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Aloiza [94]
3 years ago
5

The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5

2 28 Complete the chart and determine the solution of the equation f(x) = g(x).
x = −2

x = −1

x = 1

x = 20

Mathematics
1 answer:
coldgirl [10]3 years ago
5 0

Given equations are

f(x)=2x+24

g(x)=5(0.5)^x

Now we have to complete the table so that we can find for what value of x, both f(x) and g(x) are equal.

values in table are not clear so i will draw a fresh table using values x=-2,-1,0,1,2,3,4

I will show you calculation for x=-2

plug x=-2 into f(x) and g(x)

f(-2)=2(-2)+24=-4+24=20

g(-2)=5(0.5)^{-2}=5(\frac{1}{2})^{-2}=5(\frac{1}{2^{-2}})=5(2^2)=5(4)=20

Similarly you can find other values to complete the table.

From table we see that f(x) and g(x) both are equal to 20 when x=-2

Hence x=-2 is the final answer.

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Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answer
spayn [35]

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.


Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

4 0
2 years ago
Im a lil stuck on this :v
12345 [234]

Answer:

C-----> x<-7

Step-by-step explanation:

first u do this to turn x in positive and consequently change the > to an <:

(-1).(-4x)>28.(-1)

so:

4x<-28

x<-7

# when multiplying each side by (-1), you have to change the symbol (>) to an (<), or (<) to an (>)

6 0
3 years ago
A blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if sh
Semenov [28]

Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4

There are 4 trees, and there are 18x+4 acorns or 76 acorns.

Hope you have a nice day, and also you should mark brainliest :)

8 0
1 year ago
Read 2 more answers
Which symbol creates a true sentence when x equals 3?
kondaur [170]

Answer:

C

Step-by-step explanation:

8×3-4×2=16

7(10-3)=14

so 16 is greater

7 0
3 years ago
Ayuuuuuuddddaaaaaa!!!
Fofino [41]

Answer:

Los triangulos son iguales porque tienen dos lados y el angulo comprendido  respectivamente iguales, por tanto

3x = x+8\\2x=8\\x=4\\

8 0
3 years ago
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