5^{x+1}-5^{x+2}=-2500. Find x

Answers

Answer 1

Answer:

x is 3

Step-by-step explanation:

[tex] {5}^{(x + 1)} - {5}^{(x + 2)} = - 2500 \\ [/tex]

divide all sides by -1:

[tex] {5}^{(x + 2)} - 5 {}^{(x + 1)} = 2500[/tex]

from law of indices:

[tex]( {5}^{x} . {5}^{2} ) - ( {5}^{x} . {5}^{1} ) = 2500[/tex]

factorise out 5^x:

[tex] {5}^{x} ( {5}^{2} - {5}^{1} ) = 2500 \\ {5}^{x} (20) = 2500 \\ {5}^{x} = 125 \\ {5}^{x} = {5}^{3} \\ x = 3[/tex]


Related Questions

Which diagram shows an angle bisector

Answers

B

if it is not correct sory

Diagram B is a proper demonstration of an angle bisector.

Letter A is wrong because they are a set of intersecting ines.

Letter C is wrong because they are a set of parallel lines.

Letter D is wrong because they are also a set of perpendicular lines.

So, now, we know that Letter B is the correct answer. The reason for this is also because ∠ACD is bisected by line B.

I hope that this helped answer your question. Have a good day!

X-18.6
_____=-0.326
15.3

Answers

Answer:

13.6122

Step-by-step explanation:

(x-18.6)/15.3=-0.326

x-18.6=-0.326*15.3

x-18.6=-4.9878

x=-4.9878+18.6

x=13.6122

what are the exponent and coefficient of the expression 4b^-3

Answers

Answer:

exponent is -3 and coefficient is 4

Order the numbers from least to greatest

Answers

Answer:

B

Step-by-step explanation:

It just is

determine the area and perimeter​

Answers

Answer:

Area is the total surface covered by the shape and perimeter is the total length of the shape.

(Urgent please!!) Given the lines AB and CD, determine the slope of line CD. Type a numerical answer in the space provided. If necessary. Use the /key to represent a fraction bar. Do not put spaces in your answer

Answers

Answer:

-5/4

Step-by-step explanation:

C is at the point (2,3) and D is at the point (6,-2)

-2-3 = -5 which would be the top part and 6-2=4 and that's the bottom part.

3. Solve and plot your answer on the number line below:
9.28 + 2x = 18.14

Step by step

Answers

1. Isolate your variable (2x) by subtracting 9.28 from both sides
2. Your equation should now look like 2x=8.86
3. Divide both sides by 2
4. Your equation should now say x=4.43
5. Plot on the appropriate spot

Determine the range of the following graph:
y
12
11
10
9
8
7
2
1
-12-11-10-9-8-7-6-5-4-3-2-11
1 2 3 4 5 6 7 8 9 10 11 12
- 2
-3
-4
-8
-9
-10
-11
-12

Answers

Answer:

r = (-4,9]

Step-by-step explanation:

hope this will help

Answer:

-4<y≤2

Step-by-step explanation:

The range of a graph is the range of the y values.

of the 420 students enrolled in basic math only 41% are first-year students. How many
are first-year students? How many are not?

Answers

Answer:

Step-by-step explanation:

There are 420 students.

41% are first year students.

41% = 41/100

420 * 41/100 = 172.4

What do you do about the 0.4? I would just round to the nearest whole number which is 172.

There are 420 - 172 = 248 who are not first year students.

Help me please!!!٩(๑꒦ິȏ꒦ິ๑)۶
the 1st one ​

Answers

9514 1404 393

Explanation:

Add sin(θ)

  cos(θ) = sin(θ)

Divide by cos(θ)

  1 = sin(θ)/cos(θ) = tan(θ)

Square both sides

  1 = tan²(θ)

Add 1

  2 = tan²(θ) = sec²(θ)

Take the square root

  √2 = sec(θ) . . . . for 0 < θ < π

_____

Additional comment

The equation cos(θ) -sin(θ) = 0 has two solutions: θ = π/4 and θ = 5π/4. For the first-quadrant solution, sec(θ) = √2. For the third-quadrant solution, sec(θ) = -√2.

Santo chose c as the correct

Answers

Is this a question or an answer

Use the number to add the fraction: -5/8 + 3/4: *
Use the number ine to add the fraction
2
1
1
1
5
-
-
-
O
2
-9/10
-4/5
-1/8
1/8
2/5
1/2
7/10

Answers

Answer:

c

Step-by-step explanation:

thats the anser

6927÷19 plz help me

Answers

When dividing 6927 by 19 you get 364.58
it equals 364 r11 (i’m pretty sure)

a continuous random variable is uniformly distributed in the interval a<X<b the Lower quartile is 5 and upper quartile is 9 find
a. the values of a and b
b. p(6<X<7)
c. the cumulative distributive function

راز​

Answers

(a) X has a probabiliity density of

[tex]f_X(x) = \begin{cases}\dfrac1{b-a}&\text{if }a<x<b\\0&\text{otherwise}\end{cases}[/tex]

If the lower quartile is 5 and the upper quartile is 9, then

[tex]\displaystyle \int_a^5 f_X(x)\,\mathrm dx = 0.25 \text{ and } \int_9^b f_X(x)\,\mathrm dx = 0.25[/tex]

Computing the integrals gives the following system of equations:

[tex]\displaystyle \int_a^5\frac{\mathrm dx}{b-a} = \frac{5-a}{b-a} = 0.25 \\\\ \int_9^b \frac{\mathrm dx}{b-a} = \frac{b-9}{b-a} = 0.25[/tex]

5 - a = 0.25 (b - a)   ==>   0.75a + 0.25b = 5   ==>   3a + b = 20

b - 9 = 0.25 (b - a)   ==>   0.25a + 0.75b = 9   ==>   a + 3b = 36

Eliminate a :

(3a + b) - 3 (a + 3b) = 20 - 3×36

-8b = -88

==>   b = 11   ==>   a = 3

and so P(X = x) = 1/(11 - 3) = 1/8 for all 3 < x < 11.

(b)

[tex]\displaystyle P(6<X<7) = \int_6^7f_X(x)\,\mathrm dx = \int_6^7\frac{\mathrm dx}8 = \boxed{\frac18}[/tex]

(c) The distribution function is then

[tex]\displaystyle F_X(x) = \int_{-\infty}^x f_X(t)\,\mathrm dt = \begin{cases}0&\text{if }x\le3 \\ \dfrac x8 &\text{if }3<x<11 \\ 1&\text{if }x\ge11\end{cases}[/tex]

The temperature in a town is 33.6°F during the day and - 17.3°F at night. Find the difference in the temperatures.
The difference in temperature is
F.

Answers

Answer:

the difference between the temperatures is -50.9. f=-50.9

Step-by-step explanation:

33.6°F+17.3°F=50.9

33.6°F+F= -17.3°F

33.6°F+(-50.9°F= -17.3°F

so, F=-50.9°F

Step-by-step explanation:

d=T2-T1=(-17.3-33.6)=-50.9°F

Help finding the sketch of a graph pls i’ll rate brainliest

Answers

Answer:

A

Step-by-step explanation:

X^3+1

Y int = 1

X int = -1

We can clearly see that the x int(when y = 0) for c = -3 so C is incorrect.

b is wrong because it's a quadratic(ax^2+bx+c) and d wrong because it linear(y=mx+c).

Knowing all this we can safely say that A is the correct answer choice.

Answer:

we firstly need to find x intercept and y intercept

Translate into a variable expression. the quotient of 43 less than m and twice m

Answers

Answer:

(m - 43)/2m

Step-by-step explanation:

If a = b, then a^2 = b^2

What is the proof of this statement?

Answers

Step-by-step explanation:

=

since a=b, therefore we can write a in place of b or b in place of a,

= or =

Hence, it is proved.

I hope it helped U

I hope it helped Ustay safe stay happy

Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.​

Answers

Answer: B

Step-by-step explanation:

The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.

What is pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

From the given patterns

Figure 1 has 5 lines and it is blue in color.

Figure 2 has 4 lines and it is red in color.

Figure 3 has 3 lines and it is blue in color.

So, Figure 4 must has 2 lines and red in color.

Therefore, option B is the correct answer.

Learn more about the pattern here:

https://brainly.com/question/23136125.

#SPJ7

how to complete this question?

Answers

Answer:

f(x) = [tex]-2^{x+1}-1[/tex]

Step-by-step explanation:

I. If you see (0, -3) point on the green line

II. Perform x = 0, if y = -3 means the statement is true

    = [tex]-2^{0+1} - 1[/tex]

    = [tex]-2^{1}[/tex] - 1

    = -2 - 1

  y = -3

Got more question or somethin to discuss? Leave comment below

     

Sam hits a golf ball from a elevated tee

Answers

First take a derivative,

[tex]\frac{d}{dx}-5t^2+10t+30=-10t+10=-10(t-1)[/tex]

Now compute the critical point where the slope is 0,

[tex]-10(t-1)=0\implies t-1=0\implies t=1[/tex]

And done.

The maximum height is at [tex]t=1[/tex] of [tex]h(1)=-5+10+30=35[/tex].

Hope this helps :)

X:3/2+1/2x=2x
I need to solve for x

Answers

Answer: x = 1

Step-by-step explanation:

Given

3/2 + (1/2)x = 2x

Multiply 2 on both sides to cancel out the denominator

2 · [3/2 + (1/2)x] = 2 · 2x

3 + x = 4x

Subtract x on both sides

3 + x - x = 4x - x

3 = 3x

Divide 3 on both sides

3 / 3 = 3x / 3

[tex]\boxed {x=1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

If (x,-3) is a solution to the equation 4x = 5y - 1, what is the value of x?

Answers

9514 1404 393

Answer:

  x = -4

Step-by-step explanation:

Put the given point in the equation and solve for x.

  4x = 5(-3) -1

  4x = -16 . . . . . . simplify

  x = -4

Milan sold an article for Rs 450 with a loss of 10%. Find his CP. At what price it should be sold so as to gain 5 %.

Pls-- help request!!​

Answers

Hope it helps you.The answer of this question is 25.

helpppp!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Below

Step-by-step explanation:

DO=15

OB=3x+7

DB=9x-2

O is between D and B

So,

OB+DO=DB

or, 9x-2+3x+7=15

or, 12x=15-5

or, x=10/12

Thus, x=5/6

the answer is x=5/6
you are welcome
sorry if it’s wrong

Please help!!!! I have no clue how to do this

Answers

Answer:

It'll be the same figure- an acute isoceles triange

Step-by-step explanation:

Reflection is just copying the same shape across the x-axis (the main horizontal line on graphs) or the y-axis (the main vertical line on graphs). It's like looking at yourself in the mirror, like a reflection!

You buy butter for $4 per pound You need 4oz of butter for your formula How much does the butter for 1 portion cost?

Answers

2 I think :) hope this helped

which equation shows the valur of -2/5- (-9/15)

Answers

Answer:

3/15

Step-by-step explanation:

-2/5=-6/15

(-6-(-9))/15=(-6+9)/15=3/15

2/8 of a rope is 28 meters.What is the length of the rope?​

Answers

let length be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]

[tex]\\ \sf\longmapsto x=4(28)[/tex]

[tex]\\ \sf\longmapsto x=112[/tex]

Really need to someone to break this down so I can understand it
(a) Find the slope of the curve y= x^2 - 2x - 3 at the point ​P(2,​ -3​) by finding the limit of the secant slopes through point P.
(b) Find an equation of the tangent line to the curve at P(2, -3)

Answers

Answer:

Part A)

The slope is two.

Part B)

[tex]\displaystyle y = 2x - 7[/tex]

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

[tex]\displaystyle y = x^2 - 2x - 3[/tex]

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]

Since we want to find the slope of the curve at P(2, -3), x = 2.

Substitute:

[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]

Simplify. Note that f(2) = -3. Hence:

[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]

Substitute. m = 2. Therefore, our equation is:

[tex]\displaystyle y + 3 = 2(x-2)[/tex]

We can rewrite this into slope-intercept if desired:

[tex]\displaystyle y = 2x - 7[/tex]

We can verify this by graphing. This is shown below:

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