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mrs_skeptik [129]

3 years ago

10

Olivia is making hot sauce. Her recipe calls for five red jalapeño peppers. If she only wants to make 60 percent of the recipe,

how many red jalapeño peppers does she need?
3 red jalapeño peppers
11 red jalapeño peppers
8 red jalapeño peppers
2 red jalapeño peppers

1 answer:

AleksandrR [38]3 years ago

3 0

The answer is three peppers.

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Consider the polynomial p(x) = x^3 + 4x^2 + 6x − 36.

Nady [450]

Answer:

a. attached graph; zero real: 2

b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

Step-by-step explanation:

p(x) = x³ + 4x² + 6x - 36

a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.

p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0

b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.

2 | 1 4 6 -36

1 6 18 0

x² + 6x + 18 = 0

Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²

√Δ = 6i

x = -6±6i/2 = 2(-3±3i)/2

x' = -3-3i

x" = -3+3i

p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)

c. the solutions are 2, -3-3i and -3+3i

4 0

3 years ago

If a car travels at an average speed of x miles per hour, how far would the car travel in 90 minutes?

professor190 [17]

Answer:

1 1/2x

Step-by-step explanation:

90 minutes is 1 and 1/2 hours so I put that with the x on the end so when you get the number times it by that

4 0

3 years ago

An investment of $900 earns 6% annual interest and is compounded semi-annually. Write an equation

nalin [4]

Answer:

$A=900(1+\frac{0.06}{2})^{2(t)}$

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

First, change 6% into a decimal:

6% -> $\frac{6}{100}$ -> 0.06

Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:

$A=900(1+\frac{0.06}{2})^{2(t)}$

4 0

2 years ago

A city park commission received a donation of playground equipment from a parents' organization. The area of the playground need

dalvyx [7]

Answer:

Length = 20.49 yards and Width = 12.49 yards.

Step-by-step explanation:

The area of the rectangular playground is given by 256 yards square. It is also known that one of the sides of the playground is 8 yards longer than the other side. Therefore, let the smaller side by x yards. Then the longer side will be (x+8) yards. The area of the rectangle is given by:

Area of the rectangle = length * width.

256 = x*(x+8)

x^2 + 8x = 256. Applying the completing the square method gives:

(x)^2 + 2(x)(4) + (4)^2 = 256 + 16

(x+4)^2 = 272. Taking square root on both sides gives:

x+4 = 16.49 or x+4 = -16.49 (to the nearest 2 decimal places).

x = 12.49 or x = -20.49.

Since length cannot be negative, therefore x = 12.49 yards.

Since smaller side = x yards, thus smaller side = 12.49 yards.

Since larger side = (x+8) yards, thus larger side = 12.49+8 = 20.49 yards.

Thus, the length and the width to minimize the perimeter of fencing is 20.49 yards and 12.49 yards respectively!!!

7 0

3 years ago

Find the effective rate of interest for 1% compounded monthly.

natima [27]

Answer:

Find the effective rate of interest for 1% compounded monthly

Step-by-step explanation:

8 0

3 years ago