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lbvjy [14]
3 years ago
7

Scarlet has $85 to spend at the pet store. She is definitely buying a catfish for $12, a rainbow fish for $13, and a betta fish

for $14. Scarlet wants to use whatever money she has left over to buy some hermit crabs, which cost $8 each. There is no tax on the purchases.
Write the inequality that Scarlet can use to describe how many hermit crabs she can buy. Use x to represent the number of hermit crabs.
Mathematics
2 answers:
miv72 [106K]3 years ago
6 0

Answer:

She has enough money to buy 5 crabs.

Step-by-step explanation:

Subtract the total of the 3 fish she is buying from the amount of money she has:

85 - (12 + 13 + 14) = 85 - 39 = 46

She has $46 to spend on crabs.

Divide the amount she has to spend by the price on one crab:

46 / 8 = 5.75

Since it isn't a whole number you need to round down, since she cant buy 0.75 of a crab.

alexgriva [62]3 years ago
3 0

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you.

Step-by-step explanation:

56

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2 years ago
What would y=x^2 +x+ 2 be in vertex form
balu736 [363]

Answer:

y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

Step-by-step explanation:

y =  {x}^{2}  + x + 2

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

y = a(x - h)^{2}  + k

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{4a}

We substitute the value of these terms from the standard form.

y = a {x}^{2}  + bx + c

h =  -  \frac{1}{2(1)}  \\ h =  -  \frac{ 1}{2}

Our h is - 1/2

k =  \frac{4(1)(2) - ( {1})^{2} }{4(1)}  \\ k =  \frac{8 - 1}{4}  \\ k =  \frac{7}{4}

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

f(x) = a {x}^{n}

Therefore our derivative of f(x) —

f'(x) = n \times a {x}^{n - 1}

From the standard form of the given equation.

y =  {x}^{2}  +  x + 2

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times  {x}^{1 - 1} ) + 0

Any constants that are differentiated will automatically become 0.

f'(x) = 2 {x}+ 1

Then we substitute f'(x) = 0

0 =2x + 1 \\ 2x + 1 = 0 \\ 2x =  - 1 \\x =  -  \frac{1}{2}

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

y =  {x}^{2}  + x + 2

y = ( -  \frac{1}{2} )^{2}  + ( -  \frac{1}{2} ) + 2 \\ y =  \frac{1}{4}  -  \frac{1}{2}  + 2 \\ y =  \frac{1}{4}  -  \frac{2}{4}  +  \frac{8}{4}  \\ y =  \frac{7}{4}

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

y = a {(x - h)}^{2}  + k \\ y = (x - ( -  \frac{1}{2} ))^{2}  +  \frac{7}{4}  \\ y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

7 0
3 years ago
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