Which equation shows the commutative property of addition?

Answer:

(- 8, - 2)

Step-by-step explanation:

Assuming you mean the inverse function

Then any coordinate point (x, y ) in f(x) → (y, x) in the inverse

Given

(- 2, - 8 ) is on the graph of f(x), then

(- 8, - 2) is on the graph of [tex]f^{-1}[/tex](x)

The corresponding point on the graph of function f(x)-1 for a given point (-2,-8) from the graph of function f(x) is (-2, -9). All corresponding x-values remain the same, while the y-values are decreased by 1.

The given point (-2,-8) is on the graph of the function f(x). Now, you're asked to find the corresponding point for the function f(x)-1. When we modify a function like this, it affects the y-values (output) of the function. The x-values (input) remains constant.

In this case, for any x-value in the function f(x), the corresponding y-value in the function f(x)-1 is simply the y-value of f(x) minus one. So the corresponding point on the graph of f(x)-1 for the given point (-2,-8) from the graph of f(x) would be (-2, -9), because -8 (the y-value from f(x)) minus 1 equals -9 (the y-value for f(x)-1). Hence, the point (-2, -9) is on the graph of the function f(x)-1.

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Answer:

15

Step-by-step explanation:

term 1 is equal to 5.

term 2 is equal to 5  + (1)                 = 5 + 1   = 6

term 3 is equal to 6  + (1 + 2)             = 6 + 3   = 9

term 4 is equal to 9  + (1 + 2 + 3)         = 9 + 6   = 15

term 5 is equal to 15 + (1 + 2 + 3 + 4)     = 15 + 10 = 25

term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40

Vertical Angles have to be congruent and have the same vertex.

The correct options are:

B.  Have the same vertex.

C.  be congruent.

Vertical Angles--

Answer:

[tex]\large\boxed{x\approx-4.19\ \vee\ x\approx1.19}[/tex]

Step-by-step explanation:

[tex]x^2+3x-5=0\qquad\text{add 5 to both sides}\\\\x^2+3x=5\\\\x^2+2(x)(1.5)=5\qquad\text{add}\ 1.5^2=2.25\ \text{to both sides}\\\\x^2+2(x)(1.5)+1.5^2=5+2.25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1.5)^2=7.25\Rightarrow x+1.5=\pm\sqrt{7.25}\\\\x+1.5\approx\pm2.69\\\\x+1.5\approx-2.69\ \vee\ x+1.5\approx2.69\qquad\text{subtract 1.5 from both sides}\\\\x\approx-4.19\ \vee\ x\approx1.19[/tex]

Answer:

Step-by-step explanation:

A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?

f(x) = 1500(1.15)x  

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

The answer to this problem is a f(x) = 1500(2.15)x

Answer:

[tex]f(x) = 1500(2.15)^x[/tex]

Step-by-step explanation:

Let the function that represents the population of bacteria after x hours is,

[tex]f(x)=ab^x[/tex]

For x = 0, f(x) = 1500,

[tex]1500=a(1+r)^0[/tex]

[tex]1500=a[/tex]

Now, the population increases at a rate of 115% each hour,

So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,

That is, for x = 1, f(x) = 3225,

[tex]3225 =ab[/tex]

[tex]3225=1500(b)[/tex]

[tex]\implies b =2.15[/tex]

Hence, the function that represents the given scenario is,

[tex]f(x)=1500(2.15)^x[/tex]

Answer:  [tex]\bold{\dfrac{69}{16}}[/tex]

Step-by-step explanation:

[tex]4.3125=\dfrac{43125}{10000}\\\\\\\dfrac{43125}{10000}\div\dfrac{625}{625}=\large\boxed{\dfrac{69}{16}}[/tex]

Answer:Correct. He transformed the triangle according to the rule (x, y) → (-y, x).

Answer:

Option A.

Step-by-step explanation:

Consider the below diagram is attached with this question.

Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x).

From the below figure it is clear that the vertices of triangle FGH are F(3,2), G(1,2) and H(4,5).

The vertices of image after transformation are F'(-2,3), G'(-2,1) and H'(-5,4).

The relation between preimage and image is defined by the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

Since Quinton transformed the triangle according to the rule (x, y) → (–y, x), therefore he is correct.

Thus the correct option is A.

Answer:

b) 3a + 5b = 3

Step-by-step explanation:

It is an exact replica of the Standard Formula [Ax + By = C]. The Standard Formula is an example of a linear equation.

Answer:

3a + 5b = 1 is a linear equation

Step-by-step explanation:

Required?

To state which equation is linear...

An equation is said to be linear if it obeys the following.

1. For Single variables: y = b

An example is y = 4

2. For 2 Variables; it can take any of the following form: Ax + By = C.

An example 3x + 5y = 4

.from option A through D, only option B fits the description.

Note that the arithmetic sign could take the negative form and the position of x and y or any other constraints can take an interchanged forms.

The key thing to watch out when naming a linear equation is that the highest power is 1.

Hence, the 3a + 5b = 1 is a linear equation

Answer:

120°

Step-by-step explanation:

The arc ABC is twice that of the angle created at D. This is the central angle theorem extension.

So we can say that arc ABC = 2* 120 = 240

We know total circle angle is 360 degrees so, arc ADC + arc ABC = 360

Hence,

arc ADC + 240 = 360

arc ADC = 360 - 240 = 120

Answer:

0x + 2y = 22 ✔️

Step-by-step explanation:

To substract the equations, we should do the following:

5x + 4y = 25

5x + 2y = 3

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

0x + 2y = 22 ✔️

The value of y is: y = 11 ✅✅

The value of x is: x = 3.8 ✅✅

Answer:

To substract the equations, we should do the following:

5x + 4y = 25

5x + 2y = 3

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

0x + 2y = 22

Step-by-step explanation:

Answer:

5/12 ≈ 0.41667

Step-by-step explanation:

If the first die rolls a 1 and the second die rolls a 1, then the sum is 2.

If the first die rolls a 1 and the second die rolls a 2, then the sum is 3.

Repeating this, we can build a table showing all the possible outcomes:

[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]

As we can see, of the 36 possible outcomes, 15 are greater than seven.  So the probability is 15/36, which reduces to 5/12.

Mike can determine the width of his scale model car by setting up and solving a proportion. Using the ratio of the actual car's dimensions, calculate an equivalent ratio for the model. The width of the model car should be 6 inches.

To solve this problem, you can set up a proportion based on the known dimensions of the actual car and Mike's model. Given the actual car's length and width are 8 feet and 4 feet, and Mike's model length is 12 inches, we can set up the proportion like this:

8 feet : 4 feet = 12 inches : X

First, we need to convert all measurements to the same unit. Let's use inches since Mike's model is in inches (remember that 1 foot equals to 12 inches). So, the car's length is 96 inches and its width is 48 inches. Now, the proportion would be:

96 inches : 48 inches = 12 inches : X

To find the value of X (the width of the model), we can cross-multiply:

(96 * X) = (48 * 12)

Solve for X by dividing each side by 96, we get:

X = 6 inches

So, Mike's model car should be 6 inches wide to maintain the same ratio as the actual car.

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Answer:

3

Step-by-step explanation:

5x-3y=23

4x-4y=20

---------------I'm going to try to set this up for elimination. I notice the bottom equation contains terms that are divisible by 4 so I'm going to divide both sides by 4 on that last equation only...

5x-3y=23

 x-  y=  5

Now I'm going to multiply the bottom equation by -3 so the y terms will be opposite. When you add opposites you do get 0.  That is the whole point of elimination.  

5x-3y=23

-3x+3y=-15

------------------ adding

2x+0=8

2x    =8

 x    =4

So  using that second equation x-y=5 I will find y given that x=4.

4-y=5

-y =1

 y=-1

So the solution to the system is (4,-1)

You are asked to find x+y

So x+y=4+(-1)=3

Answer: AD = 5

because AB equals 10, logically we assume AD equals 5, hopefully this helps you.

Answer:

AD=5

Step-by-step explanation:

We are given that

[tex]\angle 1=\angle 2[/tex]

AB=10, AC=6 BC=6

We have to find the value of AD.

Let AD=x

BD=AB-AD

BD=10-x

By angle bisector theorem

[tex]\frac{AC}{AD}=\frac{BC}{BD}[/tex]

Substitute the values then we get

[tex]\frac{6}{x}=\frac{6}{10-x}[/tex]

[tex]\frac{10-x}{x}=\frac{6}{6}[/tex]

[tex]\frac{10-x}{x}=1[/tex]

[tex]10-x=x[/tex]

[tex]x+x=10[/tex]

[tex]2x=10[/tex]

[tex]x=\frac{10}{2}=5[/tex]

Hence, the value of AD=5 units

Answer:

m=4

Step-by-step explanation:

add 10 to both sides m-10+10=-6+10

m=4

Answer:

Step-by-step explanation:

Answer:

0 and 1 have the same y values for the x values.

Answer:

Attached below

Step-by-step explanation:

Given f(x) =1/x    and g(x) = x-2   then;

f.g (x) = f (g(x) )

         =f(x-2)

        =1/x⇒⇒⇒1/x-2

    f.g(x)    =  

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

C. to show the populations of major cities in 1500

Answer:

C. to show the populations of major cities in 1500

Step-by-step explanation:

correct on edge

Answer:

8

Step-by-step explanation:

8y-8=24

+8 +8

8y=32

32/8 = 4

y=4

4*2=8

Answer:

8

Step-by-step explanation:

8 y - 8 = 24

( + 8 )

8 y = 32

( ÷ 4 )

y = 4

Find the value of 2 y

y = 4 so 2 y = 8

Answer:

14 1/4

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

x is a tangent line, 56-7 is a secant line.  The length is equal to the outside segment times the entire segment. Notice that the length of the outside of the segment is equal to the entire segment for the tangent line.

[tex]x^2=7(56+7)\\\\x^2=7(63)\\\\x=\sqrt{7(63)}\\\\x=\sqrt{7(7\cdot 9)}\\\\x=7\cdot 3\\\\\large\boxed{x=21}[/tex]

Answer:

   = x^2 +4x +3

Step-by-step explanation:

f(x) = 2x^2 - 5

g(x) = x^2 - 4x - 8

(f - g)(x)=2x^2 -5 - (x^2 -4x-8)

Distribute the minus sign

    = 2x^2 -5 -x^2 +4x+8

Combine like terms

   = x^2 +4x +3

Answer:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Step-by-step explanation:

We have the function f(x) = x^2 − x − 12  and g(x) = x^2 − 16 and we need to find the multiplication of both functions.

f(x) × g(x) = ( x^2 − x − 12)(x^2 − 16) = x^4 - 16x^2 -x^3 + 16x -12x^2 + 192

Simplifying:

f(x) × g(x)= x^4 - x^3 - 28x^2 + 16x + 192

Answer: [tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Step-by-step explanation:

Given the function f(x) and g(x):

[tex]f(x)=x^2 - x -12\\\\g(x)= x^2 - 16[/tex]

We need to multiply them. To do this we need to remember the Product of power property, which states:

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

And the multiplication of signs:

[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]

Then:

[tex]f(x)*g(x)=(x^2 - x -12)(x^2 - 16)\\\\f(x)*g(x)=x^4-16x^2-x^3+16x-12x^2+192[/tex]

Adding like terms, we get:

[tex]f(x)*g(x)=x^4-x^3-28x^2+16x+192[/tex]

Answer:

5 blocks

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for AC

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AC² = AB² + BC² ← substitute values

AC² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

AC = [tex]\sqrt{25}[/tex] = 5

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The formula of a slope:

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

Substitute the coordinates of the given points G(-4, 1) and H(2, -2):

[tex]m=\dfrac{-2-1}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]

J(1, 3). Let other point (x, y).

Substitute to the slope:

[tex]\dfrac{y-3}{x-1}=\dfrac{-1}{2}[/tex]            cross multiply

[tex]2(y-3)=-1(x-1)[/tex]    use the distributive property

[tex]2y+(2)(-3)=-x+(-1)(-1)[/tex]

[tex]2y-6=-x+1[/tex]        add 6 to both sides

[tex]2y=-x+7[/tex]      divide both sides by 2

[tex]y=-\dfrac{1}{2}x+\dfrac{7}{2}[/tex]

Check the equality for coordinates of each point:

[tex](-3, 5)\\\\5=-\dfrac{1}{2}(-3)+\dfrac{7}{2}\\\\5=\dfrac{3}{2}+\dfrac{7}{2}\\\\5=\dfrac{10}{2}\\\\5=5\qquad\bold{CORRECT}[/tex]

[tex](1,\ 5)\\\\5=-\dfrac{1}{2}(1)+\dfrac{7}{2}\\\\5=-\dfrac{1}{2}+\dfrac{7}{2}\\\\5=\dfrac{6}{2}\\\\5=3\qquad\bold{FALSE}[/tex]

[tex](3,\ -2)\\\\-2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\-2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\-2=\dfrac{4}{2}\\\\-2=2\qquad\bold{FALSE}[/tex]

[tex](3,\ 2)\\\\2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\2=\dfrac{4}{2}\\\\2=2\qquad\bold{CORRECT}[/tex]

[tex](5,\ 1)\\\\1=-\dfrac{1}{2}(5)+\dfrac{7}{2}\\\\1=-\dfrac{5}{2}+\dfrac{7}{2}\\\\1=\dfrac{2}{2}\\\\1=1\qquad\bold{CORRECT}[/tex]

To identify which points could be on a line that is parallel to another and passes through a specific point, we need to know the slope of the original line or the coordinates of the given point. Without this information, it is impossible to accurately determine which points from the list might be on the parallel line.

The question asks, Which points could be on the line that is parallel to and passes through point J? This problem is a part of geometry in mathematics where we study about points, lines, and planes.

The location of point J was not specified, but the line that is parallel to another would have the same slope, regardless of its y-intercept. As such, to find the points that can lie on a line that is parallel, we must know the slope of the primary line. If we are given the slope 'm', any points that fall on the line would satisfy the equation of a line, y = mx + b, where 'b' is the y-intercept. The points whose 'y' value remains constant in the given x-y pairs would lie on the line parallel to the original line.

Without the proper information about the slope of the line or the position of point J, it is impossible to accurately determine which points from the given list can lie on the line that is parallel and passes through point J.

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[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{\textit{average rate of change}~\hfill }{slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}}\implies \cfrac{9-6}{-5-(-2)}\implies \cfrac{9-6}{-5+2}\implies \cfrac{3}{-3}\implies -1[/tex]

Answer:

6m

Step-by-step explanation:

The area of the rectangular plot is

A = l*w

   = 4*9

    = 36 m^2

To find the area of the square plot

A = s^2

36 = s^2

Take the square root of each side

sqrt(36) = sqrt(s^2)

6 = s

The length of the side of the square plot is 6 m

Answer:

Option C. Seven was not multiplied by 5/8

Step-by-step explanation:

we know that

To determine the height of a stack of 7 books that are each 2 5/8  inches thick. multiply 7 by 2 5/8

so

[tex]7(2\frac{5}{8})\\ \\7(2+\frac{5}{8})\\ \\7*2+7*\frac{5}{8}\\ \\14+\frac{35}{8}\\ \\14+4+\frac{3}{8}\\ \\18\frac{3}{8}\ in[/tex]

therefore

Seven was not multiplied by 5/8

Answer:

Option B.

Step-by-step explanation:

Giovanna did the calculations to determine the height of a stacks of 7 books having [tex]2\frac{5}{8}[/tex] inches thickness of each book.

[tex]7(2\frac{5}{8})[/tex]

[tex]=7(2+\frac{5}{8})[/tex]

[tex]=(7\times 2)+7(\frac{5}{8})[/tex]

[tex]=14+\frac{35}{8}[/tex]

[tex]=14+4+\frac{3}{8}[/tex]

=18+[tex]\frac{3}{8}[/tex]

[tex]=18\frac{3}{8}[/tex]

Now when compare this solution with Giovanna's solution we find error in 3rd step, in which she hasn't mutiplied the fraction [tex]\frac{5}{8}[/tex] by 7.

Therefore, option B is the correct one.