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Sphinxa [80]
1 year ago
8

Diego and Amit were trying to solve the equation: x^2-8x=1x 2 −8x=1x, squared, minus, 8, x, equals, 1 Diego said, "I can solve b

y completing the square. If I add 161616 to each side, I can rewrite the equation as (x-4)^2=17(x−4) 2 =17left parenthesis, x, minus, 4, right parenthesis, squared, equals, 17." Amit said, "I'll subtract 111 from each side and rewrite the equation as x^2-8x-1=0x 2 −8x−1=0x, squared, minus, 8, x, minus, 1, equals, 0. Then I'll use the quadratic formula with a=1a=1a, equals, 1, b=-8b=−8b, equals, minus, 8, and c=-1c=−1c, equals, minus, 1." Whose solution strategy would work? Choose 1 answer: Choose 1 answer: (Choice A) A Only Diego's (Choice B) B Only Amit's (Choice C) C Both (Choice D) D Neither
Mathematics
1 answer:
labwork [276]1 year ago
5 0

Answer:

Both.

Step-by-step explanation:

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A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat
allsm [11]
Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 =  3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h
6 0
1 year ago
A ball is thrown down from a balcony with a vertical velocity (in ft/s) given by
fenix001 [56]

Answer:

–90 < –32t – 10 < –58

Step-by-step explanation:

We want the velocity to be BETWEEN -90 and -58.

Whenever we need a quantity, let it be A, to be between two numbers, p and q (p is less than q), we can write it as:

p < A < q

Similarly, here we need the velocity, -32t-10 to be BETWEEN -90 and - 58 (with -90 being the smaller number). Thus we can write:

–90 < –32t – 10 < –58

This is the correct choice, 2nd choice.

4 0
1 year ago
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A plot of land is in the shape of a square. The shaded square inside is covered with gravel. the rest of the square plot is cove
aleksklad [387]
This is how you do the math to get it.

6 0
1 year ago
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A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. Josh decides to make the house addition smaller, and
emmasim [6.3K]
It is decreased by a factor of 3. You can determine this by realizing that one inch original equals 3.3 feet, but the equals 1.1 feet, and 3.3/1.1 = 3.
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This relationship is given by the equation, v = gt. In this equation, g is the acceleration due to gravity, t is the number of s
DENIUS [597]

v=gt,

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t=0 s, v=0 m/s means that object’s initial velocity 0 m/s.

v=gt, and g is a constant g=9.8 m/s². We can write v=9.8*t.

Rate of change 9.8 means the acceleration due to gravity is 9.8 m/s².

Answer: C. The initial value is 0. That means that object’s initial velocity 0 m/s. The rate of change is 9.8. That means the acceleration due to gravity is 9.8 m/s2.

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