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4 years ago

(t-1)(t+1)(t²+1) = t⁴-1 But how

Mathematics

1 answer:

Fantom [35]4 years ago

8 0

(t-1)(t+1) = t^2-1 through the difference of squares rule

So,

(t-1)(t+1)(t^2+1)

(t^2-1)(t^2+1)

(x-1)(x+1) ... let x = t^2

x^2-1 .... another application of the difference of squares rule

(t^2)^2 - 1... plug in x = t^2

t^4 - 1

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50 points. Only solve 6-10. And show work

sineoko [7]

Answer :

6 : Margaret has 30 50-cent coins and 26 10-cent coins

let 'x' represent the number of 50-cent coins, then '56-x' represents the number of 10-cent coins

17.60 = 0.5x + 0.1(56-x)

solving for 'x' we have x=30

56-30 = 26

7 : Total money = $29.40

mich money = m dollar,

amy money = (3/4)m dollars,

Total = m + 3m/4 = 29.40,

4m+3m = 4*29.4,

7m = 117.6,

m = 117.6/7 = 16.8

Hence,

Michelle's money = $16.80

Amy money = $12.60

8 : (a) The amount of milk in a carton is normally distributed with a mean of 260 millilitres (mL) and a standard deviation of 8 mL. Every milk carton is labelled with the serving size as 250 mL. (i) What is the probability that a randomly selected carton has more than the labelled serving? [3 marks) (ii) Determine the amount of milk in a carton for which only 7.08% of cartons fall below this amount. [3 marks (iii) Find an interval around the mean y = 260mL such that 95% of all milk cartons fall within this interval. (5 marks)

9 : a=3, b=5

So b+2 = a+4 = 4a-b

b=a+2

3a=b+4

b=2a-1

Hence

2a-1=a+2

10 : original dimensions of rectangle, length = 18cm and width = 10cm

Let length and width = L and W.

from statement "A rectangle has perimeter 56 cm. If 4 cm is taken from the length and added to the width, the rectangle becomes a square", you can deduce

2L + 2W = 56 ( its sides make up its perimeter )

L - 4 = W + 4

L = W + 8

sub L = W + 8 into 2L + 2W = 56

2 ( W + 8 ) + 2W = 56

2W + 16 + 2W = 56

4W = 40

W = 10

sub W = 10 into L = W + 8

L = 10 + 8 = 18

8 0

3 years ago

Read 2 more answers

I need the answer please

Veseljchak [2.6K]

The trick to solving this problem is to know and remember that the sum of all the interior angles of a triangle is always 180 degrees.

Thus, (6x+1) + (5x-17) + (9x-24) = 180.

20x = -40, so x = -2 (answer)

7 0

4 years ago

Find an equation in standard form for the hyperbola with vertices at (0,plus or minus 6) and asymptotes at y= (plus or minus 3/5

antoniya [11.8K]

Answer:

$\frac{(y)^2}{36}-\frac{(x)^2}{100}=1$

Step-by-step explanation:

Given:

Vertices of Hyperbola : (0 ± 6) or (0,6) and (0,-6)

and asymptotes at y= (±3/5)x 0r y= 3/5 x and y=-3/5 x

The vertices are of vertical hyperbola. The equation used will be:

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\\$

The Center of hyperbola (h,k) =(0,0)

The Distance from vertices to center is a and a = 6 (given)

For equation we have value of h,k and a and need to find value of b

we know,

y= k ± a/b (x-h)

Values of h and k are zero

y= 0 ± a/b (x-0)

y= (± a/b ) x

We are given asymtotes at y= (± 3/5)x which is equal to y= (± a/b ) x

as a = 6 then b= 10 i.e The simplified form of 6/10 is 3/5 so value of b=10

Putting values of a,b,h and k in equation we get,

$\frac{(y-0)^2}{(6)^2}-\frac{(x-0)^2}{(10)^2}=1\\\\\frac{(y)^2}{36}-\frac{(x)^2}{100}=1$

7 0

4 years ago

Match the name of the sampling method descriptions given.Situations 1. divide the population by age and select 5 people from eac

USPshnik [31]

Answer:

1. ⇔ b.

2. ⇔ a.

3. ⇔ c.

4. ⇔ e.

5. ⇔ d.

Step-by-step explanation:

We conclude that:

5. asking people on the street Sampling is (d.) Convenience.

4. randomly select two tables in the cafeteria and survey all the people at those two tables is (e.) Cluster.

3. choosing every 5th person on a list is (c.) Systematic.

1. divide the population by age and select 5 people from each age is (b.) Stratified.

2. writing everyones name on a playing card, shuffling the deck, then choosing the top 20 cards is (a.) Simple Random.

6 0

4 years ago

What will the length of segment I' J' be?<br>

Ymorist [56]

Answer:

5.333

Step-by-step explanation:

To find the length of dilated I' J' we need to dilate the shape.

To do this you multiply each coordinate by 8/3.

Ex: (x,y) ---> (8/3x, 8/3y)

H: (0,3) ---> (8/3*0, 8/3*3)

I: (1,1) ---> (8/3*1, 8/3*1)

J: (3,1) ---> (8/3*3, 8/3*1)

K: (2,5) ---> (8/3*2, 8/3*5)

Now we plot this. (Picture attached)

The new I' coordinate: (2.667, 2.667)

The new J' coordinate: (8, 2.667)

The new length would be 8 - 2.667 so we can find the distance between the two points.

Note we are subtracting the y coordinates and not x because x coordinates represent height and y represents length

8 - 2.667 equals 5.333

So the length of segment I' J' will be 5.333

5 0

2 years ago