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OLga [1]
2 years ago
14

Solve 64^x = 16^(x−1). (1 point) Select one: a. x = −2 b. x = −1 c. x = negative 1 over 4 d. x = negative 1 over 3

Mathematics
2 answers:
Ainat [17]2 years ago
8 0

Answer:

\huge \boxed{x=-2}

Step-by-step explanation:

64^x = 16^(x-1)

Rewrite the bases with base of 4.

(4^3)^x = (4^2)^(x-1)

Multiply exponents.

4^(3x) = 4^(2(x-1))

Cancel same bases.

3x = 2(x-1)

Expand brackets.

3x = 2x - 2

Subtract 2x from both sides.

x = -2

LekaFEV [45]2 years ago
6 0

Answer:

a. x = -2

Step-by-step explanation:

64ˣ = 16⁽ˣ⁻¹)

64 = 4³

16 = 4²

4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)

4³ˣ = 4²ˣ⁻²

3x = 2x - 2

x = -2

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A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season,
8_murik_8 [283]

Answer:

f(x) = -6x +120

Step-by-step explanation:

Let's call y the number of patients treated each week

Let's call x the week number.

If the reduction in the number of patients each week is linear then the equation that models this situation will have the following form:

y = mx + b

Where m is the slope of the equation and b is the intercept with the x-axis.

If we know two points on the line then we can find the values of m and b.

We know that During week 5 of flu season, the clinic saw 90 patients, then we have the point:

(5, 90)

We know that In week 10 of flu season, the clinic saw 60 patients, then we have the point:

(10, 60).

Then we can find m and b using the followings formulas:

m=\frac{y_2-y_1}{x_2-x_1}   and b=y_1-mx_1

In this case: (x_1, y_1) = (5, 90) and (x_2, y_2) = (10, 60)

Then:

m=\frac{60-90}{10-5}

m=-6

And

b=90-(-6)(5)

b=120

Finally the function that shows the number of patients seen each week at the clinic is:

f(x) = -6x +120

7 0
3 years ago
Read 2 more answers
What is the exterior angle of #9 ?
Alexxandr [17]

Answer:

55

Step-by-step explanation:

3x-12=2x

    +12

3x=2x +12

    -2x

x=12

4(12)+ 9

48+9

=55

6 0
3 years ago
Translation: 6 units down s(-4,1), 7(-3, 5), (0,2 )​
tia_tia [17]
(-4,-5) (-3,-1) (0,-4)
4 0
2 years ago
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
Komok [63]

<u>Answer</u>

2/3


<u>Explanation</u>

For f(x) = g(x) we should equate the two functions to get the value of x.

f(x) = g(x)

−3x + 4 =  2

-3x + 4 - 4 = 2 - 4

-3x = -2

Dividing by -3 on both sides;

(-3x)/-3 = (-2)/-3

  x = 2/3

4 0
2 years ago
Read 2 more answers
Haley bought 8 pencils and 3 folders for $10.39. Nicole bought 5 pencils and 4 folders for $10.51. How much does a folder cost?
cupoosta [38]

Answer:

$1.89

Step-by-step explanation:

1) 8p+3f=$10.39

2) 5p+4f=$10.51

where p represents pencil & f represents folder.

multiply the first equation by 5 and the second equation by 8.

40p+15f=$51.95

40p+32f=$84.08

Subtract

17f=$32.13

f=$32.13/17 =$1.89

6 0
3 years ago
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