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Naddik [55]
3 years ago
6

Rick, John, and Kevin are playing catch. Rick throws the ball to John, John throws the ball to Kevin, and Kevin throws the ball

to Rick. John knows that the distance between him and Rick is 20 yards and the distance between him and Kevin is 20 yards. He also knows that the angle created between Rick, himself, and Kevin has a measure of 30°. Which person is making the shortest throw?
Mathematics
1 answer:
pishuonlain [190]3 years ago
6 0

Answer:

Kevin and Rick

Step-by-step explanation:

RJ - 20 y

JK - 20square root 3

M<RJK - 30 y

Let’s find the length segment KR by using law of cosines

KR^2 = RJ^2 + JK^2 - 2(RJ)(JK)cos(<RJK)

KR^2=400

KR=20 yards

Kevin and Rick throwing same distance, but John’s distance is longer.

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Adam currently runs about 20 miles per week,aND he wants to increase his weekly mileage by 30% How many miles will Adam run per
mel-nik [20]
20miles increased by 30%=new mileage added

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NOTE you can also use 1.3 instead of .3 as the percent to get the answer with out addition.

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3 years ago
Which number belongs to the solution set of the equation below? 8x=120
vlabodo [156]
8x = 120
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4 0
3 years ago
Find all real zeros of 4x^3-20x+16
Pani-rosa [81]

Answer:

  {1, (-1±√17)/2}

Step-by-step explanation:

There are formulas for the real and/or complex roots of a cubic, but they are so complicated that they are rarely used. Instead, various other strategies are employed. My favorite is the simplest--let a graphing calculator show you the zeros.

___

Descartes observed that the sign changes in the coefficients can tell you the number of real roots. This expression has two sign changes (+-+), so has 0 or 2 positive real roots. If the odd-degree terms have their signs changed, there is only one sign change (-++), so one negative real root.

It can also be informative to add the coefficients in both cases--as is, and with the odd-degree term signs changed. Here, the sum is zero in the first case, so we know immediately that x=1 is a zero of the expression. That is sufficient to help us reduce the problem to finding the zeros of the remaining quadratic factor.

__

Using synthetic division (or polynomial long division) to factor out x-1 (after removing the common factor of 4), we find the remaining quadratic factor to be x²+x-4.

The zeros of this quadratic factor can be found using the quadratic formula:

  a=1, b=1, c=-4

  x = (-b±√(b²-4ac))/(2a) = (-1±√1+16)/2

  x = (-1 ±√17)2

The zeros are 1 and (-1±√17)/2.

_____

The graph shows the zeros of the expression. It also shows the quadratic after dividing out the factor (x-1). The vertex of that quadratic can be used to find the remaining solutions exactly: -0.5 ± √4.25.

__

The given expression factors as ...

  4(x -1)(x² +x -4)

5 0
3 years ago
Read 2 more answers
Which triangle congruence shortcuts don't exist?
gogolik [260]
OSSA
does not exist.
7 0
2 years ago
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