describe the domain and range of y=2(3)^x-2+5

The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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A triangle has three sides, three angles, and three vertices (also known as corners).

A triangle is a geometric shape that consists of three line segments that connect three non-collinear points.

Each of these line segments is called a side of the triangle. The three points where these sides meet are called the vertices (singular: vertex) of the triangle.

The triangle also has three interior angles formed by its sides. These angles are located inside the triangle, and their sum is always equal to 180 degrees.

In summary, a triangle is defined by its three sides, three angles, and three vertices.

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Answer:

Step-by-step explanation:

Answer: 11 yds

Step-by-step explanation: 1 yd=3 ft

Answer:

11 yards is the correct answer

Step-by-step explanation:

a yard = 3 feet

33/3 = 11 yards

Answer:

See below ~

Step-by-step explanation:

Unit Conversion :

1 quart = 2 pints

1 quart = 4 cups

He wants the 3 quart birdbath to be 3/4 filled.

Hence,

He can fill it with 4.5 pints and using cups :

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

B. -pi/6

Step-by-step explanation:

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:  The Answer Is A Because if u just add the numbers then divide them

The solution of the system of equations is (8, 2).

Given is a system of equations x-2y = 4 and x+3y = 14, we need to find the solution of the system of equations,

So, the equations are =

x-2y = 4

x = 2y + 4......(i)

x+3y = 14

x = -3y + 14..........(ii)

Equating the equations since their LHS is same,

2y + 4 = -3y + 14

5y = 10

y = 2

Put y = 2 in any equation to find the value of x,

So,

x = 2(2)+4

x = 8

Hence the solution of the system of equations is (8, 2).

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Answer:

k=77

steps:

k/11=7

k=7*11

k=77

Answer:

Step-by-step explanation:

\(\tt \cfrac{k}{11} =7\)

The opposite of division is multiplication, so we need multiply both sides by 11:-

\(\tt \cfrac{k}{11}\times 11 =7\times 11\)

\(\tt k=7\times 11\)

\(\tt k=77\)

______________________

Hope this helps! :)

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

h230  8.0 mol =h2330

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

2(H2) + 02 -> 2(H2O) this is a correct balanced equation

now to solve for grams of H20 with 8 grams of O2 you must turn 8 grams O2 into moles then use the coefficients of the O2 and the H2O, then turn moles of H2O into grams of H20.

8 grams O2 x 1 mol O2 / 32 grams O2 (molar mass)

2 mol H20 (coefficients) / 1 mol O2 (coefficients)

18.02 grams H2O (molar mass) / 1 mol H20

this is 9 grams H20

If you need more help, don't hesitate to ask!

May I have brainliest please?

the answer is 11+4+2=17  

\(\large\huge\red{\sf{➡ANSWER ⤵}}\)

Answer:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Step-by-step explanation:

A two-digit number can be written as:

a*10 + b

Where a and b are single-digit numbers.

a is the tens digit

b is the units digit.

the reverse number is:

b*10 + a

We know that:

"If you add the digits together and multiply the result by 10, you will get 9 more than the reverse number"

Then:

(a + b)*10 = b*10 + a + 9

We now need to solve this for a and b, where the other restriction that we have is that a and b can be any whole number of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Then:

(a + b)*10 = b*10 + a + 9

a*10 + b*10 = b*10 + a + 9

subtracting b*10 in both sides, we get:

a*10 = a + 9

solving this for a, we get:

a*10 - a = 9

a*(10 - 1) = 9

a*9 = 9

a = 9/9

a = 1

and notice that we do not have any restriction for b.  So b can be any number of the set.

for example, if b = 2

a*10 + b = 12

now let's test the property:

10*(1 + 2) = 2*10 + 1 + 9

30 = 20 + 10 = 30

now if b = 4, we have:

a*10 + b = 1*10 + 4 = 14

10*(1 + 4) = 4*10 + 1 + 9

50 = 50

So we can see that for any value of b, this will work.

So the only restriction that we have, is that a must be equal to 1.

Then the numbers are:

10, 11, 12, 13, 14, 15, 16, 17, 18, 19

The possible numbers are 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19

Assume the digits of the two-digit number are x and y, where:

So, the original number (n) is:

\(n = 10 \times x + y\)

When the digits are added, and multiplied by 10, we have the following equation:

\((x + y) \times 10 = 9 + (y \times 10 + x)\)

Expand the equation

\(10x + 10y = 9 + (10y + x)\)

Remove bracket

\(10x + 10y = 9 + 10y + x\)

Subtract 10y from both sides

\(10x = 9 + x\)

Subtract x from both sides

\(9x = 9\)

Divide both sides by 9

\(x = 1\)

Recall that the number is represented as:

\(n = 10 \times x + y\)

So, we have:

\(n = 10 \times 1 + y\)

\(n = 10 + y\)

This means that, the possible numbers are from 10 to 19

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We have to find the equation of the line that passes through the points (-1, -8) and (3, 4).

We can calculate the slope m as:

Then, we can write the equation in slope-point form as:

In this form, the equation does not match any of the options, but if we use the other point (3,4) to write the equation, we get another version:

This match the first option.

Answer: y - 4 = 3(x - 3)

9514 1404 393

Answer:

  (a) 11·10^21

Step-by-step explanation:

"Scientific notation" has a mantissa that has one digit to the left of the decimal point. The number 11·10^21 has two digits to the left of the decimal point, so is not in the form required by scientific notation.

  11·10^21 is not in scientific notation

_____

It would be correctly written in scientific notation as as 1.1·10^22.

Answer:

A) 11 ⋅ 10^21

Answer: y

Step-by-step explanation:

For this, you would just add everything and then tag a y on the end.

3y-10y=-7y

-7y+y= -6y (y is the same thing as 1y)

-6y+7y= 1y which is just y

It is important to understand that you can only do this with like terms. So for example if you were asked to simplify:

5x+2x+3y+5y

the answer would be 7x+8y (you cannot combine x and y)

Hope this helps :)

Answer: y

Step-by-step explanation: I personally like to combine all the +y values first, which is equal to 11y. And then I minus 10y.

Answer:

Step-by-step explanation:

Let P be the population of the community

So the population of a community increase at a rate proportional to the number of people present at a time

That is

\(\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0\)

Solve this equation we get

\(p(t)=p_0e^{kt}---(1)\)

where p is the present population

p₀ is the initial population

If the  initial population as doubled in 5 years

that is time t = 5 years

We get

\(2p_o=p_oe^{5k}\\\\e^{5k}=2\)

Apply In on both side to get

\(Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}\)

Substitute \(k=\frac{In2}{5}\)  in \(p(t)=p_oe^{kt}\) to get

\(\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}\)

Given that population of a community is 9000 at 3 years

substitute t = 3 in \({p(t)=p_oe^{\frac{In2}{5}t }}\)

\(p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8\)

Answer:

69

Step-by-step explanation:

Answer:

-3/5

Step-by-step explanation:

Just ask.

Hope this helps! :)

The perimeter of Sam's string is 178 inches.

Given information:

Sam has a rectangular shaped window.

Length = 65 inches.

Width = 24 inches.

To find the perimeter:

you can use the formula:

Perimeter = 2 x (Length + Width)

Substituting the values into the formula, we have:

Perimeter = 2 x (65 + 24)

Perimeter = 2 x 89

Perimeter = 178 inches

Therefore, the perimeter of the rectangular window is 178 inches.

So, the perimeter of the rectangular window is 178 inches. This means that if you were to walk along the outline of the window, you would cover a total distance of 178 inches. It's important to note that the perimeter represents the total length of all the sides combined, and it is measured in the same unit (in this case, inches) as the length and width of the window.

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Answer:

The answer is 3

Step-by-step explanation:

- 3 in

3 out

The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

x - 2y = -8

2y = x + 8

y = x/2 + 4

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

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