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Eva8 [605]
2 years ago
14

The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise mo

ney for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.

Mathematics
1 answer:
Sidana [21]2 years ago
6 0
We need to find the distance between (7, 5) and (10, 11) and double it, since they run it twice. We can do this as follows: 2√(11-5)² + (10-7)² = 2√36 + 9 = 2√45 = 6√5.
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Hope this helps!
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Find the 25th of sequence 3,5,7,9,11
zubka84 [21]

Answer: The 25th term of the sequence is 75

Step-by-step explanation:

The given sequence depicts an arithmetic progression. The consecutive terms differ by a common difference. We will apply the formula for arithmetic progression.

Tn = a + (n-1)d

Tn = The value of the nth term of the arithmetic sequence.

a = first term of the sequence.

d = common difference (difference between a term and the consecutive term behind it)

n = number of terms in the sequence.

From the information given,

a = 3

d = 5-3 = 7-5 = 2

We want to look for the 25th term, T25

So n = 25

T25 = 3 + (25-1)2 = 3+ 24×2

T25 = 3 + 72 = 75

5 0
1 year ago
Betsy is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? f(x) g(x) graph of the function f
agasfer [191]

Consider the quadratic function f(x)=\frac{1}{3}x^2-2x

and the linear function g(x) defined as

\text{at  }x=1, g(x)=1; \text{ at }x=2, g(x)=2 \text{ and at }x=3, g(x)=3

\text{so the linear function is }
g(x)=x\\
\\
\text{now to check whehter the quadratic function f(x) and linear function }g(x)\\
\text{intersects, we solve the equations }f(x)=g(x)\\
\\
\Rightarrow \frac{1}{3}x^2-2x=x\\
\\
\Rightarrow \frac{1}{3}x^2-3x=0\\
\\
\Rightarrow x\left ( \frac{1}{3}x-3 \right )=0\\
\\
\text{now using the zero product rule, we get}\\
\\
x=0 , \text{ and } \frac{1}{3}x-3=0

\Rightarrow x=0, \text{ and }\frac{1}{3}x=3\\
\\
\Rightarrow x=0, \text{ and }x=9\\
\\
\text{so the functions intersect at x=0 and x=9.}

4 0
1 year ago
Read 2 more answers
Find a line that lies entirely in the set defined by the equation x2 + y2 − z2 = 1.
RUDIKE [14]

Answer:

x=1\,,\,y=t\,,\,z=t

Step-by-step explanation:

A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.

A line segment is a line that has two end-points and a ray is a line that has one end-point.

Given equation is x^2+y^2-z^2=1

To find : a line that lies entirely in the set defined by the given equation.

Solution:

Take x=1\,,\,y=t\,,\,z=t

Check:

L.H.S=1^2+t^2-t^2=1+0=1=R.H.S

Therefore, x=1\,,\,y=t\,,\,z=t satisfy the given equation.

8 0
1 year ago
An arc on a circle measures 250°. Within which range is the radian measure of the central angle? 0 to StartFraction pi Over 2 En
Alex Ar [27]

Answer:

The central angle is within the range π to 3π/2

Step-by-step explanation:

To convert from degrees to radians, we multiply the angle in degrees by 180/π.

To convert from radians to degree, we multiply the angle in radians by 180°/π.

π/2 = π/2 X 180°/π= 90°

π rad = π X 180°/π= 180°

3π/2 = 3π/2 X 180°/π= 270°

2π = 2π X 180°/π= 360°

Therefore the angle 250 which is between 180 and 270 is within the range :

π to 3π/2

4 0
2 years ago
Read 2 more answers
silvia compro la misma licuadora que daniela, que costaba $355.5, pero como abonó con tarjeta de credito, le recargaron un 16%,
Debora [2.8K]

Answer:

Costo final= $412.38

Step-by-step explanation:

Dada la siguiente información:

Costo inicial= $355.5

Recargo de la tarjeta= 16% = 0.16

<u>Para calcular el costo final que debe pagar Silvia, debemos usar la siguiente información:</u>

Costo final= costo inicial*(1 + recargo)

Costo final= 355.5*1.16

Costo final= $412.38

4 0
1 year ago
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