What is the greatest common factor of 8m, 36m3, and 12

Logarithm functions are the inverses of exponential function.In the given graphs the graph number 2 is plotted with the above points. Hence the option 2 is correct.

The function given in the question is,

[tex]f(x)=log_3x[/tex]

Logarithm functions are the inverses of exponential function.

To plot the graph of the given function we have to find the asymptotes;

vertical asymptote  [tex]x=0[/tex]

Find the points at [tex]x=1[/tex]

[tex]f(0)=log_3(0)[/tex]

[tex]f(0)=0[/tex]

Find the points at [tex]x=3[/tex]

[tex]f(3)=log_3(3)[/tex]

[tex]f(0)=1[/tex]

Find the points at [tex]x=9[/tex]

[tex]f(9)=log_3(9)[/tex]

[tex]f(9)=2[/tex]

Hence, the points for the given function are (1,0) (3,1) and (9,2).

In the given graphs the graph number 2 is plotted with the above points. Hence the option 2 is correct.

Learn more about the Logarithm functions, here;

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Answer:

x = 6

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x, that is

sin30° = [tex]\frac{AB}{AC }[/tex] = [tex]\frac{x}{12}[/tex]

Multiply both sides by 12

12 × sin30° = x, hence

x = 6

Answer:

0

Step-by-step explanation:

We find the determinant of a matrix by the method below. If we have a matrix:

[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

The determinant is [tex]ad-bc[/tex]

Now, using cramer's rule, we find x-value by the formula:

[tex]x=\frac{D_x}{D}[/tex]

Where D is the determinant of the original problem and [tex]D_x[/tex] is the determinant of the x-value matrix. How do we get those?

To get original matrix and thus D, we set up the matrix as the coefficients of x and y (s) of both the equations and to get matrix of x-value and thus [tex]D_x[/tex], we replace the x values of the matrix with the numbers in the right hand side of the 2 equations. We show this below:

To get D:

[tex]\left[\begin{array}{cc}3&4\\1&-6\end{array}\right] \\D=(3)(-6)-(1)(4)=-18-4=-22[/tex]

To get [tex]D_x[/tex]:

[tex]\left[\begin{array}{cc}12&4\\-18&-6\end{array}\right] \\D_x=(12)(-6)-(-18)(4)=0[/tex]

Putting into the formula, we get:

[tex]x=\frac{D_x}{D}=\frac{0}{-22}=0[/tex]

Thus, the value of x is 0

The triangles cross the center of the circle CAD is the same as CBD.

The answer is B) 40 degrees.

Answer:

90

Step-by-step explanation:

The formula for right triangular prisms is simple; 1/2 × a × b × c. So simply plug in your numbers (doesn't matter the order you plug in).

1/2 × 12 × 5 × 3 = 90

Answer:90

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{4}{5}[/tex] and (a, b) = (9, - 1), hence

y - (- 1) = [tex]\frac{4}{5}[/tex](x - 9), that is

y + 1 = [tex]\frac{4}{5}[/tex](x - 9) ← in point- slope form

Answer:

WoodChuck-Prairie Dog

WoodChuck-Beaver

WoodChuck-Chipmunk

PrairieDog-Beaver

PrairieDog-Chipmunk

Beaver-Chipmunk

Answer:

A chipmunk and a beaver

Answer:

a=3

b=12

c=13

Step-by-step explanation:

(see attached)

The value of 'a' is 3, 'b' is 12, and 'c' is 13 and this can be determined by using the arithmetic operations.

Given :

Expression -  [tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}=2^c[/tex]

The value of a, b, and c can be determined by following the below calculations:

[tex]\dfrac{2^5\times 8^4}{16}=\dfrac{2^5\times (2^a)^4}{2^4}[/tex]

Further, simplify the above expression:

[tex]\dfrac{2^5\times (2^3)^4}{2^5}=\dfrac{2^5\times (2^a)^{4}}{2^4}[/tex]

the above equation holds good when the value of 'a' is 3.

[tex]\dfrac{2^5\times 8^4}{2^4}=\dfrac{2^5\times 2^b}{2^4}[/tex]

Further, simplify the above expression:

[tex]\dfrac{2^5\times 2^{12}}{2^5}=\dfrac{2^5\times 2^b}{2^4}[/tex]

the above equation holds good when the value of 'b' is 12.

[tex]\dfrac{2^5\times 2^{12}}{2^5}=2^c[/tex]

Further, simplify the above expression.

[tex]\dfrac{2^{17}}{2^4}=2^c[/tex]

[tex]2^{13}=2^c[/tex]

the above equation holds good when the value of 'c' is 13.

For more information, refer to the link given below:

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Step-by-step explanation:

y = x - 2

x + y = 12

Substitute the first expression for y into the second equation.

x + (x - 2) = 12

2x - 2 = 12

2x = 14

x = 7

Now plug into either equation to find y.

y = 7 - 2

y = 5

So the solution is (7, 5).

Answer: I believe the last numbers are $3.40 and $2.75

Step-by-step explanation:

5.35 minus 4.70 equals 0.65 and that is continually going so you should subtract each number by 0.65 to get the next. If that makes sense

Final answer:

The cost for Mrs. Beusse to buy 100 personalized pencils is $405.00.

Explanation:

According to the chart, the cost of pencils depends on the number of pencils being purchased. For 1-20 pencils, the cost is $5.35 each. For 21-40 pencils, the cost is $4.70 each. For 41-60 pencils, the cost is $4.05 each. Since Mrs. Beusse needs to buy 100 personalized pencils, we need to determine which price range this falls into. 100 pencils falls within the range of 81-100, so the cost per pencil will be $4.05.

Therefore, the total cost for 100 personalized pencils will be $4.05 x 100 = $405.00.

Answer:

1. k(x) = (3g + 5h)(x) = -24x+40

2. k(x) = (h - g)(x)  = 0

3. k(x) = (g + h)(x) = -6x+10

4. k(x) = (5g + 3h)(x) = -24x+40

5. k(x) = (3h - 5g)(x) = 6x-10

6. k(x) = (5h - 3g)(x) = 10-6x

Step-by-step explanation:

Given

h(x) = 5 - 3x

and

g(x) = -3 x + 5

1. k(x) = (3g + 5h)(x)

3*g(x) = 3(-3 x + 5)

=> -9x+15

5*h(x) = 5(5 - 3x)

=>25-15x

(3g + 5h)(x)=3*g(x)+5*h(x)

= -9x+15+25-15x

=-9x-15x+15+25

=-24x+40

2. k(x) = (h - g)(x)

(h - g)(x) = h(x) - g(x)

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

=5-3x+3x-5

= 0

3. k(x) = (g + h)(x)

(g+h)x = g(x) + h(x)

= -3 x + 5 + 5 - 3x

= -6x+10

4. k(x) = (5g + 3h)(x)

5*g(x) = 5(-3 x + 5)

=-15x+25

3*h(x) = 3(5 - 3x)

=15-9x

(5g + 3h)(x) = 5*g(x) + 3*h(x)

= -15x+25+15-9x

= -15x-9x+25+15

=-24x+40

5. k(x) = (3h - 5g)(x)

(3h - 5g)(x) = 3*h(x)-5*g(x)

=15-9x-(-15x+25)

=15-9x+15x-25

=-9x+15x+15-25

=6x-10

6. k(x) = (5h - 3g)(x)

5*h(x)-3*g(x) = 25-15x - (-9x+15)

= 25-15x+9x-15

= 25-15-15x+9x

=10-6x

Answer:

1. k(x) = (5g + 3h)(x) ---------------- 5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x) ---------------- 6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ---------------- 1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x) ----------------- 3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x) ----------------- 2. k(x)=3^x-3x

6. k(x) = (g + h)(x) ----------------- 4. k(x)=10-3^x-3x

Answer:

B. 1.81

Step-by-step explanation:

Simply divide [tex]\frac{6.98}{3.86}[/tex] to get [tex]1.8082...[/tex].

This is closer to [tex]1.81[/tex] than it is to [tex]1.80[/tex], so that is how it is rounded.

Then, you have your answer.

Answer:

Step-by-step explanation:

You need an x value to determine what number to multiply that will give you three numbers that are in the ratio of 3:1:4

Let the number = x

Set the equation up as 3x + x + 4x = 500

3x + x + 4x = 500           Combine the left

8x = 500                         Divide both sides by 8

x = 500/8                        Divide by 8.  

x = 62.5

So 3x = 3*62.5 = 187.5

1x       = 1 * 62.5 =  62.5

4x      = 4 * 62.5 = 250    The total should be 500

Answer:

{187.50, 62.50, 250}

Step-by-step explanation:

Add up the numbers in the ratio:  Add up 3, 1 and 4.  We get 8.

Then we divide up 500 into eight parts, each 62.5.

The ratio we are to follow is 3:1:4.

3 parts of 62.5 each comes out to 187.5;

1 part of 62.5 each comes out to      62.5; and

4 parts of 62.5 each comes out to 250.

If we have done this correctly, these 3 results add up to 500:

187.50

 62.50

250

-------------

   500

So, 500 divided up in the ratio 3:1:4 is {187.50, 62.50, 250}

Answer: THIRD OPTION.

Step-by-step explanation:

Given the trapezoid in the figure, you know the coordinates of  two points:

(0,c) and (a,b)

You can observe that the point (a,b) and the point P have the same x-coordinate, because both points are "a" units from the origin.

Then, the x-coordinate of P is:

[tex]x=a[/tex]

Now, in order to find the y-coordinate of the point P, you need to remember that when the line touches the x-axis, the value of "y" is equal to zero. Therefore, the y-coordinates of the point P is:

[tex]y=0[/tex]

Then the answer is:

[tex](a,0)[/tex]

Answer: 14.9

I have to write this in order to have enough characters.

7.45 divided by 0.5 equals 14.9. This is calculated by converting the divisor 0.5 to a whole number and doing the same operation on the dividend, then performing the division.

Dividing Decimals

To find what 7.45 divided by 0.5 is, one approach is to think of 0.5 as one-half, so you are essentially finding out how many halves there are in 7.45. Another way to approach this is to manipulate the numbers to make the division easier. Since 0.5 is equivalent to the fraction 1/2, dividing by 0.5 is the same as multiplying by 2 (which is the reciprocal of 0.5). Here are the steps to perform the division:

Therefore, 7.45 divided by 0.5 equals 14.9.

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Answer: 72and 108

Step-by-step explanation: that is the correct answer don’t be a fool

Answer:

the answer is that D is false

Step-by-step explanation:

the relative frequency chart shows that 0.35 of her total freshman and sophomores take biology (Bottom left corner of the chart).

Answer: D

Step-by-step explanation: Apex said so

Answer: $82,975.68 APEX

Everywhere you see x in the equation replace it with 1 like so...

3(1) + y = 5

3 + y = 5

Finish isolating y. To do this first subtract 3 to both sides (what you do on one side you must do to the other). Since 3 is being added, subtraction (the opposite of addition) will cancel 3 out (make it zero) from the left side and bring it over to the right side.

3 - 3 + y = 5 - 3

0 + y = 2

When x is 1 then y is 2

Check:

3(1) + 2 = 5

3 + 2 = 5

5 = 5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y=2

Step-by-step explanation:

3x + y =5

3(1) + y = 5

3 + y = 5

5-3= y which is 2

The answer is:

[tex]f(3)=|x|+(-2x^{2})=-15[/tex]

Evaluating a function means replacing the variable with the given value (3 for this case).

To evaluate the function, we need to remember that the absolute value guarantees a possitive value, for example:

[tex]|-3|=3\\|-4|=4[/tex]

So, we are given the function:

[tex]f(x)=|x|+(-2x^{2})[/tex]

Then, evaluating we have:

[tex]f(3)=|3|+(-2*(3)^{2})=3+(-2*9)=3-18=-15[/tex]

Hence, the answer is:

[tex]f(3)=|x|+(-2x^{2})=-15[/tex]

Have a nice day!

Answer:

с. 57°

Step-by-step explanation:

The measure of the exterior angle of a triangle is equal to sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

57° is the value of y.

A triangle has three sides, three angles, and three vertices. The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle. The sum of the length of any two sides of a triangle is greater than the length of the third side

Given

The measure of the exterior angle of a triangle is equal to the sum of the opposite interior angles

114 = y+y

114 = 2y

Divide by 2

114/2 = 2y/2

57 =y

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Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x

The number of students in his class be y

According to the question he gave every student 4 pieces in the class

The pieces he gave to everyone become 4y.

Note that 4 here means he had given four to each

and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y....

Answer:

B (6,12)

Step-by-step explanation:

The distance from point A (6,5) to point B should be 7.

A- (6,5)-> (7,5) is 1 unit right

B- (6,5)-> (6,12) is 7 units up

C- (6,5)-> (6,7) is 2 units up

D- (6,5)-> (12,5) is 6 units up

Answer:

51 in² is the area of the shape.

Step-by-step explanation:

Note that there is a triangle, as well as a Parallelogram.

First, solve for the measurement for the Parallelogram. The Parallelogram has sides that measure 6 in. & 7 in. respectively.

Note the measurement of the left length, which is 13. The right length is 7. To solve for the length of the triangle, subtract the two:

13 - 7 = 6

The triangle length is 6.

To solve for the triangle width, subtract the part from the total:

6 - 3 = 3

The triangle width is 3.

Note that the area of the triangle is found using the formula: Area = 1/2base x height (or length x width). Plug in the corresponding numbers to the corresponding variable.

A = 1/2(3)(6)

A = (3)(3)

A = 9

The triangle's area is 9 in².

Solve for the area of the parallelogram:

6 x 7 = 42

The parallelogram's area = 42 in².

Add the two measurements together:

42 + 9 = 51

51 in² is the area of the shape.

~

The above composite shape can be divided into :

●  A Rectangle with Length 7 in. and Width 6 in.

●  A Right angled Triangle with base 3 in. and height 6 in.

Let us first find the Area of Rectangle :

We know that - Area of a Rectangle is given by : Length × Width

[tex]:\implies[/tex]  Area of Rectangle = (7 × 6) in²

[tex]:\implies[/tex]  Area of Rectangle = 42 in²

Now, Let us find the Area of Right angled Triangle :

[tex]\mathsf{We\;know\;that - Area\;of\;a\;Triangle\;is\;given\;by : \dfrac{1}{2} \times base \times height}[/tex]

[tex]\implies \mathsf{Area\;of\;Right\;angled\;Triangle = \dfrac{1}{2} \times 3 \times 6\;(in^2)}[/tex]

[tex]:\implies[/tex]  Area of Right angled Triangle = (3 × 3) in²

[tex]:\implies[/tex]  Area of Right angled Triangle = 9 in²

Area of the Composite shape :

●  Area of Rectangle + Area of Right angled Triangle

[tex]:\implies[/tex]  Area of the Composite shape = (42 + 9) in²

[tex]:\implies[/tex]  Area of the Composite shape = 51 in²

Answer:

Your answer would be A

Step-by-step explanation:

First you gotta reduce that fraction. Then square root the 9 (which is 3) and as well as radicalize x^5, which is x^2/x

Answer:

FIRST OPTION.

Step-by-step explanation:

Given the expression [tex]\sqrt{\frac{2x^5}{18}}[/tex], you can find an equivalent expression simplifying.

The first step is to descompose 18 into its prime factors:

[tex]18=2*3*3=2*3^2[/tex]

Remember the Product of powers property, which states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then you can rewrite the expression in this form:

 [tex]\sqrt{\frac{2x^4x}{2*3^2}[/tex]

Knowing that [tex]\sqrt[n]{a^n}=a[/tex], you get the following equivalent expression:

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

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

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

Answer:

5n=1125

n=225 students in the school.

Answer:

The answer is 225.

Step-by-step explanation:

The explanation is in the top.

Answer:

-x

Step-by-step explanation:

You can distribute:

(x + 3)(x – 4)

x (x + 3) – 4(x + 3)

x² + 3x – 4x – 12

x² – x – 12

Or you can use FOIL (first, outer, inner, last).

(x + 3)(x – 4)

x² – 4x + 3x – 12

x² – x – 12

Answer: r = -10

Step-by-step explanation:

Move variable to the left , collect like terms, then divide both sides by 2.

Answer:

r = -10

Step-by-step explanation:

Your equation is 6r = 4r - 20

To solve this equation, find out r's value.

To do that, you must get r alone on one side of the equation

6r = 4r - 20

[Subtract 4r from both sides]

2r = -20

[Now divide both sides by 2]

r = -10

So, the answer to this equation is r = -10

I hope this helps! :)

Answer:

4  1/4

Step-by-step explanation:

Complementary angles add up to 90 degrees.

Thus if 12q - 9 and 8q + 14 are complementary,

12q - 9 + 8q + 14 = 90.

Combining like terms, we get:

20q + 5 = 90

20q = 85

Thus, q = 85/20, or 17/4, or 4  1/4

Answer:

42 and 48

Step-by-step explanation:

∵ Two angles are complementary to each other if their sum is 90°,

Given,

12q - 9 and 8q + 14 are complementary angles,

By the above statement,

12q - 9 + 8q + 14 = 90

Combine like terms,

20q + 5 = 90

Subtract both sides by 5,

20q = 85

Divide both sides by 20,

q = 4.25,

Thus, the angles are,

12(4.25) - 9 and 8(4.25) + 14

⇒ 42 and 48