Which of the following best represents the average speed of a fast runner?

10 meters per second

10 miles per minute

10 centimeters per hour

10 kilometers per second

The answer is A, B, and  E.

Just plot write the equation in a graphing calculator which shows they are the same.

a. The value of x ≈ 60°

b. The value of y ≈ 93°

The relevant relations are ...

external angle A is half the difference of intercepted arcs BC and BD

inscribed angle y° is half the measure of intercepted arc CD

the sum of arcs of a circle is 360°

Using these relations, we have ...

(a) A = (BC -x°)/2

x° = BC -2A = 112° -2(27°)

x° = 58°

(b) y° = CD/2 = (360° -BC -BD)/2 = (360° -112° -60°)/2

y° = 91°

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The equestrian's father will catch up to her at 2:00 pm by using the concept of relative speed and calculating the time it will take for him to close the gap between them.

The student's father will catch up to the equestrian at 2:00 pm. To solve this problem, we can use the concept of relative speed. The equestrian starts riding away from the house at 10 miles per hour (mph) at 10:00 am. By noon, when the father starts chasing her on his scooter at 15 mph, the equestrian is already 20 miles away (2 hours × 10 mph).

Since the father's speed is 15 mph and the equestrian's speed is 10 mph, the father is closing the gap at a speed of 15 mph - 10 mph = 5 mph. To cover the 20 miles gap, the father will need 20 miles / 5 mph = 4 hours. Therefore, if the father starts at noon, he will catch up to her at 4 hours later, which is 2:00 pm.

Answer:

D. (5x + 4)(5x – 4)

Step-by-step explanation:

This is the difference of two squares

[tex]a^{2} - b^{2}  = (a-b)(a+b)\\[/tex]

Following from above,

25[tex]25x^{2} -16[/tex]

Taking the elements of the expression

[tex]25x^{2} = 5^{2}x^{2}[/tex]

Using the law of indices,

[tex]a^{2} b^{2} = (ab)^{2}[/tex]

[tex]25x^{2} = (5x)^{2}[/tex]

[tex]16 = 4^{2}[/tex]

Therefore,

[tex]25x^{2} -16[/tex] =  [tex](5x)^{2}  - 4^{2}[/tex]

=[tex](5x-4)(5x+4)[/tex]

Hence the correct answer is Option D.

Answer:

Remainder is 24.

Step-by-step explanation:

Given dividend = 3x² + 10x - 8

and divisor = x - 2

To find: Remainder using Remainder theorem.

Remainder Theorem states that let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).

Let p(x) = 3x² + 10x - 8

using remainder theorem,

Remainder = p(2) = 3 × 2² + 10 × 2 - 8

                  = 3 × 4 + 20 - 8

                  = 12 + 12

                  = 24

Therefore, Remainder is 24.

John paid the most towards the rental.

To determine who paid the most towards the rental, we need to find out how much each person paid. Mark paid $3 and John paid <percentage> of the total. Their friend paid the remaining amount. Since the total cost to rent the video games was $10, we can calculate how much John paid by subtracting what Mark paid from $10 and finding the percentage of that remaining amount.

Subtracting $3 from $10 gives us $7. Since John paid the majority, we can say that he paid 70% of the total. Therefore, John paid the most towards the rental.

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∠Z ≅ ∠X and ∠W ≅ ∠Y is the correct answer

D

Answer:

$4

Step-by-step explanation:

In order to solve this problem you just have to create an equation, and it´s very simple, each kid ticket will be represented by the letter "x", and as we know a kid´s ticket is worth half what is worth an adult ticket, so the adult ticket = 2 kids tickets=2x

So we know that there are 2 adults and three kids, and the totla was $14, we create our equation:

[tex]2 adults+3kids=14\\2(2x)+3x=14\\4x+3x=14\\7x=14\\x=\frac{14}{7}\\ x=2[/tex]

Now we know that the kids ticket is $2, so the adult ticket would be twice that, $4 is the price of the adult ticket.

Answer: A. 4

Step-by-step explanation:

The characteristic equation of a circle is

[tex]x^2+y^2=r^2[/tex]

The characteristic equation of a hyperbola is

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

The intersection points will be obtained as the solution of the both characteristic equations.

[tex]x^2+y^2=r^2[/tex].......(1)

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

⇒[tex]y^2=r^2-x^2[/tex].....(from 1)

put this in (2)

[tex]\frac{x^2}{a^2}-\frac{r^2-x^2}{b^2}=1[/tex]

⇒[tex]y^2=r^2-x^2\\\frac{x^2}{a^2}+\frac{-x^2}{b^2}=1+\frac{r^2}{b^2}[/tex]

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

⇒[tex]y^2=r^2-x^2\\x^2(\frac{a^2+b^2}{a^2b^2})=\frac{b^2+r^2}{b^2}[/tex]

[tex]\Rightarrow\ x^2=\frac{a^2(b^2+r^2)}{a^2+b^2}\\y^2=\frac{b^2(r^2-a^2)}{a^2+b^2}[/tex]

So there are 2 different values of x and two different values of y, thus the maximum number of intersection points  is 4.

Answer:

the solution set is {0,-11}

Step-by-step explanation:

The equation is [tex]-p^2-11p=0[/tex]

The GCF of the left hand side of the expression is -p. Hence, factored out the GCF

[tex]-p(p+11)=0[/tex]

Now, apply the zero product property, we get

[tex]-p=0,p+11=0[/tex]

Now, solve the equations for p

[tex]p=0,p=-11[/tex]

Thus, the solution set is {0,-11}