation:

Difference = Division

The English phrase 'the difference of 17x2 and 5xy' translates to 17x2 - 5xy in algebraic expression.

The phrase 'the difference of 17x2 and 5xy' can be translated into an algebraic expression by replacing the words with their corresponding algebraic symbols. 'Difference' in mathematics means subtraction, '17x2' is a multiplicative expression and '5xy' is as well. So, the phrase can be translated to 17x2 - 5xy.

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Answer:

[tex]-5m^2+7m+8[/tex]

Step-by-step explanation:

We are given the equations

[tex](-m^2+6)+(-4m^2+7+2)[/tex]

We need to combine like terms. As there are no exponents or numbers outside the parenthesis, we can just drop them and add all like terms

[tex]-m^2+6-4m^2+7m+2\\\\-5m^2+7m+8[/tex]

Your Answer is top right (:

Answer:

10.8 miles

Step-by-step explanation:

You need to multiply 7.2 by .5 to get half of 7.2.

You now add this answer (which is 3.6) to 7.2 and the sum is 10.8.

This means your answer is 10.8 miles