Which of the following terms best describes a condition in which a quantity
decreases at a rate that is proportional to the current value of the quantity?
O
A. Exponential growth
O
B. Positive slope
O
C. Negative slope
O
D. Exponential decay

Answer:

Step-by-step explanation:

ANSWER

Point if discontinuity:  

{x}=  \pm3

Zero of the function is  

x = 0

EXPLANATION

The given rational function is:

f(x) =  \frac{3x}{ {x}^{2}  - 9}  

This function is not continous when  

{x}^{2}  - 9 = 0

{x}=  \pm \sqrt{9}  

{x}=  \pm3

The function is zero when,

3x = 0

x = 0

Answer:

x = 0 is the zero of this function and at x = ±4 function is discontinuous.

Step-by-step explanation:

The given function is [tex]f(x) = \frac{4x}{x^{2}-16}[/tex]

For this function we have to find the discontinuity and zeros of this function.

For zeros of the function [tex]0 = \frac{4x}{x^{2}-16}[/tex]

so zero of the function is x = 0

For x² - 16 = 0 this function not defined therefore, x = ± 4 function will be discontinuous.

Finally, x = 0 is the zero of this function and at x = ±4 function is discontinuous.

Answer:

$1x + $3y = c

Step-by-step explanation:

To write an expression you need to pick a variable to represent the cups of orange juice and lemonade.

x = cups of lemonade sold

y = cups of orange juice sold

Now you have the variables to represent the amount of cups sold, so now you need a variable to represent the total cost.

c = amount of money earned from selling drinks

Now you have all the variables, so you need to write how much is cost for that drink.

$1 for one cup of lemonade so $1x

$3 for one cup of orange juice so $3x

Now put the expression together:

$1x + $3y = c

The expression that represents the amount of money that Alice selling drinks​ is $ (a+ 3b)

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

According to the problem,

Let the number of cups of lemonade sold are a and the cups of orange juice sold are b.

Cost of 1 cup of lemonade is $ 1

∴Cost of a cups of lemonade = $ a

Similarly we can say,

Cost of 1 cup of orange juice is $ 3

∴ Cost of b cups of orange juice is $ 3b

So the total cost is represented by the expression : $(a + 3b)

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Answer:

[tex]24x -{6x}^{2} = 0 \: matches \: with \: 6x(4 - x) \: and \: the \: solution \: x = 0 \ \: or \: \: x = 4[/tex]

[tex]2 {x}^{2} + 6x = 0 \: matches \: with \: 2x(x + 3) = 0 \: and \: the \: solution \: x = 0 \: or \: x = - 3[/tex]

[tex]4x - {x}^{2} = 0 \: matches \: with \: x(4 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 4[/tex]

[tex]14x - {7x}^{2} = 0 \: matches \: with \: 7x(2 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 2

[/tex]

Answer:

(A.)A computer randomly generates 6 put of 100 numbers.

Step-by-step explanation:

This is an actual probability.

Answer: (-5,8)

Step-by-step explanation: since the radius of a circle square root of 14 so

x² + y² + 10x − 16y + 75 = 0

x² +10x + y² − 16y = -75

x² +10x + 25 + y² − 16y + 64 = -75 + 25 + 64

(x + 5)² + (y − 8)² = 14

ANSWER

The center is

[tex](-5,8)[/tex]

EXPLANATION

The given circle has equation

[tex] {x}^{2} + {y}^{2} + 10x - 16y + 75= 0[/tex]

An easy way to find the center is by comparing to the general equation of the circle

[tex] {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0[/tex]

where (-g,-f) is the center.

By comparing, we have

[tex]2gx = 10x[/tex]

[tex] \implies \: 2g = 10[/tex]

Divide both sides by 2.

[tex]g = 5[/tex]

Also,

[tex]2fy = - 16y[/tex]

[tex]2f = - 16[/tex]

Divide both sides by 2

[tex]f = - 8[/tex]

Therefore the center is

[tex](-5,- - 8) = (-5,8)[/tex]

Final answer:

The expression 7x = 8 evaluated with x = 2 results in 14, not 8. There was a misunderstanding in the question as it was not asking for a solution to the equation but rather an evaluation of the expression with a given value of x.

Explanation:

The question asks us to evaluate the expression 7x = 8 when x = 2. However, there seems to be a misunderstanding in the way the question is framed. Normally, an expression such as 7x = 8 would be an equation we solve to find the value of x. But since we are given that x = 2, it appears the task is to substitute this value into the expression 7x and see if it equals 8. Let's clarify and solve accordingly.

First, substitute x = 2 into the expression 7x:

7 * 2 = 14

Therefore, when we substitute x = 2 into the expression 7x, we get 14, not 8. It seems there was confusion in the question regarding what was being asked. If the task was to solve 7x = 8, then x would not equal 2 since 7*2 = 14. However, the original instruction was misunderstood, and the correct task was to substitute x = 2 into the expression and evaluate it, which we did correctly.

Answer:

65x^2 – 26x

Step-by-step explanation:

To determine the total number of seats, take the number of rows and multiply by the number of seats per row

f(x) * g(x)

13x * (5x-2)

65x^2 -26x

Answer:d

Step-by-step explanation:A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?65x + 2665x – 2665x2 + 26x65x2 – 26x

Answer:

[x + 3][2x² - 7]

Step-by-step explanation:

Start out by doing this: [2x³ + 6x² ] - [7x - 21]

↑ ⤻ ↑

GCF: 2x² GCF: -7

Do as so: 2x²[x + 3] -7[x + 3]

You see, one factor is already found [x + 3]. You only use it ONCE. Now, the other factor comes from your two Greatest Common Factors from both groups [2x² - 7]. Together, you end up with the above answer. That arrow under the negative tells you that it is attached to the 3 [distribution of the negative].

Well, I am joyous to assist you anytime.

Answer:

488 = r

Step-by-step explanation:

362 = -126 + r

126 +126

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

488 = r

I am joyous to assist you anytime.

Answer:

The answer is c.

This is because when it rotates a 180 degrees around its center it maps a parallelogram on to itself.

Answer:

Option D is correct.

Step-by-step explanation:

Option D is correct.

y < 2 and y >= x

Because the dotted line shows that y < 2 and y >=x is shown is represented by diagonal line.

Option: D is the correct answer.

      D.    y<2   and    y≥x

The graph of the system of linear inequalities are two lines:

1)

The first is a solid line which passes through (0,0) , (1,1)

i.e. the equation of the line is: y=x

and the inequality will be a inequality with a equality sign ( since the line is solid ) and the shaded region is above the line .

Hence, the inequality is: y≥x

2)

The second line is a dotted line.

This means that the inequality is strict.

Also, the line is a horizontal line parallel to the x-axis and the line pass through (0,2) and the shaded region is below the line.

Hence, the inequality is given by:

                    y<2

Step-by-step explanation:

(f+g)(x) means f(x) + g(x).

(f−g)(x) means f(x) − g(x).

So all you have to do is add them and subtract them.

1. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (3x − 7) + (2x − 4)

(f+g)(x) = 5x − 11

2. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (3x − 7) − (2x − 4)

(f−g)(x) = 3x − 7 − 2x + 4

(f−g)(x) = x − 3

3. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (2x + 3) + (x² + ½ x − 7)

(f+g)(x) = x² + 2½ x − 4

4. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (2x + 3) − (x² + ½ x − 7)

(f−g)(x) = 2x + 3 − x² − ½ x + 7

(f−g)(x) = -x² + 1½ x + 10

Answer:

= 70 Meters

Step-by-step explanation:

We can use the sine rule as follows:

Angle ABC=180-(70.5+38.833)

=70.667°

Using the sine rule and sides AB, AC and angles ABC and ACB:

b/Sin B=c/Sin C

Replacing with the values above we get:

AC/Sin ABC= AB/Sin ACB

105.6/Sin 70.667=AB/Sin 38.833

AB=(105.6 Sin 38.833)/Sin 70.667

=70.17 meters

The distance between the two points to the nearest meter is 70 meters

Answer:

70 m

Step-by-step explanation:

I got it correct on founders edtell

Answer:

[tex]a=\pm i\sqrt{26}}[/tex]

Step-by-step explanation:

[tex]6^2+a^2=10\\\\36+a^2=10\qquad\text{subtract 36 from both sides}\\\\a^2=-26<0\\\\\bold{NO\ REAL\ SOLUTIONS}\\\\\text{In the set of complex numbers:}\\\\i=\sqrt{-1}\\\\a^2=-26\to a=\pm\sqrt{-26}\\\\a=\pm\sqrt{(-1)(26)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\a=\pm\sqrt{-1}\cdot\sqrt{26}\\\\a=\pm i\sqrt{26}[/tex]

Answer:

B.

Step-by-step explanation:

Quarterly interest rate is 4.5 / 4 = 1.125%.

Monthly rate is 4.5 / 12 = 0.375%.

Answer:

B 1.25%-0.375%

Step-by-step explanation:

Compounded quarterly means there are 4 interest periods in 1 year, so divide the annual interest rate by 4.

4.5% ÷ 4 = 1.125%

Compounded monthly means there are 12 interest periods in 1 year, so divide the annual interest rate by 12.

4.5% ÷ 12 = 0.375%

[tex]\bf \cfrac{p^{-4}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^{-7}}{p^{-2}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^{-2}}\implies \cfrac{1}{p^{4}p^{-2}p^{-2}r^7}\implies \cfrac{1}{p^{4-2-2}r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}[/tex]

Answer:

[tex]\large\boxed{r^{-7}=\dfrac{1}{r^7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{p^{-4}q^3r^{-7}}{p^{-2}q^3p^{-2}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=p^{-4-(-2)-(-2)}q^{3-3}r^{-7}\\\\=p^{-4+2+2}q^0r^{-7}\\\\=p^0q^0r^{-7}\\\\=r^{-7}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{r^7}[/tex]

Answer:

10.2 inches

Step-by-step explanation:

Ok let's assume we don't know the larger (the c value).

So this means using [tex]a^2+b^2=c^2[/tex] we have:

[tex]12^2+15^2=c^2[/tex]

[tex]144+225=c^2[/tex]

[tex]369=c^2[/tex]

Square both sides:

[tex]c=\sqrt{369} \aprox 19.2[/tex

Now assume we know the larger is 15 (this means c=15 now), then we have

[tex]a^2+12^2=15^2[/tex]

[tex]a^2+144=225[/tex]

Subtract 144 on both sides:

[tex]a^2=225-144[/tex]

Simplify:

[tex]a^2=81[/tex]

Square root both sides:

[tex]a=9[/tex]

The difference between 19.2 and 9 is 19.2-9=10.2.

Answer:

Option 1 - 10.2 inches.                            

Step-by-step explanation:

Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.

To find : What is the difference between the two possible  lengths of the third side of the triangle?

Solution :

Since, It is a right angle triangle so we apply Pythagoras theorem,

[tex]C^2=A^2+B^2[/tex]

Where, C is the hypotenuse the longer side of the triangle

A is the perpendicular

B is the base

There will be two cases,

1) Assume that C=15 inches and B = 12 inches

Substitute the value in the formula,

[tex]15^2=A^2+12^2[/tex]

[tex]225=A^2+144[/tex]

[tex]A^2=225-144[/tex]

[tex]A^2=81[/tex]

[tex]A=\sqrt{81}[/tex]

[tex]A=9[/tex]

Assume that A=15 inches and B = 12 inches

Substitute the value in the formula,

[tex]C^2=15^2+12^2[/tex]

[tex]C^2=225+144[/tex]

[tex]C^2=369[/tex]

[tex]C=\sqrt{369}[/tex]

[tex]C=19.2[/tex]

Therefore, The possible length of the third side of the triangle is

[tex]L=C-A[/tex]

[tex]L=19.2-9[/tex]

[tex]L=10.2[/tex]

Therefore, The difference between the two possible  lengths of the third side of the triangle is 10.2 inches.

So, Option 1 is correct.

Answer: 117°

Step-by-step explanation:

Use the Law of Cosines:

c² = a² + b² - 2ab · cos C

12² = 6² + 8² - 2(6)(8)(cos C)

144 = 36 + 64 - 96 cos C

144 = 100 - 96 cos C

44 = -96 cos C

[tex]-\dfrac{44}{96}=cosC\\\\\\cos^{-1}\bigg(-\dfrac{44}{96}\bigg)=C[/tex]

117° = C

Answer:

Step-by-step explanation:

[tex]f(x)=(x-6)^2(x+2)^2\to y=(x-6)^2(x+2)^2[/tex]

x-intercepts are for y = 0.

Put y = 0 to the equation:

[tex](x-6)^2(x+2)^2=0\iff(x-6)^2=0\ \vee\ (x+2)^2=0\\\\(x-6)^2=0\iff x-6=0\qquad\text{add 6 to both sides}\\\\x=6\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\x=-2[/tex]

Answer:

the awnser is 2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

for the 2 lines to be parallel, they have to have the same slope

Answer:

Some polyhedrons are both prisms and pyramids.- False

The provided statement "Some polyhedrons are both prisms and pyramids" is false.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional and three-dimensional figures.

We have a statement:

Some polyhedrons are both prisms and pyramids.

As we know,

A polygon-based solid figure is known as a polyhedron, for instance, a soccer ball, a cuboid, etc.

A strong figure with two equal bases is a prism for instance: Cube. Cylinder, Cuboid, etc.

A polyhedron with a base and an top at the top is called a pyramid, cone, a pyramid with triangles as its base, etc.

Thus, the provided statement "Some polyhedrons are both prisms and pyramids" is false.

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Answer:

Answer in picture.

Step-by-step explanation:

First step: You must plot the point (-3,5).

To graph this point, start at the origin.  

The point says move left 3 and up 5 and put your dot (your point).

Second step: Use your slope to find a second point to plot.  The slope is [tex]\frac{-1}{2}[/tex].

Slope is rise/run.  So it says down 1 and right 2.

So starting at the first point you plotted and you count down 1 and then go right 2 and put your second point.

Third step: Connect the two points with a straight-edge. Extend in both directions.

The two points I used to graph my line is (-3,5) and (-1,4).

Step-by-step explanation:

[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\Delta y-\text{run up (+) or down (-)}\\\\\Delta x-\text{run to the right (+) or to the left (-) }\\\\\text{We have}\ slope=-\dfrac{1}{2}=\dfrac{1}{-2}\to\Delta y=1\ (\text{1 unit up}),\ \Delta x=-2\ (\text{2 units to the left})\\\\\text{Mark the point (-3, 5) in the coordinates system. Go 1 unit up}\\\text{and 2 units to the left. Mark next point.}\\\text{Draw a line passing through the given points.}\\\\\bold{Look\ at\ the\ picture.}[/tex]

Answer:

a  x+2y =5

b  x=1  y=2

Step-by-step explanation:

4x+3y = 10

So the cost of 1 banana is x and the cost of 1 peach is y

a) we want the cost of 1 banana and 2 peaches

1x+2y

That is equal to 5 dollars

1x+2y =5

x+2y =5

b

The matrixes are

1   2         x              5

         *           =

4   3          y            10

Using my calculator, x=1  y=2

Answer:

[tex]\large\boxed{\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{45y}{56x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{(5)(-9y)}{(-7x)(8)}=\dfrac{-45y}{-56x}=\dfrac{45y}{56x}[/tex]

Answer:

Step-by-step explanation:

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

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

m - slope

b - y-intercept.

Put the given y-intercept b = 2 and the coordinates of the point (1, 1) to the equation:

[tex]1=1m+2[/tex]            subtract 2 from both sides

[tex]-1=m\to m=-1[/tex]

The equation of a line:

[tex]y=-1x+2\to y=-x+2[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

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

[tex]x+y=2[/tex]         subtract 2 from both sides

[tex]x+y-2=0[/tex]

The sum of the first six terms of the geometric series will be -364. Hence, option (B) will be correct.

A geometric series is a series in which the division of any consecutive two terms will be the same.

For example 3, 6, 12, 24 here if you divide 6 by 3 then it gives you 2, and if you divide 12 by 6 then also it gives you 2, and so on.

here, we have,

Given up series is 2, – 6, 18, – 54

The common ratio of this GP is -3 by that

The remaining elements of this gp will be 162, -486

So the sum will be 2 - 6 + 18 - 54 + 162 - 486 = -364 so it will the summation of the given gp.

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Answer:

the Answer is: D

Step-by-step explanation:

so that means he makes 11 dollars an hour so at most he can make that because he can work really work however long which means he can't really have less than 11 dollars an hour therefore its D

Answer:

slope is

Step-by-step explanation:

slope of line is -3

Answer:

The answer is -3.

Step-by-step explanation:

I just got it correct.

Answer:

Symbol                    Words                              Open dot or closed dot

     >                        greater than                      open dot

    [tex] \ge [/tex]                     greater than                      closed dot

                                 or equal to

    <                          less than                          open dot

    [tex] \le [/tex]                        less than                         closed dot

                                or equal to

Answer:

The domain is all real numbers and the range is non-negative real numbers

(y ≥ 0) ⇒ answer B

Step-by-step explanation:

* Lets revise the parent function of the absolute value

- The absolute value or modulus |x| of a real number x is the

  non-negative value of x

- The absolute value of a number means the magnitude of the number

  without regard to its sign

- The parent function of the absolute value is f(x) = IxI

∵ The domain of the function is all the values of x which make the

  function defined

∵ In the function f(x) = IxI, x can be any number

∴ The domain of the f(x) is any real number

∴ The domain is (-∞ , ∞) or {x : x ∈ R}

∵ The range is the set of values of y that corresponding with the

   domain

∵ f(x) = IxI is non-negative value

∴ f(x) ≥ 0

∵ f(x) = y

∴ y ≥ 0

∴ The range is the set of real numbers greater than or equal zero

∴ The range is [0 , ∞) or {y : y ≥ 0}

* The true statement is: The domain is all real numbers and the range is

  non-negative real numbers (y ≥ 0)