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2 years ago

13

Joe works on an assembly line that fills boxes with various toy trinkets. Every sixth box gets a red ball and every fourt box ge

ts a blue whistle. How often does a box get both a red and a blue whistle

1 answer:

Genrish500 [490]2 years ago

6 0

Every 12th box gets a whistle and a ball because 12 is the lowest common factor of 6 and 4.

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What are the key features of a graph of a quadratic equation with only complex solutions

dybincka [34]

Answer:

If D< 0, the roots of the quadratic equation will b complex.

Step-by-step explanation:

Let $ax^{2} + bx + c =0$ is the given quadratic equation.

So, if the Discriminant (D) = $b^{2} - 4ac < 0$ , the the equation will have only complex solutions.

Complex roots are represented in the form of $(x \pm iy)$

1. <u> x represents the X axis (real) co ordinate,</u>

<u>y represents the Y axis (imaginary) coordinate</u>

<u />

<u />

2. Also, the graph of the with equation D < 0 NEVER CROSSES the X - axis, as there are no real roots of the equation, only complex roots.

3. Here. roots are always identical but are opposite in signs. Such pair or roots with opposite sign are called CONJUGATE PAIRS.

4 0

3 years ago

Bob's age is 4 times greater than Susanne's age. Dakota is three years younger than Susanne. The sum of Bob's, Susanne's, and Da

Ratling [72]

<span>Susanne is 16 years old.</span>

b = Bob's age

s = Susanne's age

d = Dakota's age

Bob's age is 4 times greater than Susanne's age:

b = 4s

Dakota is three years younger than Susanne:

d = s - 3

The sum of Bob's, Susanne's, and Dakota's ages is 93:

b + s + d = 93

solve these equations:

b = 4s

d = s - 3

b + s + d = 93

and get:

b = 64 years

s = 16 years

(remember that s = Susanne)

d = 13 years

6 0

2 years ago

(7x+5)(2x3-4x2+9x-3)

Zanzabum

I believe the answer is 3x(3x + 2)

Step-by-step explanation:

4 0

3 years ago

The cost of 4 cookies, 6 doughnuts, and 3 boxes of doughnut holes is $8.15. The cost of 2 cookies, 3 doughnuts, and 4 boxes of d

Naddika [18.5K]

Answer:

$1.25

Step-by-step explanation:

This can best be determined using a set of linear equations that are solved simultaneously.

This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.

Let the cost of a cookie be c, cost of a doughnut be d and that of a box of doughnut hole be h then if cost of 4 cookies, 6 doughnuts, and 3 boxes of doughnut holes is $8.15, we have

4a + 6d + 3h = 8.15

and the cost of 2 cookies, 3 doughnuts, and 4 boxes of doughnuts holes is $7.20 then

2a + 3d + 4h = 7.20

Dividing the first by 2

2a + 3d + 1.5h = 4.075

subtracting from the second equation

2.5h = 3.125

h = 1.25

The cost of a box of doughnut holes is $1.25

5 0

2 years ago

What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4

givi [52]

Answer:

The remainder will be 6.

Step-by-step explanation:

We have the function:

$f(x)=x^4-2x^3-27x^2-9x+18$

And we want to find the remainder after it is divided by the binomial:

$x+4$

We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (<em>x</em> - <em>a</em>), then the remainder will be given by P(a).

Here, our divisor is (<em>x</em> + 4). We can rewrite this as (<em>x</em> - (-4)).

Therefore, <em>a</em> = -4.

Then according to the PRT, the remainder will be:

$f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6$

The remainder will be 6.

4 0

2 years ago