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3 years ago

Is this in proper standard notation? 5x - 5y = 7

1 answer:

8 0

Yes this is in standard form Ax+By = C. In this case, A = 5, B = -5 and C = 7. We cannot simplify this any further because the GCF of the three values is 1.

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What is the equation of the midline for the function f(x) ?

Inessa05 [86]

let's recall the graph of sin(x), is simply a sinusoidal line waving about, but its midline is at the x-axis, namely y = 0.

this equation is simply a transformation of it, the 1/2 changes the amplitude by half, midline stays the same though, the +3, moves the whole thing upwards, a vertical shift of 3, meaning the midline went from 0 to 3, y = 3.

5 0

3 years ago

Find the product of the complex numbers. Express your answer in trigonometric form. z1 = 5(cos(25) + isin(25)) z2 = 2(cos(80) +

zmey [24]

solution:

Z1 = 5(cos25˚+isin25˚)

Z2 = 2(cos80˚+isin80˚)

Z1.Z2 = 5(cos25˚+isin25˚). 2(cos80˚+isin80˚)

Z1.Z2 = 10{(cos25˚cos80˚ + isin25˚cos80˚+i^2sin25˚sin80˚) }

Z1.Z2 =10{(cos25˚cos80˚- sin25˚sin80˚+ i(cos25˚sin80˚+sin25˚cos80˚))}

(i^2 = -1)

Cos(A+B) = cosAcosB – sinAsinB

Sin(A+B) = sinAcosB + cosAsinB

Z1.Z2 = 10(cos(25˚+80˚) +isin(25˚+80˚)

Z1.Z2 = 10(cos105˚+ isin105˚)

5 0

3 years ago

A fish tank has 9 goldfish, 6 tetras, 5 snails and 3 platies. What is the ratio of tetras to platies

Andrei [34K]

Answer:

6:3

Step-by-step explanation:

6 tetras and 3 platies

3 0

2 years ago

Find the values for c and d

baherus [9]

Answer:

c=-5

d=1

Step-by-step explanation:

$(cy^2)(4y^d)=-20y^3$

I'm going to reorder the left-hand side. Multiplication is commutative.

$(4c)(y^2y^d)=-20y^3$

Since the bases are the same in $y^2y^d$ and the operation is multiplication, I'm going to add the exponents giving me:

$4cy^{2+d}=-20y^3$

So this implies we have two equations to solve:

$4c=-20$ and $2+d=3$

So the first equation can be solved by dividing both sides by 4 giving you $c=-5$ .

The second equation can be solved by subtracting 2 on both sides giving you $d=1$ .

6 0

3 years ago

The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions

Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

$\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}$

The quadratic equation can now be solve using factorization method:

$\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}$

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

$\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\ \\ Width=x=5\text{ }ft \end{gathered}$

7 0

1 year ago