what is the center of dilation
a
b
c
d

Step-by-step explanation:

[tex]3\log x+\log2=\log3x-\log2\\\\\text{Domain:}\ x>0\\\\\text{Use}\\\\\log_ab^c=c\log_ab\\\\\log_ab+\log_ac=\log_a(bc)\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\===================\\\log x^3+\log2=\log\left(\dfrac{3x}{2}\right)\\\\\log(2x^3)=\log\left(\dfrac{3}{2}x\right)\iff2x^3=\dfrac{3}{2}x\qquad\text{subtract}\ \dfrac{3}{2}x\ \text{from both sides}\\\\2x^3-\dfrac{3}{2}x=0\qquad\text{multiply both sides by 2}\\\\4x^3-3x=0\qquad\text{use distributive property}\\\\x(4x^2-3)=0\iff x=0\ \vee\ 4x^2-3=0[/tex]

[tex]x=0\notin\ \text{Domain}\\\\4x^2-3=0\qquad\text{add 3 to both sides}\\\\4x^2=3\qquad\text{divide both sides by 4}\\\\x^2=\dfrac{3}{4}\Rightarrow x=\pm\sqrt{\dfrac{3}{4}}\\\\x=\pm\dfrac{\sqrt3}{\sqrt4}\\\\x=-\dfrac{\sqrt3}{2}\notin \text{Domain}\\\\\boxed{x=\dfrac{\sqrt3}{2}}\in \text{Domain}[/tex]

The equivalent equation to 3logx + log2 = log3x - log2 is x² = 3/4, which is derived by applying properties of logarithms such as combining log terms and setting the resulting expressions equal to each other.

The equation 3logx + log2 = log3x - log2 can be simplified using the properties of logarithms. To find the equivalent equation, we use the property that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b). Applying these properties:

The equivalent equation is x² = 3/4 or x = ±√(3/4), provided that x ≠ 0 since the logarithm of zero is undefined.

Answer:

3

Step-by-step explanation:

3+11t-9u=3+11(9)-9(11)=3+99-99=3

Answer:

The line which is parallel to the given line [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 1}[/tex] is [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 2}[/tex]

Step-by-step explanation:

Given that the equation of the line is

[tex]y=-\frac{4}{3}x+1\hfill (1)[/tex]

To find the equation of the line is parallel to the given line equation.

We know that the given equation is in the slope intercept form

y=mx+c where m is the slope and c is the intercept.

Compare with given equation(1) we get

[tex]m=-\frac{4}{3}[/tex]  and c=1

Now change the y intercept c=1 to a intercept of c= 2

Therefore (1) becomes

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

The above equation of the line is the parallel line to the given equation of the line

Answer:

3x - 4y = -28

Step-by-step explanation:

Based on the calculations, the interquartile range of a data set is equal to 53.

In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:

6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93

Based on the data set, the first quartile can be calculated as follows;

First quartile = [(n + 1)/4]th term

First quartile = (13 + 1)/4

First quartile = 3.5th term

First quartile = (30+9)/2

First quartile =  19.5.

For the third quartile, we have:

Third quartile = [3(n + 1)/4]th term

Third quartile = 3 × 3.5th term

Third quartile = 10.5th term

Third quartile = (75+70)/2

Third quartile = 72.5

Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:

Interquartile range of data set = Third quartile - First quartile

Interquartile range of data set = 72.5 - 19.5

Interquartile range of data set = 53.

the answer is 38

16+18+4

Answer:

46

Step-by-step explanation:

The picture are irrelevant and is used to trick you.

Let swirly hair = s

Let curly hair = c

Let flat hair = f

Ok, now we can rewrite the picture in math terms

s = 16

c = 2 + s = 2 + (16) = 18

s = 4 + f → f = s - 4 = (16) - 4 = 12

s + c + f = 16 + 18 + 12 = 46

Answer: 31.43 cm

Step-by-step explanation:

The length of an arc  is calculated using the formula:

[tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r

where : theta is the angle in degree

r = radius

If the angle is given in Radian , the length can be calculated using the formula:

L = r∅

Since , the angle is given in degree , we will use the first formula.

L = [tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r

L = [tex]\frac{120}{360}[/tex] X 2 X π X 15

L = [tex]\frac{1}{3}[/tex] X 2 X [tex]\frac{22}{7}[/tex] X 15

L = [tex]\frac{660}{21}[/tex]

L = 31.42857143

L ≈ 31.43 cm

Answer:

[tex]12x+3y\leq 60[/tex]

Step-by-step explanation:

Let

x ----> the numbers of trophies you can buy

y ----> the numbers of medals  you can buy

we know that

The term "at most" means "less than or equal to"

so

The number of trophies multiplied by $12 plus the number of medals multiplied by $3 must be less than or equal to $60

The inequality that represent this situation is

[tex]12x+3y\leq 60[/tex]

[tex]3x + 12y\leq 60[/tex]

Step-by-step explanation:

Answer:

t=44°

Step-by-step explanation:

The sum of the interior angles of any pentagon is always 540 degrees.

Let's set up an equation with this information: (all figures are in degrees)

[tex]t+3t+t+32+149+139=540[/tex]

Now we combine all like terms.

[tex]5t+320=540[/tex]

Now begin to isolate t be subtracting 320 from both sides.

[tex]5t=220[/tex]

Finally divide both sides by 5 to isolate t.

t=44°

Answer:

22 4/5 yards

Step-by-step explanation:

(7 3/5) x 3 = 22 4/5

To convert 7 3/5 feet to yards, you use the conversion 1 yard = 3 feet. After converting the mixed number to an improper fraction, you divide by 3, yielding the answer 2 8/15 yards, which corresponds to option C.

To convert feet to yards, we can use the conversion factor that 1 yard is equal to 3 feet. Since the student needs to find out how many yards are in 7 3/5 feet, we can convert mixed numbers to improper fractions to simplify the calculation.

The mixed number 7 3/5 can be converted to an improper fraction by multiplying the whole number 7 by the denominator 5 and adding the numerator 3, then placing the result over the original denominator: (7 * 5) + 3 = 35 + 3 = 38, so 7 3/5 becomes 38/5.

To convert 38/5 feet to yards, divide by 3 because there are 3 feet in 1 yard:

38/5 feet * 1 yard/3 feet = (38/5)/3 = 38/5 * 1/3

This simplifies to 38/5 * 1/3 = 38/15 yards

Then divide 38 by 15 to get 2 with a remainder of 8, so we have 2 and 8/15 yards.

Therefore, the answer is C. 2 8/15 yards.

Answer:

5 1/4 or 5.25

Step-by-step explanation:

Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.

3*7 = 21

4*1 = 4

We end up with the improper fraction 21/4. We can convert this into a mixed number.

Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25

Answer:

The solution is that there are 26 students in her class

Step-by-step explanation:

We know that 15 of her student are girls, and since there are more girls than boys in the class, there can at most be 15+14= 29 students in her class.

We need to find a number x between 16 (in the case where there is only one boy in the class) and 29, for which x/4 gives a remainder of 2, and x/5 gives a remainder of 1.

The numbers between 16 and 29, which when divided by 4 gives a remainder of 2 are:

18, 22, and 26

You can check yourself that these give a remainder of 2.

So it is one of these numbers. But the solution must also fulfill that the number divided by 5 gives a remainder of 1.

18/5 = 15 + remainder=3

22/5 = 4 + remainder=2

26/5 = 5 + remainder=1

Thus the only possible solution is 26.

To find the total number of students, we can use modular arithmetic and the Chinese Remainder Theorem. The number of students is 40k + 27, where 'k' is an integer.

To solve this problem, we can use the concept of modular arithmetic. Let's assume the number of students as 'x'. We are given that when the students are divided into groups of 4, there are 2 students left over. This can be written as x % 4 = 2. Similarly, when the students are divided into groups of 5, there is 1 student left over, which can be written as x % 5 = 1.

To find the value of 'x', we can solve these congruences simultaneously. One way to solve this is by brute force by trying different values of 'x'. However, a more efficient approach is to use the Chinese Remainder Theorem. By solving the congruences, we get x ≡ 21 (mod 20). This means that the number of students can be expressed as x = 20k + 21, where 'k' is an integer.

Since we are given that there are 15 girls and more girls than boys, we can say that the number of boys is 'x - 15'. Substituting the value of 'x' from the previous equation, we get the number of boys as 20k + 21 - 15 = 20k + 6. Therefore, the total number of students is 20k + 21 + 20k + 6 = 40k + 27.

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Answer:

[tex]3,462\ bacteria[/tex]

Step-by-step explanation:

In this problem we have a exponential function of the form

[tex]y=a(b^x)[/tex]

where

x is the time in hours

y is the numbers of bacteria

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

we have that

[tex]a=3,000\ bacteria[/tex]

For x=8, y=3,300

substitute in the exponential function

[tex]3,300=3,000(b^8)[/tex]

solve for b

[tex]1.1=(b^8)[/tex]

[tex]b=\sqrt[8]{1.1}[/tex]

[tex]b=1.0120[/tex]

Find the value of r

[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]

The equation is equal to

[tex]y=3,000(1.012^x)[/tex]

For x=12 hours

substitute the value of x in the equation

[tex]y=3,000(1.012^{12})[/tex]

[tex]y=3,462\ bacteria[/tex]

Answer:

5/3

Step-by-step explanation:

30/18=5/3

Answer:we multiply by the reciprocal of a fraction when completing a division problem because it is a rule in mathematics that when you divide two fraction, you change the division sign to multiplication and flip the fraction at the right of the multiplication sign.

Step-by-step explanation:

For example if you have 4÷ 1/2. It basically means how many 1/2 can one get in 4. And the answers is 8.

Therefore multiplying by the reciprocal of a fraction when completing a division problem is a short cut method that has been tested and proven to be correct.

For this case we can express the rates as:

[tex]\frac {2.40} {12} * \frac {dollars} {pen} = 0.2 \frac {dollars} {pen}[/tex]

Option A

[tex]\frac {12} {2.40} * \frac {pen} {dollars} = 5 \frac {pens} {dollar}[/tex]

Option C

If the pen package contains 12, then the cost of the package is $2.40.

Option B

Answer:

Option A, B, C

Answer: 1, 2, and 3

Step-by-step explanation: I did the question

If the boy has 10, and his sister has 2 1/2 times as many as him, you would first multiply 10 times 2 to get 20. After that you would automatically 1/2 of 10 is 5, which would bring you to the conclusion that his sister has 25 cookies. Thus, you answer is 25 cookies.

Answer:

25

Step-by-step explanation:

10×2.5=25

and heres some other random stuff so brainly will let me tell you this

The expression that gives the number of bacteria after 3 hours is

500 x  1.2³.

Given,

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

There were initially 500 bacteria.

We need to find an expression that gives the number of bacteria after 3 hours.

Suppose we have a number 3 that gets multiplied by 2 every 1 minute.

So in 3 minutes, we have,

3 x 2 = 6

6 x 2 = 12

12 x 2 = 24

We see that we need to multiply the previous answer by the required factor till the required number of times.

We have,

The initial number of bacteria = 500

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

This means the number of bacteria after one hour:

= 500 x 1.2

= 600 bacteria

After two hours,

= 600 x 1.2

= 720 bacteria

After 3 hours

= 720 x 1.2

= 864 bacteria

The expression that gives the number of bacteria is 500 x [tex]1.2^{h}[/tex] where h is the number of hours.

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The number of bacteria after 3 hours, given an initial count of 500 and a growth factor of 1.2 per hour, can be calculated as 500 × 1.2^3, resulting in 864 bacteria.

The number of bacteria in a petri dish growing exponentially can be modeled mathematically. If the number of bacteria is multiplied by a factor of 1.2 every hour, and we began with 500 bacteria, the expression for the number of bacteria after 3 hours can be found using exponential growth formula.

To find the number of bacteria after 3 hours, we would start with the initial amount of 500 bacteria and multiply it by 1.2 for each hour that passes. Therefore, after 3 hours, the expression would be:

Number of bacteria after 3 hours = Initial number × (growth factor)number of hours = 500 × 1.23

Using a calculator, we can compute this to find:

500 × 1.23 = 500 × 1.728 = 864

Thus, there would be 864 bacteria in the petri dish after 3 hours.

Step-by-step explanation:

A line that passes through the origin is proportional (y = mx).  But a line that doesn't pass through the origin isn't proportional (y = mx + b).  So all proportional relationships are linear, but not all linear relationships are proportional.

proportional relationship is just a linear relationship where the line passes through the origin (0, 0).

Answer:

Multiples:

2: 2 4 6 8 10 12 14 16 18 20

3: 3 6 9 12 15 18 21 24 27 30

The LCM is 6 (underlined)

Answer:

86/1

Step-by-step explanation:

Answer:

B)

Step-by-step explanation:

Do the zero property.

x-7=0, x+6=0

x=0+7=7,

x=0-6=-6

Answer:

b 100% true

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

T1 =2 , Tn = 1 /tn-1 For The Geometricseries 6 + 3 + 3/2 + 3/4 + .

Step-by-step explanation:

Answer:

2, 5, 8, 11, 14

Step-by-step explanation:

Find the first 5 terms by substituting n = 2, 3, 4, 5 into the recursive formula

t₂ = t₁ + 3 = 2 + 3 = 5

t₃ = t₂ + 3 = 5 + 3 = 8

t₄ = t₃ + 3 = 8 + 3 = 11

t₅ = t₄ + 3 = 11 + 3 = 14

The first 5 terms are 2, 5, 8, 11, 14

Check the picture below.

Answer:

520 eggs

Step-by-step explanation:

5%*2 is 10%.

10%*10 is 100%,that is the full carton of eggs.

26*2*10 is 520.

There were 520 eggs in the carton altogether.

Hope this helps :)

To find the total number of eggs in the carton, we use the information that 26 eggs (5% of the total) were broken. By solving the equation 0.05x = 26, we determine there were 520 eggs in the carton.

The question at hand is, "26 eggs in a carton were broken. This was 5% of the total number of eggs in the carton. How many eggs were in the carton altogether?"

To solve this problem, let us consider the total number of eggs in the carton as x. Given that 5% of x is equal to 26 eggs, we can write this relationship as an equation: 0.05x = 26. To find x, we divide both sides of the equation by 0.05, yielding x = 26 / 0.05. Calculating this result, we find that x = 520.

Therefore, there were 520 eggs in the carton altogether.

Answer:

The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%

Step-by-step explanation:

Given:

Total  bagels brought to school = 10

Number of Asiago cheese bagels = 7

To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.

Solution:

Let probability of choosing an Asiago cheese bagel be the successful event.

Probability of choosing one Asiago cheese bagels = [tex]\frac{7}{10}=0.7[/tex]

Probability of success = 0.7

Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]

Using Bernoulli Trials

To calculate the binomial probability of obtaining  exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:

⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]

where [tex]p\rightarrow[/tex] Probability of success

[tex]q\rightarrow[/tex] Probability of failure

Thus,  probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :

⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]

⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]

⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]

⇒ [tex]10(0.343)(0.09)[/tex]

⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)

ln z + ln 7 = ln 63

When adding two logarithms of the same base, you can combine them into a single logarithm where the input is the product of both previous inputs

ln 7z = ln 63

Take the exponential of e to both sides

7z = 63

Divide both sides by 7

z = 9

Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

Here, the "whole number" is the portion of the number to the left of the decimal point: 593.

The "remainder" is the portion left after the whole number is subtracted: 0.5625.

0+6/10+2/100+4/100

Hope this helped! (plz mark me brainliest)

The answer is 120 cubic inches.

There are 120 cubic inches contained inside the box.

The volume of space occupied by a substance or item, or the space enclosed within a container.

Volume = L * B * H (unit^3)

Given length of the cuboid = 12 inches

Given breadth of the cuboid = 5 inches

Given height of the cuboid = 2 inches

Volume of cuboid = 12 * 5 * 2 = 120 inch^3

Hence there are 120 cubic inches contained inside the box.

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