What the additional information fill in the blanks

Answer:

Step-by-step explanation:

taking the inverse is essentially saying

x = (f(x) + 3)^2

root(x) - 3 = f(x) and -root(x) -3 = f(x)

(you have to take both the positive and negative roots)

plug in 49 for x and get 4 and -10.

The value of the inverse function, to the function f(x) = (x + 3)², at f(x) = 49, is; f⁻¹(49) = 4

The notation f⁻¹(x) represents the inverse of the function f(x). The inverse function, f⁻¹(x) undoes the the effect of the function f(x), meaning, that if y = f(x), then x = f⁻¹(y)

The value of f⁻¹(49) for the function, f(x) = (x + 3)² is the x-value, such that f(x) = 49, which can be obtained by solving the equation f(x) = (x + 3)², for x as follows;

Taking the square root of both sides of the equation, we get;

√(f(x)) = √((x + 3)²)

√(f(x)) = (x + 3)

Subtracting 3 from both sides, we get;

√(f(x)) - 3 = x + 3 - 3 = x

√(f(x)) - 3 = x

The above function is the inverse function, f⁻¹(x) that takes an output value, f(x), to produce the corresponding input value, x of the original function;

The inverse function, f⁻¹(x) = √(f(x)) - 3, takes the original output, f(x) to produce the original input x

When the output value is f(x) = 49 we get;

f⁻¹(49) = √(49) - 3 = ±7 - 3

Restricting the domain of the original function, f(x) to (x + 3) ≥ 0, or x ≥ -3, so that its inverse is also a function and produces only one value, we get;

f⁻¹(49) = 7 - 3 = 4

f⁻¹(49) = 4

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3 rolls would cost $1.17.

There exists a direct proportion between two values when one exists as a multiple of the other.

In direct proportion, if one quantity exists increased or decreased then the other quantity increases or declines, respectively. But in indirect or inverse proportion, if one quantity increases then the different quantity decreases and vice-versa.

If 7 rolls of tape cost $2.73,

Then 1 roll of tape would cost $2.73/7 = $0.39

Now, the cost of 3 roll of tapes would be 0.39*3 = $1.17

Therefore, at same rate the 3 rolls of tape would cost $1.17.

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Answer:

m,4+ a+b

Step-by-step explanation:

an exterior angle equals the sum of the 2 opposite interior angles

Answer:

35.2

Step-by-step explanation:

tan(58) = x/22

or, x = 22×tan(58)

or, x = 35.2 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

The 2nd one is 3x+1

The 3rd answer is x+3

Step-by-step explanation:

Given g(x)=4x-1 and f(x)=x-2

Subtracting both

4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1

The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3

Answer:

-7/5

Step-by-step explanation:

I think let me know

Answer:

7/-5  or -7/5

Step-by-step explanation:

This shall be quite an easy problem, I shall be doubting that this is high school, however, I am happy to aid :)

We shall begin by labeling the points given to us to prepare for inputting the values in the slope formula

(3,4).     (8,-3)

x1,y1     x2,y2

Slope Formula:

y1 - y2

x1 - x2

Inputting the values:

4 - (-3)

3 - 8

Solve:

7

-5

The slope of the line passing through the points (3,4) and (8,-3) shall be 7/-5 or -7/5 negatives shall go both ways of fractions

Answer:

no solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

I get no solution also (the answer is imaginary).

Answer:

12 miles

Step-by-step explanation:

1/3 of an hour = 20 minutes = 4 miles

1 minute = 4/20 miles

60 minutes = 4/20 x 60 miles

                   = 4 x 3 miles

                   = 12 miles

60 minutes = 1 hour

=> 1 hour = 12 miles

Jacks unit rate is 12 miles/hr

Answer:

12

Step-by-step explanation:

There are two ways of doing this problem. I think the easiest way is to use a decimal in the denominator and round

4/0.333333333 = 12.000000001

The answer is obviously meant to be 12.

The other way is more sophisticated, but more accurate.

4/1 // 1/3               This is a 4 tier fraction. The rule is to invert the denominator (turn the bottom fraction upside down) and multiply.

4/1 * 3/1 = 12

The first method is easier to understand. The second is more accurate and more useful for physics.

Answer:

Step-by-step explanation:

the answer is a)

Answer:

Area of the rectangular trench = 1 square meter

Step-by-step explanation:

length of the garden = 2 1/2 m width of the garden = 2 m

length of both garden and trench = 3 1/2 m

width of both garden and trench = 3m

Length of the trench = Difference in length

= 3 1/2 m - 2 1/2 m

= 7/2 - 5/2

= (7 - 5) / 2

= 2/2

= 1 m

Length of the trench = 1 m

Width of the trench = difference in width

= 3 m - 2 m

= 1 m

Width of the trench = 1 m

Area of the rectangular trench = length × width

= 1 m × 1 m

= 1 m²

Or

1 square meter

Area of the rectangular trench = 1 square meter

[tex] - \frac{2}{5} [/tex]

Explanation:

The x coordinates are -4 and 14. They add up to -4+14 = 10. Then this cuts in half to get 10/2 = 5. This is the x coordinate of the midpoint.

We'll follow this same idea for the y coordinates as well.

10+0 = 10 which cuts in half to 10/2 = 5, and this is the y coordinate of the midpoint.

Therefore, the midpoint is (5,5).

Coincidentally, the x and y coordinates are the same for the midpoint (both are 5). This won't always happen.

Answer:

Hello the answer is 5x - y = 30!

Step-by-step explanation:

m = (0 (-5))/(6 - 3) = (0 + 5)/(3) = 5/3

y = mx + b

O = (5/3)(6) + b

O = (30/3) + b

O = 10 + b

-10 = b

3y = 5x - 30

3y + 30 = 5x

5x - 3y = 30

this is a number is can not devide

Answer:

x = 44.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 48 = 30/x

x cos 48 = 30

x = 30 / cos 48

x=44.83429

Rounding to the nearest tenth

x = 44.8

Answer:

5sqrt2

Step-by-step explanation:

Using the pythagorean theorem, we get 5^2+5^2=c^2. C is the diagonal here. 25+25=c^2, c^2=50. c=sqrt50. Simplifying it, we get the diagonal as 5sqrt2.

Answer:

2.5%

Step-by-step explanation:

Given :

Mean, μ = 190

Standard deviation, σ = 30

Probability that more than 250 books are borrowed ;

x = 250

P(Z > z)

Z = (x - μ) / σ

P[Z > (x - μ) / σ] = P[Z > (250 - 190) / 30]

P(Z > z) = P(Z > 2)

P(Z > 2) = 1 - P(Z < 2) = 1 - 0.97725

P(Z > 2) = 1 - P(Z < 2) = 0.02275

(0.02275 * 100)% = 2.275%

2.5% is closest to 2.275%

Answer:

.574

Step-by-step explanation:

This can be inputted in a calculator to achieve .57357643

To three decimal places that is .574

Answer:

B: Subtraction property of equality

Answer:

Answer is in the picture.

Answer:

45:13/36

46:86/63

47:19/42

48:9/10

49:1/12

Answer:

$95.52

Step-by-step explanation:

Number of robots = 3

Cost of each robots = $398

Tax rate = 8%

Amount of tax of each robots = 8% of $398

= 8/100 × $398

= 0.08 × $398

= $31.84

TOTAL TAX to be paid = Amount of tax of each robots × Number of robots

= $31.84 × 3

= $95.52

TOTAL TAX to be paid = $95.52

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.

Answer:

The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.

Answer:

The distance between C and D is 4.2768 inches.

Step-by-step explanation:

As from A to B the distance is 5.625 inches and actual is 1688 miles

so,

1 mile = 5.625/1688 = 0.0033 inches

So, the distance between C and D is 1296 miles

= 1296 x 0.0033 inches = 4.2768 inches  

Answer:

[tex]79\%[/tex]

Step-by-step explanation:

The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.

Formulas used:

The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:

Area of square: [tex]A=2^2=4[/tex]

Area of circle:

[tex]A=1^2\pi=\pi[/tex]

Therefore, the probability that the point will be inside the circle is:

[tex]\frac{\pi}{4}=0.78539816339\approx \boxed{79\%}[/tex]

Answer:

4th option, 7/4 and

5th option, 3

Step-by-step explanation:

The line seems like it will have a positive slope and will not be 0 since it's not passing through the origin

so, possible values are 7/4 and 3

Answered by GAUTHMATH

Answer: The answer would be 7/4, 3

Step-by-step explanation:

Answer:

[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]

Answer:

choice A is the answer

Step-by-step explanation:

[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]

but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.

Answer:

is there anything underneath it? it says which of the following

Step-by-step explanation: