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3 years ago

15

The school cafeteria serves pizza every sixth day and applesauce every eighth day.suppose that pizza and applesauce are both on

today's menu.In how many days will they be together on a menu again?

1 answer:

valentina_108 [34]3 years ago

6 0

Least common multiple

First factor each

6=2*3

8=2*2*2*2=3*8=24

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If B=3x-1 and C=2x^2+x+9, find an expression that equals 2B+2C in standard form.

Anestetic [448]

Answer:

$4x^2 +8x + 16$

Step-by-step explanation:

2 (3x - 1) + 2 (2x^2 + x + 9)

6x - 2 + 4x^2 +2x + 18

4x^2 + 8x +16

3 0

3 years ago

Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading co

oksano4ka [1.4K]

f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.

<h3>Find the required equation:</h3>

The zeroes or roots of a polynomial function are x values for which f(x) = 0

If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is

⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)

where a is the leading coefficient

Here in the question it is given that,

Polynomial should be with degree 3
zeros of f(x) are − 3 , 4 , − 3

By using the formula of polynomial function we get,

⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)

⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))

⇒ f(x) = 1(x + 3)(x - 4)(x + 3)

⇒ f(x) = (x + 3)(x² - x - 12)

⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36

⇒ f(x) = x³ + 2x² - 15x - 36

Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.

Learn more about polynomial function here:

brainly.com/question/12976257

#SPJ1

4 0

1 year ago

Tossing 2 fair coins and both landing heads up what would be the fraction for that

Anon25 [30]

The chance of One heads occurring is 1/2.
The chance of the second occurring separately is 1/2 as well. Joint together, it is 1/2x1/2: which is 1/4.

So your answer is 1/4 chance

I hope this Helps!

5 0

3 years ago

Read 2 more answers

NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she

Goshia [24]

Answer:

The distance from hot air balloon to the ground $AC=50.1457 ft$ .

Step-by-step explanation:

Labelled diagram of given scenario is shown below.

Given that,

An angle of elevation of Hot air balloon by Angie is $40$ °.

When she stepped back $200 ft$ then angle of elevation was $10$ °.

Height of Angie is $5.5 ft$ .

To find: How far off the ground is a hot air balloon.

So, from figure

Height of Angie $(BC) = 5.5ft$

In triangle Δ $ABD$ ,

⇒ $tan {40\si {\degree}} = \frac{AB}{BD}$

⇒ $AB = tan (40) \times BD$ ....................(1)

Now, In triangle Δ $ABE$

⇒ $tan (10)= \frac{AB}{200+BD}$

⇒ $AB = tan(10)\times (200+BD)$

Here, substituting the value $AB$ from Equation (1) we get,

$tan(10)\times (200+BD)= tan(40)\times BD$

$tan(10)\times 200+tan(10)\times BD= tan(40)\times BD$

⇒ $BD\times (tan(40)-tan(10))=tan(10)\times 20$

⇒ $BD\times 0.6628 = 35.2654$

⇒ $BD = \frac{35.2654}{0.6628} =53.2067 ft$

Now, finding the value of $AB$ from equation (1)

$AB= tan(40)\times 53.2067=0.8391\times 53.2067$

$AB=44.6457 ft$

Therefore Length of $AC= AB+BC$ = $(44.6457 + 5.5) ft$

$AC=50.1457 ft$ .

Hence,

The distance from hot air balloon to the ground $AC=50.1457 ft$ .

6 0

3 years ago

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm^3/s) when the diameter is 60

nexus9112 [7]

Answer:

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere is given by the following equation:

$V = \frac{4\pi r^3}{3}$

In which r is the radius.

Implicit derivatives:

This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So

$\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$

The radius of a sphere is increasing at a rate of 4 mm/s.

This means that $\frac{dr}{dt} = 4$

How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?

This is $\frac{dV}{dt}$ when $r = \frac{d}{2} = \frac{60}{2} = 30$ . So

$\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$

$\frac{dV}{dt} = 4\pi*(30)^2*4$

$\frac{dV}{dt} = 1508$

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

7 0

3 years ago