Which relationship in the triangle must be true?
sin(B) = sin(a)
sin(B) = cos(90 -B)
cos(B) = sin(180-B)
cos(B) cos(A)

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:

[tex]\bf (-3yz)(-3yz)(-3yz)(-3yz)\implies (-3yz)^1(-3yz)^1(-3yz)^1(-3yz)^1 \\\\\\ (-3yz)^{1+1+1+1}\implies (-3yz)^4\implies (-3)^4 y^4 z^4\implies 81y^4 z^4[/tex]

The expression (-3yz) (-3yz) (-3yz) (-3yz) is  (-3yz) ⁴

  ⇒(-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹=(-3yz)¹⁺¹⁺¹⁺¹

   ⇒ (-3yz)¹ (-3yz)¹ (-3yz)¹ (-3yz)¹ = (-3yz)⁴

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Answer:

1st and 3rd options

Step-by-step explanation:

We have been given three scatter plots. We are asked to choose the plots with cluster.

We know that cluster in a dot plot is formed when many data points lie in a small interval.

We can see that graphs represented by 1st option and 3rd option have many data points in a small interval, therefore, 1st and 3rd options are correct choice.

Answer:

Step-by-step explanation:

Answer:

[tex]y - 7 = \frac{1}{4}(x + 2)[/tex]

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are. Plus, perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES] so −4 becomes ¼.

I am joyous to assist you anytime.

The answer is:

The volume of the sand is approximately 0.015605 m3

To solve the problem, and find the volume of the sand that Zed purchased, we need to use the formula to calculate the density and isolate the volume from it.

So, solving we have:

[tex]density=\frac{mass}{volume}[/tex]

From the statement we know that:

The mass of the sand is 25 kg

The density of the dry sand is 1,602 kg/m3

So, substituting and solving we have:

[tex]density=\frac{mass}{volume}\\\\volume=\frac{mass}{density}\\\\volume=\frac{25kg}{1,602\frac{kg}{m^{3}}}=0.015605m^{3}[/tex]

Hence, the volume of the sand is approximately 0.015605 m3

Have a nice day!

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

Answer:

x = -5/2 y +4

Step-by-step explanation:

2x+5y = 8

Subtract 5y from each side

2x+5y -5y = -5y+8

2x = -5y+8

Divide each side by 2

2x/2 = -5y/2 +8/2

x = -5/2 y +4

Answer:

main number

Step-by-step explanation:

Final answer:

A base number in mathematics is the number raised to a power, where in scientific notation it is always 10, whereas in economic terms, a base year is a reference year for economic measurements.

Explanation:

The definition of a base number in mathematics generally refers to the number that is being raised to a certain power. In the context of scientific notation, the base number is always 10. This is used to succinctly represent very large or very small numbers in the form N x 10^n, where N is a number greater than or equal to 1 and less than 10, and n is a positive or negative integer; for example, 10^0 = 1. However, the concept of a base extends beyond just the number 10; any number can act as a base in different mathematical contexts.

When discussing numbers in a positional numeral system, the base determines the value of each digit in the number and how those digits are combined to represent the overall number. For instance, in the base-10 system, the digits 0 through 9 are used, and the position of each digit indicates how many multiples of powers of 10 it represents. Finally, in the context of economic indexes, a base year is a reference year against which economic growth or inflation is measured.

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]

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: no

Step-by-step explanation:

Linear functions are straight lines and are also written in the form y=mx+b

The linearity of 3[g(x)] = x depends on the form of g(x). If g(x) is linear, such as g(x) = ax, then the equation is linear. Otherwise, if g(x) involves non-linear operations, the overall equation will not represent a linear function.

Whether or not the equation 3[g(x)] = x represents a linear function depends on the form of g(x). If g(x) is a linear function, then the equation represents a linear transformation. If g(x) is nonlinear, then the overall function is not linear.

For example, if g(x) = exp(3x), the relationship is non-linear due to the exponential function. However, if the g(x) function is a simple linear function like g(x) = a₁x, with a constant coefficient, the equation maintains its linearity. In this scenario, the function could even represent a constant multiple of the identity function, where g(x) = x/3.

It is important to note that in the context of mathematics, understanding whether a function is linear involves recognizing if it can be written in the form of g(x) = mx + b, where m and b are constants, and the function results in a straight line on a graph.

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.

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When it asks for descending order of the polynomial it wants you to put the exponents in order from largest to smallest like so...

C. [tex]x^{12} +3x^{7} + 4x^{3}  -9x[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option C

Step-by-step explanation:

In this question the given polynomial is 4x³ + 3x⁷ - 9x + x¹²

If we rewrite it in the descending order of the powers then the polynomial will be

x¹² + 3x⁷ +4x³ + 9x

This polynomial matches with option C.

Option C is the answer.

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:

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.

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:

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:

[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:

y-intercept is [0, -4]

Step-by-step explanation:

Straight lines NEVER have rate of changes [slopes].

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:

3.5 liters

Step-by-step explanation:

2 liters + 1.5 liters = 3.5 liters

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:

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)

Answer:

40 square units

Step-by-step explanation:

The surface area is given by

LA = 2(wh+lh)

where h is the height l is the length and w is the width

We do not include the top or bottom

We know l=6 w=4 and h=2

LA = 2 ( 4*2 + 6*2)

lA = 2( 8+12)

    = 2 (20)

    = 40

Answer:

{19, 29, ... , 79, 89}

Step-by-step explanation:

Multiples of 10 are {10, 20, 30, 40, ... , 90}

Numbers which are each 1 less than these multiples of 10 would be:

                               {9, 19, 29, ... , 79, 89}.

Note that the last number, 89, is less than 91.

We must omit 9 from this set, since 9 is not a 2-digit number.  Then our final list is {19, 29, ... , 79, 89}.

Answer:

The numbers are 19,29,39,49,59,69,79,89

Step-by-step explanation:

2 digit numbers starts from 10 and ends on 99.

2 digit numbers less than 91 starts from 10 and ends at 90.

2 digit numbers less than 91 and multiple of 10 are 10,20,30,40,50,60,70,80,90.

2 digit numbers less than 91 and which are 1 less than a multiple of 10 are 19,29,39,49,59,69,79,89.

The numbers are 19,29,39,49,59,69,79,89

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: [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]

[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.

Answer:

D) 120pi yd2

Step-by-step explanation: