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Keith_Richards [23]
3 years ago
6

Two minor league baseball players got a total of 210 hits. Washington had 12 more hits than Sanchez. find the number of hits fro

m
each player
Mathematics
1 answer:
mote1985 [20]3 years ago
8 0
Washington: 117 Hits
Sanchez: 93 Hits

Hope this helps, have a nice day!
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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
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Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1
geniusboy [140]

Answer:

Step-by-step explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

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2 years ago
Factorising quadratics 2nd page
mihalych1998 [28]
A^2-b^2=(a+b)(a-b)

1: x^2-4=(x+2)(x-2)
2: (x+8)(x-8)
3: (x+10)(x-10)
4: (x+14)(x-14)
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3 years ago
Plis help with this problem! (Screenshot attached)
Diano4ka-milaya [45]

Answer: The total surface area is 633.9

Step-by-step explanation:

12.25 times 15.75, then divide by 2 = 96.46875 (this is the area of the triangle

Then times 4 = 385.875 (Because there are four triangles

15.75 times 15.75 = 248.0625 (The area of the square)

The sum is 633.9375

Rounded = 633.9

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2 years ago
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What is the image point of (3, 8) after a translation right 3 units and down 5 units
shusha [124]

Answer:

<h3>               (6, 3)</h3>

Step-by-step explanation:

Translation right (or left) means change of the x-coordinate.

Translation down (or up) means change of the y-coordinate.

(3, 8)   →    (3+3, 8-5) = (6, 3)

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3 years ago
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