MATHEMATICS HIGH SCHOOL

If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?A.) There are two complex roots.
B.) There are two real roots.
C.) There is one real root.
D.) There is one complex root.

Answers

Answer 1
Answer:

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the roots of the quadratic equation of the form  ax^(2) +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^(2)-4ac}}{2a}

where

The discriminant of the quadratic equation  is equal to

b^(2)-4ac

if  (b^(2)-4ac)> 0 ----> the quadratic equation has two real roots

if  (b^(2)-4ac)=0 ----> the quadratic equation has one real root

if  (b^(2)-4ac)< 0 ----> the quadratic equation has two complex roots

in this problem we have that

the discriminant is equal to -8

so

the quadratic equation has two complex roots

therefore

the answer is the option A

There are two complex roots
Answer 2
Answer:

Answer:

There are two complex roots

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The figure shows line AC and line PQ intersecting at point B. Lines A'C' and P'Q' willbe the images of lines AC and PQ, respectively, under a dilation with center P andscale factor 2.Which of the following statements about the image of lines AC and PQ would beTRUE under the dilation.Line AC will be parallel to line AC, and line P Q will be the same line as line PQ.Line AC will be perpendicular to line AC, and line P Q will be parallel to line PQ.Line AC will be parallel to line AC and line P Q will be perpendicular to PQ.Line AC will be parallel to line AC, and line P Q will be parallel to line PQ.

Help me on this I don't understand it​

Answers

Answer:

  B has the greatest range for a given amount of fuel

Step-by-step explanation:

In the US, fuel efficiency is measured in terms of miles per gallon. This value is found by dividing the number of miles traveled by the corresponding number of gallons used.

When calculations are repetitive, it is often useful to use a spreadsheet to do them. You can enter the formula once, and have it operate on all the different data sets. Here, the formula divides the number in the miles column (range) by the number on the same row in the gallons column (fuel).

We find the greatest miles per gallon (best efficiency) is given by Option B.

__

Additional comment

Many places in the world measure fuel efficiency by the amount of fuel required to deliver a certain outcome. In this problem, that would be expressed as gallons per some number of miles, perhaps 100 miles. Using that measure, a lower value indicates better performance.

I HAVE 5 MATH QUESTIONS AND I NEED HELP ASAP. ONLY COMMENT IF YOU'RE GONNA HELP ME PLEASE. THANKS! QUESTIONS ARE PASTED BELOW.

Answers

1. (2,3)
2. (-1,-1)
3. infinitely many
4. coincident
5. consistent independent, coincident, inconsistent (in that order)

Which point is located at (4, -2)?y
5
ТА
4
3
2+
1
2 3
Х
-5 -4 -3 -2 -11
-2
4 5
B
-4
D
b

Answers

Answer:

Point B of 4the quertant

An auto weighing 2,500 pounds is on a street inclined at 10 with the horizontal. Find the force necessary to prevent the car from rolling down the hill. Round your answer to the nearest whole number. Do not use a space or decimal in your answer or it will be marked wrong.

Answers

Answer:

13892 lb-ft/sec^2

Step-by-step explanation:

Given that An auto weighing 2,500 pounds is on a street inclined at 10 with the horizontal.

Here acceleration due to gravity is the pulling factor against which the car should be stopped from rolling down the hill.

Weight of the car =2500 pounds

Vertical component of gravity = 32cos (90-10)=32sin 10 = 32(0.1736)

Force required = mass x acceleration

=2500x0.1736x32

=13892 lb ft/sec^2
Make sure your calculator is set to DEGREES and not RADIANS when performing your sinθ calculation. sin(10) = -0.54402 sin(10°) = 0.17365 You could also try using trig tables if you're unsure how to do this. So: 2500sin(10°) = 434 lb

To determine the appropriate landing speed of an airplane, the formula D = .1x 2 − 3x + 22 is used, where x is the initial landing speed in feet per second and D is the distance needed in feet. If the landing speed is too fast, the pilot may run out of runway; if the speed is too slow, the plane may stall. What is the appropriate landing speed if the runway is 800 feet long? Show all of your work or explain how you came up with your solution

Answers

800=0.1x^2-3x+22\n0.1x^2-3x-778=0\n\Delta=(-3)^2-4\cdot0.1\cdot(-778)=9+3112=3121\n√(\Delta)=√(3121)\nx_1=(-(-3)-√(3121))/(2\cdot0.1)=(3-√(3121))/(0.2)=15-5√(3121)\approx-264.3\nx_2=(-(-3)+√(3121))/(2\cdot0.1)=(3+√(3121))/(0.2)=15+5√(3121)\approx294.3

Approx. 294.3 ft/s

Why can't you factor 2cosx^2+sinx-1=0 ?

Answers

2cos^2x+sinx-1=0\n\n2(1-sin^2x)+sinx-1=0\n\n2-2sin^2x+sinx-1=0\n\n-2sin^2x+sinx+1=0\n\n-2sin^2x+2sinx-sinx+1=0\n\n-2sinx(sinx-1)-1(sinx-1)=0\n\n(sinx-1)(-2sinx-1)=0\iff sinx-1=0\ or\ -2sinx-1=0\n\nsinx=1\ or\ -2sinx=1\n\nsinx=1\ or\ sinx=-(1)/(2)\n\nx=(\pi)/(2)+2k\pi\ or\ x=-(\pi)/(6)+2k\pi\ or\ x=(7\pi)/(6)+2k\pi\ where\ k\in\mathbb{Z}
2cosx^2+sinx-1=2(1-sin^2x)+snx-1=\n\n=2(1-sinx)(1+sinx)-(1-sinx)=(1-sinx)[2(1+sinx)-1]=\n\n=(1-sinx)(2+2sinx-1)=(1-sinx)(1+2sinx)\n\n2cosx^2+sinx-1=0\ \ \ \Leftrightarrow\ \ \ (1-sinx)(1+2sinx)=0\n\n1-sinx=0\ \ \ \ \ or\ \ \ \ \ 1+2sinx=0\n\n1)\ \ \ 1-sinx=0\ \ \ \Rightarrow\ \ \ sinx=1\ \ \ \Rightarrow\ \ \ x= ( \pi )/(2) +2k \pi ,\ \ \ k\in I\n\n

2)\ \ \ 1+2sinx=0\ \ \ \ \ \ \Rightarrow\ \ \ sinx=- (1)/(2)\n\n \Rightarrow\ \ \ x_1=( \pi + ( \pi )/(6) )+2k \pi ,\ \ \ \ \ \ x_2=( - ( \pi )/(6) )+2k \pi,\ \ \ \ \ \ k\in I\n\n.\ \ \ \ \ \ x_1=(7 \pi )/(6) +2k \pi ,\ \ \ \ \ \ \ \ \ \ \ \ x_2=-( \pi )/(6) +2k \pi,\ \ \ \ \ \ \ \ \ k\in I\n\nAns.\ x=-( \pi )/(6) +2k \pi\ \ \ or\ \ \ x= ( \pi )/(2) +2k \pi\ \ \ or\ \ \ x=(7 \pi )/(6) +2k \pi,\ \ \ k\in I
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