Find the volume of the figure: a cone with a square pyramid of the same height cut out. The pyramid has height l, and its square base has area l2.

Answer:

(f º f)(3) = 30, when f(x) = x² - x

Step-by-step explanation:

This is a great example of composite functions and how to multiply one function by another.  (f º f) really means f(f(x)), or replacing every x in the original function f(x) with the function f(x).

Step 1: State the original function.

[tex]f(x) = x^{2} -x[/tex]

Step 2: Insert the function f(x) wherever there is an x.

[tex]f(f(x))=(x^{2} -x)^{2} -(x^2-x)[/tex]

Step 3: Expand anything that has an exponent. Remember: [tex](x+y)^2 = (x+y)(x+y)[/tex]

[tex]f(f(x))=(x^{2} -x)(x^{2} -x) -(x^2-x)[/tex]

Step 4: Foil the parts of the equations in brackets by multiplying the first terms, outside terms, inside terms and last terms in each bracket.

[tex]f(f(x))=(x^{4}-x^3-x^3+x^{2}) -(x^2-x)[/tex]

Step 5: Now you can remove the brackets (don'f forget to switch the symbols for the second brackets because you are subtracting) and sum the like terms.

[tex]f(f(x))=x^{4}-x^3-x^3+x^{2} -x^2+x[/tex]

[tex]f(f(x))=x^{4}-2x^3+x[/tex]

Step 6: Finally, substitute the given x value, which is 3, into the new equation.

[tex]f(f(x))=(3)^{4}-2(3)^3+(3)[/tex]

[tex]f(f(x))=81-54+3[/tex]

[tex]f(f(x))=30[/tex]

Therefore the answer is (f º f)(3) = 30.

Answer:

30

Step-by-step explanation:

Method 1:

ƒ(x) = x² - x

(f∘f)(x) = f(f(x)) = f(x²-x) = (x² - x)² - (x² - x) = x⁴ - 2x³ + x² - x² + x =  x⁴ - 2x³ + x

(f∘f)(3) = 3⁴ - 2(3)³ + 3 = 81 - 54 + 3 = 30

Method 2:

f(3) = 3² - 3 = 9 - 3 = 6

(f∘f)(3) = f(f(3)) = f(6) = 6² - 6 = 36 - 6 = 30

x=-52

w=15

b=4.8

s=9.7

p=15

m=3.2

Q1.

[tex]x + 20 = - 32[/tex]

Add -20 to both sides of the equation.

[tex]x + 20 - 20 = - 32 - 20[/tex]

Simplify

[tex]x = - 52[/tex]

Q2.

[tex]w + 10 = 25[/tex]

Add -10 to both sides of the equation.

[tex]w + 10 - 10 = 25 - 10[/tex]

[tex]w = 15[/tex]

Q3.

[tex]7.2 + b = 12[/tex]

Add -7.2 to both sides of the equation.

[tex] - 7.2 + 7.2 + b = 12 - 7.2[/tex]

[tex]b = 4.8[/tex]

Q4.

[tex]5.3 + s = 15[/tex]

Add -5.3 to both sides to get,

[tex]s + 5.3 - 5.3 = 15 - 5.3[/tex]

Simplify:

[tex]s = 9.7[/tex]

Q5.

[tex]p + ( - 25) = - 10[/tex]

Add 25 to both sides,

[tex]p - 25 + 25 = - 10 + 25[/tex]

[tex]p = 15[/tex]

Q6.

[tex]m + - 1.6 = -4.8[/tex]

Add 1.6 to both sides of the equation;

[tex]m + - 1.6 + 1.6 = - 4.8 + 1.6[/tex]

[tex]m = - 3.2[/tex]

Answer:

$12

Step-by-step explanation:

Let p be the store's cost (cost to buy the product wholesale).

Then the selling price is p + markup, or

                                         p + 0.80p = 1.80 p

and this comes to $21.60.

Dividing $21.60 by 1.80 results in p = $12.

The cost to the store is $12.

Simplifying

0.5p + -3.45 = -1.2

Reorder the terms:

-3.45 + 0.5p = -1.2

Solving

-3.45 + 0.5p = -1.2

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '3.45' to each side of the equation.

-3.45 + 3.45 + 0.5p = -1.2 + 3.45

Combine like terms: -3.45 + 3.45 = 0.00

0.00 + 0.5p = -1.2 + 3.45

0.5p = -1.2 + 3.45

Combine like terms: -1.2 + 3.45 = 2.25

0.5p = 2.25

Divide each side by '0.5'.

p = 4.5

Simplifying

p = 4.5

The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 0.5p-3.45=-1.2

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

0.5p-3.45=-1.2

0.5p= -1.2+3.45

0.5p= 2.25

p= 2.25/0.5

p= 4.5

Therefore, the value of p is 4.5.

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Answer:

A and E

Step-by-step explanation:

thats what it is

D is the correct answer

Answer: D

Hope this Helps!

Answer:

X=2 F=6 This works for both equations. Hope this helps!

Step-by-step explanation:

Answer:

The exponential function [tex]f(x)=2(3^x)[/tex] has an initial value of 2. The correct option is 1.

Step-by-step explanation:

The general form of an exponential function is

[tex]g(x)=ab^x[/tex]

Where, a is initial value and b is growth or decay factor.

In option 1, the given function is

[tex]f(x)=2(3^x)[/tex]

Here, the initial value is 2 and growth factor is 3. Therefore the correct option is 1.

In option 2, the given function is

[tex]f(x)=3(2^x)[/tex]

Here, the initial value is 3 and growth factor is 2. Therefore option 2 is incorrect.

Answer:

The border is 105 cm long

Step-by-step explanation:

The length of the border of the mirror is 105 cm.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The mirror is in the shape of a triangle.

Each side of the triangle.

Now,

The perimeter of the mirror.

= 3 x side

= 3 x 35 cm

= 105 cm

Thus,

The length of the border is 105 cm.

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Answer:

144 in³

Step-by-step explanation:

The volume of a pyramid of base area A and height h is

V = (1/3)(A)(h).

Here,

V = (1/3)(6 in)²(12 in) = 144 in³

The volume of the given pyramid with a square base whose side measures 6 inches and the altitude of the pyramid measures 12 inches is 144 cubic inches. The value is obtained by applying the formula for the volume of the pyramid as  [tex]\frac{1}{3} B_{A}h[/tex].

The volume of the pyramid is given by the formula:

[tex]V=\frac{1}{3} B_{A}h[/tex]

Where,

[tex]B_A[/tex] is the area of the base of the pyramid and

h is the height or altitude of the pyramid

As shown in the diagram,

The pyramid has a square base whose side measures 6 inches and the altitude of the pyramid is 12 inches

Thus,

Area of the square base,

[tex]B_A =a^{2}[/tex]

⇒ [tex]B_A=6^2[/tex]

⇒ [tex]B_A=36[/tex] sq. inches

Height of the pyramid h = 12 inches

On substituting the values in the formula,

[tex]V=\frac{1}{3}B_Ah[/tex]

⇒ [tex]\frac{1}{3}[/tex] × 36 × 12

⇒ 4 × 36

⇒ 144 cubic inches

Therefore, the volume of the given pyramid is 144 cubic inches.

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Answer:

See explanation

Step-by-step explanation:

If PK and PF are tangent to the circle, then the radii OK and OF are perpendicular to the lines PK and PF respectively.

Consider quadrilateral PFOK. The sum of the measures of all interior angles in quadrilateral PFOK is equal to 360°. Since OK and OF are perpendicular to the lines PK and PF, you have that

∠FOK+90°+∠KPF+90°=360°,

∠FOK=360°-90°-90°-∠KPF=180°-∠KPF.

Angles FOK and KOE are supplementary angles, then

∠KOE=180°-∠FOK=180°-(180°-∠KPF)=∠KPF.

Since angle KOE is central angle, the arc EK has the same measure as angle KOE and as angle KPF.

Given [tex]\(PK\) and \(PF\)[/tex] tangents to circle [tex]\(O\),[/tex] angles [tex]\( \angle P \) and \( \angle EK \)[/tex] are equal by the properties of tangents.

To prove that [tex]\( m\angle P = m\angle EK \)[/tex] given the diagram, we can use properties of tangents and circles. Here is a step-by-step proof:

1. Identify the given information:

  - [tex]\( PK \) and \( PF \)[/tex] are tangents to circle [tex]\( k(O) \) at points \( K \) and \( F \),[/tex] respectively.

  - [tex]\( O \)[/tex] is the center of the circle.

  - [tex]\( PK \) and \( PF \)[/tex] are tangent to the circle, meaning they touch the circle at exactly one point.

2. Use properties of tangents:

  - A tangent to a circle is perpendicular to the radius at the point of tangency.

  - Thus, [tex]\( OK \perp PK \) and \( OF \perp PF \).[/tex]

3. Mark the right angles:

[tex]- \( \angle OKP = 90^\circ \)[/tex]

[tex]- \( \angle OFP = 90^\circ \)[/tex]

4. Connect the points to form a triangle:

  - Draw the line segment [tex]\( OP \).[/tex]

5. Use the exterior angle theorem:

  - In [tex]\(\triangle OKP\),[/tex] [tex]\( \angle OPK \)[/tex] is an exterior angle for [tex]\(\angle OKP\) and \(\angle PKO\).[/tex]

  - Since [tex]\( \angle OKP = 90^\circ \)[/tex] and [tex]\(\angle PKO\)[/tex] is another angle in the triangle, we have:

[tex]\[ \angle OPK = 180^\circ - (\angle OKP + \angle PKO) = 180^\circ - (90^\circ + \angle PKO) = 90^\circ - \angle PKO. \][/tex]

6. Similarly, in [tex]\(\triangle OFP\):[/tex]

  -[tex]\( \angle OFP = 90^\circ \) and \(\angle PFO\)[/tex] is another angle in the triangle.

  - Using the same logic as before:

[tex]\[ \angle OEP = 180^\circ - (\angle OFP + \angle PFO) = 180^\circ - (90^\circ + \angle PFO) = 90^\circ - \angle PFO. \][/tex]

7. Note that [tex]\( \angle OKP = \angle P \)[/tex] and [tex]\( \angle OFP = \angle EK \):[/tex]

  - By the property of the tangents from the same external point, [tex]\( PK = PF \).[/tex]

  - [tex]\( \angle PKO \) and \( \angle PFO \)[/tex] are complementary to [tex]\(\angle P\)[/tex] and [tex]\(\angle EK\)[/tex] respectively.

Therefore, it follows that:

[tex]\[ m\angle P = m\angle EK \][/tex]

Thus, the proof is complete.

Circumference is 2 times the radius times PI.

2 x 3 = 6

6 x 3.14 = 18.84  

The circumference is 18.84 inches.

Answer:

y-2=x-5

Step-by-step explanation:

First, I don't remember about how to solve point slope form, just go and search about how to solve point slope form on Google.

Answer:

Parallel is undefined

Perpendicular is 0

Step-by-step explanation:

The line x = -42 is a vertical line through the x-axis. As such its slope is undefined. All parallel lines have the same slope and will also be undefined. Perpendicular lines will be lines horizontal through the y-axis. This means the slope of any perpendicular line to it will be 0.

Answer:

16 bags

Step-by-step explanation:

To find this, we divide 2 over 1/8, to see how many units of 1/8 fits into that of 2.

[tex]\frac{2}{\frac{1}{8} }[/tex] can be rewritten as 2*8. 2*8 = 16 bags.

Answer:

16 bags

Step-by-step explanation:

We are given that Lin is making small bags of trail mix for campers and has 2 pounds of raisins.

If she puts 1/8 pound in each bag, we need to find out how many bags can she fill before she runs out of raisins.

To find this, we just need to divide the pounds of raisins by the amount of raisins she is putting in each bag.

Number of bags Lin can fill = [tex]\frac{2}{\frac{1}{8} }[/tex] = 16

The circle area can be defined as x2 + y2 < 3.46^2.

For point M, x2 + y2 = 13.

Since 3.46^2 is about 12, point M is outside the circle!

Answer:

outside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius = 3.46410161514, hence

x² + y² = 3.46410161514²

x² + y² = 12 ← equation of circle

To determine where a point (x, y) lies

• If x² + y² < r² then point is inside the circle

• If x² + y² = r² then point lies on the circle

• If x² + y² > r² then point lies outside the circle

For (- 3, 2)

(- 3)² + 2² = 9 + 4 = 13 > 12

Hence point (- 3, 2) lies outside the circle

Answer:

C

Step-by-step explanation:

The volume (V) of a sphere is calculated using the formula

V = [tex]\frac{4}{3}[/tex]πr³

If the radius is doubled, that is r = 2r , then

V = [tex]\frac{4}{3}[/tex]π (2r )³

(2r)³ = 8r³, thus the volume is multiplied by 8

Answer:

-3x - 9y = 36

If x = 0

Step-by-step explanation:

1. Plug 0 to x:

-3(0) - 9y = 36

2. Simplify

0 - 9y = 36

3. Cross out the 0 to make the question faster to solve, which now you are left with:

-9y = 36

4. Divide both sides by -9:

-9y/-9 = 36/-9

5. Simplify:

y = -4 <--------Answer

Hope this Helped!!!!!

~Shane

The value of y when x equals 0 in the equation -3x - 9y = 36 is -4.

To find the value of y when x equals 0 in the equation -3x - 9y = 36, we can simply substitute 0 for x and solve for y.

Substituting 0 for x, the equation becomes:

-3(0) - 9y = 36

This simplifies to:

-9y = 36

Dividing both sides of the equation by -9, we get:

y = 36 / -9

This gives us:

y = -4

Therefore, the value of y when x equals 0 is -4.

Answer:

Step-by-step explanation:

8x - 2y + x + x        combine like terms

= (8x + x + x) - 2y

= 10x - 2y

Answer:

Step-by-step explanation:

To end his suffering

Answer:

He wanted to make a hit on broadway.

Step-by-step explanation:

Answer:

3(p + 2q)(p + 3q)

Step-by-step explanation:

Factor out 3 from each term

3(p² + 5pq + 6q²) ← factor the quadratic by

Consider the factors of the q² term which sum to give the coefficient of the pq- term

The factors are + 2 and + 6, since

2 × 3 = 6 and 2 + 3 = 5, hence

3p² + 15pq + 18q²

= 3(p + 2q)(p + 3q)

The quadratic expression [tex]3p^2+15pq+18q^2[/tex] can be factorized by first taking out a factor of 3, then factorizing the remaining quadratic expression. The result is 3(p+2q)(p+3q).

To answer your question about factorizing the quadratic expression [tex]3p^2+15pq+18q^2,[/tex] it's important we understand the factorization process.

First, we can take out a factor of 3.
So,[tex]3p^2+15pq+18q^2[/tex] = 3([tex]p^2+5pq+6q^2[/tex])

Now, we factor the quadratic expression [tex]p^2+5pq+6q^2.[/tex]
To factor it, we need to look for two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fulfill this property. Therefore, we can write [tex]p^2+5pq+6q^2[/tex] = (p+2q)(p+3q)

So the factorization of the original expression is 3(p+2q)(p+3q)

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Answer:

The answer is A (APEX)

Answer:

Step-by-step explanation:

Given is table of x,y as follows:

x   y

1    4

2    8

3   27

4  85

5  250

6  600

The nearest seems to be from

y = 1.24(2.84)^x

Answer:

Yes! I use this site all the time and my questions always get answered quickly!

Step-by-step explanation:

Final answer:

Brainly can be a good resource for interactive learning in Algebra. Key areas of study include algebraic expressions, equations, and graphing polynomials. Collaborative activities and practice are recommended for mastering these concepts.

Explanation:

It seems like you're looking for a good online resource to help with Algebra. Brainly can be a good choice for interactive learning and assistance.

When studying Algebra, some key areas you will explore include algebraic expressions, equations, exponents, number patterns, functions, finance and growth, trigonometry, analytical geometry, and statistics.

An excellent way to develop your algebra skills is through practice and application. This includes simplifying algebraic expressions by eliminating terms wherever possible and always checking if your answer is reasonable. Also, engaging in group activities can enhance your understanding as you discuss and solve problems collaboratively.

When learning about graphing polynomials, understanding how the shape of the curve changes as the constants are adjusted is crucial. This graphical perspective reinforces the algebraic concepts taught and provides a visual aid in comprehending the material.

Answer:

The correct answer option is: Yes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow .

Step-by-step explanation:

We are given that Elias writes the numbers 1 through 20 on separate slips of paper.

Given that there are 16 white slips and four yellow slips and  eight odd numbers on white slips, and the rest of the odd numbers are on yellow slips, we can conclude that the events are odd and yellow independent because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow .

Answer:

c

Step-by-step explanation:

Answer:

oats = (18/100)*(2 lb) = 0.36 lb

Step-by-step explanation:

Answer:

L: 8in W: 2in H: 22in

Step-by-step explanation:

Answer:

Place one dot at (0,2) and then make the a dot where the line touches a grid square every 2 times

Step-by-step explanation:

The y intercept is 2 and the slope is 2

Answer:

Place one dot at (0,2) and then make the a dot where the line touches a grid square every 2 times

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

it would be one because then it wouldn't have been dilated cause dilation is a non-rigid transformation and would no have kept the congruence of the original shape.

Final answer:

The volume of the triangular pyramid is calculated using the formula V = 1/3 × base area × height. With a base area of 330 square yards and height of 18 yards, the volume is found to be 1,980 cubic yards. Therefore, the correct answer is C.

Explanation:

The volume of a triangular pyramid can be calculated using the formula V = 1/3 × base area × height. Given that the base area is 330 square yards and the height of the pyramid is 18 yards, we can calculate the volume by substituting these values into the formula: V = 1/3 × 330 × 18 = 1980 cubic yards. Therefore, the correct answer is C. 1,980 yd³.

The volume of the triangular pyramid is 1,980 cubic yards, making the correct answer option C.

To find the volume of the triangular pyramid, we first need to determine the area of the base triangle. Since the base has an area of 330 square yards, we can use the formula for the area of a triangle, which is 1/2 * base * height. Let's denote the base of the triangle as b and the height as h. We can rearrange the formula to solve for b:

[tex]\[ 330 = \frac{1}{2} \times b \times h \][/tex]

Given that the height of the pyramid is 18 yards, we can plug this value in and solve for the base:

[tex]\[ 330 = \frac{1}{2} \times b \times 18 \][/tex]

330 = 9b

[tex]\[ b = \frac{330}{9} \][/tex]

b = 36.67

Now, we have the base length of the triangle. Next, we can calculate the volume of the pyramid using the formula for the volume of a pyramid, which is [tex]\( \frac{1}{3} \times base\ area \times height \)[/tex]. Let's denote the volume as V:

[tex]\[ V = \frac{1}{3} \times 330 \times 18 \][/tex]

V = 1980

So, the volume of the pyramid is 1980 cubic yards. Therefore, the correct answer is option C: 1,980 yd.

Answer:

6.48074069841

Step-by-step explanation:

We can enter this on a calculator or can be estimated

Answer:

They will have to borrow $ 31,211

(23% of the purchase price)

Step-by-step explanation:

Total price : $135,700

Down payment:  20% of total price

Closing costs :  3% of total price

The Colburns will have to borrow 23% of the total price.

0.23*$135,700 =  $ 31,211