Which runner lost the race?

Answer:

710 is the answer.

Step-by-step explanation:

7.1 x 10^2

10^2= 10 x 10 = 100

so,

7.1 x 100 = 710

Answer:

The correct option is;

[tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]

Step-by-step explanation:

The given parameters are

The equation of motion of one (the first) object is r = 4·cos(θ)

The equation of motion of the other (the second) object is r = -1 + 2·cos(θ)

Equating both equations gives;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -1/2

θ = Arccos(-1/2) = 120° = 2·π/3

Therefore, the two equations are equal when θ = 2·π/3 for which we have;

r = 4·cos(2π/3) = -2 and r = -1 + 2·cos(2π/3) = -2

∴ r = 4·cos(2π/3) = -1 + 2·cos(2π/3) = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore [tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex])

Given that ,

The first object is moving around the screen r = 4 cos(0)

The second object is moving around the screen r = -1 + 2cos(0)

We have to find ,

The coordinates represent a possible collision point of the objects.

According to the question,

Coordinate represent collision points to object ,

Equating both equations ;

4·cos(θ) = -1 + 2·cos(θ)

4·cos(θ) - 2·cos(θ) = -1

2·cos(θ) = -1

cos(θ) = -[tex]\frac{1}{2}[/tex]

θ = [tex]cos^{-1} (\frac{1}{2} )[/tex] = 120°

[tex]\theta[/tex] = [tex]\frac{-2\pi }{3}[/tex]

Therefore, the two equations are equal when θ = [tex]\frac{2\pi }{3}[/tex]

We have;

r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -2

And r = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex]) =

r = -2

r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex])

r = -2

The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore r = -2 and [tex]\theta = \frac{2\pi }{3}[/tex] .

Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex]) .

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Answer:

[tex]Eric= \$22.86[/tex]

[tex]Shiloh = \$17.14[/tex]

Step-by-step explanation:

Represent Eric with E and Shiloh with S;

[tex]E:S = 4:3[/tex]

[tex]Total = \$40[/tex]

Required

Determine the how much money each have

We have to convert the ratio to fraction;

For Eric, we have

[tex]Eric= \frac{E}{E + S} * Total[/tex]

[tex]Eric= \frac{4}{4 + 3} * \$40[/tex]

[tex]Eric= \frac{4}{7} * \$40[/tex]

[tex]Eric= \frac{\$160}{7}[/tex]

[tex]Eric= \$22.86[/tex]

[tex]Shiloh = Total - Eric[/tex]

[tex]Shiloh = \$40 - \$22.86[/tex]

[tex]Shiloh = \$17.14[/tex]

Answer: Add 2 to each side

We do this to undo the "minus 2" or "subtract 2" that is happening to the variable f. Addition is the opposite of subtraction.

Solving that inequality leads to [tex]f \le 5[/tex] meaning f can be 5 or smaller.

Answer:

[tex]4.99\times 10^{-10}\ m[/tex]

Step-by-step explanation:

Given that,

The diameter of a proton is 1.7 x 10⁻¹⁵ meters

The diameter of an atom is 5 x 10⁻¹⁰ meters.

We need to find the difference in the diameters.

[tex]D=5\cdot10^{-10}-1.7\cdot10^{-15}\\\\=4.99\times 10^{-10}\ m[/tex]

So, the difference in the diameter is [tex]4.99\times 10^{-10}\ m[/tex].

Answer:

t>2.034s and t>0.154s

Step-by-step explanation:

Given the quadratic function h(t)=-16t^2+35t+5 which represents the height of the balloon, h, in feet t seconds after it is thrown.

To determine when the balloon is more than 10feet above the ground, we will substitute h = 10 into the expression to have;

h(t)=-16t^2+35t+5

-16t^2+35t+5>10

-16t^2+35t+5-10>0

16t^2-35t+5>0

Find t;

t > 35±√35²-4(16)(5)/2(16)

t>35±√1225-320/32

t>35±√905/32

t>35±30.08/32

t > 35+30.08/32 and t > 35-30.08/32

t>65.08/32 and t>4.92/32

t>2.034s and t>0.154s

Hence the balloon is more than 10feet above the ground at when t>2.034s and t>0.154s

Answer: d n = 2p

Step-by-step explanation:

Answer:

8x+(-27)=y

Step-by-step explanation:

To find an equation of a line, you use the formula mx+b=y

M=slope

x=x cooridnates

y=y coordinates

b=y intercept

Slope:

You use the formula y2-y1/x2/x1 to find slope.

5-(-3)/2-5

5+3/-3

8/-3

8

Y intercept:

8(5)+b==3

40+b=-3

b=-37

Equation: 8x+-37=y

The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line passes through each pair of points (5,-3), (2,5)

We know that, the equation of a line passing through two points (x1, y1) and (x2, y2) is given by,

(y-y1) = (y2-y1)/(x2-x1)(x-x1)

Where, (y2-y1)/(x2-x1) is, representing the slope of the line.

Here, x1 = 5, x2 = 2 and y1 = -3, y2 = 5

Equation of the line =

(y+3) = (5+3)/(2-5)(x-5)

y+3 = -8/3(x-5)

3y+9 = -8x+40

3y = -8x+31

Hence, The equation of the line that passes through each pair of points (5,-3), (2,5) is 3y = -8x+31

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Answer: [tex]\frac{1}{16}[/tex]

Step-by-step explanation:

1. Original Equation: [tex]4^4(4^-^7)(4)[/tex]

2.Simplify: [tex]4^4(4^-^7)(4) ----> 4^4* 4^-^7 * 4\\[/tex]

3.Apply exponent rule: [tex]4^4^-^7^+^1[/tex]

4. Simplify: [tex]4^-^2\\[/tex]

5.Apply exponent rule: [tex]\frac{1}{4^2}[/tex]

6.Simplify: [tex]\frac{1}{16}[/tex]

Answer:

B 4/3

Step-by-step explanation:

3^32^9/3^42^7

B 4/3

Answer:

1/3x

Step-by-step explanation:

Subtract x by x and y by y to find the distance/difference

36            163

24,          127

= 12/36 = rise/run

Now reduce to find the slope, reduce until you can't anymore.

12/36

6/18

3/9

1/3 (that's your slope)

Answer:

what is a crown

Step-by-step explanation:

they should stop eating out

Answer:

Step-by-step explanation:

The answer is 64 because If you multiply 2x2x2x2x2x2 It equals 64

Answer:

Step-by-step explanation:

rational

Answer:

Rational

Explanation:

18/42 is 4.258 which is a rational number

Answer: [tex]2x+y^2[/tex]

Step-by-step explanation:

[tex]x\:+\:x\:+\:y\:\cdot \:y[/tex]

[tex]x+x+yy[/tex]

[tex]2x+yy[/tex]

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

Answer:

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

Answer:

15/8 quartz of grape juice

Step-by-step explanation:

Given that:

Standard Recipe requirement :

1 1/2 quartz of sparkling water requires 3/4 quatz of grape juice

Number of grape juice required for 15/4 of sparkling water ;

Let quartz of grape juice required = x

1 1/2 sparkling water = 3/4 grape juice

15 /4 sparkling water = x grape juice

3/2 = 3/4

15/4 = x

Cross multiply ;

3/2 x = 15/4 * 3/4

3/2x = 45/ 16

x = 45/16 ÷ 3/2

x = 45/16 * 2/3

x = 90/48 = 15/8

x = 15/8 quartz of grape juice

Answer:

83 photos each

2 photos left over

Answer:

Each Family gets 83 photos each and 2 photos are left over

Step-by-step explanation:

Answer:

En la caja registradora hay 200 monedas de cinco pesos, 20 monedas de 10 pesos y 582 monedas un peso.

Step-by-step explanation:

De acuerdo a la información, puedes escribir las siguientes ecuaciones:

x+y+z=802 (1)

5x+10y+z=1782 (2)

x=10y (3)

Primero debes reemplazar (3) en (1) y (2):

10y+y+z=802

11y+z=802 (4)

5(10y)+10y+z=1782

50y+10y+z=1782

60y+z=1782 (5)

Ahora, tienes dos ecuaciones:

11y+z=802 (4)

60y+z=1782 (5)

Puedes despejar z en (4):

z=802-11y (6)

Después, puedes reemplazar (6) en (5):

60y+802-11y=1782

49y=1782-802

y=980/49

y=20

Puedes reemplazar el valor de y en (3) para encontrar x:

x=10y

x=10(20)

x=200

Puedes reemplazar el valor de y en (6) para encontrar z:

z=802-11(20)

z=802-220

z=582

De acuerdo a esto, en la caja registradora hay 200 monedas de cinco pesos, 20 monedas de 10 pesos y 582 monedas de un peso.

Answer:

y=1/3x+11/3

Step-by-step explanation:

y=mx+b

y=1/3x+b

3=1/3(-2)+b

3 = -2/3+b

+2/3 +2/3

11/3=b

So the equation of the line that perpendicular to y= -3x + 3/5 that Goes through point (-2, 3 ) is y=1/3x+11/3.

Answer:

X represents the value you can multiply with the slope to get the answer.

y = 0.007x

  = 0.007(6)

  = 0.042

Therefore, 0.042 inches of rain falls in 6 minutes.

Answer:

1) 1.267x10^9

2) 2

Step-by-step explanation:

Answer:

b = 1/4

Step-by-step explanation:

We will use 4 as a common denominator.

3 × 2 = 6        2 × 2 = 4

Now we have the equation 6/4 + b = 7/4

Answer:

50%

Step-by-step explanation:

hope this helped

you need 10 8' planks of wood because 15x3= 45+9x4= 77, then 77÷8= 9.625, but you can't get .625 of a plank, so 10. hope you get a good grade!

Answer:

(2, -4) would be point b.

Step-by-step explanation:

This is because -2 was on the negative side of the x axis before the refection and now it's on the positive side of the x axis

Answer:

it would be (2,-4)

Step-by-step explanation:

correct me if I'm wrong

Stay Safe

Stay Strong

Stay Awesome

Answer:

$20,232.75

Step-by-step explanation:

I hope it helped

Answer:

c=-5

Step-by-step explanation:

Answer:

c = -5

Step-by-step explanation:

This is the answer because:

1) We first have to isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helps!