Part 3: Find the inverse function, f –1(x), for the function f (x) = x2 + 10x + 28.

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Explanation:

If we plugged (x,y) = (0,8) into the first inequality, then we get

y < x^2+6

8 < 0^2+6

8 < 0+6

8 < 6

which is false. So we can rule out choice A.

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Trying choice B leads us to

y < x^2+6

2 < 4^2+6

2 < 16+6

2 < 22

That last statement is true, so the first inequality is true for (x,y) = (4,2)

Let's try the other inequality

y > x^2-4

2 > 4^2-4

2 > 16-4

2 > 12

That's false. Since one of the inequalities is false (it doesn't matter which one), this means the entire system is false. We cross choice B off the list.

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Now onto choice C

You should find that y < x^2+6 becomes -4 < 10 after plugging in (x,y) = (-2,-4). Since -4 < 10 is true, we move onto the next inequality.

The inequality y > x^2-4 becomes -4 > 0 after plugging in those mentioned x,y values. The inequality -4 > 0 is false.

We cross choice C off the list.

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The only thing left is choice D. It has to be the answer.

Let's find out if we get true inequalities when plugging in (x,y) = (2,6)

y < x^2+6

6 < 2^2+6

6 < 10 ... true

and

y > x^2-4

6 > 2^2-4

6 > 4-4

6 > 0 .... also true

Both inequalities are true, so the entire system is true. Therefore, (x,y) = (2,6) is one of the infinitely many solutions to this system.

Choice D is confirmed as the answer

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Refer to the diagram below. I've graphed the two dashed boundary curves and the shaded region between. This region is above the y = x^2-4 curve, and below the y = x^2+6 curve. So we're ignoring the stuff above the y = x^2+6 curve.

Points A through D represent the four answer choices in the order given. We see that point D is the only point in the shaded region, so that visually confirms we have the correct answer.

Note: points on the dashed boundaries do not count as solutions.

Answer:

Draw a C plane and plot the dots if the coordinates

Answer:

it's a triangle draw the chart

Answer:

12.75

Step-by-step explanation:

c = π x d

40.035= 3.14 x d

40.035/3.14 = 12.75

9 <= 17 -4x

Subtract t 17 from both sides:

-8 <= -4x

Divide both sides by-4,

2 <= x

Rewrite the inequality with the x on the left side.

Answer: x <=2

Answer:

The answer to the question: "Will Hank have the pool drained in time?" is:

Step-by-step explanation:

To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:

Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:

Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:

Now, we use a rule of three:

If:

And we calculate:

At last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:

As we know, Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes.

Answer:

Step-by-step explanation:

The lengths of the tangents drawn from an external point tot he circle are equal.

RA = RB = 12.2

QA = QC = 5.9

PC = PQ - QC = 27.4 - 5.9 = 21.5

PC = PB = 21.5

QR = QA + RA = 5.9 + 12.2 = 18.1

PR = PB + RB = 21.5 + 12.2 = 33.7

Perimeter = PQ  +  QR + PR

                 = 27.4 +  18.1 + 33.7

                 = 79.2

Answer:

in orange you cost 5.52

in apple you cost 3.9

Step-by-step explanation:

1 1/2=2×1+1=3

so multiplied the 3 in the price per pound

so in orange you got this solution

3×1.84=5.52

and in apple you got this solution

3×1.30=3.9

#CARRY ON LEARNING

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#100% SURE

Answer: B. 4.11

Step-by-step explanation:

Using Binomial distribution  ( as the arrival times of workers are independent).

Formula for standard deviation: [tex]\sqrt{{p(1-p)}{n}}[/tex], where p= population proportion, n= sample size.

As per given ,

p= 0.06, n=300

Required standard deviation= [tex]\sqrt{0.06\left(1-0.06\right)300}[/tex]

[tex]=\sqrt{(0.06)(0.94)(300)}\\\\=\sqrt{16.92}\approx4.11[/tex]

Hence, the correct option is B.

Answer:

(1 + 2h)(1 - 2h)

Step-by-step explanation:

[tex]1 - 4h^2 = 1 ^2 - (2h)^2[/tex]

          [tex]=(1 - 2h)(1 + 2h)[/tex]                       [tex][ \ a^2 - b^2 = (a - b)(a+b) \ ][/tex]

Answer:  54

The angles of a triangle add up to equal 180.

Since we already know two angles, we can just use simple math to find the third.

120 + 6 = 126

180 - 126 = 54

Answer:

54°

Step-by-step explanation:

A triangle ALWAYS measure a 180° Angle in total so if the first and second angle is 120° and 6°, just add it together and will form a 126° Angle so subtract it to 180° Angle and it will result in a 54° Angle

Thank you and please mark me as brainliest ^^

Step-by-step explanation:

a. represent the man's current age by n. Two years ago his age was n - 2.

b. Multiplication of n by the product of y and z would be (y×z)×n.

Answer:

2

Step-by-step explanation:

Answer:

infinity zeros are there

Step-by-step explanation:

please make me brainlsit answer

Answer:

not sure but I think the answers c

Answer:

y = 5x

Step-by-step explanation:

y = kx

65 = k (13)

65/13 = k

k = 5

~~~~~~~~~~~~

y = 5x

B. [tex] \sqrt{x} + \sqrt{x - 1} [/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \\ \\= \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \times \frac{ \sqrt{x} + \sqrt{x - 1} }{ \sqrt{x} + \sqrt{x - 1} } \\ \\ = \frac{ \sqrt{x} + \sqrt{x - 1} }{ ({ \sqrt{x} })^{2} - { (\sqrt{x - 1} })^{2} } \\\\ [∵(a + b)(a - b) = {a}^{2} - {b}^{2} ] \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{x - (x - 1)} \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{ x - x + 1} \\ \\= \sqrt{x} + \sqrt{x - 1} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

216

Step-by-step explanation:

Answer:

In common notation: lcm (27,72) = 216

Answer:

B) y=6x

Step-by-step explanation:

6×11-x= -72

hope you understood it please mark me as brainliest

Answer:

sinT = [tex]\frac{15}{17}[/tex]

Step-by-step explanation:

We require to calculate RT before obtaining sinT

Using Pythagoras' identity in the right triangle

RT² = 30² + 16² = 900 + 256 = 1156 ( take the square root of both sides )

RT  = [tex]\sqrt{1156}[/tex] = 34 , then

sinT = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{RS}{RT}[/tex] = [tex]\frac{30}{34}[/tex] = [tex]\frac{15}{17}[/tex]

Answer:

4x

Step-by-step explanation:

[tex]\sqrt{x} \cdot \sqrt{x} = \sqrt{x^2} = x^{ 2 \times \frac{1}{2}} = x[/tex]

[tex]given :\\\\ \sqrt{x} \cdot 4\sqrt{x} = 4 \cdot\sqrt{x} \sqrt{x} = 4 \sqrt{x^2} = 4x[/tex]

Answer:

Step-by-step explanation:

7.3

Answer:

7.3

Step-by-step explanation:

22/3 = 22/3

(Decimal: 7.333333)

Answer:

176

Step-by-step explanation:

11 pints is 176 US fluid ounces

Given:

Kiosk is the combination of a cylinder and a cone.

Diameter of cylinder and cone = 5 m

Height of the cylinder = 3 m

Height of the cone = 2 m

To find:

The volume of the kiosk.

Solution:

We know that the radius is half of the diameter. So,

Radius of cylinder and cone = [tex]\dfrac{5}{2}[/tex] m

                                               = [tex]2.5[/tex] m

Volume of the cylinder is:

[tex]V_1=\pi r^2h[/tex]

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

Putting [tex]\pi =3.14, r=2.5, h=3[/tex] in the above formula, we get

[tex]V_1=(3.14)(2.5)^2(3)[/tex]

[tex]V_1=(3.14)(6.25)(3)[/tex]

[tex]V_1=58.875[/tex]

Volume of a cone is:

[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]

Where, r is the radius and h is the height of the cone.

Putting [tex]\pi =3.14, r=2.5, h=2[/tex] in the above formula, we get

[tex]V_2=\dfrac{1}{3}(3.14)(2.5)^2(2)[/tex]

[tex]V_2=\dfrac{1}{3}(3.14)(6.25)(2)[/tex]

[tex]V_2\approx 13.083[/tex]

The volume of the kiosk is the sum of volume of cylinder and the volume of cone.

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

[tex]V=58.875+13.083[/tex]

[tex]V=71.958[/tex]

[tex]V\approx 72[/tex]

Therefore, the volume of the kiosk is 72 cubic meter.

Answer:

[tex]1\frac{13}{23}[/tex]

Step-by-step explanation:

6² ÷ 23

36 ÷ 23

[tex]1\frac{13}{23}[/tex]

Answer:

40

Step-by-step explanation:

f(4) = 3(4²) - 2(4)

= 3(16) - 8

= 48 - 8

= 40

when x=4, f(x) = 40

Answer: The surface of the ocean

Answer: It represents being at the surface

Negative values are below the surface, while positive values are above the surface.

In other words, -9 means 9 feet below sea level. The value 0 is at sea level. Something like 12 means you're 12 feet above sea level.

i think its C.No;the system has many solución

Answer:

thanks the quark is w wl1pp39iejbs sthe akwyve s akw9u27 2babe

Answer:

13 miles

Step-by-step explanation:

the distance from the soccer field to the library is 8 miles

the distance between home and soccer field is a hypotenuse, use Pythagorean theorem to find the distance.

[tex]a^2+b^2=c^2\\\\4^2+3^2=c^2\\\\16+9=c^2\\\\c^2=25\\\\c=5[/tex]

the distance is 5 miles

5 + 8 = 13 miles total