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VARVARA [1.3K]
3 years ago
5

For a quadratic function ƒ(x)=ax2+bx+c, ƒ(−1)<1, ƒ(1)>−1, and ƒ(3)<−4. What could be the sign of a?

Mathematics
1 answer:
denis23 [38]3 years ago
4 0

Answer:

"a" must be negative

Step-by-step explanation:

The slope between points (-1, 1) and (1, -1) is a minimum of (-1-1)/(1-(-1)) = -1.

The slope between points (1, -1 and (3, -4) is a maximum of (-4-(-1))/(3-1) = -3/2.

Thus, as x increases, the slope is decreasing. In order for that to be the case, the value of <em>a</em> must satisfy a < 0.

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A 8-foot tall man is standing beside a 32-foot flagpole. The flagpole is
kipiarov [429]

Answer:

The flagpole's shadow is 16.875 feet longer than the man's shadow

Step-by-step explanation:

The total length of the shadow is expressed by taking its actual length by a factor that depends on the position of the sun which is constant for the man too. The expression is as follows;

Height of the shadow=actual height of the flagpole×factor

where;

length of the flagpole's shadow=22.5 feet

actual height of the flagpole=32 feet

factor=f

replacing;

22.5=32×f

32 f=22.5

f=22.5/32

f=0.703125

Using this factor in the expression below;

Length of man's shadow=actual height of man×factor

where;

length of man's shadow=m

actual height of man=8 feet

factor=0.703125

replacing;

length of man's shadow=8×0.703125=5.625 feet

Determine how much longer the flagpole's shadow is as follows;

flagpoles shadow-man's shadow=22.5-5.625=16.875 feet

The flagpole's shadow is 16.875 feet longer than the man's shadow

7 0
3 years ago
Suki split five dog treats equally among her six dogs. Which fraction represents this division.
anzhelika [568]
5 treats divided by six groups of one dog, or in easier terms, five dog treats divided up for 6 dogs. As a fraction, just remove the words except for 5, divided by, and 6, to give you 5/6. Hope this helped.
5 0
3 years ago
The answer to this word problem usinf discriminant
solniwko [45]
\bf h=-9.8t^2+45t+1.2\implies 64.5=-9.8t^2+45t+1.2&#10;\\\\\\&#10;0=-9.8t^2+45t-63.3\\\\&#10;-------------------------------

\bf \qquad \qquad \qquad \textit{discriminant of a quadratic}&#10;\\\\\\&#10;0=\stackrel{\stackrel{a}{\downarrow }}{-9.8}t^2\stackrel{\stackrel{b}{\downarrow }}{+45}t\stackrel{\stackrel{c}{\downarrow }}{-63.3}&#10;~~~~~~&#10;\stackrel{discriminant}{b^2-4ac}=&#10;\begin{cases}&#10;0&\textit{one solution}\\&#10;positive&\textit{two solutions}\\&#10;negative&\textit{no solution}&#10;\end{cases}&#10;\\\\\\&#10;(45)^2-4(-9.8)(-63.3)\implies -456.36

the discriminant is a negative value, thus no solution for such quadratic, meaning if we use h=64.5 like we did, there's no "t" seconds at which point the ball hits the batting cage.
8 0
3 years ago
I think it the third one but need a double check
makkiz [27]

Answer:

The first answer is correct.

Step-by-step explanation:

Line 5 says that the reason is due to substitution

Line 3 says m∠ SQT equals 180°

If we substitute 180° into the spot for m∠ SQT in line 4, we get solution option 1

8 0
3 years ago
HELPPPPP PLEASEEEE!!!!!Find the Area of the Rectangle:
tangare [24]

Answer:

62

Step-by-step explanation:

IM NOT SURE I THINK BUT hope this helps :)

7 0
3 years ago
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