Answer:
A: -11
B: Two complex solutions
Step-by-step explanation:
The discriminant of this equation is 3^2-20=9-20=-11. Since the discriminant is negative, its square root will be an imaginary number, and there will be two complex solutions. Hope this helps!
118 handle bars tells us that there's 118 bikes
if all 118 bikes were regular bikes
118*2 = 236
we would be 33 wheels short
118*1 = 118
we would be 17 seats short
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if 101 of the bikes are regular and 17 are tandem
101*1 = 101
17*2 = 34
we would have the right amount of seats
101*2 = 202
17*2 = 34
202 + 34 = 236
we would be 33 wheels short.
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if 17 bikes are tandem, 33 are tricycle, and 68 are regular
17*2 = 34
33*3 = 99
68*2 = 136
we would have the right amount of wheels
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Answer:
There are 68 bicycles, 17 tandem bicycles, and 33 tricycles.
This question isn't hard, it just takes longer since it's based off of guess and check.
B. 17.16 represents a credit of $17.16; "credits" mean that you're receiving something, so it's added. A is incorrect because it shows the money being taken away and that isn't what a credit does. C and D aren't even the same amount of money in the question, so they aren't your answer either.
The simple/ <span>common sense method:
</span>The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore <u>c=19</u>.
The new equation is: <u>y=x^2+19 </u>
<span>
<span>The most complicated/thorough method:
</span></span>This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore <u>(0,9) </u>
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
<u>(0, 19) </u>
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore <u>g(x)=x^2+19</u>
Answer:
12 cm = 21.62 miles
6 cm = 11.04 miles
Step-by-step explanation:
To find the distance, set up a proportion. A proportion is two equal ratios set equal to each other. We form the ratios by using corresponding values. We write a ratio of 
and simplify.
We know 
. We know the distance on the map is 12 cm and 6 cm whish converts to 4.7 inches and 2.4 inches. We can write 
and 
We set them equal.
and
To solve each proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.
and
