Is abc~def? If so, identify the similarity postulate or theorem that applies.

Answer: [tex]\bold{64g^9h^6k^{12}}[/tex]

Step-by-step explanation:

[tex]\text{Apply the product rule:} (a^b)^c=a^{b*c}\\\\(4g^3h^2k^4)^3\\\\=4^{(1*3)}g^{(3*3)}h^{(2*3)}k^{(4*3)}\\\\=4^3g^9h^6k^{12}\\\\=64g^9h^6k^{12}[/tex]

Answer:  15,600,000

Step-by-step explanation:

26 x 25 x 24 =15,600 combinations of letter with no repeats

10 x 10 x 10 = 1000 with repeating numbers

15,600 x 1000 = 15,600,000

The total number of possible license plates is 26*25*24*10*9*8.

The number of possible license plates with no repeated letters can be calculated by multiplying the number of choices for each position. Since no letter can be repeated, the choices for the first position would be 26 letters, then 25, and then 24 for the three positions. For the digits, there are 10 choices for each position.

So, the total number of possible license plates would be 26*25*24*10*9*8.

Answer:

2.44x10^-9

1.05x10^-6

3.75x10^4

1.49x10^5

3.81x10^8

Final answer:

Values in scientific notation are ordered by their exponent values. First, compare the sign and size of the exponents, and then compare the coefficients if necessary. The ordered values from least to greatest are: 2.44 x 10^-9, 1.05 x 10^-6, 3.75 x 10^4, 1.49 x 10^5, 3.81 x 10^8.

Explanation:

To order the given values in scientific notation from least to greatest, we look at the exponent to determine their relative sizes. The values with negative exponents will be smaller than those with positive exponents, and among those with the same sign exponents, the one with the smaller absolute value of exponent is smaller. Then we compare the coefficients if necessary, that is if the exponents are the same.

[tex]2.44 x 10^-9[/tex]

[tex]1.05 x 10^-6[/tex]

[tex]3.75 x 10^4[/tex]

[tex]1.49 x 10^5[/tex]

[tex]3.81 x 10^8[/tex]

Answer:

1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.

Step-by-step explanation:

A number cubed is x^3. Difference of this and 1 is x^3 - 1.

Finall we have 1/2 of this:

= 1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.

Answer:

[tex]\frac{x^3-1}{2}[/tex]

Step-by-step explanation:

We must follow what the statement asks us, starting from the last thing and going forward from there.

A number cubed: [tex]x^3[/tex]

The difference of a number cubed and one: [tex]x^3-1[/tex]

And finally:

one-half of the difference of a number cubed and one, this would be one half of the expression we already found:

[tex]\frac{x^3-1}{2}[/tex]

Answer:

[tex]s\geq 4\ cm[/tex]

Step-by-step explanation:

we know that

[tex]s(V)=\sqrt[3]{V}[/tex]

where

s is the side length, in units, of a cube

V is the volume of a cube in cubic units

For a [tex]V=64\ cm^{3}[/tex]

substitute in the formula

[tex]s=\sqrt[3]{64}[/tex]

[tex]s=4\ cms[/tex]

If Jason wants to build a cube with a minimum of 64 cubic centimeters

therefore

the minimum length side of the cube is 4 cm

[tex]s\geq 4\ cm[/tex]

Answer:

The graph that represent direct variation in the attached figure

Step-by-step explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

The graph that represent direct variation in the attached figure

Answer:

option d

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Find out the total value of each option and see which one gives a total of $3.60

For A, 12 nickels + 12 dimes = 12 x $0.05  + 12 x $0.10 = $1.80 ≠ $3.60

For B, 24 nickels + 24 dimes = 24 x $0.05  + 24 x $0.10 = $3.60 (correct)

For C, 36 nickels + 36 dimes = 36 x $0.05  + 36 x $0.10 = $5.40 ≠ $3.60

For D, 48 nickels + 48 dimes = 48 x $0.05  + 48 x $0.10 = $7.20 ≠ $3.60

Answer:

For my opinion, the best option it B.

Answer:

x=7

Step-by-step explanation:

The other angle is equivalent to 45 degrees. According to the 45-45-90 triangle theorem, the hypotenuse is a times the square root of 2 and the legs are equivalent to a. In this scenario a is equivalent to 7. X is another leg and therefore is also 7.

Given.

6a - 5b

Plug in values.

6(-3) - 5(4) =

-18 - 20 =

-38

For this case we have the following expression:

[tex]6a-5b[/tex]

We must evaluate the expression when:

[tex]a = -3\\b = 4[/tex]

Then, replacing the values we have:[tex]6 (-3) -5 (4)[/tex]

Taking into account that according to the law of the signs of multiplication, it is fulfilled that:

[tex]+ * - = -[/tex]

So:

[tex]-18-20 =[/tex]

Equal signs are added and the same sign is placed:

-38

Answer:

-38

[tex] \frac{7}{8} \times 24 = 21 \\ [/tex]

You multiply 7/8 to the number of hours in a day which 24

Gerard's baby brother sleeps for 7/8 of the day, which equals 21 hours when calculated (7/8 * 24 hours).

Gerard's baby brother spends 7/8 of his day sleeping.

To calculate how many hours this is, we need to know how many hours there are in a full day.

A full day has 24 hours. So, we multiply 7/8 by 24 to find out the total hours spent sleeping.

Here's the step-by-step calculation:

Therefore, Gerard's baby brother sleeps for 21 hours a day.

For this case we must multiply the following expression:

[tex]\sqrt [3] {x ^ 2} * \sqrt [4] {x ^ 3}[/tex]

By definition of properties of otencias and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

We rewrite the terms of the expression:

[tex]\sqrt [3] {x ^ 2} = (x ^ 2) ^ {\frac {1} {3}} = (x ^ 2) ^ {\frac {4} {12}}\\\sqrt [4] {x ^ 3} = (x ^ 3) ^ {\frac {1} {4}} = (x ^ 3) ^ {\frac {3} {12}}[/tex]

So, we have:

[tex](x ^ 2) ^ {\frac {4} {12}} * (x ^ 3) ^ {\frac {3} {12}} =[/tex]

Applying the above definition we have:

[tex]\sqrt [12] {(x ^ 2) ^ 4} * \sqrt [12] {(x ^ 3) ^ 3} =[/tex]

We multiply the exponents:

[tex]\sqrt [12] {x ^ 8} * \sqrt [12] {x ^ 9} =[/tex]

We combine using the product rule for radicals.

[tex]\sqrt [12] {x ^ 8 * x ^ 9} =[/tex]

By definition of multiplication properties of powers of the same base, we put the same base and add the exponents:

[tex]\sqrt [12] {x ^ {8 + 9}} =\\\sqrt [12] {x ^ {17}} =\\\sqrt [12] {x ^ {12} * x ^ 5} =\\x \sqrt [12] {x ^ 5}[/tex]

Answer:

Option C

Answer:

its c

Step-by-step explanation:

Answer:  the answer would be -1/11

Step-by-step explanation: the reason being the slope of the green is a negative slope because it is going down ward not upwards therefore it is negative and because the the lines are parallel they are equal so the slope of both lines are -1/11

Answer:

Dimetri says that a function that is made of terms

where the variable is raised only to an odd power

will be an odd function. Do you agree with

Dimetri?

Step-by-step explanation:

If g is an odd function and f is an odd function then g ◦ f is odd.

g ◦ f (x) = g (f (x)) = g (−f (−x)) = −g (- (- f (−x))) = −g (f (−x)) = - g ◦ f (−x)

The answer is: No, I am not agree with Dimetri, statement is false because there are so many counterexamples.

Answer:

Sample Response: He is correct only if there is no constant term. −x to an odd power is −x, so the signs will change on the terms with the variable but not on the constant term.

Step-by-step explanation:

Answer:

D. (-∞,4]

Step-by-step explanation:

The range is the y values

The lowest y values is negative infinity

The highest y values is 4

( - inf, 4]

We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4

For this case we have:

[tex]10 ^ {- 20}[/tex], we must run the decimal point 20 spaces to the left.

[tex]0.00000000000000000010 \ kg[/tex]

[tex]10 ^ {- 12}[/tex], we must run the decimal point 12 spaces to the left.

[tex]0.000000000010 \ kg[/tex]

Thus, it is observed that the mass of a small virus is smaller!

We subtract and obtain:

[tex]10 ^ {-11}[/tex]

ANswer:

The mass of a small virus is less!

Answer: -10kg

Step-by-step explanation:

10-20 =-10

10-22 =-12

-10 is lesser

Answer:I think that in this problem you need a right angle with a circle in it

Answer:

[tex]\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points from the graph (-5, 2) and (5, -1).

Substitute:

[tex]m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}[/tex]

We have the equation in form:

[tex]y=-\dfrac{3}{10}x+b[/tex]

Put the coordinates of the point (5, -1) to the equation:

[tex]-1=-\dfrac{3}{10}(5)+b[/tex]

[tex]-1=-\dfrac{3}{2}+b[/tex]

[tex]-\dfrac{2}{2}=-\dfrac{3}{2}+b[/tex]            add 3/2 to both sides

[tex]\dfrac{1}{2}=b\to b=\dfrac{1}{2}[/tex]

let's bear in mind that perpendicular lines have negative reciprocal slopes...... hmmmm what's the slope of the given line anyway?

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{4-(-4)}\implies \cfrac{1+3}{4+4}\implies \cfrac{4}{8}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]

so, we're really looking for a line whose slope is -2 and runs through (-4 , 3)

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-2[x-(-4)] \implies y+3=-2(x+4) \\\\\\ y+3=-2x-8\implies y=-2x-11[/tex]

Answer:

4

Step-by-step explanation:

When multiplying, the greatest common factor of each is four.

8= 4 x 2

36= 4 x 9

The greatest common factor (GCF) of 8 and 36 is 4. The correct option is  B.

GCF stands for "Greatest Common Factor." It refers to the largest positive integer that divides evenly into two or more given numbers. In other words, the GCF is the largest number that is a factor of all the given numbers.

Finding the GCF is useful in various mathematical operations, such as simplifying fractions, finding equivalent fractions, or solving equations. It helps in identifying common factors and simplifying calculations.

To find the GCF, you can identify the common factors of both numbers and determine the largest one they share.

The factors of 8 are 1, 2, 4, and 8.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The largest factor that both 8 and 36 share is 4.

Therefore, the greatest common factor of 8 and 36 is 4.

To learn more about the greatest common factor click:

https://brainly.com/question/2352983

#SPJ6

Answer:

3.5 liters

Step-by-step explanation:

2 liters + 1.5 liters = 3.5 liters

Answer:

x = 12

Step-by-step explanation:

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

Distribute

5x - 30 = 2x + 6

Put like terms on each side by subtracting both sides by -2x and adding 30 on each side

3x = 36

Simplify

3x/3 = 36/3

x = 36/3

x = 12

Plug is back in to check

5(12) - 30 = 2(12) + 6

60 - 30 = 24 + 6

30 = 30

Answer:

x=12

Step-by-step explanation:

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

Distribute

5x-30 = 2x+6

Subtract 2x from each side

5x-2x -30 = 2x-2x+6

3x-30 =6

Add 30 to each side

3x-30+30 = 6+30

3x=36

Divide each side by 3

3x/3 = 36/3

x =12

Answer: The difference cannot be found because the indices of the radicals are not the same.

Step-by-step explanation:

To find the difference you need to subtract the radicals. But it is important ot remember the following: To make the subtraction of radicals, the indices and the radicand must be the same.

In this case you have these radicals:

[tex]\sqrt[ {8ab}^{3} ]{{ac}^{2} }- \sqrt[ {14ab}^{3}]{{ac}^{2} }[/tex]

You can observe that the radicands are the same, but their indices are not the same.

Therefore, since the indices are different you cannot subtract these radicals.

Answer:

-6

Step-by-step explanation:

The formula for finding the rate of change is:

[tex]Rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]

The interval is [1,5]

So, a = 1 and b=5

[tex]f(1) = 17 - (1)^2\\ =17-1\\=16\\f(5) = 17-(5)^2\\=17-25\\=-8[/tex]

Putting in the values

[tex]Rate\ of\ change = \frac{f(5)-f(1)}{5-1} \\=\frac{-8-16}{5-1}\\= \frac{-24}{4}\\ =-6[/tex]

The average rate of change is -6 ..

Answer:

-6

Step-by-step explanation:

For this case we have the following equation:

[tex]-2 (x + 5) = - 2 (x-2) +5[/tex]

We apply distributive property to the terms within parentheses:

[tex]-2x-10 = -2x + 4 + 5[/tex]

We add similar terms to the right side of the equation:

[tex]-2x-10 = -2x + 9[/tex]

We add 2x to both sides of the equation:

[tex]-10 = 9[/tex]

Equality is not fulfilled, so the equation has no solution.

Answer:

It has no solution

Answer: Yuto's equation has no solution.

Step-by-step explanation:

To find the solution  to Yuto’s equation, you need to solve for the variable "x":

Apply Distributive property:

[tex]-2(x+5)=-2(x-2)+5\\\\-2x-10=-2x+4+5\\\\-2x-10=-2x+9[/tex]

Add [tex]2x[/tex] to both sides of  the equation:

[tex]-2x-10+2x=-2x+9+2x\\\\0x-10=9\\\\-10=9\ (False)[/tex]

Therefore, the equation has no solution.

Answer:

y-intercept is [0, -4]

Step-by-step explanation:

Straight lines NEVER have rate of changes [slopes].

To find the mean you must add all the numbers together then divide the sum by the total amount of numbers in the data set

71 + 92 + 94 + 93 + 98 + 85 + 66 + 70 + 68 + 93 + 87 + 71 + 85 + 52 + 61 + 62 + 85 + 69 + 95 + 79 = 1576

There are at total of 20 numbers in this data set so you must divide 1576 by 20

1576 / 20 = 78.8

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

A

Step-by-step explanation:

We can see that the slope is positive, which means that the x-term must be positive.

If you expand and simply both equations into the form y = mx + b, you will find that m is positive for A and negative for B, hence A is the correct answer.

Answer:

6 + 2[x - 1) , where x > 0. I think.

Answer:

f(x) = 6+2Lx-1), where x > 0

Step-by-step explanation:

To answer this you need to understand two things, variables and constants, the constant price of the shipping is $6 so that is a constant, now the company would charge you with $2 for every fraction or pound extra over the one pound that you are charged for the $6, so your variable is the weight of the package, and this will be expressed by X

So the function would look like this:

[tex]f(x)= 6+ 2(x-1) when x > 0[/tex]

If the weight of your package is less than oneyou´d just pay the 6 bucks, since when the weight is bigger than 1 pound you would pay 2 extra bucks, you just need yo know how many extra buck you´ll pay that´s why it´s expressed with the Lx-1)

The expression 81x⁴ - 1  can be factored completely by identifying it as a difference of squares. First, factor it into (9x² + 1)(9x² - 1) and then further factor (9x² - 1) into (3x + 1)(3x - 1). The final factored form is (9x² + 1)(3x + 1)(3x - 1).

We are given the expression 81x⁴ - 1 and need to factor it completely. This is a difference of squares, which can be written as:

The difference of squares formula is a²- b² = (a + b)(a - b). Applying this formula, we get:

Next, notice that 9x²- 1 is also a difference of squares:

Again using the difference of squares formula, we get:

Putting everything together, the complete factorization of 81x⁴ - 1 is:

Answer:

1/6

Step-by-step explanation:

there are 6 dresses altogether and 1 blue dress.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

We have been given that Maria has three red dresses, 2 white dresses, and one blue dress. We are asked to find the probability that Maria will wear a blue dress at her party.

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]

We know that number of blue dresses is 1, so number of favorable outcomes is 1.

Total dresses = 3 Red dresses + 2 White dresses + 1 Blue dress = 6 dresses.

[tex]\text{Probability that Maria will wear a blue dress at her party}=\frac{1}{6}[/tex]

Therefore, our required probability is [tex]\frac{1}{6}[/tex].