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3 years ago

8

A restaurant offered cooking classes on 24 of the 30 days in November. What decimal is equivalent to the fraction of days in Nov

ember that classes were offered at the restaurant?

1 answer:

zvonat [6]3 years ago

3 0

Assuming they mean the fraction is 24/30 the answer is 0.8 (24÷30 is the equation to use)

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Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60

TEA [102]

Answer: the rate at which the distance between the boats is increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

6 0

3 years ago

Which expression is equivalent to 8(− 5+1.25x)−105(0.6x+1)?

Mice21 [21]

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<em>Good</em><em> </em><em>luck</em><em> </em><em>on</em><em> </em><em>your</em><em> assignment</em>

6 0

3 years ago

Read 2 more answers

What is the discontinuity and zero of the function f(x) = the quantity of 3 x squared plus x minus 4, all over x minus 1? A. Dis

Firlakuza [10]

Answer:

The correct option is D. Discontinuity at (1, 7), zero at (negative four thirds, 0)

Step-by-step explanation:

$\text{The function is given to be : }f(x)=\frac{3x^2+x-4}{x-1}\\\\\implies f(x)=\frac{(3x+4)(x-1)}{(x-1)}$

To find the point of discontinuity :

Put the denominator equal to 0

⇒ x - 1 = 0

⇒ x = 1

Also, if the factor (x - 1) gets cancel, then it becomes a hole rather than a asymptote , ⇒ y = 3x + 4 at x = 1

⇒ y = 7

So, Point of discontinuity : (1, 7)

And the zero is : after cancelling the factor (x - 1) put the remaining factor = 0

⇒ 3x + 4 = 0

⇒ 3x = -4

⇒ x = negative four thirds ( zero of the function)

Therefore, The correct option is D. Discontinuity at (1, 7), zero at (negative four thirds, 0)

4 0

3 years ago

Read 2 more answers

What is the remainder when (3x4 + 2x3 − x2 + 2x − 19) ÷ (x + 2)?<br><br> 0<br> 5<br> 10<br> 15

Elanso [62]

Answer: Second option is correct.

Explanation:

Since we have given that

$f(x)=3x^4+2x^3-x^2+2x-19$

And $g(x)=x+2$

To find the remainder, we use the Remainder Theorem, which states that when f(x) is divided by (x-c) then the f(c) is the required remainder.

So,

Here, we have,

$x+2=0\\\\x=-2$

So, we will find f(-2) which will give us the required remainder,

$f(-2)=3(-2)^4+2(-2)^3-(-2)^2+2(-2)-19\\\\f(-2)=(3\times 16)-(2\times 8)- 4-4-19\\\\f(-2)=48-16-36-4-19\\\\f(-2)=5$

Hence, Second option is correct.

7 0

3 years ago

Draw an obtuse angle big. place a point p inside the angle. now construct perpendiculars from the point to both sides of the ang

never [62]

I have drawn three obtuse angles showing three different positions.

then taken a point p inside it.

Now to draw perpendicular from a point to a given line

we draw a line parallel fom that point to that given line.

After that from that point we draw perpendicular to that line.

Now the question arises which side is closer to point p ,

The answer is if length of perpendicular from p to the line is longer that side is farther from the point p , and if the length of perpendicular is shorter then that that line is nearer to point P.

8 0

3 years ago