Y = (x+3)² – 64 how do you write this in standard form

What is the value of z in the figure shown? 45.6 1148

kupik [55]

Answer:

45

Step-by-step explanation:

8 0

3 years ago

a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

xenn [34]

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83. $\underline{\overline 3}$ feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

the fence, we have;

Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

$\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x$

$y = \mathbf{250 - \dfrac{3}{2} \cdot x}$

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

$\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2$

$\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}$

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, $\dfrac{dA}{dx} = 0$

Finding the value of x at the maximum point, we get;

$\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0$

Therefore;

$\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}$

$\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125$

The length of the plot that will give the most area, y = 125 feet

Learn more here:

brainly.com/question/16337916

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6 0

3 years ago

PLZ HELP FOR BRAINLIEST!!

worty [1.4K]

C

Using Descartes' rule of signs

look for the number of sign changes in f(x)

+ / + / - / -

There is 1 sign change hence 1 positive zero

f(-x) = -x³ + x² + 8x - 8

look for the number of sign changes in f(- x)

- / + / + / -

there are 2 sign changes hence 2 possible negative zeros

3 0

3 years ago

Answer to question first

andrey2020 [161]

Answer:

C. But be careful. It depends if you have been told what I was having trouble with.

Step-by-step explanation:

The question is a little unclear. If the actual interest is constant for all situations, the answer is C. The more times you compound, the more interest you will accumulate. Banks don't do it that way. It they compound every three months, then they cut the interest rate by a quarter.

So the interest would look like (1 + 0.022/4)*principle. Whoever made the question has to make clear what is going on. My guess is the intended answer is C.

5 0

3 years ago

a person driving along the road moves rates of 56 miles per hour driven.How far does the person drive in 1.5 hours?

tester [92]

56 miles : 1 hour
/2. /2
28 miles : 30 minutes
56+28. 1h+30m
84 miles : 1 hour 30 minutes

84 is the answer

8 0

3 years ago

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