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
WINSTONCH [101]
3 years ago
9

Solve the linear equation:

title="4^{2x+7} = 8^{2x-3}" alt="4^{2x+7} = 8^{2x-3}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
g100num [7]3 years ago
8 0

Answer:

  x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

  2(2x+7) = 3(2x -3)

  0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

  0 = 2x -23 . . . . . . . . . . . . . simplify

  0 = x - 23/2 . . . . . . . . . . . . divide by 2

  11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

_____

<em>Check</em>

This value of x makes the equation become ...

  4^(2·23/2 +7) = 8^(2·23/2 -3)

  4^30 = 8^20 . . . . . true

You might be interested in
Can you help me out with this one?
shepuryov [24]

Answer: 98

Step-by-step explanation:

98 / (-7) = -14

7 0
3 years ago
Read 2 more answers
Brainliest. follow anything . box of chocolates contains seven milk chocolates and six dark chocolates. Five of the milk chocola
Olenka [21]

Answer:

8/13

Step-by-step explanation:

has the slightly lower numbers meaning 11/13 would be milk chocolate with peanuts, and 8/13 would be the dark chocolate

6 0
3 years ago
Read 2 more answers
0.004 of all math majors at a certain university double major in music. Express this decimal as a percent.
RUDIKE [14]
I think  the answer is 4%
3 0
3 years ago
HELP, I AM UTTERLY CONFUSED *20 points
Studentka2010 [4]
Ok so this question is a bit complicated, but it's easier to understand if you break it down into smaller parts!

1) First, you know that ABGF is half the perimeter of ACDE. This means that the length of one side of ABGF must be 1/2 the length of one side of ACDE.
>> You can think of this by putting in random numbers. Say the perimeter of the larger square is 24 and the perimeter of the smaller square is 12. That means one side of the larger square of 24/4 (b/c four sides) = 6 and one side of the smaller square is 12/4 = 3!

2. Ok know you know the lengths of the sides relative to each other, but you're only given one value: 4in. Since the smaller square has sides that are 1/2 the larger squares, you know that it makes up 1/4 of the larger square! So imagine 4 of those smaller squares filling up that larger square to make a 2 by 2. It just so happens that 4in is the diagonal going through one of our imaginary squares, which is equal in size to ABGF!

3. Now use the 45-45-90 rule to figure out the length of one side of that imaginary square because the 4in diagonal splits that imaginary square into two of those 45-45-90 triangles. You know the hypotenuse of that triangle is 4in. That means one of the legs is 4/✓2 (since the rule says that the hypotenuse and the leg are in a ✓2:1 ratio). And like we said before the length of that leg is the length of the side of our imaginary square. And our imaginary square must be the same size as ABGF! So now we know the side of the smaller square to be 4/✓2!

4. Multiply the side of the smaller square by 2 to get the side of our larger square. (4/✓2)*2=8/✓2

5. Now to find the area of the shaded region, just find the area of the smaller square ABGF and subtract from the larger square ACDE. Use equation for the area of a square!
a =  {s}^{2}
where s=the length of one side.

The length of one side of the smaller square is 4/✓2. So it's area is:
{( \frac{4}{ \sqrt{2} }) }^{2}  =  \frac{16}{2}  = 8

The length of one side of the larger square is 8/✓2. So it's area is:
{ ( \frac{8}{ \sqrt{2} }) }^{2}  =   \frac{64}{2}   = 32

Now subtract. 32-8=24! :)

Hope this helps! Let me know if you have any questions.
3 0
3 years ago
How would you simplify 5-6w-4+7w?
Natasha2012 [34]
You add the like terms. In this case, the like terms are -6w,+7w & 5,-4.
-6w + 7w = 1w.
5 - 4 = -1.
The coefficients (terms with variables - letters) comes firm, then the terms (numbers) 
.
so the final answer is: 1w -1   :)
6 0
2 years ago
Other questions:
  • Can you help me solve this
    9·2 answers
  • The first five terms of a pattern are given below. 38, 41, 44, 47, 50.... Which expression can be used to determine the nth term
    11·1 answer
  • What is the product of 63 and -59??
    5·1 answer
  • If tim spends 1/3 each weekday sleeping and about 7/24 each weekday in school what fraction of a weekday does Tim spend either s
    13·1 answer
  • Find two solutions for f(x) = x2 + x - 6​
    8·1 answer
  • What does -8(6x - 2) equal? How do I get my answer?
    15·2 answers
  • Can you please help me solve for the area
    13·1 answer
  • The point (4, 10) is in each scatterplot. In which one is it an outlier? On a graph, points (4, 10) and (6, 1) are outside of th
    7·2 answers
  • Write the equation of the line that passes through the points (-8,3) and (0,2). Put your answer in fully reduced point-slope for
    14·1 answer
  • the ratio of boys to girls in a chorus is 5:6. which shows an equivalent ratio. Use a proportion to solve. A 10 boys to 12 girls
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!