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Eddi Din [679]
3 years ago
5

Francis scores 3 more than 2 times the number of points that riad scores if r represents the number of points riad scores which

expression represents the number of points francis scores A. 5r B. 6r C. 2r + 3 D. 3r +2
Mathematics
2 answers:
Alex_Xolod [135]3 years ago
7 0
The answer is C. 2r+3
Gnoma [55]3 years ago
7 0

Francis scores 3 more than 2 times the number

3 more is + 3

2 times is 2×

number is r

(2 × r) + 3

2r + 3

C. 2r + 3

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Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length
Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola:   y=k (x-\frac13)^2

<u />

<u>Part 1</u>

If the curve passes through point (\frac23 ,1), this means that when x=\dfrac23, y = 1

Substitute these values into the equation and solve for k:

\implies 1=k \left(\dfrac23-\dfrac13\right)^2

\implies 1=k \left(\dfrac13 \right)^2

Apply the exponent rule \left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c} :

\implies 1=k \left(\dfrac{1^2}{3^2} \right)

\implies 1=\dfrac{1}{9}k

\implies k=9

<u>Part 2</u>

  • The chord of a parabola is a line segment whose endpoints are points on the parabola.  

We are told that one end of the chord is at (\frac23 ,1) and that the chord is horizontal.  Therefore, the y-coordinate of the other end of the chord will also be 1.  Substitute y = 1  into the equation for the parabola and solve for x:

\implies 1=9 \left(x-\dfrac13 \right)^2

\implies \dfrac19 = \left(x-\dfrac13 \right)^2

\implies \sqrt{\dfrac19}  = x-\dfrac13

\implies \pm \dfrac13  = x-\dfrac13

\implies x=\dfrac23, x=0

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:  

\implies \dfrac23-0=\dfrac23

**Please see attached diagram for drawn graph. Chord is in red**

6 0
2 years ago
Convert 2 Liters to gallons. Use the fact that 1 gal.= 3.8L.
iris [78.8K]

we know that

1 gal.= 3.8L

we can also write as

3.8L=1 gal

Firstly, we will find for 1L

so, we can divide both sides by 3.8

\frac{3.8}{3.8} L=\frac{1}{3.8}gal

1 L=\frac{1}{3.8}gal

now, we will multiply both sides by 22

22*1 L=22*\frac{1}{3.8}gal

22L=5.78947 gal

22L=5.8 gal

so, option-b.............Answer

8 0
3 years ago
If I charged 30$ a hair cut the whole year how many times would each customer have to come in to get 17,510$
V125BC [204]
You would need to come in 583.6 or 584 times
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100 POINTS!!!!! WILL GIVE BRAINLIEST!!!!!!! <br> Show that: (a + bi)^2 = (a + b)(a − b) + 2abi
inna [77]

Step-by-step explanation:

(a+bi)2

=a2 +2abi +b2i2

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The anwser is 4,520. :D
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