Write two and thirty-one hundredths as a decimal number.
A) 0.231
B) 2.031
C) 2.31
D) 231.00

Answer:

x = e^2 = 7.39

Step-by-step explanation:

We have been given the logarithmic equation;

6+In x=8

The first step is to subtract 6 on both sides of the equation;

6 + ln x - 6 = 8 - 6

ln x = 2

We then introduce the exponential function, since the exponential function and the natural log function are inverses of each other;

[tex]e^{lnx}=e^{2}\\\\x=e^{2}=7.38906[/tex]

Answer:

Step-by-step explanation:

6 + ln(x)  = 8

ln(x) = 8 - 6

ln(x) = 2

x = [tex]e^{2}[/tex]

x = 7.38905609893

x = 7

Answer:

3²

Step-by-step explanation:

Add the indices together

3⁸ ₓ 3⁴ = 3¹²

3² ₓ 3⁸ = 3¹⁰

Now we minus the indices since we are dividing

3¹² - 3¹⁰ = 3²

Answer:

Option B is correct

Step-by-step explanation:

Given:

f(x) = -20x^2 +14x +12 and

g(x) = 5x - 6

We need to find f/g and state its domain.

f/g = -20x^2 +14x +12/5x - 6

Taking -2 common from numerator:

f/g = -2(10x^2 - 7x - 6) / 5x -6

Factorize 10x^2 - 7x - 6= 10x^2 - 12x +5x -6

Putting in the above equation

f/g = -2(10x^2 - 12x +5x -6)/ 5x -6

f/g = -2(2x(5x-6) + 1 (5x-6)) / 5x-6

f/g = -2 ( (2x+1)(5x-6))/5x-6

cancelling 5x-6 from numerator and denominator

f/g = -2(2x+1)

f/g = -4x -2

The domain of the function is set of all values for which the function is defined and real.

So, our function g(x) = 5x -6 and domain will be all real numbers except x = 6/5 as denominator will be zero if x=5/6 and the function will be undefined.

So, Option B is correct.

ANSWER

-4x-2; all real numbers except x=6/5

Option B is correct.

EXPLANATION

The given functions are:

[tex]f(x) = - 20 {x}^{2} + 14x + 12[/tex]

We factor to get,

[tex]f(x) = - 2(10 {x}^{2} - 7x - 6)[/tex]

Split the middle term:

[tex]f(x) = - 2(10 {x}^{2} + 5x - 12x - 6)[/tex]

[tex]f(x) = - 2(5x(2{x} + 1)- 6(2x + 1))[/tex]

[tex]f(x) = - 2(2{x} + 1)(5x - 6)[/tex]

and

[tex]g(x) = 5x - 6[/tex]

[tex]( \frac{f}{g} ) = \frac{f(x)}{g(x)}[/tex]

[tex]( \frac{f}{g} ) = \frac{ - 20x + 14x + 12}{5x - 6}[/tex]

where 5x-6≠0

x≠6/5

[tex]( \frac{f}{g} ) = \frac{- 2(2{x} + 1)(5x - 6)}{5x - 6}[/tex]

Cancel the common factors to get,

[tex]( \frac{f}{g} ) = - 2(2{x} + 1)[/tex]

[tex]( \frac{f}{g} ) = - 4{x} - 2[/tex]

Answer:  $277.91

Step-by-step explanation:

The average of the 2 highest salaried quarters is:

[tex]\dfrac{\$13,500+\$12,775}{2}=\dfrac{\$26,275}{2}=\$3,137.50[/tex]

Divide that by 26 (weeks) to find out her average weekly salary:

[tex]\dfrac{\$3,137.50}{26}=\$505.29[/tex]

Multiply that by 55% (0.55) to calculate her weekly unemployment benefit:

[tex]\$505.29(0.55)=\$277.908[/tex]

Round to the nearest penny --> $277.91

Answer:

y = 3x-9

Step-by-step explanation:

y = -1/3 x +2

The slope is -1/3

We want a line perpendicular to it

Perpendicular lines have negative reciprocal slopes

The new slope is -(-3/1) = 3

We have a slope  m=3 and a point (5,6)

We will use point slope form to find the line

y-y-1 = m(x-x1)

y-6 = 3(x-5)

In slope intercept form

Distribute

y-6 = 3x-15

Add 6 to each side

y-6+6 = 3x-15+6

y = 3x-9

Answer:

[tex]x_1=i\sqrt{7}[/tex]

[tex]x_2=-i\sqrt{7}[/tex]  

Step-by-step explanation:

Given the equation [tex]x^2=-11+4[/tex], you need to solve for the variable "x".

You can follow this steps:

Step 1: you need to make the addition indicated in the equation:

[tex]x^2=-7[/tex]

Step 2: Apply square root to both sides of the equation:

[tex]\sqrt{x^2}=\±\sqrt{-7}[/tex]

[tex]x=\±\sqrt{-7}[/tex]

Step 3: Since [tex]i=\sqrt{-1}[/tex], then you need to rewrite it as:

[tex]x=\±i\sqrt{7}[/tex]

Therefore the solutions are:

[tex]x_1=i\sqrt{7}[/tex]

[tex]x_2=-i\sqrt{7}[/tex]

Answer:

3/11

Step-by-step explanation:

A ratio for 3 cups to 8 cups is written as 3:8.

To turn this into a fraction, you must put the first number over the sum of both numbers.

3/3+8

3/11

Answer:

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Step-by-step explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

  = √25(1-sin^2t)

   = 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t  in given rectangular equation, we get

y= -3(2-t) +4

 = -6+3t+4

 = -2+3t !

Answer:

C

Step-by-step explanation:

ln 1 = 0, so f(1) = 0 + 2 = 2.  So we need to find a graph that passes through (1, 2).  Only graph C fits.

The graph of the function f(x) = In x + 2 is the graph b

The parent function for the natural log function is f(x) = ln(x).

To transform the graph of f(x) = ln(x) to the graph of f(x) = ln(x) + 2, we perform the following transformation:

Vertical Shift:

The graph is shifted two units upward.

This is because adding 2 to the output of the function has the same effect as shifting the graph two units upward.

So, the graph of f(x) = In x + 2 is b

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She is 3 years older than her brother and has (x+3) in the equation means that x is being used as her brothers age. (She is adding 3 to her brothers age)

The answer is Amy's brother's age.

Answer:

B

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

let's take a peek, we have two fractions, let's get the LCD of all fractions, in this case the LCD of 2 and 5, hmmmm that'd be 10.

now, let's multiply both sides by the LCD of 10 to do away with the denominators and proceed.

[tex]\bf \cfrac{x}{2}+\cfrac{2x}{5}=18\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{x}{2}+\cfrac{2x}{5} \right)=10(18)}\implies 5x+4x=180 \\\\\\ 9x=180\implies x=\cfrac{180}{9}\implies x=20[/tex]

Using the Pythagorean theorem, given a right triangle with one leg 20 m and the hypotenuse 25 m, the length of the other leg is approximately 15 m.

To find the length of the third side of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, if the lengths of the two legs are a and b, and the hypotenuse is c, the theorem is expressed as a^2 + b^2 = c^2.

Since we know the length of the hypotenuse (25 m) and one leg (20 m), we need to find the length of the other leg. Let's denote it as b. Therefore, the equation will be 20^2 + b^2 = 25^2. Solve for b, we get b = sqrt(25^2 - 20^2), which equals approximately 15 m.

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Final answer:

To find the correct product of (5x − 11)² , apply the squaring of a binomial formula to get an expanded form 25x² − 110x + 121.

Explanation:

The student is asked to find the correct product of the expression (5x − 11)² . To solve this, we can apply the squaring of a binomial rule, which is an application of the distributive property (also known as the FOIL method for binomials). According to this rule, the square of a binomial (a − b)² is equal to a² − 2ab + b² .

Substituting 5x for a and 11 for b, we get:

(5x)² = 25x²  (the square of the first term)

2 × 5x × 11 = 110x (double the product of the two terms)

11² = 121 (the square of the second term)

Putting it all together:

(5x − 11)² = 25x − 110x + 121

This is the expanded form of the given expression.

[tex]\bf \textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 75\cdot 2\implies 150\qquad \qquad \qquad \cfrac{150}{2}\implies 75 \\\\[-0.35em] ~\dotfill\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-cos(150^o)}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1-\left( -\frac{\sqrt{3}}{2} \right)}{2}}[/tex]

[tex]\bf sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{\frac{2+\sqrt{3}}{2}}{2}} \\\\\\ sin\left( \cfrac{150^o}{2} \right)=\pm\sqrt{\cfrac{2+\sqrt{3}}{4}}\implies sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill sin\left( \cfrac{150^o}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{2}~\hfill[/tex]

The value of sin75 by using half angle identity is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Value of sin75 by using half angle identity is calculated as:-

Half angle identity for is,

[tex]sin\dfrac{\theta}{2}=\pm\sqrt{\dfrac{1-cos\theta}{2}[/tex]

[tex]\dfrac{\theta}{2}=\dfrac{150}{2}[/tex]

[tex]sin\dfrac{150}{2}=\pm\sqrt{\dfrac{1-cos150}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{{1+\dfrac{\sqrt{3}}{2}}}{2}[/tex]

[tex]sin \dfrac{150}{2}=\pm\sqrt{\dfrac{2+\sqrt{3}}{4}[/tex]

[tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Hence, the value of sin75 is [tex]sin\dfrac{[150^0]}{[22]}=\pm\dfrac{\sqrt{2+\sqrt{3}}}{2}[/tex].

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Answer:

A is the answer

Step-by-step explanation:

(0, -5):

-5 = 2(0) - 5 >>>   -5 = -5

-5 = (0)^2 - 5 >>>   -5 = -5

(2, -1):

-1 = 2(2) - 5 >>>   -1 = 4 - 5 >>>   -1 = -1

-1 = (2)^2 - 5 >>>   -1 = 4 - 5 >>>   -1 = -1

The solutions of the given set of equations are (0, -5) and (2, -1) so option (A) will be correct.

The equation is a combination of variable and constant. Which could be in addition multiplication or subtraction.

Given y = 2x -5 and y = x² - 5

By putting the y value into another equation

2x -5 = x² - 5

x² - 2x = 0

x(x - 2) = 0

x = 0 and x = 2.

Now y corresponding to x = 0 is y = -5 and corresponding to x= 2 is y = -1.

Hence the possible set of coordinates among the options are (0, -5) and (2, -1).

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Answer:

259 divided by 170,000 gives you the % 259 is out of 170,000 which is .0015. Move the decimal two spaces to the right to get the actual commission rate=.15%

Answer:

Q = 25°

Step-by-step explanation:

Given

cos(Q + 60) = 0.0872, then

Q + 60 = [tex]cos^{-1}[/tex] (0.0872 ) = 85° ( nearest degree )

Q = 85° - 60° = 25°

Answer: median

Step-by-step explanation: Statistical Mathematics

7, 10, 16, 21, 26, 30, 40, 43

Here we have an even number of the data entries so we get two values in the mid.

Now take the average of those mid values:

Answer:

The possible values of n are -0.5 and -3.5

Step-by-step explanation:

Analyze two cases

1) n-(-2)=1.5

Solve for n

n+2=1.5

n=1.5-2

n=-0.5

2) -2-n=1.5

n=-2-1.5

n=-3.5

see the attached figure

Answer:-0.5,-3.5

Step-by-step explanation:i did this

Answer: Option D

D. 0.92

Step-by-step explanation:

The correlation coefficient "r" is a number between -1 and 1 that indicates how related are two variables X and Y.

The stronger the nearest correlation is, the value of r a -1 or a 1.

A negative correlation indicates that when X increases Y decreases.

A positive correlation indicates that when X increases Y increases.

A correlation close to zero implies that there is very little correlation of the variables. When this happens, the points are scattered in the graph.

In this case you can see in the graph that the points are not scattered, but aligned. You can also observe that when X increases Y increases also.

This allows us to conclude that the correlation is strong and positive. Therefore the correct option is option D.

[tex]r = 0.92[/tex]

-4x<-12

-4x<-12 | /(-4)

x>3

Answer:

r

0.15r

1.15r

Step-by-step explanation:

The problem states that r cm of rain fell on the garden on Thursday, so the first answer is:

The centimeters of rain on Thursday    r

On Saturday, 15% more rain fell than on Thursday. The extra amount of rain on Saturday, as compared to Thursday is 15% of r. 15% of r is the same as 15% times r. 15% can be written as a decimal as 0.15, so 15% of r is the same as 0.15r. This is the answer to the second line.

How many more centimeters of rain fell on Saturday than on Thursday   0.15r

The amount of rain on Saturday is the amount of rain on Thursday plus the additional 15%. We already know that the additional 15% of rain is 0.15r. The total amount of rain on Saturday is r + 0.15r = 1r + 0.15r = 1.15r. That answers the third question.

The centimeters of rain on Saturday     1.15r

Answer:

y = x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x is in this form

with slope m = 1 and c = 0

• Parallel lines have equal slopes, thus

y = x + c ← is the partial equation of the parallel line

To find c substitute (2, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = x + 2 ← equation of parallel line

The equation of the line parallel to y = x and passing through the point (2, 4) is y = x + 2.

In mathematics, two lines are said to be parallel if they have the same slope. The given line is y = x, and because its slope is 1 (the coefficient of x), the line we're looking for, which is parallel to this, will also have a slope of 1.

To find the equation of a line with a given slope that passes through a certain point, we use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the point. Substituting 1 for m, and the given point (2, 4) into this equation gives us y - 4 = 1(x - 2), which simplifies to y = x + 2, the equation of the line we were seeking.

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Answer: All values make a true statement.

Step-by-step explanation: Since f(x) and g(x)=x, f(x)=g(x) can also be written as x=x. That is a true statement so all values of x works.

Hope this helps!

Answer:

y - 8 = -2(x - 6)

Step-by-step explanation:

Given the slope and one point on the line, we should use the point-slope formula:

y - k = m(x - h), where (h, k) is the point and m is the slope.

Here, we have y - 8 = -2(x - 6)

Answer:

y = - 2x + 20

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2, so

y = - 2x + c ← is the partial equation

To find c substitute (6, 8) into the partial equation

8 = - 12 + c ⇒ c = 8 + 12 = 20

y = - 2x + 20 ← equation of line

Answer:

One year has 365 days

Step-by-step explanation:

The question in English is

How many days does the year have?

we know that

[tex]1\ year=12\ months[/tex]

[tex]1\ year=52\ weeks[/tex]

[tex]1\ year=365\ days[/tex]

therefore

One year has 365 days

Answer:

365

Step-by-step explanation:

Angle 4: 64.76 degrees because vertical angles are equal to each other

Angle 6: 180-64.76= 115.24 degrees.

I forget the names of these rules lol

<4 is also 64.76 because alternate interior angles are congruent

<6 is the same-side interior angle to <4 so they are supplementary angles. 180 - 64.76 = 155.24 degrees.

<6 is 155.24 degrees

30 x 30=900 square meters

The area of the square helicopter landing pad is equal to 900 square meters.

In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;

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

Where:

By substituting the given side lengths into the formula for the area of square, we have the following;

Area of square, A = 30 × 30

Area of square, A = 900 square meters.

In this context, we can logically deduce that the area of the square helicopter landing pad is equal to 900 square meters.

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Answer:

52 IN. FOR SURE

Step-by-step explanation:

Formula: A=2(wl+hl+hw)

Fill the formula and you'll understand I promise or search formula for surface area of a rectangular prism fill the numbers and your all set!!!

PLZZZ MARK BRAINLIST!!! PLZZ

Answer:

13

Step-by-step explanation:

Triangles consists of 180 degrees. 132 + 13 = 145      180 - 145 = 35, therefore the smallest measurement of the triangle is 13 since 132 and 35 are larger numbers.