It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?

A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r

The volume of the pyramid is 1280 cubic feet.

To find the volume of a pyramid, we can use the formula:

Volume = (1/3) * Base Area * Height

Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:

[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]

The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:

[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]

Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:

Volume = (1/3) * 256 * 15

Volume = (1/3) * 3840

Volume = 1280 cubic feet

Therefore, the volume of the pyramid is 1280 cubic feet.

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Answer: the answer above is pretty much right, the answe is B

Final answer:

To determine the number of terms in the given arithmetic sequence, we calculate the common difference and apply the formula for the nth term. With a common difference of -8 and an nth term of -225, we find that there are 31 terms in the sequence.

Explanation:

To find out how many terms are in the arithmetic sequence 15, 7, -1, -9,..., -225, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

In this sequence, the common difference d is 7 - 15 = -8. Now we use the formula with an = -225, a1 = 15, and d = -8 to find n.

Plugging these values into the formula, we get:
-225 = 15 + (n - 1)(-8)
-225 = 15 - 8n + 8
-225 = 23 - 8n
-248 = -8n
n = 31

Therefore, there are 31 terms in the arithmetic sequence.

9km is greater than 145cm due to the conversion factor between kilometers and centimeters.

9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.

The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.

so

the answer is the option

A. the remote interior angles

In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The four types of conic section are the hyperbola, the parabola, the circumference and the ellipse.

For the problem we have this parametric equation:

(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]

From geometry, we know that we can express a circumference in terms of parameters like this:

(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]

being r the radius of the circumference.

On the other hands, we know that a ellipse can be expressed in terms of parameters like this:

(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]

Therefore, we will have three answers that are the cases for the values a and b, namely.

Case 1: Circumference

To the case of a circumference, the more simple ordinary equation is given by:

(4) [tex]x^{2} + y^{2} = r^{2}[/tex]

Substituting (1) into (4):

[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]

But because of the equation (2), necessarily:

[tex]a = b = r[/tex]

Case 2: Ellipse (focal axis matches the x-axis) 

In this case, the simple ordinary equation is given by:

(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]

being a and b semi-major axis and semi-minor axis respectively. 

Given that a an b are variables of the parametrization, and a and b are variables of the ellipse as well, to avoid confusion we will modify the equation (5) like this:

(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]

So, substituting (2) into (6):

[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]

Necessarily:

[tex]a=a'[/tex]  and  [tex]b=b'[/tex] 

and given that the focal axis matches the x-axis, then:

[tex]a>b[/tex] 


Case 3: Ellipse (focal axis matches the y-axis) 

In this case, applying the same previous reasoning, the simple ordinary equation is given by:

(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]

being a' and b' semi-major axis and semi-minor axis respectively. 

So, substituting (2) into (7):

[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]

Necessarily:

[tex]a = b'[/tex]  and  [tex]b = a'[/tex] 

and given that the focal axis matches the y-axis, then:

[tex]a<b[/tex] 

Finally, the conclusions are:

1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)

2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)

3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)

How the values of a and b determine which conic section will be traced was discussed thoroughly.

A conic section is a curve obtained as the intersection of the surface of a cone with a plane.

The given parametric equations are:

[tex]x=acos t[/tex]

[tex]\frac{x}{a} =cost[/tex]....(1)

[tex]y=bsint[/tex]

[tex]\frac{y}{b} =sint[/tex]....(2)

Adding the squares of (1) and (2)

[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]

We know [tex]cos^{2} t + sin^{2} t=1[/tex]

So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)

If [tex]a=b[/tex], (3) will be reduced into:

[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.

If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.

if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.

Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.

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Answer:4.8cm^3

Step-by-step explanation:I got it right on edge.

Answer:

D edge

Step-by-step explanation:

Final answer:

The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.

Explanation:

To calculate the monthly payments, you can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^-n)

Where:

Using the given values, we can calculate:

P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)

P ≈ $61.02

Therefore, the monthly payments would be approximately $61.02.

To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:

Total Interest = (P * n) - PV

Total Interest ≈ ($61.02 * 48) - $2469

Total Interest ≈ $1704.96 - $2469

Total Interest ≈ -$764.04

Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.

The answer to the above question can be explained as under -

We know that, the sum of angles of triangle is 180°.

So, vertex angle plus base angles are equal are equal to 180°.

Let the vertex angle be represented by "v" and base angles be represented by "b".

Thus,  v + b + b = 180°

So,  v + 2b = 180°

Next, the question says, the vertex angle is 20° less than the sum of base angles.

Thus, 2b - 20° = v

Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v

The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.

The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:

To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.

Answer:

The alternate exterior angles with angle 11 are angle 13 and angle 5.

Step-by-step explanation:

Two angles are called Alternate exterior angles if

1. They are on the exterior side of parallel lines and

2.  Lie on the opposite sides of the transversal line.

It is given that

[tex]r\parallel s[/tex] and [tex]t\parallel u[/tex]

From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.

Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.

Answer:

The alternate exterior angles with angle 11 are angle 13 and angle 5.

Step-by-step explanation:

Answer:

1 and 4 i believe

Step-by-step explanation:

The value of volume of cube is,

⇒ V = 1.728 meter³

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

Given that;

A cube has a side length of 120 cm.

Since, We know that;

1 m = 100 cm

Hence,

120 cm = 120 / 100 m

            = 1.2 m

So, Volume of cube is,

⇒ V = side³

⇒ V = 1.2³

⇒ V = 1.728 meter³

Thus,  volume of cube is,

⇒ V = 1.728 meter³

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The value of the expression ∛27x⁹ is 9x³.

The given expression is ∛27x⁹.

Cube root of twenty seven times of x power nine.

We can split the terms inside the cube root.

27=3×3×3

∛x⁹ = x³

Now let us plug in the above expression.

= 3√3³ × x⁹

= 3√3³ × √ x⁹

= 3 × 3 × x³

= 9x³.

Hence, the value of the expression ∛27x⁹ is 9x³.

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Answer:

C) 2 tan θ

E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)

Step-by-step explanation:

This is essentially what the other person said, but in a better format.