MATHEMATICS HIGH SCHOOL

A straight line has gradient m and passes through the points (0,-2). Find the two values for m for which the line is tangent to the curve y=x^2-2x 7. And for each value of m, find the coordinates of the points where the line touches the curve

Answers

Answer 1
Answer:

Answer:

when m=2 or -2, the line is tangent to the curve at the points (2.7) and (0,7)

Step-by-step explanation:
Answer 2
Answer:

Answer:

Hi,

Step-by-step explanation:

The curve is y=x^²-2x+7

The tangent  has for equation: y=mx-2

Let's find the intersection of the tangent and the curve.

mx-2=x^2-2x+7\n\nx^2+(-2-m)x+9=0\n\Delta=(-2-m)^2-4*9=m^2+4m-32\nThe\ point\ must\ be \ unique: \Delta=0\n\nm^2+4m-32=0\n\delta=4^2+4*32=144=12^2\n\nm=(-4-12)/(2) =-8\ or\ m=(-4+12)/(2) =4\n\nx^2+(-2-m)x+9=0\ and\ \Delta=0 = > x=(2+m)/(2) \n\nif\ m=-8\ then\ x=(2+(-8))/(2)=-3\ and\ y=mx-2=(-8)*(-3)-2=22\n\nif\ m=4\ then\ x=(2+4)/(2)=3\ and\ y=mx-2=4*3-2=10\n\n\nCoordinates\ of\ the\ points\ are (-3,22)\ and\ (3,10)\n

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there are 750 spectators in the stadium,of which 420 are women and the rest are men what percent of the spectators are women? and what percent of the spectators are men?

Answers

The percentage of women spectators is 56%.

The percentage of men spectators is 44%.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of spectators = 750

Number of women = 420

Number of men = 750 - 420 = 330

The percentage of women.

= 420/750 x 100

= 56%

The percentage of men.

= 330/750 x 100

= 44%

Thus,

56% of women are spectators.

44% of men are spectators.

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number \ of\ men=750-420=330\n\n(420)/(750)*100\%=(42000)/(750)\%=56\%\n\n100\%-56\%=44\%\n\nWomen\ are\ 56\%\ of\ spectators\ and\ men\ are\ 44\%.

fifteen percent of the workers at nationwide industries earn minimum wage. if 24 workers earn minimum wage, how many total workers are there at nationwide industries?

Answers

if you do 100 divided by 15 times 24 you get 160
Let the total number of workers be x

Since its given in statement, that 15% of workers earn minimum wage and that is equal to 24.
i.e 15 % of x = 24
x*15/100 = 24
x = 24*100/15
x = 160
therefore total number of workers are 160

Solve in picture. Mathematics problem.

Answers

Cross Multiplication!
(4)/(7) = (x-3)/(21)
4 × 21 = 7 × (x-3)
Distribute 7 into the parenthesis:
84 = 7x - 21
Take 21 to the other side:
84 + 21 = 7x
105 = 7x
Divide by 7 on both sides:
(105)/(7) = (7x)/(7)
( 7 and 7 cancels out )
15 = x
x = 15

Which of the following choices is the subject of this simple sentence? The corn grew as tall as the fence.

Answers

The answer is corn it is the subject

Final answer:

The subject of the simple sentence "The corn grew as tall as the fence." is "the corn".

Explanation:

The subject of the simple sentence "The corn grew as tall as the fence." is "the corn". The subject is the noun or pronoun that the sentence is about or that performs the action of the verb. In this sentence, the corn is the noun that grows, so it is the subject.

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Answers

The answer to that question is $4,750
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