If f(x) =1/9 x-2, what is f-1(x)?

Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

 downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

 decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

 form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

The function g(x) = |x+11|-7 is a transformed absolute value function, which is decreasing on the interval (-infinity, -11) due to the horizontal shift to the left by 11 units.

The question is asking about the transformation of the absolute function f(x) = |x| into a new function g(x). The function provided, g(x) = |x+11|-7, is a transformed version of f(x) where the graph has been shifted horizontally and vertically. To determine on which interval g(x) is decreasing, we need to consider the properties of the absolute value function and its transformations.

The graph of the standard absolute value function, f(x) = |x|, is shaped like a 'V', increasing for x > 0 and decreasing for x < 0. When we introduce a horizontal shift to the function (such as adding 11 to x), this shifts the vertex of the 'V' horizontally. For g(x), the graph is shifted to the left by 11 units due to the '+11' inside the absolute value. Therefore, the function will be decreasing on the interval (-infinity, -11) since the function will decrease to the left of the vertex (which is now located at x = -11). The vertical shift (subtracting 7) simply moves the graph down but does not affect the intervals of increasing or decreasing behavior.

Answer: 8x^4+x^3-4x^2+1

Step-by-step explanation:

To simplify this polynomial expression, we first combine like terms. The simplified expression will be 8x^4 - x + 1.

The expression provided in your question is a polynomial that contains terms with variables raised to different powers. In simplifying this kind of polynomial, you first need to combine like terms, which are those terms that have the same variable and the same exponent.

Therefore, let's organize and combine like terms: x4 - 2x + x and 3x2 - 5x2 + x2 and . As a result, we get 8x4, or 8x to the power of 4, -x, and 1. Thus, the final simplified expression is: 8x4 - x + 1

Hope this helps in your understanding of simplifying polynomials!

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Answer:

x=-5

Step-by-step explanation:

Vertical lines have the same x value all the time.  They are of the form x=

Since it passes through the point (-5,-2) the x value must be -5

x=-5

Answer:

This is B because as we can see the X axis increases in value to y decreases making it negetive

Answer:

the answer is B because the X axis increases in value  as y decreases making it negative

Step-by-step explanation:

Answer:

She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.

Step-by-step explanation:

Francesca made her first error in step 3 because her sine, cosine, and tangent trigonometric ratio values are incorrect.

The correct steps to use in this regards are as follows;

Step 1;

A unit circle is shown. A ray intersects point (-2, -10) in quadrant 3. θ is the angle formed by the ray and the x-axis in quadrant 1.

Step 2;

r = √[(-2)² + (-10)²] = √104 = 2√26

Step 3;

cos θ = -2/(2√26) = -1/√26 = -(√26)/26

sin θ = -10/(2√26) =-5/√26 = -5(√26)/26

tan θ = -10/-2 = 5

sec θ = 1/sin θ = 1/-(√26)/26 = -26/√26

cosec θ = 1/cos θ = 1/-5(√26)/26 = -(√26)/5

cot θ = 1/tan θ = 1/5

Thus, Francesca made her first error in step 3 because the correct sine, cosine, and tangent ratios above differ from hers which was incorrect which lead to incorrect values of cosecant, secant, and tangent functions.

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The probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.

To calculate the probability that the four-digit number formed is not divisible by 4, we need to determine the total number of possible arrangements of the digits I through 4 and then find the number of arrangements that are not divisible by 4.

Total number of arrangements:

Since there are four digits (I, 2, 3, 4), there are 4! (4 factorial) ways to arrange them without repetition.

4! = 4 × 3 × 2 × 1 = 24

Now, let's find the arrangements that are not divisible by 4:

For a number to be divisible by 4, the last two digits must form a number divisible by 4. The possible combinations of the last two digits that are divisible by 4 are: 12, 24, and 32.

So, we have three combinations (12, 24, and 32) where the number formed is divisible by 4.

Now, to find the arrangements that are not divisible by 4, subtract these three combinations from the total:

Arrangements not divisible by 4 = Total arrangements - Divisible by 4 arrangements

Arrangements not divisible by 4 = 24 - 3 = 21

Now, we can calculate the probability:

Probability = (Number of arrangements not divisible by 4) / (Total number of arrangements)

Probability = 21 / 24

Probability ≈ 0.875

So, the probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.

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Answer:

Option B 6 30 am

Step-by-step explanation:

step 1

Sum all the times

(45+5+10+30+15)=115 minutes

Convert minutes to hours

we know that

60 minutes = 1 hour

so

115 minutes=60+55= 1 hour 55 minutes

Subtract 1 hour 55 minutes from 8 25 am

(8 25 am)-(1 hour 55 minutes)=(8 25 am-1 hour)-(55 minutes)

=7 25 am-55 minutes

=7 25 am-(25+30) minutes

=(725 am-25 minutes)-(30 minutes)

7 00 am-30 minutes

=6 30 am

Answer:

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(8)\\\\x^2+2x=17\\\\x^2+(2)(x)(1)=17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(1)+1^2}_{(*)}=17+1^2\\\\(x+1)^2=18\iff x+1=\pm\sqrt{18}\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt{18}\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24[/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

We have the equation

[tex]y-36x-1=0[/tex]     add 36x and 1 to both sides

[tex]y-36x+36x-1+1=36x+1[/tex]

[tex]y=36x+1[/tex]

Therefore

the slope: m = 36

the y-intercept: b = 1

Answer:

A 2

Step-by-step explanation:

When we divide x by 9 there is some whole number we will call y plus a remainder of 4

x/9 = y  remainder 4

Writing this in fraction form

x/9 = y + 4/9

Multiplying each side by 9

9*x/9 = 9* y + 4/9 *9

x = 9y +4

Multiply each side by 2

2x = 2*(9y+4)

2x = 18y +8

Add 3 to each side

2x+3 = 18y +8+3

2x+3 = 18y +11

Divide each side by 9

(2x+3)/9 = 18y/9 +11/9

              = 2y + 9/9 +2/9

               =(2y+1 + 2/9)

  We know y is a whole number and 1 is a whole number so we can ignore 2y +1 when looking for a remainder)

2/9 is a fraction

Taking this back from fraction form to remainder from

                 (2y+1) remainder 2

Answer:

Third side must be greater than 7 and less than 17

Step-by-step explanation:

If a triangle has two sides of lengths 5 and 12, the value for the length of the third side be greater than 7 and less than 17.

Answer:   The perimeter of ΔYXZ6.4

Answer:6.4

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

Line AB and BC are tangents to the given circle.

[tex] \angle \: ABC = \frac{1}{2} ( 210 - 150)[/tex]

[tex] \angle \: ABC = \frac{1}{2} (60) = 30 \degree[/tex]

Alternatively, <ABC and <AOC are supplementary because AB and BC are tangents.

[tex] \angle \: ABC + 150 \degree = 180 \degree[/tex]

[tex] \angle \: ABC = 180 \degree - 150 \degree = 30 \degree[/tex]

The correct choice is A.

Answer:30

Step-by-step explanation:

Answer:

2b2t

Step-by-step explanation:

2b2t

Answer:

x = 3, x = - 3, x = - 1 with multiplicity 2

Step-by-step explanation:

Given that x = 3 and x = - 3 are zeros then

(x - 3) and (x + 3) are factors and

(x - 3)(x + 3) = x² - 9 ← is a factor

Using long division to divide the polynomial by x² - 9 gives

quotient = x² + 2x + 1 = (x + 1)² and equating to zero

(x + 1)² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2

Hence the zeros of the polynomial are

x = 3, x = - 3, x = - 1 with multiplicity 2

Answer:

V=1884 Cubic mm

Step-by-step explanation:

We know that the volume of the Sphere is given by the formula

[tex]V= \pi r^2h[/tex]

Where r is the radius and h is the height of the cylinder

We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.

[tex]V=V_1-V_2[/tex]

[tex]V=\pi r_1^2 \times h-\pi r_2^2 \times h[/tex]

[tex]V=\pi \times h \times (r_1^2-r_2^2)[/tex]

Where

[tex]V_1[/tex] is the the volume of solid cylinder with radius [tex]r_1[/tex] and height h

[tex]V_2[/tex] is the volume of the cylinder being carved out with radius [tex]r_2[/tex] and height h

where

[tex]r_1 = 7[/tex] mm ( Half of the bigger diameter )

[tex]r_2 = 5[/tex] mm ( Half of the inner diameter )

[tex]h=25[/tex] mm

Putting these values in the formula for V we get

[tex]V=\pi \times 25\times (7^2-5^2)[/tex]

[tex]V=3.14 \times 25 \times(49-25)[/tex]

[tex]V=3.14 \times 25 \times 24[/tex]

[tex]V= 1884[/tex]

Answer:

3/10

Step-by-step explanation:

because the pattern is -0.15;

9/10= 0.9

3/4= 0.75

3/5= 0.6

9/20= 0.45

3/10= 0.3

Answer:

Opposite sides are congruent; All right angles are congruent

Step-by-step explanation:

Answer: 3y/2 - 5

Step-by-step explanation:

Expand

-(-3y/2 + 5)

Simplify the brackets

3y/2 - 5

Answer:

x=-2/9 or

x = negative 2 over 9

Step-by-step explanation:

We need to solve:

[tex]\frac{2}{5}(x-2)=4x[/tex]

and find the value of x.

Solving:

[tex]\frac{2}{5}(x-2)=4x\\\frac{2x}{5}-\frac{4}{5}=4x\\ Adding \,\,4/5\,\,on\,\,both\,\,sides\\\frac{2x}{5}-\frac{4}{5}+\frac{4}{5}=4x+\frac{4}{5}\\\frac{2x}{5}=4x+\frac{4}{5}\\subtract \,\,4x\,\,from both sides\\\frac{2x}{5}-4x=\frac{4}{5}\\\frac{2x-20x}{5}=\frac{4}{5}\\\frac{-18x}{5}=\frac{4}{5}\\-18x=\frac{4}{5}*5\\-18x=4\\x=\frac{4}{-18}\\x=\frac{-2}{9}[/tex]

x=-2/9 or

x = negative 2 over 9

Answer:

Monthly Payment = $457.5

Total amount Henry end up paying for the boat overall = $35,960

Step-by-step explanation:

Total Amount to be paid = $32,000

Down Payment = $ 14,000

Interest rate = 5.5%

Total time for Amount to be paid = 4 years

Rest of the payment to be paid = 32,000 - 14,000

= 18000

Amount of interest = P*r*t

P= Principal Amount

r = rate

t = time

Putting values

Amount of interest= 0.055 *18000*4 = 3960

Total Remaining payment = 18000+3960 = 21,960

As Payment to be paid in 4 years, So number of months = 4*12 = 48 months

Monthly payment = Total Payment / Months = 21,960/48 = 457.5

So, Monthly Payment = $457.5

Total amount Henry end up paying for the boat overall = Down Payment + Remaining Payment

=14,000+21960

= 35960

So, Total amount Henry end up paying for the boat overall = $35,960

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 → (0, b)

If m > 0, then the function is increased

If m < 0, then the function is decreased

We have

[tex]m=\dfrac{2}{3}>0[/tex] - the function is increased

[tex]b=-4[/tex] - the y-intercept is -4 → (0, -4)

Therefore the line passes through III, IV and I quadrant.

========================================

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

========================================

We have [tex]y\leq\dfrac{2}{3}x-4[/tex] → ≤ - shaded region below the line.

Therefore the inequal the inequality exist in I, III and IV quadrant.

Look at the picture.

The inequality exists in quadrants A.I, III, and IV.

The answer is option A

            slope(m)=tan∅=y axis/x axis.

If m > 0, then the function is increased

If m < 0, then the function is decreased

=function is increased

=y-intercept is -4 = (0, -4)

    Therefor the line passes through III, IV and I quadrant.

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Answer:

The perimeter of Δ WXY is 14.50 cm ⇒ the last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- There is a fact in any triangle; the segment joining the midpoints of

  two side of a triangle is parallel to the 3rd side and half its length

* Lets use this fact to solve the problem

- In Δ WXY

∵ Q is the midpoint of WX

∵ R is the midpoint of XY

∵ S is the midpoint of YW

- By using the fact above

∴ QR = 1/2 WY

∴ RS = 1/2 WX

∴ SQ = 1/2 XY

- Lets calculate the length of the sides of Δ WXY

∵ QR = 1/2 WY

∵ QR = 2.93

∴ 2.93 = 1/2 WY ⇒ multiply both sides by 2

∴ WY = 5.86 cm

∵ RS = 1/2 WX

∵ RS = 2.04

∴ 2.04 = 1/2 WX ⇒ multiply both sides by 2

∴ WX = 4.08 cm

∵ SQ = 1/2 XY

∵ SQ = 2.28

∴ 2.28 = 1/2 XY ⇒ multiply both sides by 2

∴ XY = 4.56 cm

- Lets find the perimeter of Δ WXY

∵ The perimeter of Δ WXY = WX + XY + YW

∴ The perimeter of Δ WXY = 5.86 + 4.08 + 4.56 = 14.50

* The perimeter of Δ WXY is 14.50 cm

In this exercise we have to use the knowledge of the perimeter of a figure to calculate its value, and then:

Letter D

So from some information given in the statement and in the image, we can say that:

So solving, you will have to:

[tex]QR = 1/2 WY\\RS = 1/2 WX\\SQ = 1/2 XY[/tex]

Now with both information we can calculate the perimeter value as:

[tex]QR = 1/2 WY\\QR = 2.93\\2.93 = 1/2 WY\\ WY = 5.86 cm\\RS = 1/2 WX\\ RS = 2.04\\2.04 = 1/2 WX\\WX = 4.08 cm\\SQ = 1/2 XY\\SQ = 2.28\\2.28 = 1/2 XY \\XY = 4.56 cm\\ WXY = WX + XY + YW\\WXY = 5.86 + 4.08 + 4.56 = 14.50[/tex]

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See attachment for the answer.

Answer:

X=5, X=1

Step-by-step explanation:

Okay so the | means absolute value and it is similar to a parentheses, except everything inside it becomes positive. Since there is a variable (x) inside it, you will have two scenarios then, one where everything inside is positive and where it's negative (so -3x +9 = -6 and 3x -9 =-6) You then solve for x in both equations.

Answer:

x=5   x=1

Step-by-step explanation:

-3|x - 3|= -6

Divide each side by -3

-3|x - 3|/-3= -6/-3

|x - 3|= 2

To get rid of the absolute value signs, we get two equations, one positive and one negative

x-3 =2           x-3 = -2

Add 3 to each side

x-3+3 = 2+3        x-3+3 = -2 +3

x =5                         x = 1

Answer: B) 15 + 5i

Step-by-step explanation:

(7 + 4i) + (8 + i)

Add like terms: (7 + 8) + (4i + i)

Simplify: 15 + 5i.

Step-by-step explanation:

i think its 4.2m^2+1.5n

Answer:

4.2m^2+1.5n

Step-by-step explanation:

1.7m^2 + 6.5n - 4n + 2.5m^2 - n

First, rearrange the numbers so that they can be added or subtracted with their like terms.

It would look like this:

(1.7m^2 + 2.5m^2) + (6.5n - 4n - n)

All you have to do is solve from here

this would simplify into:

4.2m^2+1.5n

Hope this helped!

Answer:

20875

Step-by-step explanation:

Given:

y = 5500 ln (9t + 4

y is number of mowers sold

t is years after a particular model is introduced

f(t)= 9t+4

How many mowers will be sold 4.5 years after a model is introduced?

t=4.5

putting t=4.5 in given function we get,

y= 5500ln(9(4.5) +4)

       = 20875.19

20875 mowers will be sold 4.5 years after a model is introduced!

no your wrong its 85.2

Answer:

126.5 ft

Step-by-step explanation:

It's further for the catcher to throw to

The catcher must throw approximately 127.3 feet to get a runner out at second base on a square baseball diamond. The Pythagorean theorem is used to calculate the diagonal from home plate to second base. Runners often try to steal second base due to the longer throw required and being in scoring position.

The question involves calculating the distance a catcher must throw the ball to get a runner out at second base on a baseball diamond, which is a square with sides of 90 feet. To find this distance, we must determine the diagonal of the square, as the catcher throws the ball from one corner (home plate) to the opposite corner (second base). Applying the Pythagorean theorem to the square, the diagonal distance D is given by D = √(90² + 90²). So, D = √(8100 + 8100) = √16200 feet, which approximately equals 127.3 feet. Runners are inclined to steal second base more often because it is generally easier to steal with the catcher having to make a longer throw, and once on second base, the runner is in scoring position with two bases potentially available to advance.

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Answer:

1. multiply (2) by -2 and add to (1)

-2x-2y=-1320

add to (1) we get

4y-2y=1440-1320

2y=120

y= $60 cost of silver ring.

2. Multiplying (distributive property, we get the equivalent equation

x+72=3x-216

Adding 216 to both sides of the equal sign, we get

x+72+216=3x-216+216 --> x+288=3x

Subtracting x from both sides, we get

x+288-x=3x-x --> 288=2x

Logan and Izzy had initially had 188 stickers between the two of them.

3.

a = d before Anna gives away 50 marbles.

5 (a-50) = a +50 after Anna gives away 50 marbles.

5a - 250 = a + 50

4a = 300

a = 75

Anna has 75 marbles at the beginning and so did David.

Together they have 150 marbles.