1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andreas93 [3]
2 years ago
8

Solve for 'x' in the following equation, explaining each step. 3^ (-3x+7) = 3^ (7x-13)

Mathematics
1 answer:
Yanka [14]2 years ago
5 0

Answer:

x = 2

Step-by-step explanation:

In order to have the two sides of the equation be equal, the exponents must equal.

-3x + 7 = 7x - 13

Add 3x to both sides.

7 = 10x - 13

Add 13 to both sides.

20 = 10x

Divide by 10.

2 = x

Check:

3^(-3•2+7)=3^(7•2-13)

3^1 = 3^1

3 = 3

You might be interested in
Simplify 5 over -32 squared simplified
Brilliant_brown [7]

Answer:

Step-by-step explanation:

5

−322

=

5

−1024

=

−5

1024

8 0
3 years ago
Read 2 more answers
X2 - 49 = 0 solve for x
Bogdan [553]

x^2 - 49 = 0

Add 49 to both sides:

x^2 = 49

Take the square root of both sides:

X = 7

8 0
3 years ago
The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by p
yawa3891 [41]
500=4πr^2. first divide 500 from four which will equal 125, then divide 125 with π and it will equal 39.788 . finally √39.788. the answer will be r=6.3 or 6
8 0
3 years ago
find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive
wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

  • n = number of terms,
  • a = first term and
  • d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

#SPJ1

4 0
2 years ago
Systems with three variables. please help
kirza4 [7]
X= 6
Y= 0
Z= -2

CHECK
3x + y -2z =22
3(6) + 0 -2(-2) =22
18 + 0 +4= 22
22=22

x+5y+z =4
6 +5(0)+ -2 =4
6 + 0 +-2 = 4
4=4

x+3z=0
6 + 3(-2) =0
6 -6 = 0
0=0
3 0
3 years ago
Other questions:
  • In a math class, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. What is the probability that in a randomly
    5·1 answer
  • Elin has made twenty-nine note cards for her friends. She plans to send out a total of forty cards. What percentage of the cards
    14·1 answer
  • Which way shows how to make a ten to solve 13-7
    5·1 answer
  • If $1600 earned simple interest of $56.24 in 2 months, what was the simple interest rate? The simple interest rate is % (Do not
    6·1 answer
  • A nut wholesaler sells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If
    12·2 answers
  • A group of 12 runners each drink 64 ounces of water every day.How many ounces of water will they drink in 45 days?
    8·2 answers
  • Which of the following is the equation of a line that passes through the point (3,2) and is parallel to the y-axis? A. x = 2 B.
    14·2 answers
  • Solve the system by substitution <br><br> -x-y-z= -8<br><br> -4x+4y+5z= 7<br><br> 2x+2z= 4
    8·2 answers
  • Solve the system by substitution.<br> x = 9y<br> x-5y=20
    8·1 answer
  • I NEED ANSWERS FAST PLEASE ILL GIVE BRAINLIEST
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!