The graphically and algebraically

ans = 0.00369913687

hope it helps...!!!!

Answer: [tex]f^-1(1)=-1[/tex]

Step-by-step explanation:

From the graph given we can derive the function  [tex]f(x)[/tex]

[tex]f(x) = .5x + 1.5[/tex]

To solve  [tex]f^-1(1)[/tex] we need to find the inverse function of [tex]f(x)[/tex].

Inverse functions are functions that essentially "reverse" the mapping of the domain ([tex]x[/tex]) and range ([tex]y[/tex]) of the parent function.

To find the inverse function  [tex]f(x)[/tex] we need to solve for x in terms of y.

[tex]y = .5x + 1.5[/tex]

[tex]y - 1.5 = .5x[/tex]

[tex]\frac{y - 1.5}{.5} = \frac{.5x}{.5}[/tex]

[tex]x=2y-3[/tex]

from this, we can derive that

[tex]f(y)^-1=2y-3[/tex]

this can also be written as a function of x

[tex]f(x)^-1 = 2x-3[/tex]

both functions are identical.

take one of these functions and you can find that

[tex]f^-1(1) = 2(1) - 3[/tex]

[tex]f^-1(1) = -1[/tex]

Step-by-step explanation:

I only know the answer for the second task

The given equation represents a function and inverse of the function exist if x ≥ 6.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y = 2(x – 5)² – 6

Part A:

Using vertical line test, we can find the whether the graph is a function or not.

After drawing a graph for the given curve, and drawing a vertical line.

The vertical line touches only one point for the one input.

The given equation represents a function.

Part B:

Replace x → y and y → x

x = 2(y – 5)² – 6

2(y – 5)² = x + 6

[tex]\rm y^-^1 = \sqrt{\dfrac{x+6}{2}} +5[/tex]

Plug x = 1 in the y:

y = 26

Plug  [tex]\rm y ^-^1[/tex] = 1 in inverse of a function:

x = 26

Thus, the given equation represents a function and inverse of the function exist if x ≥ 6.

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Step-by-step explanation:

divide equation by 2

subtract 6

-x

Answer:

1600 / 1.1^10 = $616.87

Step-by-step explanation:

Im not so sure, but here

the value of the diamond ring 10 years ago was approximately $419.47

To find the value of the diamond ring 10 years ago, we need to calculate its original value before the annual appreciation.

Let's assume the original value of the ring 10 years ago was "x" dollars.

After 10 years, with an annual appreciation rate of 12%, the value of the ring became $1200.

The formula to calculate the future value (FV) of an investment with compound interest is:

FV = PV * (1 + r)ⁿ

where:

FV = future value

PV = present value (original value)

r = annual interest rate (as a decimal)

n = number of years

In this case, we have:

FV = $1200 (present value after 10 years)

r = 12% (0.12 as a decimal)

n = 10 years

Now, we can rearrange the formula to find the original value (PV):

PV = FV / (1 + r)ⁿ

PV = $1200 / (1 + 0.12)¹⁰

PV = $1200 / 2.85610019

PV ≈ $419.47

So, the value of the diamond ring 10 years ago was approximately $419 (rounded to the nearest dollar).

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Answer:

20 cm²

Step-by-step explanation:

If the given shape has been enlarged by scale factor 2, then each of the side lengths will be increased from 1 cm to 2 cm, as 1 × 2 = 2

Area of the given shape is 5 cm².

As we are working with area, we cannot simply multiply the area of the given shape by the scale factor.  Area is measured in square units, therefore we need to multiply the area of the given shape by the square of the scale factor.

⇒ area of the enlarged shape = area of given shape × sf²

                                                  = 5 cm² × 2²

                                                  = 5 cm² × 4

                                                  = 20 cm²

(see attached image for proof)

A current asset is an asset that can reasonably be expected to be sold, consumed, or exhausted through the normal operations of a business within the current fiscal year

Your information is incomplete. Therefore, an overview of the current asset will be given. Current assets are those that you can convert into cash within one year, such as short-term investments and accounts receivable.

Current assets include cash, cash equivalents, accounts receivable, stock inventory, marketable securities, pre-paid liabilities, and other liquid assets.

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Answer: See below

Step-by-step explanation:

[tex]$$Find the possible rational roots using the rational root theorem:$$x^{3}+x^{2}-3 x+12=0$$Select the coefficient of the leading term and the constant term:$1 x^{3}+x^{2}-3 x+12=0$\\Find the positive divisors of 12 and 1: \\\\Divisors of $12: 1,2,3,4,6,12$\\Divisors of $1: 1$\\Divide each of the divisors of 12 by 1 :\\$\frac{1}{1}, \frac{2}{1}, \frac{3}{1}, \frac{4}{1}, \frac{6}{1}, \frac{12}{1}$2, \pm 3, \pm 4, \pm 6, \pm 12$$[/tex]

[tex]$$Because both positive and negative values are valid candidates, the possible rational roots of $x^{3}+x^{2}-3 x+12=0$ are:$$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12[/tex]

Answer:

35%

Step-by-step explanation:

Percent increase is (new number - old number) / old number

(162 - 120) / 120 = 42 / 120 = 0.35 = 35%

Using the slope concept, it is found that the kite is 46.50 feet above the ground.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem:

Hence:

tan(24º) = (3.5 + x)/105.

3.5 + x = 105tan(24º)

x = 105tan(24º) - 3.5

x = 43.25 ft.

Hence, the height of the kite is:

43.25 ft + 3.25 ft = 46.50 feet.

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Answer:

Step-by-step explanation:

�

105

105

x

​

sin

24

1

=

1

sin 24

​

=

�

105

105

x

​

105

sin

24

=

105 sin 24=

�

x

Cross multiply.

�

=

42.707347...

x=42.707347...

Type into calculator.

Add 3.25, the distance from the ground to his hand:

Add 3.25, the distance from the ground to his hand:

42.707347...

+

3.25

=

42.707347...+3.25=

45.957347...

45.957347...

≈

≈

46

46

Round to the nearest tenth.

The kite is 46 feet above the ground.

The kite is 46 feet above the ground.

Answer:

need pictures of questions

Step-by-step explanation:

please

Answer:

The common denominator is 8

Step-by-step explanation:

It depends on what you mean. The denominator is 8 in both of the fractions that is being added together

Answer:

The GCF of 12 and 28 is 4

hope it helpsss

Answer: is 4 thats the answer

Step-by-step explanation: i have none im not good at explaining math welp have a good day

Answer:

$20.90

Step-by-step explanation:

If we want to find Aiden's hourly rate, and we know how long he worked, and how much money he made, then we can simply divide his profit by how long he worked. This will give us the precise amount of money he made per hour.

So,

$334.40 / 16 hours = 20.9

This means Aiden earned approximately $20.90 per hour.

Hope this helped!

Answer:

See the photo above

Step-by-step explanation:

Hope this helps and have a nice day

Answer:Triangular Pyramid Solved Examples Example 1: Find the surface area of a triangular pyramid with the base area is 28cm.sq., the perimeter is 20cm, slant length is 5cm. Solution: Surface area = [Base area] + ½ × Perimeter × [Slant length] = 28 + ½ × 20 × 5 = 28 + 50 = 78 cm.sq.

Step-by-step explanation:

Answer:

Angle #1 is 45 degrees

Angle #2 is 60 degrees

Angle #3 is 75 degrees

Step-by-step explanation:

x- angle #1

y- angle #2

(180-x-y)- angle #3

3x=180-x

4x=180

x=45

180-x-y=y+15

y=60

180-60-45=

180-105= 75

The velocity of the jogger will be 0.18 miles per minute.

Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.

Given that:-

The velocity will be calculated as:-

V   =   Distance  ÷   Time

V   =   8     ÷    45

V   =   0.18 miles per minute

Therefore the velocity of the jogger will be 0.18 miles per minute.

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Answer:

254/54797

Step-by-step explanation:

image attached

Answer:

should be 3^X = 7 and X = log7/log3

Step-by-step explanation:

Answer:

[tex]3^x = 7\\x = \frac{log7}{log3}[/tex]

Answer:

5x-7y+35=0.

Step-by-step explanation:

1) according to the condition it is possible to make up the required equation:

[tex]\frac{x}{-7} =\frac{y}{5} =1;[/tex]

note, the numbers -7 and 5 are from the given coordinates;

2) if to re-write the equation into common form, then

5x-7y+35=0.

Answer:

Clyde has 14 pencils in his backpack

Step-by-step explanation:

Let x be the number of pencils that Clyde has in his backpack.

We can translate this statement “Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack” mathematically like this :

[tex]17=5+\frac{6}{7} x \\\\ \Longleftrightarrow 17-5=\frac{6}{7} x \\\\ \Longleftrightarrow 12=\frac{6}{7} x \\ \\\Longleftrightarrow x=\frac{12\times 7}{6} =14[/tex]

Let he has n pencils

So

[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}+5=17[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}=12[/tex]

[tex]\\ \rm\hookrightarrow 6n=84[/tex]

[tex]\\ \rm\hookrightarrow n=14[/tex]

Answer:

[tex]709*68=48212[/tex]

ans = 48212

Answer:

54 yards²

Step-by-step explanation:

First, we can find the area of the figure as a whole.

6 x 11 = 66

Now we have to find the area of the smaller rectangle

3 x 4 = 12

Finally, we subtract the whole and the smaller rectangle

66 - 12 = 54

The probability of at least one of the coins showing heads is 4