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2 years ago

4^(4x-1)=32 How do I solve this problem? Do I do 4 to the fourth power first?

Mathematics

2 answers:

yKpoI14uk [10]2 years ago

7 0

Answer:

$\large\boxed{x=\dfrac{7}{8}}$

Step-by-step explanation:

$4^{(4x-1)}=32\\\\(2^2)^{4x-1}=2^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-1)}=2^5\iff2(4x-1)=5\ \ \text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(4x)+(2)(-1)=5\\\\8x-2=5\qquad\text{add 2 to both sides}\\\\8x=7\qquad\text{divide both sides by 8}\\\\x=\dfrac{7}{8}$

eduard2 years ago

3 0

This is the answer to the problem

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You row a canoe x miles per hour down a river for 20 minutes. On the return trip, you travel 1 mile per hour slower. The return

ozzi

Answer:

Total Distance = 2 miles

Step-by-step explanation:

We know D = RT where

D is distance

R is rate (speed)

T is time

First Leg:

Rate = x mph

Time = 20/60 = 1/3 hour

Hence, D = RT, Distance = x * 1/3 = x/3 miles

Second Leg:

Rate = x - 1

Time = 30/60 = 1/2 hour

Distance = (x - 1) * 1/2 = (x-1)/2

Total distance is the sum of both the legs, hence,

Total distance = $\frac{x}{3}+\frac{x-1}{2}=\frac{2x+3(x-1)}{6}=\frac{2x+3x-3}{6}=\frac{5x-3}{6}$ miles

Since both the distance are equal we can equate and solve:

$\frac{x}{3}=\frac{x-1}{2}\\2x=3x-3\\x=3$

Plugging this x = 3 into the total distance expression, we get:

$\frac{5x-3}{6}\\\frac{5(3)-3}{6}\\=2$

Total distance, 2 miles

5 0

3 years ago

Find g. (-9) g(+)= r^2 + 3r

oee [108]

Answer:

g(-9) = 64

Step-by-step explanation:

Given function:

g(r) = r² + 3r

Find g(-9):

g(-9) = (-9)² + 3(-9) = 81 - 27 = 64

7 0

2 years ago

IMPORTANT PLEASE!! 10 POINTS :)

s344n2d4d5 [400]

Answer:

The domain is all the possible inputs for this function. The range is all the possible outputs for this function.

The line starts at the x-value of 0 and ends at the x-value of 12. Therefore, your domain is D: [0, 12].

The line starts at the y-value of 9000 and ends at the y-value of 0. Therefore, your range is R: [0, 9000].

5 0

2 years ago

A hallow metal pipe has an outer diameter of 3 inches and a thickness of 1/4 inch. The length of the pipe is 12 inches. Compute

saveliy_v [14]

Answer:

Step-by-step explanation:

I don"t really know the answer but i might have and explanation to help. Hollow everyday circular objects appear differently than drawn two-dimensional circles. Objects like pipes and hoses have two different diameters. The outside diameter measures the distance of a straight line from one point on the outside of the object, through its center, and to an opposite point on the outside. The internal diameter measures the inside of the object. Calculating the internal diameter depends on the outside diameter and the thickness of the outer circle.

3 0

2 years ago

a bee flies at 9 feet per second directly to a flower bed from its hive. the bee stays at the flower bed for 15 minutes then fli

qaws [65]

Answer:

Assuming the question is asking how much time it takes each way, the answer would be 2 minutes from the hive to the flowerbed and 3 minutes back.

Assuming the question is the amount of distance between the hive and the flower bed, the answer is 1080 feet.

Step-by-step explanation:

So the total amount of time it was away from the hive was 20 minutes. Out of those 20 minutes, 15 minutes were spent in the flowerbed. So that means travel time was 5 minutes. Now, going is 9 and coming back is 6, so 9+6=15, 5/15=1/3, 1/3*9=3 and 1/3*6=2

Knowing that information, lets solve what the question could be because I have no idea. The amount of distance from the hive to the flower bed is 1080 feet. I got this by doing 9 (the amount of feet per second) times 120 (the amount of seconds in 3 minutes.) You could do this with 6 but I found it easier to multiply 9*120 compared to 6*180.

If it's the commute time, we already solved that.

If I didn't answer the real question, please just comment on this.

6 0

3 years ago