what is the true solution to 3 ln 2+ln 8=2ln(4x)

Answer:

x = - 5

Step-by-step explanation:

Using the rule of exponents

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

Given

[tex](1/2)^{x}[/tex] = 32

[tex]\frac{1}{2^{x} }[/tex] = 32

[tex]2^{-x}[/tex] = [tex]2^{5}[/tex]

Since the bases are equal, both 5, equate the exponents

Hence x = - 5

Answer:

x = 12

Step-by-step explanation:

Assuming you reqire the value of x that makes

4 : x equivalent to 5 : 15

Divide 5 by 4, that is 5 ÷ 4 = 1.25

Thus 1.25x = 15 ( divide both sides by 1.25 )

x = 12

Hence

4 : 12 = 5 : 15

To simplify the expression 3−9 · 36 · 36, we understand that 36 is 3 raised to the power of 6. Multiplying 36 by itself means adding the exponents, resulting in 3¹². Subtracting 9 (the minus sign before 9) from 12 (the exponent in 36 · 36), we get 3³, which is equal to 27.

To simplify the expression 3−9 · 36 · 36, we first need to understand the rules for cubing of exponentials and the operations of exponents.

To cube an exponential, you cube the base digit and multiply the exponent by 3.

For example, when cubing 3², we raise 3 to the power of 6 because the original exponent is multiplied by 3 (2×3=6), which gives us 3⁶, or in other words, 729.

In this case, however, we need to simplify the original expression.

We'll start by recognizing that 36 is 3 raised to the power of 6.

The expression states to multiply 36 by itself, which is essentially stating 3⁶ × 3⁶.

When multiplying exponents with the same base, we simply add the exponents, in this case, 6 + 6, which gives us 3¹².

Hence, the expression can be simplified to 3−9 · 3¹².

Now we are subtracting exponents (because of the minus sign), which means we take 9 away from 12 giving us 3³, or 3 cubed, which equals 27.

Answer:

(0, 0)

Step-by-step explanation:

The y-intercept refers to the point where the graph of a function intersects or crosses the y-axis. The value of x is usually zero at this particular point since the y-axis has the equation;

x = 0

From the alternatives given, the ordered pair (0, 0) could be the y-intercept of a function since x has a value of 0.

Answer:

28

Step-by-step explanation:

There are five numbers so the average must be x/5.

25= x/5

x= 125

30+29+25+20 = 104

Therefore the final number of the five must be 125-104=21

The 3 largest are still 30,29,25.

So their average is (30+29+25)/3

= 28

The average of the three larger numbers is 28

Let y be the 5th number.

Next, we shall determine the value of y. This can be obtained as follow:

Average = Sum of data / number of data

25 = (30 + 29 + 25 + 20 + y) / 5

25 = (104 + y) /5

Cross multiply

25 × 5 = 104 + y

125 = 104 + y

Collect like terms

y = 125 – 104

y = 21

Thus, the correct data are: 30, 29, 25, 20, 21

Finally, we shall determine the average of the three larger numbers.

Average = Sum of data / number of data

Average = (30 + 29 + 25) / 3

Average = 84 / 3

Average = 28

Therefore, the average the three larger numbers is 28

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Answer: 209 i think. hope it helped

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

Each day she increased by 12 jumps. 12 x 17= 204 (you would multiply 12 by 17 instead of 18 since you wouldn't count the first day) 204+21=225

Answer:

999 is the largest number that has 3 digits

Step-by-step explanation:

Answer:

the correct answer is B

Answer:

second option

Step-by-step explanation:

Given expression is:

[tex]\sqrt[3]{64a^6b^7c^9}[/tex]

Converting the expression in the exponents of multiples of three

[tex]\sqrt[3]{4^3*a^6*b^6*b*c^9}[/tex]

Solving the radical

[tex]={4^{(3*\frac{1}{3})} *a^{(6*\frac{1}{3})}*b^{(6*\frac{1}{3})}*b^{(\frac{1}{3})}*c^{(9*\frac{1}{3})}}\\=4a^2b^2c^3\sqrt[3]{b}[/tex]

Hence,

2nd option is correct ..

Answer:

25

Step-by-step explanation:

Here we are supposed to find the distance between two coordinates ( 4,10) and (-3,-14).

Let us do this step by step with detailed explanation.

We will use distance formula in order to find the distance between them. The distance formula is given as

[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]

Here we have

[tex]x_{2}=-3\\x_{1}=4\\y_{2}=-14\\y_{1}=10\\[/tex]

Replacing them in the formula we get

[tex]D=\sqrt{(-3-4)^{2} +(-14-10)^{2} }\\D=\sqrt{(-7)^{2} +(-24)^{2} }\\D=\sqrt{49+ 576 }\\D=\sqrt{625 }\\D=25\\[/tex]

Hence our distance is 25 units

Final answer:

The distance between the points (4,10) and (-3,-14) on the coordinate plane is 25 units, calculated using the distance formula.

Explanation:

The distance between the points (4,10) and (-3,-14) on the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

To calculate the distance:

The distance between the points is 25 units.

Answer:$0.46

Step-by-step explanation

there are 6 pens so divide 2.76 by 6

Answer:

A

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = half the product of the diagonals

here AC = 13 and BD = 15 ← diagonals, hence

A = 0.5 × 13 × 15 = 97.5 units² → A

Answer:

Its A. 97.5

Step-by-step explanation:

just took the test

Answer:

f(3) = 9

Step-by-step explanation:

when we have f(x) that means function of any number. when we have a number in that function we plug it in our equation for all X's. Therefore, when we have f(3) we plug it in to all X's which looks like this

[tex]f(3) = \frac{2 \times 2 + 5}{(3 - 2)} = 9[/tex]

notice how I multiplied at the top first. you also want to apply the rules of PEMDAS.

Hope this helps!

Answer:

-2/7

Step-by-step explanation:

1. simplify the right side of equation by mult

2. divide by seven

3. whatever is being multiplied by x is the slope

please MARK ME BRAINLIEST

The slope of the linear equation 7Y= -2(X - 4) will be negative 2/7.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

7Y= -2(X - 4)

Simplify the equation in the slope-intercept form will be

7Y= -2X + 8

Y = (-2/7)X + 8/7

Then the slope of the linear equation 7Y= -2(X - 4) will be negative 2/7.

More about the linear equation link is given below.

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Answer:

144.5cm^2

Step-by-step explanation:

First find area of the rectangle

Area of a rectangle = L*B

= 9*13 = 117cm^2

Now find area of the triangle

Area of triangle. = 1/2 base * height

Height = 13 - 8 =5cm

Area of the triangle = 1/2 *11 *5 = 27.4

Now area of the who figure is area of rectangle + area of triangle

= 117 + 27.5

= 144.5cm^2

For this case we have that the area of the figure is given by the area of a rectangle plus the area of a triangle.

The area of a rectangle is given by:

[tex]A = a * b[/tex]

Where a and b are the sides of the rectangle.

According to the figure we have:

[tex]a = 13 \ cm\\b = 9 \ cm[/tex]

So, the area of the rectangle is:

[tex]A = 13 * 9\\A = 117 \ cm ^ 2[/tex]

On the other hand, the area of a triangle is given by:

[tex]A = \frac {1} {2} b * h[/tex]

Where b is the base of the triangle and h the height. According to the figure we have:

[tex]b = 13-8 = 5 \ cm\\h = 11 \ cm[/tex]

Substituting:

[tex]A = \frac {1} {2} 5 * 11\\A = 27.5 \ cm ^ 2[/tex]

Adding up we have the total area is:

[tex]A_ {t} = 117 \ cm ^ 2 + 27.5 \ cm ^ 2\\A_ {t} = 144.5 \ cm ^ 2[/tex]

Answer:

Option B

Answer:

Part A

to the 10th power will be positive and to the 11th power is negative. When the exponent is even it will be positive. When it is odd it will be negative

Part B

The one with the negative enclosed will be positive. The second one, the exponent is only effecting the number and not the sign. The outcome will always be negative.

Answer:

7/6 is the answer, or as a mixed fraction, 1 1/6

Step-by-step explanation:

Turn 2 1/3 into an improper fraction. This gives 7/3. Since dividing by 3 is the same as multiplying by 1/2, 7/3 * 1/2 multiply top and bottom with each other to get 7/6 as your answer.

Hope this helps!

Answer:

[tex]\frac{7}{9}[/tex]

Step-by-step explanation:

2[tex]\frac{1}{3}[/tex] ÷3

= [tex]\frac{7}{3}[/tex] ÷3

= [tex]\frac{7}{3}[/tex] x [tex]\frac{1}{3}[/tex]

= [tex]\frac{7}{9}[/tex]

Answer:

d

Step-by-step explanation:

the angle is less than 90 degrees

Answer:

the correct choice is an acute angle have a great day

Step-by-step explanation:

Answer:

With pass cost = $25

Without pass cost = 3x number of days going the the class

Answer:

[tex]y =25[/tex] and [tex]y=3x[/tex]

Step-by-step explanation:

Given : An exercise class has two options a $25 pass for all sessions during the month or $3 per lesson

To Find: write an equation to model the cost of going to the exercise class for a month using a pass and another equation for paying a fee for each lesson​.

Solution:

Let the total cost be y

Option 1) a $25 pass for all sessions during the month

So, equation for option 1 : [tex]y =25[/tex]

Option 2) $3 per lesson

Let x be the number of lessons

So, cost of x lessons = 3x

So, Total cost: [tex]y=3x[/tex]

So, equation for option 2 : [tex]y =3x[/tex]

Hence an equation to model the cost of going to the exercise class for a month using a pass and another equation for paying a fee for each lesson​ is [tex]y =25[/tex] and [tex]y=3x[/tex]

Step-by-step explanation:

the correct answer is C equilateral hope this helps have a great day

There are six (C). Equilateral triangles in a regular hexagon

An equilateral triangle exists in a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, exist equal in measure.

Option(C). Equilateral exists the correct option.

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Step-by-step explanation:

f(x) + n - move the graph n units up

f(x) - n - move the graph n units down

f(x + n) - move the graph n units to the left

f(x - n) - move the graph n units to the right

====================================================

We have f(x) = 2ˣ.

g(x) = f(x) + 1 - move the graph of f(x) one unit up.

(look at the picture)

Answer:

Step-by-step explanation:ik

Final answer:

To find the variance, calculate the average of the squared differences between each data point and the mean. The standard deviation is found by taking the square root of the variance.

Explanation:

To calculate the variance, follow these steps:

Find the mean of the data set.

For each data point, subtract the mean and square the result.

Find the average of the squared differences.

To calculate the standard deviation, take the square root of the variance.

For example, if the data set is {2, 4, 6, 8, 10}, the mean is 6. The squared differences are {(2-6)^2, (4-6)^2, (6-6)^2, (8-6)^2, (10-6)^2}, which equals {16, 4, 0, 4, 16}. The average of the squared differences is (16+4+0+4+16)/5 = 40/5 = 8. Therefore the variance is 8. The standard deviation is the square root of the variance, so in this case, the standard deviation is √8 = 2.83.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$375\\ r=rate\to 2.1\%\to \frac{2.1}{100}\dotfill &0.021\\ t=years\dotfill &12 \end{cases} \\\\\\ A=375[1+(0.021)(12)]\implies A=375(1.252)\implies A=469.5[/tex]

The new account balance in 12 years can be calculated using the simple interest formula. William's new balance after 12 years will be $469.50, after earning a simple interest of $94.50 on his initial deposit of $375.

William's new account balance in 12 years can be calculated using the simple interest formula, which is: Principal (P) x Rate (R) x Time (T).

We already know from the question that the principal (P) is $375, the rate (R) is 2.1% or 2.1/100 = 0.021, and the time (T) is 12 years.
Plugging these values into the formula, we get:
Simple Interest (SI) = PRT
= $375 * 0.021 * 12
= $94.50.
The new balance in the account would be the sum of the initial amount and the simple interest earned. Therefore, the new balance = $375 (Initial deposit) + $94.50 (Interest) = $469.50.

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The exact value of trigonometric function sin(15 degrees) is √6 - √2 divided by 4.

To find the exact value of sin(15 degrees), we can use the sum-to-product trigonometric identity, which states that:

sin(A) + sin(B) = 2 × sin((A + B) / 2) × cos((A - B) / 2).

In this case, we can write sin(15) as sin(45 - 30) and use the identity.

First, we have sin(45 degrees) and sin(30 degrees), which are known values of √2/2 and 1/2, respectively. Plugging these values into the identity, we get sin(15) = 2 × sin(7.5) × cos(7.5).

Now, we can use the half-angle formulas for sine and cosine to simplify further. Sin(7.5 degrees) can be expressed as (√6 - √2) / 4, and cos(7.5 degrees) as (√6 + √2) / 4. So,

sin(15 degrees) = 2 × [(√6 - √2) / 4] × [(√6 + √2) / 4], which simplifies to (√6 - √2) / 4.

In conclusion, the exact value of sin(15 degrees) is (√6 - √2) / 4. This value can be derived using trigonometric identities and the half-angle formulas for sine and cosine.

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The exact value of sin 15 is 0.2588.

The exact value of sin 15 is 0.2588.

To find this value, we can use the fact that sin 30 = 0.5. Since 15 degrees is half of 30 degrees, we can use the half angle formula for sine to calculate sin 15.

Using the half angle formula, sin (15) = sqrt((1 - cos(30))/2) = sqrt((1 - sqrt(3)/2)/2) = 0.2588.

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Final answer:

The joint frequency of being a senior and wanting to have a park cleanup is 26, which represents the number of seniors who preferred the project of park cleanup.

Explanation:

The joint frequency of being a senior and wanting to have a park cleanup can be determined by looking at the frequency table. According to the table, there are 26 seniors who want to have a park cleanup. Therefore, the joint frequency of being a senior and wanting to have a park cleanup is 26.

This answer represents the number of seniors who preferred the project of park cleanup. It shows the specific combination of being a senior (belonging to the senior students group) and wanting to have a park cleanup project.

[tex]x^2-x-90=0\\x^2+9x-10x-90=0\\x(x+9)-10(x+9)=0\\(x-10)(x+9)=0\\x=10 \vee x=-9[/tex]

Answer:

Step-by-step explanation:

c, b, because 6 multiplied by x will equal the amount of time she spent running around the block plus the 8 minutes stretching, if you solve for x the answer is also 5 times around the block

Subtracting the stretching time from the total exercise time gives the jogging time, which when divided by the time per lap, gives the total laps. Leticia jogged around the block 5 times.

The question asks how many times Leticia jogged around the block given that she stretched for 8 minutes and then jogged, with each lap taking 6 minutes to complete, and she spent a total of 38 minutes exercising.

To solve this problem, we need to first determine how much time she spent jogging after stretching. To do this, we subtract the time spent stretching from the total exercise time:

38 minutes total - 8 minutes stretching = 30 minutes jogging.

Next, we divide the jogging time by the time it takes to run around the block once: 30 minutes jogging / 6 minutes per lap = 5 laps. The correct equation that models this situation is C.

Equation: 8 + 6x = 38 and the correct number of times she jogged around the block is B. Answer: 5 times around the block.

Answer:  C, -1.9

Step-by-step explanation:

Its obviously a negative, so it can't be D.

And it's a greater negative then A, so its not B.

And then A is just toooo far away.

So the answer is C

Hope this helps ;)

Just follow PEMDAS

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

56+50*2

Do Multiplication first

56+50*2=56+100

56+100=156

Answer is 156

Answer:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

56+50 × 2

Multiplication first then addition

50 × 2 = 100

56 + 100 = 156

The student's mathematics problem requires solving a quadratic equation derived from the statement that the square of '9 less than a number' equals '3 less than the number'. By expanding, rearranging, and factoring the quadratic equation, we find that the number in question is 12.

The student's question involves solving an algebraic equation to find an unknown number.

Let's denote the unknown number as x.

The problem states that the square of 9 less than the number is 3 less than the number itself.

This can be represented as the equation:

(x - 9)^2 = x - 3

To solve for x, we will follow these steps:

Therefore, the two possibilities for the unknown number are 7 and 12.

We must check which one satisfies the original equation, and we find that x = 12 is the correct solution.

=