Curriculum 2.0 Geometry: Unit 3-Topic 1, SLT 9

Applying Volume Formulas to Pyramids and Cones


3. Determine the volume of the cone shown below. Give your answers in terms of u and then round your

answer to the nearest thousandth.

V = 58.667pi


4. Find the dimensions of a cone that is similar to the one given above and sketch the cone.

Explain how you determined your answers.

Answer:

Two solutions were found :

x = 6

x = -1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (3x2 -  15x) -  18  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  3x2 - 15x - 18  =   3 • (x2 - 5x - 6)  

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 5x - 6  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    x2 - 6x + 1x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-6)

            Which is the desired factorization

Equation at the end of step  3  :

 3 • (x + 1) • (x - 6)  = 0

In Conclusion, the answer would be 0.

Answer:

1,7,49

Step-by-step explanation:

Answer: 7 squared

Step-by-step explanation:

49 = 1 x 49 or 7 x 7.

Factors of 49: 1, 7, 49.

Prime factorization: 49 = 7 x 7

which can also be written 49 = 7².

Answer:

sales tax on a bottle of window cleaning solution = $0.1533

sales tax on a gel pen=$0.1925

Step-by-step explanation:

The price of bottle of window cleaning solution = $2.19

Sales tax =7%

Applying the tax, 7/100 * 2.19 = $0.1533

The price of a gel pen = $2.75

Applying the sales tax;

7/100 * 2.75 = $0.1925

The 7% sales tax on a $2.19 bottle of window cleaning solution and a $2.75 gel pen is around $0.35.

To calculate the 7% sales tax on a $2.19 bottle of window cleaning solution and a $2.75 gel pen, you first need to find the total cost of the items. Add $2.19 and $2.75 which equals $4.94. This is your base amount on which you will calculate the sales tax.

To get the tax amount, multiply the total cost by the tax rate as a decimal (7% = 0.07). So, $4.94 * 0.07 = $0.35 approximately. This will be the sales tax charged on these items.

Therefore, if you buy a window cleaning solution and gel pen, you would pay around $0.35 in taxes assuming a 7% sales tax.

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Answer: p = 16

Step-by-step explanation: 125 divided by 5 is 25

then subtract 25 by 9 to get 16 so p = 16

hope this helps please mark brainliest

Answer:

39 or 100

Step-by-step explanation:

45 47 54 56 81 94

Range is 94 - 45 = 49

Either add 100 or 39 to the set.

94+6 = 100

45-6 = 39

Exterior Angle Property

Step-by-step explanation:

Interior Angle :

The angle formed with in the closed boundary of the triangle is called an interior angle.

In the given figure,  α ,  β and γ are interior angles.

Exterior Angles:

The angle formed outside the closed boundary of the triangle is called an exterior angle.

In the given figure,  γ' is an exterior angles.

Sum of the measures of the two non-adjacent interior angles  is EQUAL to  measure of an exterior angle of a triangle.

⇒   α +    β   = γ'

This property is known as " Exterior Angle Property"

Also, here angles  γ and γ' are making a linear pair.

γ +     γ'  =  180°

Answer:

9/10

Step-by-step explanation:

first you find the lowest common denominator. 1/2 becomes 5/10, 2/5 becomes 4/10. 5/10+4/10=9/10

Answer: 466.67 calories in 2 cups of spaghetti

Step-by-step explanation: if there are 350 calories in 1 1/2 cups of spaghetti you only need have a cup to make 2 cups then 1/3 of 350 calories is 116.67

so 350 + 116.67= 466.67

please give brainliest

This question pertains to Health in Middle School.

The subject of this question is Health and the grade level is Middle School.

Answer:

(x - 2)² + (y + 3)² = 9

Step-by-step explanation:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - (-3))² = 3²

(x - 2)² + (y + 3)² = 9

The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

The correct option is (B).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

As per the given data:

We are given the coordinates for the center of a circle and the measure of the radius of the circle. We have to find out the equation of the circle

The coordinates of the center of the circle (O) = (2, -3)

The radius of the circle = 3

The standard equation of the circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

By substituting (h, k) ⇒ (2, -3) and r = 3

(x - 2)^2 + (y + 3)^2 = 3^2

= (x - 2)^2 + (y + 3)^2 = 9

The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

Hence, The equation of the circle is (x - 2)^2 + (y + 3)^2 - 9 = 0.

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Answer:

Step-by-step explanation:

D.The left end goes up and the right end goes down because this is a first order function

The end behavior of the function f(x) = -2(x - 2)^5 is that the left end goes up and the right end goes down. This is determined by the odd degree and negative leading coefficient of the function.

The end behaviors of a function can be determined by looking at the highest degree term, also known as the leading term. In this case, for the function f(x) = -2(x - 2)^5, the highest degree is odd (5), and the coefficient, -2, is negative.

Odd degree with a negative leading coefficient means that the end behaviors of this function will be: as x approaches negative infinity (moves left), the function values will go toward positive infinity (up), and as x approaches positive infinity (moves right), the function values will go toward negative infinity (down).

So the correct option here is: D. The left end goes up; the right end goes down.

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Answer:

13

Step-by-step explanation:

14+9+20+5+17+13 = 78

78/6= 13

To find the mean you always add all the data and then divide it by the amount of data.

Answer: irrational number

Step-by-step explanation:

4π is an irrational number.

The number 4π is an irrational number. An irrational number is a number that cannot be expressed as a fraction. In this case, 4π is the product of the rational number 4 and the irrational number π. Since π is an irrational number, their product, 4π, is also an irrational number.

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Answer:

$13.14

Step-by-step explanation:

60 mi/1 hour = x mi/1.5 hours

x = 90 mi to drive to work

25 mi/1 gallon = 90 mi/y gallons

y = 3.6 gallons to get to work

$3.65/1 gallon = $z/3.6 gallons

z = $13.14

Justin spends $13.14 on gas to get to work.

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The average speed of Justin when he goes to work is 60 miles/hour.

The time taken to reach to work is 1 hour 30 minutes.

Justin's car travels 25 miles for 1 gallon of gas.

The cost for one gallon of gas is $3.65 per gallon.

The total miles travelled is 60 miles/ hour * 1 hour 30 minutes.

Total miles travelled = 60 * (1.5)

Total miles travelled = 90 miles

The gas used for 25 miles is 1 gallon

The gas used for 90 miles is 90/25 = 3.6 gallon.

The cost of gas is $3.65 per gallon

The cost of 3.6 gallon is 3.65 *3.65

The cost of the gas used to get to work is $13.14.

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Answer:

-121

Step-by-step explanation:

-11² = -1 × 11² = -1 × 121 = -121

Answer:

If the negative is included in the square, that makes the number positive.

(-11)^2 = 121

If the negative is not included in the square, that makes the number negative.

-(11^2) = -121

Answer:

190 cm^2

Step-by-step explanation:

Base: 10 × 3 = 30 (×2 = 60)

Small faces: 5 × 3 = 15 (×2 = 30)

Larger faces: 5 × 10 = 50 (×2 = 100)

Add: 100 + 60 + 30 = 190

The Simplification of the expression of 2x + x  can be written as 3x

A mathematical expression is simplified when it is expressed in the simplest way possible. The expression is usually reduced to its simplest form by using fundamental features of numbers, exponents, algebraic principles, etc. to eliminate any repetitions or redundancies.

Given that 2x + x

Then we can factorize as

x(2+1)

=(x*3)

=3x

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Answer:

This is khan answear

Assign a number to each student, and use a computer program to generate 150150150 random numbers between 111 and 150015001500. Ask those students whose numbers are selected.

Step-by-step explanation:

Answer:

Assign a number to each student, and use a computer program to generate 150 random numbers between 1 and 150. Ask those students whose numbers are selected.

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

It says to work out what is in parentheses first, (PEMDAS).

For example:

2(5 - 3) - 1    

5 - 3 = 2 so we have:

2 * 2 - 1

= 4 - 1

= 3.

Answer:

3+n

Step-by-step explanation:

Simple questions but it can be technical atimes, according to the question we are to solve in terms of n, simple...

The sum of 3 and n can be written as 3+n

This cannot be solved further because there are two different variables and it is impossible to add them together

Therefore the final answer is 3+n

But in case a value is given for n we can then substitute and solve further

Hope this will help you

Answer:

Step-by-step explanation:

n+3

3+n

Answer:

The answer is 216 I got It wrong at first but the other answer has it right so I changed mine so no one gets confused.

Step-by-step explanation:

Answer:

216 inches is the volume

Step-by-step explanation:

multiply length times width times height

Answer:

A. 5x + 2x - 4 = 2x2  <- Yes

x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

B. x^2 - 6x - 7 = 2x    <- Yes

x = 4 + sqrt(23) or x = 4 - sqrt(23)

C: 5x^2 – 3x+ 10 = 2x2    <- Yes

x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)  

D . 2x^2 – 3x+ 10 = 2x^2 + 21x = -11/3     <- No

Step-by-step explanation:

Solve for x over the real numbers:

5 x + 2 x - 4 = 2 x^2

5 x + 2 x - 4 = 7 x - 4:

7 x - 4 = 2 x^2

Subtract 2 x^2 from both sides:

-2 x^2 + 7 x - 4 = 0

Divide both sides by -2:

x^2 - (7 x)/2 + 2 = 0

Subtract 2 from both sides:

x^2 - (7 x)/2 = -2

Add 49/16 to both sides:

x^2 - (7 x)/2 + 49/16 = 17/16

Write the left hand side as a square:

(x - 7/4)^2 = 17/16

Take the square root of both sides:

x - 7/4 = sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

x = 7/4 + sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

Answer: x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

______________________________________________

Solve for x over the real numbers:

x^2 - 6 x - 7 = 2 x

Subtract 2 x from both sides:

x^2 - 8 x - 7 = 0

Add 7 to both sides:

x^2 - 8 x = 7

Add 16 to both sides:

x^2 - 8 x + 16 = 23

Write the left hand side as a square:

(x - 4)^2 = 23

Take the square root of both sides:

x - 4 = sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

x = 4 + sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

Answer: x = 4 + sqrt(23) or x = 4 - sqrt(23)

_________________________________________________

Solve for x:

5 x^2 - 3 x + 10 = 2 x^2

Subtract 2 x^2 from both sides:

3 x^2 - 3 x + 10 = 0

Divide both sides by 3:

x^2 - x + 10/3 = 0

Subtract 10/3 from both sides:

x^2 - x = -10/3

Add 1/4 to both sides:

x^2 - x + 1/4 = -37/12

Write the left hand side as a square:

(x - 1/2)^2 = -37/12

Take the square root of both sides:

x - 1/2 = 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

x = 1/2 + 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

Answer: x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)

________________________________________________

Solve for x over the real numbers:

2 x^2 - 3 x + 10 = 2 x^2 + 21

Subtract 2 x^2 + 21 from both sides:

-3 x - 11 = 0

Multiply both sides by -1:

3 x + 11 = 0

Subtract 11 from both sides:

3 x = -11

Divide both sides by 3:

Answer: x = -11/3

Answer: A. 5x + 2x - 4 = 2x2  <- Yes

x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

B. x^2 - 6x - 7 = 2x    <- Yes

x = 4 + sqrt(23) or x = 4 - sqrt(23)

C: 5x^2 – 3x+ 10 = 2x2    <- Yes

x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)  

D . 2x^2 – 3x+ 10 = 2x^2 + 21x = -11/3     <- No

Solve for x over the real numbers:

5 x + 2 x - 4 = 2 x^2

5 x + 2 x - 4 = 7 x - 4:

7 x - 4 = 2 x^2

Subtract 2 x^2 from both sides:

-2 x^2 + 7 x - 4 = 0

Divide both sides by -2:

x^2 - (7 x)/2 + 2 = 0

Subtract 2 from both sides:

x^2 - (7 x)/2 = -2

Add 49/16 to both sides:

x^2 - (7 x)/2 + 49/16 = 17/16

Write the left-hand side as a square:

(x - 7/4)^2 = 17/16

Take the square root of both sides:

x - 7/4 = sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

x = 7/4 + sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

Answer: x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

______________________________________________

Solve for x over the real numbers:

x^2 - 6 x - 7 = 2 x

Subtract 2 x from both sides:

x^2 - 8 x - 7 = 0

Add 7 to both sides:

x^2 - 8 x = 7

Add 16 to both sides:

x^2 - 8 x + 16 = 23

Write the left-hand side as a square:

(x - 4)^2 = 23

Take the square root of both sides:

x - 4 = sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

x = 4 + sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

Answer: x = 4 + sqrt(23) or x = 4 - sqrt(23)

_________________________________________________

Solve for x:

5 x^2 - 3 x + 10 = 2 x^2

Subtract 2 x^2 from both sides:

3 x^2 - 3 x + 10 = 0

Divide both sides by 3:

x^2 - x + 10/3 = 0

Subtract 10/3 from both sides:

x^2 - x = -10/3

Add 1/4 to both sides:

x^2 - x + 1/4 = -37/12

Write the left-hand side as a square:

(x - 1/2)^2 = -37/12

Take the square root of both sides:

x - 1/2 = 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

x = 1/2 + 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

Answer: x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)

________________________________________________

Solve for x over the real numbers:

2 x^2 - 3 x + 10 = 2 x^2 + 21

Subtract 2 x^2 + 21 from both sides:

-3 x - 11 = 0

Multiply both sides by -1:

3 x + 11 = 0

Subtract 11 from both sides:

3 x = -11

Divide both sides by 3:

Answer: x = -11/3

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Given:

ABCD is a cyclic quadrilateral.

m∠C = 43°

To find:

The measure of ∠A.

Solution:

In cylic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ m∠A + 43° = 180°

Subtract 43° from both sides.

⇒ m∠A + 43° - 43° = 180° - 43°

⇒ m∠A = 137°

The measure of ∠A is 137°.

Answer:

$103.75

Step-by-step explanation:

we know that

Karen earns $62.25 for working 9 hour

so

using proportion

Find out  how much she will  earn for working 15 hours

[tex]\frac{62.25}{9}\ \frac{\$}{h}=\frac{x}{15}\ \frac{\$}{h}\\\\x=62.25(15)/9\\\\x=\$103.75[/tex]

2cm=6ft.

Length=6cm=3×(2cm)=>3×6=18ft

Width=4cm=2×(2cm)=>2×6=12ft.

Answer: 3rd option, length=18ft, width=12ft

On Wednesday, 64 people were sent the message as each of the 16 recipients forwarded the message to 4 other people.

To determine the number of people sent the message on Wednesday, we need to consider the number of people who received the message on each day. On Monday, Zach sent the message to 4 friends, so there were 4 recipients. On Tuesday, each of the 4 friends forwarded the message to 4 other people, resulting in a total of 4 friends x 4 recipients = 16 recipients. On Wednesday, each of these 16 recipients forwarded the message to 4 other people, resulting in a total of 16 recipients x 4 recipients = 64 people sent the message on Wednesday.

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Answer:

∠ K = 35° and ∠ L = 105°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

let ∠ K = x then ∠ L = 3x

Sum the angles and equate to 180

3x + x + 40 = 180, that is

4x + 40 = 180 ( subtract 40 from both sides )

4x = 140 ( divide both sides by 4 )

x = 35

Thus

∠ K = 35° and ∠ K = 3x = 3 × 35 = 105°

Answer:

[tex]\frac{2}{13}[/tex]

Step-by-step explanation:

In probability,

"OR" means "addition"

"AND" means "multiplication"

We want probability of A "OR" B, that means we find each individual probability and "ADD" them.

P(A) means P(choosing a 3 card):

There are 4 three-cards, 1 from each suit, and a total of 52 cards, so

P(A) = 4/52 = 1/13

P(B) means P(choosing a 7 card):

There are 4 seven-cards, 1 from each suit, and a total of 52 cards, so

P(B) = 4/52 = 1/13

Now,

P(A or B) = P(A) + P(B) = 1/13 + 1/13 = 2/13

The answer is  [tex]\frac{2}{13}[/tex]

Answer: 2/13

Step-by-step explanation:

Answer:

3 seconds

Step-by-step explanation:

We have to give us the following function h (t) = - 16 * t ^ 2 + 48 * t + 3

Now, they tell us that the height is 3 feet, therefore replacing that value we have left:

3 = -16 * t ^ 2 + 48 * t + 3, operating cancels 3. And it would be:

-16 * t ^ 2 + 48 * t = 0

Removing common factor -16 * t, it would be:

(-16 * t) * (t - 3) = 0

We have two solutions:

-16 * t = 0 ---> t = 0

 t - 3 = 0 ---> t = 3

Because the time cannot be 0 seconds, the time it would take the ball in the air is 3 seconds.

The ball was in the air for 3 seconds.

To find how long the ball was in the air when the catcher caught it 3 feet above the ground, we need to solve for t in the equation -16t^2 + 48t + 3 = 3. Simplifying the equation, we get -16t^2 + 48t = 0. Factoring out 16t, we have 16t(-t + 3) = 0. Setting each factor equal to zero, we find two solutions: t = 0 and t = 3 seconds. Since we are only interested in the time the ball was in the air, we discard the solution t = 0 and conclude that the ball was in the air for 3 seconds.

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