A regulation basketball hoop has a rim with an 18-inch diameter. What is the approximate length around the rim of a regulation basketball hoop?

Answer:

x= [tex]2-\sqrt{3}[/tex]          and          x=[tex]2+\sqrt{3}[/tex]

Step-by-step explanation:

- transfer the -1 to the other side so that the equation reads as [tex]x^{2} -4x+1[/tex]

- factor! think about what numbers add -4 but also multiply to be 1

- you may then realize that there are no numbers with those characteristics

- since that is the case, we have to use the quadratic formula, which is:

               [tex]\frac{-b+\sqrt{b^{2}-4ac }}{y}[/tex]        and         [tex]\frac{-b-\sqrt{b^{2}-4ac }}{y}[/tex]

- the equation is shown as [tex]a^{2}+b^{2}=c^{2}[/tex]

- using the numbers that correspond with those lettered values, plug it in the quadratic formulas

the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

To find the solutions to the equation [tex]\( x^2 - 4x = -1 \)[/tex], we can follow these steps:

1. Move all terms to one side of the equation to set it equal to zero:

 [tex]\[ x^2 - 4x + 1 = 0 \][/tex]

2. We can solve this quadratic equation using the quadratic formula:

  [tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

  where [tex]\( a = 1 \), \( b = -4 \), and \( c = 1 \).[/tex]

3. Plug in the values and simplify:

  [tex]\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)} \] \[ x = \frac{4 \pm \sqrt{16 - 4}}{2} \] \[ x = \frac{4 \pm \sqrt{12}}{2} \] \[ x = \frac{4 \pm 2\sqrt{3}}{2} \] \[ x = 2 \pm \sqrt{3} \][/tex]

So, the solutions to the equation [tex]\( x^2 - 4x = -1 \) are \( x = 2 + \sqrt{3} \) and \( x = 2 - \sqrt{3} \)[/tex].

Answer:

21

Step-by-step explanation:

(9g+4)-55=

(72+4)-55=

76-55=

21

Final answer:

To find the answer, first multiply 9 by 8, then add 4, resulting in 76. Finally, subtract 55 to get the answer, which is 21.

Explanation:

To solve the problem, we need to first calculate the sum of 9g and 4 when g=8. This will be 9 × 8 + 4.

After calculating the sum, we will subtract 55 from this amount to get the final answer.

Following the steps:

Therefore, when g = 8, subtracting 55 from the sum of 9g and 4 results in  21.

Answer: 2713 cubic centimeter

Step-by-step explanation:

Answer:

339 cubic centimeters

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]. In this case, a ball with the radius of 3 centimeters would have a volume of [tex]\frac{4}{3}\pi \cdot 3^3=113.04[/tex] cubic centimeters. Multiplying this by the three soccer balls, you get about 339 cubic centimeters, or the third option. Hope this helps!

Answer:

B. Opposite angles add up to 180 degrees.

Step-by-step explanation:

Answer Choice B is incorrect because opposite angles are actually congruent. However, adjacent angles of a parallelogram do add up to 180 degrees.

Answer:

8

Step-by-step explanation:

3m + 9 -9m = 2m + 25

3m + 9 = 11m + 25

9 = 8m + 25

16/2 = 8m/2

M = 8

Answer:

Step-by-step explanation:

[tex](\frac{a^{4}}{-7b^{3}})^{2}=\frac{(a^{4})^{2}}{(-7b^{3})^[2}}\\\\=\frac{a^{4*2}}{(-7)^{2}b^{3*2}}\\\\=\frac{a^{8}}{49b^{6}}[/tex]

Answer:

Three students voted for horns.true

Step-by-step explanation:thats all i know

Answer:

B, D, E, F

Step-by-step explanation:

Three students voted for horns.

Thirteen students voted for piano or guitar.

Twice as many students voted for piano as horns.

Eleven students voted for flute or guitar.

Answer:

im not sure

Step-by-step explanation:

so sorry i didnt know the answer.

Answer:

the perimeter of the rectangle is 23.75 feet.

Step-by-step explanation:

5 5/8 × 2 = 11 1/4.

6 1/4 × 2 = 12 1/2

11 1/4 + 12 1/2 = 23 3/4 or 23.75

Answer:

The center of data is a single number that summarizes the entire data set.

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

-4x < 8

-8 < 4x

-2 < x

x > -2

We have been given a sphere with radius 8.6 ft. We are asked to find the surface area of the given sphere.

We know that surface area of a sphere is equal to [tex]4\pi r^2[/tex].

[tex]A=4\pi r^2[/tex]

Upon substituting [tex]r=8.6\text{ ft}[/tex] in surface area formula, we will get:

[tex]A=4\pi (8.6\text{ ft})^2[/tex]

[tex]A=4\pi \cdot 73.96\text{ ft}^2[/tex]

[tex]A=295.84\pi\text{ ft}^2[/tex]

[tex]A=929.4087706\text{ ft}^2[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]A\approx 929.41\text{ ft}^2[/tex]

Therefore, the surface of the given sphere would be approximately [tex]929.41\text{ ft}^2[/tex].

Answer:

18 is for the top

6 is for the bottom

Answer:

1. C

2. D

Step-by-step explanation:

Answer:

$114.17

Step-by-step explanation:

First we need to convert cubic yard to cubic feet.

One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.

So the cost of one cubic feet is 64/27 = $2.3704

We also need to convert from inches to feet.

One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet

Now we need to find the volume of the slab:

Volume = 17 * 17 * (1/6) = 48.1667 ft3

Now, to find the cost, we can use a rule of three:

1 cubic feet -> $2.3704

48.1667 cubic feet -> X

X = 48.1667 * 2.3704 = $114.1743

Answer:

x=2 x=-2

Step-by-step explanation:

f(x)=4x^2−16

f(x)=4(x^2-4)

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

x=2 x=-2

Hope this helps! Please mark brainliest :)

The zeros of the function f(x) = 4x2 − 16 are found by factoring the quadratic equation, which results in two solutions x = -2 and x = 2.

To find the zeros of the function f(x) = 4x2 − 16, we need to set the function equal to zero and solve for x:

0 = 4x2 - 16

To solve this quadratic equation, you can factor out the common factor of 4:

0 = 4(x2 - 4)

We now have a difference of squares, which can be factored further:

0 = 4(x + 2)(x - 2)

Set each factor in the parentheses equal to zero:

So the zeros of the function are x = -2 and x = 2.

Answer:

416 x 5 = 2080

721 x 8 = 5768

5768 + 2080 = 7848. Have a great day.

Answer:

The answer is $321,631.08

Step-by-step explanation:

I just did a test on it. Got it wrong, but it showed me the right answer.

Answer:

321,621,numbers

Step-by-step explanation:

Let r represent the radius of cylinder.

We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].

We will use lateral surface area of pyramid to solve our given problem.

[tex]LSA=2\pi r h[/tex], where,

LSA = Lateral surface area of pyramid,

r = Radius,

h = height.

Upon substituting our given values in above formula, we will get:

[tex]LSA=2\pi r\cdot (1.5)r[/tex]  

Now we will find the total surface area of cylinder.

[tex]TSA=2\pi r(r+h)[/tex]

[tex]TSA=2\pi r(r+1.5r)[/tex]

[tex]TSA=2\pi r(2.5r)[/tex]

[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]

[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]

[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]

[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]

Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].

To increase £258 by 43%, convert the percentage to a decimal, calculate the increased amount, and add it to the original amount. The increased amount to the original amount is £368.94

To increase £258 by 43% using the multiplier method:

Convert the percentage to a decimal: 43% = 0.43

Calculate the increased amount: £258 x 0.43 = £110.94

Add the increased amount to the original amount: £258 + £110.94 = £368.94

the actual distance between the two towns is 360 miles.

The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.

Given, On a map, the distance between two towns is 12 centimeters.

Also given, 3 centimeters represent 90 miles on the map.

Since 12 centimeters represent the distance between the two towns on the map, we can set up the proportion:

3 centimeters : 90 miles = 12 centimeters : x miles

where x represents the actual distance between the two towns in miles.

To solve for x, we can cross-multiply and simplify:

3 centimeters * x miles = 90 miles * 12 centimeters

3x = 1080

x = 360

Therefore, the actual distance between the two towns is 360 miles.

Learn more about scale here:

https://brainly.com/question/1287267

#SPJ6

Answer:

see below

Step-by-step explanation:

V = l*w*h for the rectangular  tank

V = 70* 40*40

  =112000 cm^3 = 1mL

The water is 84000

Make this a fraction

84000/112000  = 3/4

The water fills 3/4 of the tank

1-3/4 = 1/4

It is 1/4 from the top

Find the volume of the treasure chest

V = 12*10*8 =960

Tower

V = pi r^2

  3.14 * 10^2 *10

  =3140

Water + chest + tower

84000+960+3140 =88100

This is less than 112000 so the water will not overflow

Answer:

a) 10 cm

b) Will not overflow

Step-by-step explanation:

8400 = base area × height

84000 = 70 × 40 × h

h = 30

From the top: 40 - 30 = 10cm

b) Capacity of the tank:

70 × 40 × 40

112,000 cm³

Combined volume of the two vessels:

(12 × 10 × 8) + (3.14 × 10² × 10)

960 + 3140

4,100 cm³

4100 = 70 × 40 × rise

rise = 1.464285715 cm

Since 1.464285715 < 10

It will not overflow

Answer:

20 pages

Step-by-step explanation:

Answer:

20 pages

Step-by-step explanation:

3/5 minute =36sec

if 36=12

.·.60= 60×12÷36=20

Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base

Step-by-step explanation:

a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula

Answer:

Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.

Step-by-step explanation:

I just did it on edge

Final answer:

The new cost of houses after a 25% increase from the original price of £100,000 is £125,000. You calculate this by finding 25% of £100,000, which is £25,000, and then add it to the original price.

Explanation:

The student is asking how to calculate the new cost of houses after a 25% price increase from the previous year when the houses cost
£100,000. To find the new price, we need to calculate 25% of £100,000 and then add that to the original price.

First, find 25% of £100,000:

0.25
(multiplier for 25%)
× £100,000
(original cost)
= £25,000
(the increase).

Next, add the increase to the original cost:

£100,000
+ £25,000
= £125,000.

Therefore, the new cost of the houses after a 25% increase is £125,000.

Answer:

[tex]y = 66.25(1.11)^x[/tex]

Step-by-step explanation:

Let's plug in 9 for x and 171 for y into the given exponential equation:

y = [tex]ab^x[/tex]

171 = [tex]ab^9[/tex]

Now do the same with (10, 190):

190 = [tex]ab^{10}[/tex]

Write them both in terms of a and set them equal:

a = 171/[tex]b^9[/tex]

a = 190/[tex]b^{10}[/tex]

171/[tex]b^9[/tex] = 190/[tex]b^{10}[/tex]

Multiply both sides by [tex]b^{10}[/tex]:

171b = 190

b = 190/171 = 10/9 ≈ 1.11

Plug this in to find a:

a = 171 / (10/9)^9 ≈ 66.25

So, the exponential model is:

[tex]y = 66.25(1.11)^x[/tex]

Answer:

y = 66.25[(10/9)^x]

Step-by-step explanation:

171 = a(b⁹)

b⁹ = 171/a

190 = a(b¹⁰)

190 = a(171/a) × b

b = 190/171

b = 10/9

(10/9)⁹ = 171/a

a = 66.24890362

In one year, the Perseid meteor shower had a meteor appear every 1 1/5 minutes on average. That same year, the Leonid meteor shower had a meteor appear every 4 2/3 minutes on average. How many more meteors fell during the Perseid meteor shower?

Answer:

325,452 meteors

Step-by-step explanation:

We all know that :

We have 365 days in a year and in each day there are 24 hours, Likewise an hour has 60 minutes

SO, the total number of minutes in a year is :

365 × 24 × 60 = 525600 minutes

For Perseid  meteor:

[tex]1 + \frac{1}{5} \\ \\ = 1 + 0.2 \\ \\ = 1.2[/tex]

So one meteor fall at 1.2 minutes interval Thus, in a year, we will have :

1 meteor - 1.2 minutes.

x meteor - 525600 minutes.

1.2x = 525600

[tex]x = \frac{525600}{1.2}[/tex]

x = 438000

∴  438,000 meteors fell during the Perseid shower.

For  Leonid meteor shower:

[tex]4 + \frac{2}{3} = 4.67[/tex]

So one meteor fall at 4.67 minutes interval Thus, in a year, we will have :

1 meteor - 4.67 minutes.

x meteors - 525600 minutes.

[tex]4.67x = 525600[/tex]

[tex]x = \frac{525600}{4.67}[/tex]

x = 112548

112,548 meteors fell during the Leonid Shower.

Finally , the numbers of more meteors that  fell during the Perseid meteor shower is calculated by the difference in the number of Perseid meteor shower and Lenoid meteor shower. i.e

438,000 - 112,548 = 325,452

325,452 more meteors fell during the Perseid meteor shower

Answer:

For Leonid meteor shower: So one meteor fall at 4.67 minutes interval Thus, in a year, we will have : 1 meteor - 4.67 minutes. x meteors - 525600 minutes

Step-by-step explanation:

Answer:

30 ,345,986

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

If e = 7, you would replace e in the expression e - 2 with 7 so that the expression becomes 7 - 2 which results in 5.

Does that help?

Answer:

360.82 units

Step-by-step explanation:

The circle has a circumference of 1,133.54 units.

The circumference of a circle is given as:

C = πD

where D = diameter

This implies that:

1133.54 = πD

=> D = 1133.54 / π

D = 360.82 units

Its diameter is 360.82 units

Answer:

5940 y

Step-by-step explanation:

Simplify the following:

-11 (-9)×5×3×4 y

-9×3 = -27:

-11×5×-27×4 y

-27×4 = -108:

-11×5×-108 y

-11×5 = -55:

-108-55 y

-55 (-108) = 5940:

Answer: 5940 y