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2 years ago

True or false? The quadratic equation 10p2 - 5p = -8 has one solution.

Mathematics

1 answer:

pav-90 [236]2 years ago

6 0

Answer: False

=============================================

Explanation:

I'll use x in place of p.

The original equation 10x^2-5x = -8 becomes 10x^2-5x+8 = 0 after moving everything to one side.

Compare this to ax^2+bx+c = 0

We have

a = 10
b = -5
c = 8

Plug those three values into the discriminant formula below

d = b^2 - 4ac

d = (-5)^2 - 4(10)(8)

d = 25 - 40*8

d = 25 - 320

d = -295

The discriminant is negative, which means we have no real solutions. If your teacher has covered complex or imaginary numbers, then you would say that the quadratic has 2 complex roots. If your teacher hasn't covered this topic yet, then you'd simply say "no real solutions".

Either way, this quadratic doesn't have exactly one solution. That only occurs when d = 0. Therefore, the original statement is false.

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A rowing team rowed 90 miles while going with the current in the same amount of time as it took to row 10 miles going against th

pishuonlain [190]

Answer:

The speed in still water is 5 miles per hour.

Step-by-step explanation:

distance with current = 90 miles

distance against current = 10 miles

speed in still water = s

speed of current = 4 mph

speed with current = s + 4

speed against current = s - 4

time = t

speed = distance/time

distance = speed * time

With current:

90 = (s + 4) * t

Against the current:

10 = (s - 4) * t

We have a system of equations:

90 = (s + 4) * t

10 = (s - 4) * t

90 = ts + 4t

10 = ts - 4t

Subtract the second equation from the first equation.

80 = 8t

10 = t

t = 10

10 = t(s - 4)

10 = 10(s - 4)

1 = s - 4

s = 5

Answer: The speed in still water is 5 miles per hour.

8 0

3 years ago

A hotel has $504 to buy new pillows. If the cost of each pillow is $6, how many pillows will the hotel be able to buy? A) 78 B)

Naddik [55]

Hello there!
You can use the equation:
504 ÷ 6
84
The hotel can buy 84 pillows.
Hope this helped! :D

4 0

3 years ago

Read 2 more answers

Kenyl covers the front of a circular bulletin board with fabric that costs 1.48 per square foot. The bulletin board has a radius

Gnoma [55]

Answer:

Step-by-step explanation:

In this question we are trying to calculate the cost of exact amount of fabric used given the cost per area of the fabric.

To answer this question mathematically, we need to know the area of the bulletin board. To do this , we employ a mathematical approach. We know that the bulletin board is circular in shape from the question and thus we calculate the area of this shape.

Mathematically, the area of the circular bulletin board is pi * r^2 where r refers to the radius. From the question, we can identify that this radius is 2.5 feet. let’s insert this into the equation we have.

mathematically A = 2.5^2 * pi = 19.63 sq. feet

The cost of the fabric per square feet is 1.48.

now the cost for this area that we have will be 1.48 * 19.63 = 29.0524

This is nearest to 29

7 0

3 years ago

For what value of c is the function defined below continuous on (-\infty,\infty)?

kozerog [31]

$f(x)= \left \{ {{x^2-c^2,x \ \textless \ 4} \atop {cx+20},x \geq 4} \right
$

It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
A function, f, is continuous at x = 4 if
 $\lim_{x \rightarrow 4} \ f(x) = f(4)$

In notation we write respectively
 $\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)$

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just 4c + 20.

On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
$\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2$

Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c²

$c^2+4c+4=0
\\(c+2)^2=0
\\c=-2$

That is to say, if c = -2, f(x) is continuous at x = 4.

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers $(-\infty, +\infty)$