Solve for x and graph the solution on the number line. If possible, resolve your answer to a single inequality. In case of no solution leave the number line blank.

22>=-3x+7 and -3x + 7 >-17

Answer:

1/8

Step-by-step explanation:

144 ÷ 18 = 8

so, it 1/8

The value of the stock after 2 years was 0.6497xx.

What is Mathematical expression?

The combination of number and variable by using addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

Christopher bought stock in a company two years ago that was worth xx dollars.

In the first year that he owned the stock, then it decreased by 11%.

In the second year the value of the stock decreased by 27%.

Now,

The multiplier of value for the first year was (1 - 11%) = 0.89

The multiplier of value for the second year was (1 - 27%) = 0.73

Then the multiplier of value for the two years was = 0.89 * 0.73

                                                                             = 0.6497

Hence, The value of the stock after 2 years was 0.6497xx.

Learn more about the mathematical expression visit:

https://brainly.com/question/14462529

#SPJ1

Inverse of the given function F(x) = ( x + 3 )² + 1 is F⁻¹(x) = [√( x - 1 ) ] - 3

Given is a function of x, F(x) = ( x + 3 )² + 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = ( x + 3 )² + 1 becomes y =  ( x + 3 )² + 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = 3 x³- 4, we get

x =  ( y + 3 )² + 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = ( y + 3 )² + 1

=> x + 1 =   (y + 3 )²

=> (y + 3 )² = x + 1

=> y = √( x - 1 )  - 3

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y =√( x - 1 ) - 3 becomes F⁻¹(x) = √( x - 1 )  - 3

Therefore, we get the inverse of the given function F(x) = ( x + 3 )² + 1 as F⁻¹(x) = √( x - 1 )  - 3

Learn more about Inverse of a Function here:

https://brainly.com/question/2541698?referrer=searchResults

#SPJ9

do 7 x for and you will not have any changes to your memories of your own and the fact of life that I am sure

Step-by-step explanation:

Y should have a negative side in front of it.

[tex]2x - y = 5 \\ - y = - 2x + 5 \\ y = 2x - 5[/tex]

The base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that:

The quadratic polynomial is:

= 4x² + 12x + 9

After using factor method:

= 2x² - 4x + 3x - 12

= 2x(x + 4) + 3(x - 4)

= (2x + 3)(x - 4)

Thus, the base lengths are (2x + 3) and (x - 4) meters if the area of the base of the statue is 4x² + 12x + 9.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

Answer: C. 36,000

Step-by-step explanation:

Answer:

Your answer should be about 36,000

Step-by-step explanation:

You can kind of already eliminate A. the real answer should be around 34 to 35 thousan and it is the nearest to the options that you have

hope this helps

Answer:

  2√10

Step-by-step explanation:

You want the simplest radical form of 6.32455532034.

In order for the given decimal value to have a "simplest radical form," we must assume it is an approximation of an irrational root. The given rational number is approximately equal to √40, differing in the 12th decimal place and beyond.

  6.32455532034 ≈ √40 = 2√10

__

Additional comment

The radical is simplified by removing all of the perfect squares from under the radical.

  40 = 2^3 × 5 = (2^2)(2×5) = (2^2)(10)

  √40 = 2√10

[tex]{\huge\color{yellow}{\boxed{\fcolorbox{blue}{black}{꧁ANSWER ꧂}}}} \\ \\ \frac{3}{4} + ( - \frac{1}{4} ) \\ \\ = \frac{9 - 3}{12} = \frac{6}{12} = \frac{2}{4} \\ \\ \frac{3}{8} + ( - \frac{3}{8}) = 0(cancel \: \: out)[/tex]

Answer:

3/4 + (-1/4)

-1/4 = -0.25

3/4 = 0.75

3/8 + (-3/8)

-3/8 = -0.375

3/8 = 0.375

the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.

Given that the line passes through (-5, -6), and has a slope (m) = 1/5, to find the equation of the line, do the following:

Substitute (x, y) = (-5, -6) and m = 1/5 into y = mx + b to find the value of b:

-6 = 1/5(-5) + b

-6 = -1 + b

Add 1 to both sides

-6 + 1 = -1 + b + 1

-5 = b

b = -5

Substitute m = 1/5 and b = -5 into y = mx + b

y = 1/5x + (-5)

y = 1/5x - 5

Thus, the equation of the line that has a slope of 1/5 and passes through (-5, -6) is: y = 1/5x - 5.

Learn more about equation of a line on:

https://brainly.com/question/13763238

#SPJ1

Integers are positive and negative whole number digits, where the set of integers is denoted by capital Z.

Z={-n,...,-2,-1,0,1,2,...,36,37,38,39,...,n}

So 37 is in between 36 and 38

After expanding logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_7(\sqrt{r} )+9}{s^2t^\frac{1}{3} }[/tex]

as, log (√x) = 1/2 log (x), equation becomes

[tex]= \frac{\frac{1}{2} log_7(r) + 9}{s^2t^\frac{1}{3} } \\[/tex]

now, after rationalize this equation

[tex]= \frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

Thus, after expanding the logarithm equation is : [tex]\frac{t^{\frac{2}{3}}(\frac{1}{2} log_7(r)+9)}{s^2t}[/tex]

To know more about logarithms, visit :

brainly.com/question/5956809

#SPJ4

The function y = (x + 3)² is the result of translating the function y = x² 3 units in the -x direction.

In this question we have a function of the form y = f(x), which is modified by transformation rules. The statement defines the original function as y = x² and we see that the resulting expression is y = (x + 3)². By direct observation, we that the latter function is the consequence of using an horizontal translation of the form:

g(x) = f(x - k), where k < 0.

This transformation rule indicates a horizontal translation in the - x direction. To be specific, a horizontal translation 3 units in the -x direction. Graphically specific, the graph of f(x) is moved 3 units in the - x direction.

To learn more on translations: https://brainly.com/question/12463306

#SPJ1

Based on the information, the percentage increase for the area s greater as it is 600% greater

Here, we have a square of side length 3 cm

The area of the square is 3² = 9 cm²

Perimeter of the square = 4L = 4 * 3 = 12 cm

When we triple the length of the square, its new length becomes 3 ,× 3 = 9 cm

Area here will be 9 * 9 = 81 cm²

Perimeter = 4 L = 4 * 9 = 36cm

To calculate percentage change, we use the formula;

(new value - old value)/old value * 100%

For the perimeter;

(36-12)/12 * 100% = 24/12 * 100% = 2 * 100% = 200%

For the area;

(81-9)/9 * 100% = 72/9 * 100% = 8 * 100% = 800%

The percentage increase of the area is greater by: 800% - 200% = 600%

Learn more about percentages on:

https://brainly.com/question/843074

#SPJ1

The side length of the square shown is tripled.

3 cm

Which percent of increase is greater the percent of increase for the perimeter of the square or the percent of increase for the area

The answer to the question is T= - 7.5°C - 8.5°C = -16°C

The initial temperature in the late afternoon was -7.5°C.

It  dropped by 8.5 degrees by midnight.

Change in temperature (in midnight) = -8.5°

Here negative sign represents the decrease in the temperature

.Let T be the total change in the temperature.

So, total change in the temperature is T =  - 8.5°C 

Therefore the required temperature in the midnight =temperature in late afternoon+the temperature dropped in night.

Final temperature at night =-7.5°C-8.5°C=-16°C

Learn more about Temperature change here:https://brainly.com/question/13315138

#SPJ9

Answer:

In the image above

Step-by-step explanation:

Vertical line: A vertical line is a collection of points whose x -coordinate is the same for any y -coordinate. The equation of a vertical line is given by: x=c where c is a real number.

Check the picture below.

The rate at which the temperature of the compound rose is 2 degree per hour.

To figure this problem we will use unitary method where unitary method is a method where we find the value of the single unit and then multiply the value of single unit to the number of units to get the necessary value.

But according to the question we have find the value of only single unit.

Therefore we have been given that

     every [tex]1\frac{3}{4}[/tex] hours = temperature of compound rose [tex]3\frac{1}{2}[/tex] degrees

Now applying unitary method we get,

         [tex]1\frac{3}{4} = 3\frac{1}{2} \\\\ \frac{7}{4} = \frac{7}{2} \\\\ 1 = \frac{7}{2} /\frac{7}{4}[/tex]

            = 2 degrees per hour

Hence the rate that the temperature of the compound rose is 2 degree per hour.

Learn more about unitary method here : https://brainly.com/question/24587372

#SPJ9

Answer:

1. E K H and F K G

2. E K F and H K G

3. E K F or G K H

4. F K G and G K J

5. G K J

Step-by-step explanation:

The equation only has real solutions, x = 2/√5  and x = –2/√5

Let p = x².

Then we can write 25 x⁴-40 x²+16 = 0 as:

25 p²- 40 p +16 = 0

This is a quadratic equation.

There are three ways to find the solutions of a quadratic equation:

Let us factoring method.

25 p²- 40 p +16 = 0

(5p - 4)(5p - 4) = 0

Hence 25 p²- 40 p +16 = 0 only has single real solution:

5p - 4 = 0

5p = 4

p = 4/5

Substitute p = 4/5 into p = x², we get:

x² = 4/5

x = ± √(4/5)

The solutions are x = 2/√5  and x = –2/√5

Learn more about the solutions of quadratic equations here:

https://brainly.com/question/19247384

#SPJ4

Answer:

Step-by-step explanation:

w(t)  =  F(t) - D(t) = water into (or out of the pool)

        =  t^2 + 8t+9      -   (t^2 +11t+4)

 w(t)        = -3t + 5       <===== shows all of the water will leak out after 5/3 hr

the two functions intersect at 5/3 hr    this is where water in = water out = dry pool

The solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

The expression is given as

22 >= -3x + 7 and -3x + 7 >-17

The above expression is an inequality expression

As a general rule:

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

So, we have

22 >= -3x + 7 and -3x + 7 >-17

Evaluate the like terms

15 >= -3x  and -3x  >-24

Divide through by -3

So, we have

-5 <= x  and x  < 8

Combine the expressions

-5 <= x < 8

Hence, the solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

See attachment for the number line

Read more about number line at

brainly.com/question/24644930

#SPJ1

Answer:

(1, 1) , (5, 2), (6, 4), (4, 7) and (2, 3)

Step-by-step explanation:

When a point is rotated 180° about the origin(either clockwise or anticlockwise), the transformed coordinates are the negatives of the original coordinates.

Thus when a point (x, y) is rotated about the origin, its new coordinates become (-x, -y)

Given the original 5 vertices of the pentagon, the vertices of the rotated pentagon are transformed as follows

Original Vertex    ==>     Transformed Vertex

(-1, -1)                      ==>          (1, 1)
(-5, -2)                    ==>          (5, 2)
(-6, -4)                    ==>          (6, 4)
(-4, -7)                    ==>          (4, 7)
(-2, -3)                    ==>          (2, 3)

Answer:

A. x < $20 or x > $150

B. x [tex]\geq[/tex] $25

C. x [tex]\leq[/tex] 35mph

D. x [tex]\leq[/tex] $4

Step-by-step explanation:

Not sure of the format desired for item A but this is what I came up with.

Answer: 100 million or 100,000,000

Step-by-step explanation:

Do the exponent in the brackets. Then the one outside of the brackets.

10 to the power of 4=10000(which is 10 x 10 x 10 x10)

Then figure out 10000 the the power of 2.

10000 x 10000 = 100,000,000

Therefore the value of this is 100 million.

Answer:

[tex]\mathrm{88 + v}[/tex]

The correct option is (x²- 2x + 4) for the quotient.

For the given question;

The equations are given as;

(x³ + 8) = (x + 2)

For finding the quotient; this could be written as,

(x³ + 8)/ (x + 2) = 1

Thus, we have

= (x³ + 8)/ (x + 2)

Rewriting the equation as;

=  (x³ + 2³)/ (x + 2)

Apply the formula of (a³ + b³) = (a+b)(a² - ab + b²) at the numerator;

= (x + 2)(x² -2x + 4)/  (x + 2)

Cancel the value of (x+ 2)

= (x² -2x + 4)

Thus, the quotient of the division is obtained as (x² -2x + 4).

To know more about the quotient, here

https://brainly.com/question/11418015

#SPJ9

Answer:

5x+40-7<23

5x+33<23

5x<-10

x<-2