WILL MARK BRAINLIEST
The surface area of a sphere is 900pi square inches. What is the radius of the sphere?

Recall the formula SA= 4 pi r^2.
15 inches
18 inches
30 inches
60 inches

Answer:

(-2, 1)

Step-by-step explanation:

Just substitute -2 for x in y = x + 3:    y = -2 + 3 = 1.  So the solution is (-2, 1).

Answer:

Solution of the system of equations

y = x + 3

x = –2 is:

(-2,1)

Step-by-step explanation:

We have to find the solution of the system of equations:

y = x + 3

x = –2

Solution means values of x and y

x= -2

Putting it in equation y=x+3

⇒ y= -2+3

⇒ y= 1

Hence, solution of the system of equations

y = x + 3

x = –2 is:

(-2,1)

Answer:

Option B is correct.

Step-by-step explanation:

Lateral surface area of cone = π*r*l

where r is the radius and l is the height of cone.

We are given height = l  24 cm

and diameter d = 10.5 cm

we know that radius is half of diameter i.e,

r = d/2

=> r = 10.5/2

r = 5.25

Putting the values in the formula:

Lateral surface area of cone = π*r*l

Lateral surface area of cone = π*5.25*24

Lateral surface area of cone = 126 π cm^2

So, Option B is correct.

Answer: second option.

Step-by-step explanation:

We know that we can calculate the lateral surface area of a cone with this formula:

[tex]LA=\pi rl[/tex]

Where "r" is the radius and "l" is the slant heigth.

We know that the radius is half the diameter, then the radius of this cone is:

[tex]r=\frac{10.5cm}{2}\\\\r=5.25cm[/tex]

Since we know tha radius and the slant height, we can substitute values into the formula. Therefore, we get:

 [tex]LA=\pi (5.25cm)(24cm)\\\\LA=126\pi cm^2[/tex]

Answer:

(x) = 2(1/6)^x

Step-by-step explanation:

To easily solve this problem, we can graph each option using a graphing calculator, or any equation plotting tool.

Case 1

f(x) = 2(6)^x

Case 2

f(x) = 1/2*(6)^x

Case 3

f(x) = 2(1/6)^x

Case 4

f(x) = 1/2*(1/6)^x

By looking at the pictures below, we can tell that the correct option is

Case 3

f(x) = 2(1/6)^x

Since the stretch is done by a factor of 2

0.625 rounded to the nearest hundredth is 0.63

2 is in the hundredths place, and since the next number is 5 the 2 is rounded up one number giving you 0.63

Answer:

Option C

Step-by-step explanation:

we know that

The solution of the system of inequalities is the shaded area above the dashed line y=4 and above the dashed line y=x

therefore

The system of inequalities is equal to

y>4

y>x

For this case we must indicate an expression equivalent to:

[tex](2 ^ 3) ^ {-5}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

We also have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Rewriting the expression we have:

[tex](2 ^ 3) ^ {-5} = 2 ^ {-15} = \frac {1} {2 ^ {15}}[/tex]

Answer:

Option A

Answer:

12

Step-by-step explanation:

6 people

2 bagels per person

This is a multiplication problem.

2 * 6 = 12

He bought 12 bagels.

Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.

Now, Pythagoras' Theorem is defined as follows:

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:

c^2 = a^2 + b^2

24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)

b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)

b = √(24^2 - 8^2) (Take the square root of both sides)

b = √512 (Evaluate 24^2 - 8^2)

b = 16√2 (Simplify √512)

= 22.627 (to three decimal places)

I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.

Answer:

9/20 miles

Step-by-step explanation:

we know that

if the bird flies 5/6 miles north for -------------> 3/8 miles east

then

for 1 mile north------------------------------> X miles east?

X=(3/8)/(5/6)-------> 18/40-------> 9/20 miles

the answer is

9/20 miles

The bird flies 18/25 miles east for each mile travelled north.

The question is asking for the ratio of the distance a bird flies east to the distance it flies north. Given that the bird flies 3/5 mile east and 5/6 mile north, we can set up a ratio to express the distance flown east per mile flown north. This is a straightforward ratio problem, where we divide the distance east by the distance north to find the required ratio.

To find the number of miles the bird flies east for every mile it travels north, we can set up the following ratio:

Distance East / Distance North = (3/5) miles / (5/6) miles
To simplify this, we multiply by the reciprocal of the denominator, resulting in:

(3/5) * (6/5) = 18/25.

So, the bird flies 18/25 miles east for every mile it travels north.

Answer:

Each friend will get 1/3 of a bread roll.

4 bread rolls. and 12 friends.

So 4/12 = 1/3.

Hope it helps..........

Step-by-step explanation:

Answer:

1/3 is the answer.

Step-by-step explanation:

There are 12 people, and 4 bread rolls. Each person would therefore get

4 bread rolls/ 12 people, so each person would get 1/3 of a bread roll.

Answer:

$504

Step-by-step explanation:

since there is 12 months in a year , the family would pay 12$ a year.

12x12= 144

then since they paid a down payment of $360

360+144=504

so they would have paid $504

Answer:

After factorization of given expression we get 12( x + 30 ).

Step-by-step explanation:

Given:

Money Saved by Nolansky family for down payment = $ 360

x is the monthly payment for 1-year

Expression Representing the total cost of the computer = 12x + 360

To find: Factors of the given expression.

We need to factor the given expression. We do it by taking the common factor of both the term.

Consider,

12x + 360

= 2 × 2 × 3 × x +  2 × 2 × 2 × 3 × 3 × 5

= 2 × 2 × 3 × ( x + 2 × 3 × 5 )

= 12 × ( x + 30 )

= 12 ( x + 30 )

Therefore, After factorization of given expression we get 12( x + 30 ).

The speed of the commercial jet is [tex]540mi/h[/tex] while the speed of the private airplane is [tex]330mi/h[/tex]

Let's name the commercial jet as cj and private airplane as pa, so we know the following:

It takes the commercial jet 1.1 hours for the flight, so:

[tex]t_{cj}=1.1h[/tex]

It takes the private airplane 1.8 hours for the flight, so:

[tex]t_{pa}=1.8h[/tex]

The speed of the commercial jet is 210 miles per hour faster than the speed of the private airplane:

Let's name the speed of the commercial jet as [tex]v_{cj}[/tex] and the speed of the private airplane as [tex]v_{pa}[/tex], then:

[tex]v_{cj}=v_{pa}+210[/tex]

From physics we know that:

[tex]v=\frac{d}{t} \\ \\ Where: \\ \\ v: \ speed \\ \\ d: \ distance \\ \\ t: \ time[/tex]

Since the distance from Denver to phoenix is unique, then:

[tex]d_{cj}=d_{pa}=d[/tex]

Thus, from the equation [tex]v_{cj}=v_{pa}+210[/tex] and given the relationship [tex]v=\frac{d}{t}[/tex] we have:

[tex]v_{cj}=v_{pa}+210 \\ \\ \frac{d}{t_{cj}}=\frac{d}{t_{pa}}+210 \\ \\ \\ Plug \ in \ t_{cj}=1.1 \ and \ t_{pa}=1.8 \ then: \\ \\ \frac{d}{1.1}=\frac{d}{1.8}+210 \\ \\ Isolating \ d: \\ \\ d(\frac{1}{1.1}-\frac{1}{1.8})=210 \\ \\ \frac{35}{99}d=210 \\ \\ d=\frac{99\times 210}{35} \\ \\ d=594miles[/tex]

Finally, the speeds are:

[tex]\bullet \ v_{cj}=\frac{d}{t_{cj}} \\ \\ v_{cj}=\frac{594}{1.1} \therefore \boxed{v_{cj}=540mi/h} \\ \\ \\ \bullet \ v_{pa}=\frac{d}{t_{pa}} \\ \\ v_{pa}=\frac{594}{1.8} \therefore \boxed{v_{pa}=330mi/h}[/tex]

Hello :D

Answer:

[tex]\boxed{R>-1}[/tex]

The answer should have a negative sign.

Step-by-step explanation:

First, you do is divide by 17 from both sides of an equation.

[tex]\frac{17r}{17}>\frac{-17}{17}[/tex]

Then, you simplify and solve to find the answer.

[tex]-17\div17=-1[/tex]

[tex]\boxed{R>-1}[/tex], which is our answer.

I hope this helps you!

Have a great day! :D

Answer: [tex]r>-1[/tex]

Step-by-step explanation:

Given the inequality provided [tex]17r > -17[/tex], you need to solve for "r".

To do this, you can divide both sides of the inequality by 17. Then you  get the following solution:

[tex]17r > -17\\\\\frac{17r}{17}>\frac{-17}{17}\\\\(1)r>(-1)\\\\r>-1[/tex]

Now, you can expressed this solution in Interval notation form.

 Therefore, the solution of the inequality in Interval notation is:

[tex](-1, \infty)[/tex]

Answer:

34.

Step-by-step explanation:

x = 3 + 2√2

x^2 = (3+2√)^2

=  9 + 8 + 12√2

= 17 + 12√2

x^2 + 1 /x^2

= (17 + 12√2)^2 +  (1 / (17 + 12√2)

= 34.

Answer:

YZ = XZ

Step-by-step explanation:

Perpendicular Bisector:

A perpendicular bisector of a line segment 'l' is a line that is perpendicular to the line segment 'l' and cuts the line segment 'l' into two equal parts.

Given:

1. A triangle WXY.

2. A perpendicular bisector from vertex W that intersects XY at point Z.

Conclusion based on the drawing:

a. Z is the midpoint of the line segment XY because point Z lies on the perpendicular bisector of XY.

b. Hence, XZ = YZ.

Answer:

Option D.

Step-by-step explanation:

Given information: WXY is a triangle.

Steps of construction:

1. Draw a triangle WXY.

2. Constructs a perpendicular bisector from vertex W that intersects side XY at point Z.

If a line cuts a line segment exactly in half by a 90 degree angle, then it is called a perpendicular bisector.

WZ is a perpendicular bisector on XY. It means point Z divides the side XY in two equal parts.

[tex]YZ=XZ[/tex]

Therefore, the correct option is D.

Answer:

20 minutes

Step-by-step explanation:

Both will meet again at start point after LCM(60,80) seconds.

That is 240 seconds.

in time slower car completes one lap, faster one covers 1 +20/80 lap, that is 1.25 laps. After 20 laps faster by slower car car will be 5 laps ahead, time =20*60 = 1200s = 20 minutes.

hope it help

Answer:

Step-by-step explanation:

Answer:

x² + 4x - 12, remainder - 60

Step-by-step explanation:

Using synthetic division to divide

Since dividing by x - 1, evaluate for x = 1

1 | 1  3  - 16  - 48

   ↓  1     4   - 12

  ---------------------------

   1   4  - 12  - 60 ← degree 2 polynomial

quotient = x² + 4x - 12, remainder = - 60

Hence

[tex]\frac{x^3+3x^2-16x-48}{x-1}[/tex] = x² + 4x - 12 - [tex]\frac{60}{x-1}[/tex]

The division of the given polynomials x³ + 3x² - 16x - 48 by x - 1 using synthetic division results in the polynomial x² + 4x - 12 - 60/(x - 1) with a remainder of -60.

The division of two polynomials can be performed using polynomial long division or synthetic division. In this case, we have a cubic polynomial divided by a linear polynomial: x³ + 3x² - 16x - 48 divided by x - 1.

We can use synthetic division to solve this. Place the coefficients of the dividend (1, 3, -16, -48) in a row and place the zero from the divisor (x - 1= 0, x = 1) to the left. Add down the columns and multiply the result by x in each row, placing the result in the next row.

Following these steps, the coefficients become 1, 4, -12, and -60 which translates to the polynomial x² + 4x - 12 - 60/(x - 1). The remainder (-60) divided by the divisor (x - 1) is added as the last term.

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Answer:

54 degrees

Step-by-step explanation:

I would turn this into a quadrilateral by connecting C to O and O to A.

The angles of a quadrilateral add up to 360 degrees.

So we have 90+90+126+angleABC=360

                            180+126+angleABC=360

                                  306+angleABC=360

                                           angleABC=360-306=54

Answer:

ABC = 54°

Step-by-step explanation:

Two tangent have been drawn from an external point B to the circle O.

These tangents touch the circle at points A and C.

Now as per Theorem of arcs and angles.

∠ABC = [tex]\frac{1}{2}[/tex]   [m(major arc AC) - m(minor arc AC)]

          = [tex]\frac{1}{2}[/tex]  [234 - 126]

         = [tex]\frac{1}{2}[/tex]  × (108)

         = 54°

Therefore, ABC = 54°

Answer:

Second option.

Step-by-step explanation:

The angle [tex](3x+17)\°[/tex] and the angle [tex](4x-8)\°[/tex] are alternate exterior angles, then they are congruent. So we can can find "x":

[tex]3x+17=4x-8\\17+8=4x-3x\\x=25[/tex]

Then, the angle  [tex](4x-8)\°[/tex] is:

 [tex](4x-8)\°=(4(25)-8)\°=92\°[/tex]

You can observe that the angle identified in the figure attached as "3" and the angle 46° are Alternate interior angles, then they are congruent.

Since the sum of the measures of the angles that measure 92°, 46° and the angle "2" is 180°, we can find the measure of the angle "2" by solving this expression:

[tex]92\°+46\°+\angle 2=180\°\\\\\angle 2=180\°-92\°-46\°\\\\\angle 2=42\°[/tex]

Answer:I agree that 46 is correct

Step-by-step explanation:

Answer:

[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Box 1:

Number of pens = 3

Total number of items = pencils + pens = 7 + 3 = 10

Probability that a pen will be picked, P(Pen) = [tex]\frac{3}{10}[/tex]

Box 2:

Number of crayons = 3

Total number of items = color pencils + crayons = 3 + 3 = 6

Probability that a crayon will be picked, P(Crayon) = [tex]\frac{3}{6}[/tex]

P(pen from 1st box and crayon from 2nd box),

= P(Pen) x P(Crayon)

= [tex]\frac{3}{10}[/tex] x [tex]\frac{3}{6}[/tex]

= [tex]\frac{3}{20}[/tex]

Answer:

The markup is $2.48

Step-by-step explanation:

* Lets explain the problem

- There is a cost price we don't know it

- There is a selling price we know it

- There is a markup we want to find it

- The relation between the cost price , the selling price and the markup

 is ⇒ selling price - cost price = markup

∵ The percentage of the selling price is 109%

∵ The percentage of the cost price is 100%

- That means the markup rate = 109% - 100% = 9%

∵ The selling price is $29.99

- Lets use the ratio to find the cost price

∵ selling price / cost price = selling price% / cost price%

∴ 29.99 / cost price = 109 / 100

- By using cross multiplication

∴ cost price × 109 = 29.99 × 100

∴ cost price × 109 = 2999

- Divide both sides by 109

∴ cost price = $27.51

∵ The markup = selling price - cost price

∴ The markup = 29.99 - 27.51 = $2.48

* The markup is $2.48

A boy swimming at an elevation of 3 feet below sea level. This is the answer because the boy is only 3 feet away from sea level while the bird is 10 feet away form sea level.

Answer:

B. A boy swimming at an elevation of –3 feet.

Step-by-step explanation:

We have been given that a bird flies at an elevation of 10 feet. We are asked to choose the elevation that is closer to sea level than the bird.

Let us find absolute value of each elevation.

A. A fish swimming at an elevation of –18 feet.

[tex]|-18|=18[/tex]

The fish is 18 feet away from sea level.

B. A boy swimming at an elevation of –3 feet.

[tex]|-3|=3[/tex]

The boy is 3 feet away from sea level.

C. A kite flying at an elevation of 30 feet.

[tex]|30|=30[/tex]

The kite is 30 feet away from sea level.

D. A bird sitting in a tree at an elevation of 12 feet

[tex]|12|=12[/tex]

The bird is 12 feet away from sea level.

Since the distance between the boy swimming and sea level is less than other distances, therefore, the boy is closer to sea level than the bird.

The piecewise function can be graphed by graphing the two sub-functions, x+3 and 2x, separately for their defined ranges of x-values, with x+3 for 4 < x < 8 and 2x for x > 8, and combining them to form the complete graph of the piecewise function.

To graph this piecewise function, you would start by separately graphing each sub-function, x+3 and 2x, within their defined ranges of x-values, with x+3 defined for 4 < x < 8 and 2x defined for x > 8.

For 4 < x < 8, plot the line y = x + 3, but only include the section of the line where x values are greater than 4 and less than 8. Keep in mind this will not include the points where x=4 or x=8.

Next, for x > 8, plot the line y = 2x, but this time only include the section of the line where x values are greater than 8. Ensure X=8 is excluded.

The two separate lines drawn are the graphical representation of the piecewise function f(x).

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Answer:

correct answer options are ; C and D

Step-by-step explanation:

By definition, vertical angles are those that are opposite each other when two lines cross and are equal.

Observing the given options;

C. ∠LRE and ∠FRA

D.∠TRF and ∠NRL

In the other options given, it could have been correct if stated as;

A. ∠ARS and ∠ERO

B. ∠NRA and ∠TRE

Answer:

Step-by-step explanation:

1.2307692307692.

The first step is to find the proportionality constant.

The formula is

z = kx/y

1.2307692307692 = k * 4/13          Multiply both sides by 13

1.2307692307692 * 13 = 4k

16 = 4*k                                            Divide by 4

k = 16/4

k = 4

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

z = k*x/y

x = 9

y = 20

k = 4

z = 4 *9/20

z = 36/20

z = 1.8

Answer:

[tex]&\boxed{\text{1.800 000 000 0000}}[/tex]

Step-by-step explanation:

[tex]z \propto x\\\\z \propto \dfrac{1}{y}\\\\z \propto \dfrac{x}{y}\\\\z = k \left (\dfrac{x}{y} \right )[/tex]

Solve for k

[tex]\begin{array}{rcl}1.2307692307692& = & k\left (\dfrac{4}{13} \right )\\\\16.000000000000 & = & 4k\\k & = & 3.9999999999999\\\\z & = & 3.9999999999999\left (\dfrac{x}{y}\right )\\\end{array}[/tex]

Calculate the new value of z

[tex]\begin{array}{rcl}z & = & 3.999 999 999 9999 \left (\dfrac{9}{20}\right )\\\\& = &\boxed{\textbf{1.800 000 000 000}}\\\end{array}[/tex]

Answer:

The possible value of 'x' is: 3.

Step-by-step explanation:

A polynomial has no real solutions when the discriminat is less than zero. Given the following polynomial: [tex]ax^{2} +bx+c = 0[/tex] the discriminant is given by: [tex]Discriminant = b^{2}-4ac[/tex]

In this case, a=1, b=2. By substituting those values:

[tex]Discriminant = 2^{2}-4(1)c[/tex] ⇒ [tex]Discriminant = 4-4c[/tex]

Given that the discriminant should be less tha zero, then 'c' must be greater than one.

In this case, the only possible value of 'x' is: 3.

Answer:

3

Step-by-step explanation:

Given

x² + 2x + c = 0 ← in standard form

with a = 1, b = 2 and c = c

If there are no real solutions then the discriminant

b² - 4ac < 0, that is

2² - (4 × 1 × c ) < 0

4 - 4c < 0 ( subtract 4 from both sides )

- 4c < - 4

Divide both sides by - 4, reversing the sign as a consequence

c > 1

Hence a possible value of c is 3

Answer:

Step-by-step explanation:

If two equations are the same, then the system of equations has infinitely many solutions.

If two equations different only constant number, then the system of equations has no solution (coefficient at x in both equations is the same and coefficient at y is the same).

Therefore for y = 8x + 7 other equation is y = 8x - 7.

Answer:

The missing term is 3b

Step-by-step explanation:

step 1

Find the coordinates of point F

Find the midpoint AB

[tex]F(\frac{-3a+3a}{2},\frac{b+b}{2})\\ \\F(0,b)[/tex]

step 2

Find the coordinates of point E

Find the midpoint AC

[tex]E(\frac{-3a-a}{2},\frac{b-5b}{2})\\ \\E(-2a,-2b)[/tex]

step 3

Find the distance EF

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute

[tex]EF=\sqrt{(b+2b)^{2}+(0+2a)^{2}}[/tex]

[tex]EF=\sqrt{(3b)^{2}+(2a)^{2}}[/tex]

therefore

The missing term is 3b

Answer:

its 3b thats the answer

Answer:

p = 35

Step-by-step explanation:

180 - 125 = 55

180 - 90 = 90

55 + 90 = 145

180 - 145 = 35

p = 35