What is the domain of the of the exponential function shown below?

Answer:

[tex]\frac{1}{3a}[/tex]

Step-by-step explanation:

Given

[tex]\frac{a-3}{15a}[/tex] × [tex]\frac{5}{a-3}[/tex]

Cancel the factor (a - 3) on the numerator and denominator

Cancel the 5 and 15 by dividing both by 5, leaving

[tex]\frac{1}{3a}[/tex]

Answer:  The required answer is [tex]\dfrac{1}{3a},~a\neq 3.[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=\dfrac{a-3}{15a}\times\dfrac{5}{a-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since (a - 3) is present in both numerator and denominator, so we can divide them if

[tex]a-3\neq 0\\\\\Rightarrow a\neq 3.[/tex]

Then, we get from (i) that

[tex]P\\\\\\=\dfrac{(a-3)}{15a}\times\dfrac{5}{(a-3)}\\\\\\=\dfrac{5}{15a}\\\\\\=\dfrac{1}{3a}.[/tex]

Thus, the required answer is [tex]\dfrac{1}{3a},~a\neq 3[/tex]

Answer:

You can find the quotient of the expression in the images below, together with more information and a full analysis

(2x^4-3x^3-3x^2+7x-3)/(x^2-2x+1)

Answer:

The quotient is: 2x^2+x-3

Step-by-step explanation:

we need to divide (2x^4-3x^3-3x^2+7x-3) by (x^2-2x+1)

The division is attached in the figure below.

The quotient is: 2x^2+x-3

The remainder is: 0

The statement that is true in every aspect regarding his claim is:

The series is given as:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9[/tex]

which could also be written by:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n(\dfrac{1}{3})^n\cdot 3^2[/tex]

i.e.

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{-n}\cdot 3^2\\\\\\\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=\sum_{n=0}^{3} (-1)^n\cdot 3^{2-n}[/tex]

which is not equivalent to: [tex]\sum_{n=0}^{3} 3^{2-n}[/tex]

Since,  on expanding the actual series we get the sum as:

[tex]\sum_{n=0}^{3} (-\dfrac{1}{3})^n\cdot 9=(-\dfrac{1}{3})^0\cdot 9+(-\dfrac{1}{3})^1\cdot 9+(-\dfrac{1}{3})^2\cdot 9+(-\dfrac{1}{3})^3\cdot 9\\\\\\=9-\dfrac{1}{3}\times 9+\dfrac{1}{3^2}\times 9-\dfrac{1}{3^3}\times 9\\\\\\=9-3+1-\dfrac{1}{3}\\\\\\=\dfrac{22}{3}[/tex]

Now, the expansion of:

[tex]\sum_{n=0}^{3} 3^{2-n}[/tex] is:

[tex]\sum_{n=0}^{3} 3^{2-n}=3^2+3^1+3^0+3^{-1}\\\\\\=9+3+1+\dfrac{1}{3}=\dfrac{40}{3}[/tex]

Answer:

D in short

Step-by-step explanation:

Ed2021

Answer:

25 - y

Step-by-step explanation:

"subtract" = "-"

"subtract y" means to "- y"

"from 25" implies that 25 is in the front.

Put the phrases together:

"subtract y from 25" = 25 - y

25 - y is your answer.

~

First you add all the numbers together. So you add 82+93+75+89 to get 339. Once you get that, you divide it by the amount of numbers there are. In this case, it's 4. 339 divided by 4 is 84.75.

HOPE THIS HELPS!!

Answer:

The average of the John scores is 84.75.

Step-by-step explanation:

Formula of average is given as :

[tex]A=\frac{\text{Sum of all the terms}}{\text{Number of terms}}[/tex]

We have:

Test grades of John: 82, 93, 75, and 89

Number of terms - 4

Average of the score of the John;

[tex]a=\frac{82 + 93 +75 + 89}{4}=84.75[/tex]

The average of the John scores is 84.75.

And so your answer should be 60 inches, hope this helps c:

Answer: Its B

Step-by-step explanation:

Answer:

1st option

Step-by-step explanation:

By observation, we can see that the graph crosses the y-axis at y = -2. Therefore the y-intercept is -2.

we can also see that the graph intersects the axes at  (0,-2) and (3,0)

the formula for a linear slope when given two points (x1, y1) and (x2,y2) is given by :

m = (y2 - y1) / (x2 - x1)

In our case, x1 = 0, y1 = -2, x2= 3 and y2 = 0

hence m = (0 - (-2)) / (3-0) = 2/3

Hence the slope is 2/3

Only option 1 satisfies the values for both y-intercept and slope that we calculated.

Answer:

A) The slope is 2/3 and the y intercept is -2

Step-by-step explanation:

This is the correct answer for edge

Answer:

First subtract 7 from each side of the equation

Step-by-step explanation:

2x+7 = 13

First subtract 7 from each side of the equation

2x+7 -7 = 13-7

2x = 6

Next divide each side by 2

2x/2 = 6/2

x=3

Answer:

X=3

The answer should have a positive sign.

Step-by-step explanation:

First, you subtract by 7 both sides of equation.

2x+7-7=13-7

Simplify.

13-7=6

2x=6

Then, divide by 2 both sides of equation.

2x/2=6/2

Simplify, to find the answer.

6/2=3

X=3 is the correct answer.

Answer:

B. 11x^2 − x + 10

Step-by-step explanation:

(5x^2 + 2x + 1) + (6x^2 − 3x + 9)

I like to line them up vertically

  (5x^2 + 2x + 1)

+ (6x^2 − 3x + 9)

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

11 x^2  -  x   + 10

Answer:

The answer is B

Step-by-step explanation:

75 + x = 90

First, Virginia had to write an equation to solve for x.

75 - 75 + x = 90 - 75

Second, Virginia used the subtraction property of equality to isolate x.

x = 15

Third, "x = 15" was the answer Virginia got after subtracting 90 and 75.

75 + 15 = 90

Finally, she had to verify her answer

Answer:

The Multiplication  property

Step-by-step explanation:

The Multiplication  property by a constant was used

For real numbers a and b, and c different from zero:

If c is positive and [tex]a <b[/tex] then [tex]a*\frac{1}{c} <b*\frac{1}{c}[/tex].

If c is negative and [tex]a <b[/tex] then [tex]a*\frac{1}{c} >b*\frac{1}{c}[/tex].

In this case we have

[tex]5x<100[/tex]  Then  [tex]\frac{5}{5}x<\frac{100}{5}[/tex]

Finally

[tex]x<20[/tex]

Answer:

answers in pictures

Step-by-step explanation:

The greatest common factor of group 1 will be 2x so option C is correct.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution of the given equation will be as follows:-

=  2x² + 6x + 5x + 15

=  2x ( x + 3 )  + 5 ( x + 3 )

=  ( x + 3 ) ( 2x + 5 )

We can see in the second step the first group have a common factor of 2x.

Therefore greatest common factor of group 1 will be 2x so option C is correct.

To know more about quadratic equations follow

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[tex]x^2-9x+14 =x^2-2x-7x+14=x(x-2)-7(x-2)=(x-7)(x-2)[/tex]

Answer:

(x - 7)(x - 2)

Step-by-step explanation:

Consider the factors of the constant term (+ 14) which sum to give the coefficient of the x- term (- 9)

The factors are - 7 and - 2, since

- 7 × - 2 = + 14 and - 7 - 2 = - 9, hence

x² - 9x + 14 = (x - 7)(x - 2) ← in factored form

Answer:  b) 18.37

Step-by-step explanation:

Since the intial t-value is 1960 and the final t-value is 1990, then t = 30

[tex]P(30)=\dfrac{100}{1+400\cdot e^{-0.15(30)}}\\\\\\.\quad =\dfrac{100}{1+400\cdot e^{-4.5}}\\\\\\.\quad =\dfrac{100}{1+400(0.0111)}}\\\\\\.\quad =\dfrac{100}{1+4.4436}}\\\\\\.\quad =\dfrac{100}{5.4436}}\\\\\\.\quad =\boxed{18.37}[/tex]

Answer:

4x² - 4xy + y²

Step-by-step explanation:

For clarity it is essential that you use (2x - y)^2 or (2x – y)² to indicate the square of (2x - y).

Since we're squaring (2x - y), we expect 3 terms in the expansion.

(2x - y)(2x - y) = 4x^2 - 4xy + y^2, or 4x² - 4xy + y²

Next time you see "the following," please share the answer choices.  Thank you.

Answer:

The value of k =3

Step-by-step explanation:

[tex]x^2+y^2-6y-12=0[/tex] We need to solve this equation to become in standard form to find the value of k.

[tex]x^2+y^2-6y-12=0\\x^2+y^2-6y = 12\\(x)^2 +(y^2-2(y)(3)+(3)^2) = 12 +(3)^2\\(x)^2+(y-3)^2 = 12+9\\(x)^2 +(y-3)^2 = 21[/tex]

The given standard form is:

[tex]x^2+(y-k)^2=21[/tex]

Comparing it with [tex](x)^2 +(y-3)^2 = 21[/tex]

The value of k =3

Answer:

k = 3

Step-by-step explanation:

Equation of the given function has been given as x² + y² - 6y - 12 = 0.

We have to convert this equation in the standard form of x² + (y - k)² = 21 to get the value of k.

x² + y² - 6y - 12 = 0

x² + y² - 6y + 9 - 9 - 12 = 0

x² + [y²- 2(3y) + 3²] - 21 = 0

x² + (y - 3)²- 21 = 0

x² + (y - 3)² = 21

Now by comparing this equation with the standard form of the equation we get the value of k = 3

Answer:

Answer is (c) knowing that it is going to rain tomorrow, and going to bed before 9

Step-by-step explanation:

Because they are not related in any way, going to bed early doesn't effect the weather.

Option C, knowing that it is going to rain tomorrow, and going to bed before 9 p.m, represents independent events as the outcome or occurrence of one does not affect the other probabilistically.

The question at hand is asking which of the provided options are examples of independent events. In probability theory, independent events are those whose occurrence or outcome does not affect the probability of the other occurring. Going through the options provided:

It's essential to differentiate between events that may logically seem connected and those that truly affect each other's outcomes in the context of probability theory.

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Answer:

35 cubic inches

Step-by-step explanation:

V= lwh

1*5*7= 35

Answer:

The answer is 35 cubic inches.

Step-by-step explanation:

For volume problems (with prisms, such as cardboard boxes) all you have to do is multiply all the dimensions, height, width, and length.

Answer:

0.65 > 3/5

Step-by-step explanation:

3/5 is 0.6 in fraction form

0.65 is greater than 0.6.

Therefore, 0.65 is greater than 3/5.

hope this helps!

Answer:

B. Pythagorean triple

Step-by-step explanation:

To prove Pythagorean triple, we must prove that

ML² + LN² = MN²

or MN = √( ML² + LN²)

= √( 9² + 12²)

= √( 81 + 144)

= √( 225)

= 15 = value of MN given in diagram (proven)

4/6 divided by 2/6 is 2.

you multiply the 4/6 by 6/2 to get 24/12. You then simplify it and get 2 as your answer.

Answer:

Part 1)

a.1) The central angle of pentagon is 72°

a.2) The central angle of hexagon is 60°

a.3) The central angle of decagon is 36°

a.4) The central angle of dodecagon is 30°

b.1) The measure of each interior angle of pentagon is 108°

b.2) The measure of each interior angle of hexagon is 120°

b.3) The measure of each interior angle of decagon is 144°

b.4) The measure of each interior angle of dodecagon is 150°

Part 2) The central angle and the interior angle are supplementary angles

Part 3) As the number of sides increases, the central angle decreases and the interior angle increases.

Step-by-step explanation:

Part 1. For each polygon, include the following information in the paragraph box below:

a) What was the central angle you used to locate the vertices? Show your calculation.

we know that

To find the central angle divide 360 degrees by the number of sides of the polygon

case a.1) Pentagon

The pentagon has 5 sides

so

The central angle is equal to

360°/5=72°

case a.2) Hexagon

The pentagon has 6 sides

so

The central angle is equal to

360°/6=60°

case a.3) Decagon

The pentagon has 10 sides

so

The central angle is equal to

360°/10=36°

case a.4) Dodecagon

The pentagon has 12 sides

so

The central angle is equal to

360°/12=30°

b) What is the measure of each interior angle of the polygon? Show your calculation

we know that

The sum of the interior angle of the polygon is equal to

S=(n-2)*180°

where

n is the number of sides

To find each the measure of each interior angle, divide the sum of the interior angles by the number of sides

case b.1) Pentagon

The pentagon has 5 sides

so

S=(n-2)*180°

S=(5-2)*180°=540°

Divide by the number of sides

The measure of each interior angle is equal to

540°/5=108°

case b.2) Hexagon

The hexagon has 6 sides

so

S=(n-2)*180°

S=(6-2)*180°=720°

Divide by the number of sides

The measure of each interior angle is equal to

720°/6=120°

case b.3) Decagon

The hexagon has 10 sides

so

S=(n-2)*180°

S=(10-2)*180°=1,440°

Divide by the number of sides

The measure of each interior angle is equal to

1,440°/10=144°

case b.4) Dodecagon

The hexagon has 12 sides

so

S=(n-2)*180°

S=(12-2)*180°=1,800°

Divide by the number of sides

The measure of each interior angle is equal to

1,800°/12=150°

Part 2. What is the relationship between the central angle and the interior angle?

we know that

The sum of the central angle plus the interior angle is equal to 180 degrees

therefore

The central angle and the interior angle are supplementary angles

Verify

Pentagon

72°+108°=180°

Hexagon

60°+120°=180°

Decagon

36°+144°=180°

Dodecagon

30°+150°=180°  

Part 3. As the number of sides increases, how do the angles change?

we know that

As the number of sides increases, the central angle decreases and the interior angle increases.

Answer:

The profit after 4 seasons is 14.938 units

Step-by-step explanation:

To quickly solve this problem, we can use a calculator or any graphing tool

to examine both graphs

Revenue

t(x)=5x

Cost

r(x)=(1.5)^x

Profit

P = Revenue - costs = t(x) -r(x)

P = 5x - (1.5)^x

The profit after 4 seasons is 14.938 units

Answer:

14.9

Step-by-step explanation:

Answer: Infinitely many

Step-by-step explanation:

First simplify the right side by adding 5 and 2

now you have the equation 4y+7=7+4y

That is the exact same thing so any number works.

just to add to the great reply above.

[tex]\bf \begin{matrix} 4y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}+7=5+2~~\begin{matrix} +4y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\implies 7=7[/tex]

whenever you end up with something like 0 = 0, or 7 = 7, is a flag that both equations are exactly the same, in this case, the one on the right-hand-side is really the one one the left-hand-side in disguise.

So the graph of one, is the same as the graph of the other, or put in another words, let's say the graph the first one, the second one when graphed, will just be pancaked on top of the first one, and any point whatsoever on the second one, matches with the first one, and since both lines continue infinitely, then infinitely many solutions.

Answer:

Step-by-step explanation:

She has a total of 3 + 3 + 2 choices which is 8

She chooses the first one that has 3 members in it.

3/8 is the probability of that fact.

She chooses the second one from a group that also has 3 members only now there are only 7 choices total. That fact is

3/7

So your total probability is

3/8 * 3/7 = 9/56

Those two numbers are prime to one another.

Answer:

The corresponding point is (-4.-1)

Step-by-step explanation:

we know that

The point (-4,2) is on the graph of f(x)

so

For x=-4

f(x)=2

therefore

For x=-4

-(1/2)f(x)=-(1/2)*2=-1

The corresponding point is (-4.-1)

[tex]3\div\dfrac{1}{2}=3\cdot2=6[/tex]

Answer:

6

Step-by-step explanation:

3 divided by 1/2

To solve this first put a 1 as the denominator for the 3 to make it a fraction

3/1 divided by 1/2

To divide fraction you need to change the division sign to a multiplication sign and the second fraction into its reciprocal

3/1*2/1

Now multiply across

6/1 which is also 6

Answer:

The two cars will be almost 188 miles far from each other.

Step-by-step explanation:

Travel Time for Car 1 = t = 3.5 hours

Travel time for Car 2 = t-1 = 3.5 - 1 = 2.5 hours

Average speed of car 1 = 40 mph

Average speed of car 2 = 50 mph

Distance traveled by Car 1 = 40*3.5 = 140 miles

Distance Traveled by Car 2 = 50*2.5 = 125 miles

As both the roads are at a 90 degree angle. The path of the two cars and the joining line of their final position forms a right angle triangle where:

altitude = a = 140

base = b = 125

Distance of cars after 3.5 hours = c = ?

According to Pythagoras theorem:

c^2 = a^2 + b^2

c^2 = 140² + 125²

c² = 19600+15625

c = √35225

c = 187.68

Almost 188 miles.

Answer:

I attach the missing image from your question.

To easily solve this question, we must realize that the graph of the relation is very similar to that of the expression

y = √(x-a) , where a>0

If we take a look at the image attached, we have plotted the graph of

y = √(x-1) , and its correspondent inverse function.

This means that the answer is the first option

Answer:

x=-6

Step-by-step explanation:

The axis of symmetry is the lowest (or highest) point.  It is the line where it becomes the mirror image.

Looking at the graph, this is the line x=-6

x = -6