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3 years ago

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What is the range of the exponential function shown below f(x)=2•7^x

1 answer:

Gemiola [76]3 years ago

4 0

This is rather a sneaky question. You don't know exactly what numbers you can use and what numbers not.

For example, are you allowed to use x = - 3. The answer is yes

f(-3) = 2*7^(-3) = 2/7^3 = 2/147.

How about 0? If there is going to be a problem, zero is usually the number that causes the problem.

f(0) = 2*7^(0) = 2 * 1 = 2 and in this case 0 is just fine.

How about positive numbers? No they are all good.

So the range is -∞ < y < ∞

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Find mDCAˆ. the question says that the angle is 3x+19 the smaller arc is 91 and the bigger is 17x-3 it is one of those problems

valina [46]

Answer: Option C.

Step-by-step explanation:

Let as consider the below figure is attached below.

We know that angle between tangent and secant is half of difference of major and minor arcs.

$\angle ABC=\dfrac{arc(AD)-arc(AC)}{2}$

$3x+19=\dfrac{17x-3-91}{2}$

Multiply both sides by 2.

$6x+38=17x-94$

$38+94=17x-6x$

$132=11x$

Divide both sides by 11.

$12=x$

The value of x is 12.

$arc(AD)=17(12)-3$

$arc(AD)=204-3$

$arc(AD)=201^{\circ}$

Now,

$arc(DCA)=360^\circ-arc(AD)$

$arc(DCA)=360^\circ-201^{\circ}$

$m\widehat {DCA}=159^{\circ}$

Therefore, the correct option is C .

5 0

3 years ago

198 cans of food consisted of both veggies and fruits. if 1/3 of the cans were veggies how many cans were

Bas_tet [7]

Answer:

$\frac{1}{3} \times 198 = 66 \: canned \: veggies \\ \\ 198 - 66 = 132 \: canned \: fruit$

8 0

3 years ago

Two parallel lines are cut by a transversal,

Volgvan

Answer:

also 75°

Step-by-step explanation:

the angles across each other at a crossing point of 2 lines must be equal.

so, 2 = 3.

and the angles at the crossing point with a parallel line are simply a "mirror" or rather a copy of the angles at the crossing point with the first line.

so, 2 = 3 = 6 = 7

and 1 = 4 = 5 = 8

7 0

2 years ago

Two gears are adjusted so that the smaller gear drives the larger one. if the smaller gear of 3.7cm rotates through an angle of

zepelin [54]

Answer:

<em>The larger gear will rotate through 156°</em>

Step-by-step explanation:

<u>Arc Length</u>

The arc length S of an angle θ on a circle of radius r is:

$S = \theta r$

Where θ is expressed in radians.

The smaller gear of r1=3.7 cm drives a larger gear of r2=7.1 cm. The smaller gear rotates through an angle of θ1=300°.

Convert the angle to radians:

$\displaystyle \theta_1=300*\frac{\pi}{180}=\frac{5\pi}{3}$

The arc length of the smaller gear is:

$\displaystyle S_1=\frac{5\pi}{3}\cdot 3.7$

$\displaystyle S_1=\frac{18.5\pi}{3}$

The larger gear rotates the same arc length, so:

$\displaystyle S_2=\frac{18.5\pi}{3}$

$\displaystyle \theta_2\cdot r_2=\frac{18.5\pi}{3}$

Solving for θ2:

$\displaystyle \theta_2=\frac{18.5\pi}{3r_2}$

$\displaystyle \theta_2=\frac{18.5\pi}{3*7.1}$

$\theta_2=2.73\ radians$

$\displaystyle \theta_2=2.73*\frac{180}{\pi}=156$

The larger gear will rotate through 156°

7 0

3 years ago

I need help pls help

zmey [24]

Answer:

33/20

Step-by-step explanation:

I dont know if that was a minus or a plus but it looked like a minus sorry if its wrong

6 0

3 years ago

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