(2/3)^x-1=27/8, Find x. Please, a step-by-step explanation.​

(2/3)^x-1=27/8, Find X. Please, A Step-by-step Explanation.

Answers

Answer 1

Answer:

x=-2

Step-by-step explanation:

(2/3)^x-1=27/8

Rewriting the right hand side

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

We know that a^-b = 1/a^b  Hint: { 1/(3/2) = 2/3}

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

The bases are the same, so the exponents are the same

x-1 = -3

x -1+1 = -3+1

x = -2


Related Questions

Help on 36 and 37 pls, the choices for 37 are 70,77,82, and 90

Answers

Answer:

36: G-30

37: Please add the rest of the questions, so I can answer 37.

Step-by-step explanation:

I’ll mark u as a brainliest!! pls help me

Answers

Answer:

Shorter leg is 7

Bigger leg is 7√3 = 12.1 (rounded to the nearest tenth)

What is the approximate length of the line segment?
(1, -1)
(6,-8)

Answers

Answer:

8.6023

Step-by-step explanation:

length = √[(x2-x1)^2+(y2-y1)^2]

=√[(1-6)^2+(-1--8)^2] =√74 =8.6023

What are the roots of the equation x2 + 6x - 4 = 0?
A6+2V13
B.-6+2V13
C.3V13
D.-3V13

Answers

Answer:

The answer is D

Step-by-step explanation:

use the quadratic formula, plug and chug, and voila!

Inverse property of addition for real numbers

Answers

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

Find the value of x in each case

Answers

Answer: x=45

Step-by-step explanation:

To solve for x, we first need to understand the figure. We know TV and RS are parallel lines. If we extend TV to the left, we get a straight line parallel to RS. By Alternate Interior Angles, We know ∠R is equivalent to ∠T on the very left. Therefore, we can set it equal to 180° and solve.

x+2x+x=180          [combine like terms]

4x=180                  [divide both sides by 4]

x=45

Now, we know x=45.

20 points lovelys <3​

Answers

Answer:

A) 2 cm

Step-by-step explanation:

By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.

tại teamart,1 ly trà sữa có giá a đồng và 1 ly kem có giá là b đồng.Hãy viết biểu thức đại số biểu thị số tiền bạn Cúc mua 3 ly trà sữa và 4 ly kem

Answers

Answer:

3 a + 4 b

Step-by-step explanation:

Biểu thức đại số biểu thị bạn Cúc mua  3  ly trà sữa và  4  ly kem là:

3 a + 4 b

SOMEONE PLEASE HELP ME ITS URGENT (PICTURE)

Answers

Answer:

Question #1

x and its opposing side are equal in length. One of the sides have no fence.

Set up an equation to find x:

[tex]x+x+10=26\\2x=26-10\\2x=16\\x=8[/tex]

The length of the side marked x is 8.0 m.

Question #2

New length = 10 + 1 = 11 cmNew width = xNew perimeter = old perimeter = 34 cm

Set up an equation to find x

[tex]11+11+x+x=34\\2x=34-22\\2x=12\\x=6[/tex]

The new width is 6 cm.

Suppose we have a stick of length 1.a) We randomly uniformly choose a point and break the stick into two pieces.Find the expected length of the smaller piece.b) We randomly uniformly choose two points (independently) and break thestick into three pieces. Find the probability that the three resulting piecescan be arranged to form a triangle (i.e. all triangle inequalities are satisfied;i.e no piece is longer than the sum of the other two).

Answers

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

please please please answer!! will give brainliest and extra points!

Answers

Answer:

a) y = x

b) y = 10

c) x = 3

Step-by-step explanation:

a) the line passes through the points (-5, -5) and (1, 1).

Step 1. Identify the slope

M = slope

M = change in y/change in x

Two points: (-5, -5) & (1, 1)

M = (y2 - y1)/(x2 - x1)

where y2 = 1 y1 = -5 x2 = 1 & x1 = -5

M = (1 - -5)/(1 - -5)

Note: Two negative signs together makes addition!

M = 6/6

M = 1

Step 2. Find the y-intercept

The slope is 1 but then we need a y-intercept. To do this we have to take a look when the first y-intercept happened.

Answer: y-intercept undefined so therefore our final answer is y = x
••••••••••••••••••••••••••••••••••••••••••••••••••
b) the line that passes through (-2, 10) and (3, 10).

If we would’ve graphed this, we can see that they’re in line with the y-axis so there wouldn’t be any slope.

Step 1. Find the slope.

M = slope

M = change in y/change in x

Two points: (-2, 10) & (3, 10)

M = (y2 - y1)/(x2 - x1)

M = (10 - 10)/(3 - -2)

M = 0/5

M = 0

Therefore the slope is 0

Step 2. Find the y-intercept

And the y-intercept is 10 obviously so now our answer would be y = 10
•••••••••••••••••••••••••••••••••••••••••••••••••••
c) the line parallel to the y-axis that passes through the point (3, -7)

Equation of line parallel to y-axis is x = k

(3, -7) lies on our required line

-> k = 3

The equation of the required line is x = 3
••••••••••••••••••••••••••••••••••••••••••••••••••
d) & e)

I don’t know the answer to the rest I’m sorry but at least appreciate these 3 answers that I’m giving you

Have a good day!

-Unluckydoom

BC has endpoints B(5,9) and C(-4,-3). Find the coordinates of the midpoint of BC.
I need help !!

Answers

Answer:

(0.5,3)

Hope this helps..Have a good day!!

PLS HELP ASAP! 20 PTS

evaluate

Answers

Answer:

Step-by-step explanation:

Cos^-1(1/2) = 60

To get from a degree to radian, simply multiply by pi then divide by 180. So the final answer is 1/3pi or approximately 1.0472

I hope this helped! :D

find the missing side. Round it to the nearest tenth.​

Answers

Answer: x = 74.3

Step-by-step explanation:

Let 22 be reference angle

so

tan 22 = p/b

tan 22 = 30/x

or, x= 30/tan22

so, x = 74.252

so, x = 74.3

The recursive formula for a geometric sequence is: a = 4 an=an-1×3 What is the 3rd term of this sequence?​

Answers

Answer:

36

Step-by-step explanation:

a1 = 4

an=an-1 *3

a2 = a1 *3 = 4*3 = 12

a3 = a2*3 = 12*3 = 36

If 8x-4=12;then 2x - 1=

Answers

Answer: 21

Step-by-step explanation:

Step-by-step explanation:

tbh I have no idea

doing this for points

so yeah

I don’t understand how taxes and discounts work in math, could someone explain to me?

Answers

Some additional context would be helpful in providing a complete answer. But the basic idea is this:

• Object ABC has a price X set on it.

• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.

• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.

Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.

• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.

• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.

Pure mathematicsssss

Answers

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

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

Step 2: Use the complete square method.

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

Step 3: Have it to [tex]a(x+b)^{2} +c[/tex]

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

Line of symmetry:  

To find line of symmetry, we use -b/2a formula.

Based from [tex]2x^{2} -4x+1[/tex]:

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

a shopkeeper sells a pant at 10% profit, if he would have sold it at rs.150 more than profit would have been 15% find the purchased price of the pant

Answers

Answer:

selling prices =10% 10+150+15%=180

You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 1 and flipping heads? Write your answer as a fraction in simplest form.

Answers

Answer:

5/12

Step-by-step explanation:

Number cube:

Numbers greater than 1 → 5 options out of 6

Coin:

Heads → 1 out of 2

Required probability:

P(>1 & H) = 5/6*1/2 = 5/12

Answer: Probability of rolling a number more than one: 5/6

Probability of heads: 1/2

Probability of both: 1/2 + 5/6 = 4/3

Step-by-step explanation:

Find the value of f(x) at the given value of x: f(x) = (x -4)(x + 3), x = 3​

Answers

Answer:

-6

Step-by-step explanation:

f(x)= (3- 4)(3+3)

=( -1 )(6)

= -6

please help 15 points (picture)

Answers

Answer:

the first difference are all 20.

since the first differences of this relation are constant, it is a linear relation

Answer:

Linear because the account balance increases by a constant 20.

Step-by-step explanation:

→ The first difference is 20 for all values because :

20 - 0 = 20

40 - 20 = 20

60 - 40 = 20

80 - 60 = 20

100 - 80 = 20

PLEASE HELP, I'LL MARK BRAINLIEST.. Of the 37 teachers at Francesca's high school, 9 are female. What is the ratio of the number of male teachers to the total number of teachers? Please write in decimal form

Answers

The answer you are looking would be decimal 5.9

Hello! I really need some help with this (:

Answers

Answer:

y = 3x + 3

Step-by-step explanation:

As x increases, y increases by 3. Therefore, the slope of the function is 3.

Setting x = 0 will give an output of 3. Therefore, the y-intercept is (0, 3).

Overall, the function rule for the given data set is y = 3x + 3.

Whats the answer



HURRY IM BEING TIMED

Answers

Answer:

(C.

I THINK-

Step-by-step explanation:

I think the answer is c

HELPPPPPPPP
Which of the following is a geometric sequence?

Answers

Answer:

ES LA NUME  C                                        R

Step-by-step explanation:

A basketball is shot into the air. Its height is represented by the polynomial equation h(t) = –16t2 + 35t + 5, where h is the height of the basketball at t seconds. What's the height of the basketball at 1.5 seconds?
Question 4 options:

20.2 feet


18.8 feet


21.5 feet


16.7 feet

Answers

Answer:

height = 21.5 ft

Step-by-step explanation:

Substitute t = 1.5 into h(t) and evaluate

h(1.5) = - 16(1.5)² + 35(1.5) + 5

        = - 16(2.25) + 52.5 + 5

       = - 36 + 57.5

      = 21.5 ft

Answer:

21.5 feet.

Step-by-step explanation:

Let t = 1.5

[tex]h(1.5)=-16(1.5)^2+35(1.5)+5\\h(1.5)=-36+52.5+5\\h(1.5)=21.5[/tex]

Therefore, at 1.5 seconds, the basketball is 21.5 feet in the air.

f(x)=−4x
2
+5x
\text{Find }f(6)
Find f(6)

Answers

Answer:

-114

Step-by-step explanation:

f(x) = -4x^2 +5x

Let x = 6

f(6) = -4(6)^2 +5(6)

     = -4(36) +30

     - 144+30

   = -114

What is the range of the function on the graph, I hope you can see it

Answers

Answer:

Option 4. All real numbers greater than or equal to 2.

I hope this will help.

[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]

Answers

Answer:

\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}

\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}

Step-by-step explanation:

This is the simplified answer.
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