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uranmaximum [27]
3 years ago
14

Tammy is creating potpourri bowls using 40 bags of shredded bark and 20 bags of flower

Mathematics
1 answer:
Anni [7]3 years ago
5 0

Answer:

20

Step-by-step explanation:

She only has 20 bags of flower petals, so she cannot create more than that. Because 40 is divisible by 20, she can make 20 bowls.

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Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.
NeTakaya

Answer:

Option B

Step-by-step explanation:

Complex roots occur as conjugate pairs so the third root is -3 - i ( note that the sign changes from + to -).

So in factor form we have:-

(x - 2)(x - (-3 + i))(x - (-3 - i)) = 0    Let's expand the last 2 factors first:-

(x - (-3 + i))(x - (-3 - i))

= (x + 3 - i)(x + 3 + i)

= x^2 + 3x +ix + 3x + 9 + 3i - ix - 3i - i^2

= x^2 + 6x + 9 - (-1)

= x^2 + 6x + 10

Now multiplying by (x - 2):-

(x - 2)(x^2 + 6x + 10) = 0

x^3 + 6x^2 + 10x - 2x^2 - 12x - 20 = 0

x^3 + 4x^2 - 2x - 20 = 0    (answer)

Option B

5 0
3 years ago
Given the points J(4,-7) and L(-2,13), find the coordinates of point k on JL such that the ratio of jk is 1:4
Irina-Kira [14]

Answer:

The coordinates of point k are (-2.8,-3)

Step-by-step explanation:

we shall use the internal division formula to find the coordinates of point k

Mathematically, the formula is as follows;

Let’s call the coordinates of point k (x,y)

(x , y) = mx2 + nx1/(m + n) , my2 + ny1/(m + n)

From the question;

m = 1 , n = 4

x1 = 4, x2= -2

y1 = -7 , y2 = 13

Substituting these values in the equation, we have the following;

1(-2) + 4(4)/(1 + 4) , 1(13) + 4(-7)/(1+4)

(-2+16)/5, (13 -28)/5

= -14/5, -15/5

= (-2.8, -3)

3 0
3 years ago
5. Solve each equation.<br>a.<br>6(3x - 5) - 7x = 25​
Ivahew [28]

Answer:

Step 1: Simplify both sides of the equation.

6(3x−5)−7x=25

(6)(3x)+(6)(−5)+−7x=25(Distribute)

18x+−30+−7x=25

(18x+−7x)+(−30)=25(Combine Like Terms)

11x+−30=25

11x−30=25

Step 2: Add 30 to both sides.

11x−30+30=25+30

11x=55

Step 3: Divide both sides by 11.

x=5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Show that for any real number x ≥ 0 the set (x,x + 1]∩N is a singleton set
inessss [21]

Answer: First, a singleton set is the set with only one element, for example, the set {∅} or set "null" is a singleton.

now, X ≥ 0, and X ∈ R.

(x,x + 1]∩N is the intersection between the set x and x+1 with the set of natural numbers, so the result of this operation is the set of all the natural numbers between x and x+1.

if x is a rational (or irrational) number, such as 1.5, then x +1 = 2.5

in (1.5, 2.5] there is only one natural element, the 2, then (x,x + 1]∩N is the singleton {2}

if x is a positive integer number, such as 1, then x + 1 = 2

the set is (1,2] is important to notice that 1 ∉ (1,2] because the set is open in the lower limit. so this set only contains one natural number, the 2; so again; the intersection with the natural set is a singleton

So this is proven for x rational, irrational and integers.

This happens because each element in the natural set is separated by the next one by 1, and in the set (x,x + 1]  although the distance between the lower and upper limits is 1, the set is open in the lower limit, so the distance is < 1. then you never can have two natural numbers on this set.

8 0
3 years ago
What is the discount of 40 to 25 in percentage
babunello [35]

Answer:

%37.5

Step-by-step explanation:

.375 aka %37.5

If we did .375 x 40 it would be 15. 40-15=25

3 0
3 years ago
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