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4 years ago

How did the Missouri Compromise keep peace between the North and South?

1 answer:

8 0

The Missouri Compromise basically said that the next states that joined the US would be given to the north and the south. Ex: The first would go to the South and the next will go to the North. Or answer A

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If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes

anyanavicka [17]

ANSWER

$x = 2 \: \: or \: \: x = 15$

$x = - 2 \: \: or \: \: x = - 15$

EXPLANATION

The given polynomial is

$f(x) = {x}^{2} + kx + 30$

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

$m + n = - \frac{b}{a} = -k$

and the product of roots is

$mn = \frac{c}{a} = 30$

The square difference of the zeroes is given by the expression.

$( {m - n})^{2} = {(m + n)}^{2} - 4mn$

From the question, this difference is 169.

This implies that:

$( { - k)}^{2} - 4(30) = 169$

${ k}^{2} -120= 169$

$k^{2} = 289$

$k= \pm \sqrt{289}$

$k= \pm17$

We substitute the values of k into the equation and solve for x.

$f(x) = {x}^{2} \pm17x + 30$

$f(x) = (x \pm2)(x \pm 15)$

The zeroes are given by;

$(x \pm2)(x \pm 15) = 0$

$x = \pm2 \: \: or \: \: x = \pm 15$

5 0

4 years ago

I am Desperate for answer

solmaris [256]

The mean is 8 and the lower quartile is 6.

8 0

3 years ago

Suppose that the grade 7 student expected to sell between 100 and 150 hotdogs. How many packages of 12 wieners and 8 buns should

Marysya12 [62]

Assuming that 1 wiener and 1 bun required to sell 1 hotdog.

Given that there are 12 wieners and 8 buns in 1 packet of each.

Let m be the minimum numbers of hotdogs for no leftover wieners or buns.

So, m must be a number which is divisible by both 12 as well as 8.

The smallest number which is the common multiple of both 12 as well as 8 is the highest common factor (H.C.F.) of 12 and 8 which is 24.

So, m=24

At this pint, note that 24 is the minimum number of hotdogs that students can sell with no leftover wieners or buns. For this, they need 2 packets of wieners and 3 packets of buns.

So, 1 m hotdogs required 2 packets of wieners and 3 packets of buns

But, here the number of hotdogs is between 100 and 150.

The next possible number of hotdog wit no leftover wieners or buns is 48 which is 2m, the next will be 3m, and so on.

In fact, any multiple of m will be divisible by 12 as well as 8, so there will not be any leftover wieners or buns.

So, 24n hotdogs require 2n packets of wieners and 3n packets of buns,

where n is a counting number.

Now, find the multiple of 24 in between 100 and 150,

The first multiple is 24x5=120

So, 120 hotdogs require 2x5=10 packets of wieners and 3x5=15 packets of buns

The second multiple is 24x6=144

So, 144 hotdogs require 2x6=12 packets of wieners and 3x6=18 packets of buns

If the students want to sell more than 300 hotdogs:

The minimum number which is multiple of 24 is 24x13=312, the next number is 24x14=336, and so on

For this n=13, 14, 15, ...

So, they need to buy 2n packets of wieners and 3n packets of buns to sell 24n packets of hotdogs for no leftover.

For the minimum number of 312 hot dogs, they need to buy 2x13=26 packets of wieners and 3x12=36 packets of buns.

3 0

3 years ago

4. Given point A (3, 8) and point B (-5, 1). Find the following:

Anni [7]

Answer:

a) (-1,4.5)

b)10.63 units

c)7/8

Step-by-step explanation:

a) To find this, we use the midpoint formula

(x,y) = (x1 + x2)/2 , (y1 + y2)/2

(x1,y1) = (3,8)

(x2,y2) = (-5,1)

(x,y) = (3 -5)/2 , (8 + 1)/2 = (-1, 4.5)

b) To calculate the distance D between two points, we use the formula;

D = √(x2-x1)^2 + (y2-y1)^2

D = √(-5-3)^2 + (1-8)^2

D = √(-8)^2 + (-7)^2

D = √64 + 49

D = √113

D = 10.63 units

C) We use the slope formula here

m = (y2-y1)/(x2-x1)

m = (1-8)/(-5-3) = -7/-8 = 7/8

6 0

3 years ago

Find the value of X in the triangle shown below<br> X= ? ( in degrees)

frez [133]

Answer:

x=50

Step-by-step explanation:

since all triangles angles add up to 180 and x and the other corner look equal, than minus 80 from 180 and then divide by two (because of the 2 corners.) x=50 degrees

4 0

3 years ago