X - 1 4 (12 - x) = x + 3(4 - x)

Nady [450]

A gardener can increase the number of dahlia plants in an annual garden by either buying new bulbs each year or dividing the existing bulbs to create new plants . The table below shows the expected number of bulbs for each method

Part A
For each method,a function to model the expected number of plants for each year

Part B
Use the Functions to Find the expected number of plants in 10 years for each method.

Part C
How does the of plants in five years compare to the expected number of plants in 15 years !Explain how these patterns could affect the method the gardener decides to use.

8 0

3 years ago

Solve each system by graphing.

Helen [10]

They intersect at point...

(-1,4)

6 0

3 years ago

Read 2 more answers

The zeros of a parabola are 6 and −5. If (-1, 3) is a point on the graph, which equation can be solved to find the value of a in

Elena L [17]

ANSWER

$3= a( - 1 +6)( - 1 - 5)$

EXPLANATION

The equation of a parabola in factored form is

$y = a(x + m)(x + n)$

where 'a' is the leading coefficient and 'm' and 'n' are the zeros.

From the question, the zeros of the parabola are 6 and −5.

This implies that,

$m = 6 \: \: and \: \: n = - 5$

We plug in these zeros to get:

$y= a(x +6)(x - 5)$

If (-1, 3) is a point on the graph of this parabola,then it must satisfy its equation.

We substitute x=-1 and y=3 to obtain:

$3= a( - 1 +6)( - 1 - 5)$

The first choice is correct.

6 0

3 years ago

Read 2 more answers

Match the information on the left with the appropriate equation on the right.

solmaris [256]

Answer:

Step-by-step explanation:

1). Equation of a line which has slope 'm' and y-intercept as 'b' is,

y = mx + b

If slope 'm' = 1 and y-intercept 'b' = -3

Equation of the line will be,

y = x - 3

x - y = 3

2). Equation of a line having slope 'm' and passing through a point (x', y') is,

y - y' = m(x - x')

If the slope 'm' = 1 and point is (-1, 2),

The the equation of the line will be,

y - 2 = 1(x + 1)

y = x + 1 + 2

y = x + 3

x - y = -3

3). Equation of a line passing through two points $(x_1, y_1)$ and $(x_2,y_2)$ will be,

$y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

If this line passes through (-2, 3) and (-3, 4),

$y-3=\frac{(4-3)}{(-3+2)}(x+2)$

y - 3 = -1(x + 2)

y = -x - 2 + 3

y = -x + 1

x + y = 1

4 0

3 years ago

Find the y intercepts of 3x^2+24x-51. quadratic formula

julia-pushkina [17]

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , with a = x^2 coefficient, b = x coefficient, and c = constant.

Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

$y=3*0^2+24*0-51\\y=0+0-51\\y=-51$

Your y-intercept is (0,-51).

Next, using our equation plug the appropriate values into the quadratic formula:

$x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}$

Next, solve the multiplications and exponent:

$x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}$

Next, solve the addition:

$x=\frac{-24\pm \sqrt{1224}}{6}$

Now, simplify the radical using the product rule of radicals as such:

Product Rule of Radicals: √ab = √a × √b

√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

$x=\frac{-24\pm 6\sqrt{34}}{6}$

Next, divide:

$x=-4\pm \sqrt{34}$

The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).

Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

$x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83$

The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).

5 0

4 years ago

X - 1 4 (12 - x) = x + 3(4 - x) - 2x