Find the value of x in the equation without evaluating the power

Find The Value Of X In The Equation Without Evaluating The Power

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

2 ^(5+x) = 2^8            (because 256 = 2^8)

 equate the exponents    5+x = 8     then x = 3

1/3 ^(2+x) = 1 / 3^ 6        (because 729 = 3^6 )

  equate the exponents  2+ x = 6    then x = 4

Answer 2

Answer:

a) x = 3

b) x = 4

Step-by-step explanation:

Use the Exponential Power Rule.

[tex]a^x \times a^y = a^{x+y}[/tex]

Also covert the term on the right to the same base as on the left.

If you are allowed to have calculator do [tex]\log_{\text{base}} (\text{number})[/tex] to get the exponent. For example [tex]\log_{2} (256) = 8[/tex], that means [tex]256 = 2^8.[/tex]

Without calculator you can divide with base untill you have it fully factored, then count. For example:

256/2 = 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

We had to divide with base two 8 times so 256 = 2⁸.

a)

[tex]2^5 \cdot 2^x = 256\\2^{5+x} = 2^8[/tex]

Now that we have same base we can equate the exponents!

[tex]5 + x = 8\\x = 8 - 5\\x = 3[/tex]

b)

[tex](\frac{1}{3})^2 \cdot (\frac{1}{3})^x = \frac{1}{729}\\\\(\frac{1}{3})^{2+x} = \frac{1}{3^6}\\\\(\frac{1}{3})^{2+x} = (\frac{1}{3})^6[/tex]

[tex]2 + x = 6\\x = 6 - 2\\x = 4[/tex]


Related Questions

The diameter of a circle is 14 miles. What is the circle's area?
Use 3.14 for ​.

Answers

Answer:

153.86cm^2

Step-by-step explanation:

area of a circle= πr^2

where r = radius= 14/2= 7miles

area= 3.14×(7×7)

area= 3.14×49= 153.86cm^2

Which equation can be used to find A, the area of the parallelogram shown?

Answers

Answer: A = 6 x 7  

Explanation:

The area of a parallelogram is equal to base times height.

The base and height are always perpendicular to one another. Usually the base is horizontal along the ground (if not then you'd need to rotate your paper until it is, but that step is optional).

The base is 6 meters and the height is 7 meters.

Therefore, area = base x height = 6 x 7

The side of 11 meters is not used at all. It's likely put in there as a distraction.

Answer:

A = 6 * 7

Step-by-step explanation:

A parallelogram follows the same rules as a regular quadrilateral, as the only difference is that both its sides have been moved along.

What are the values of a and b? a = 14, b = 6 a = 14, b = 8 a = 17, b = 6 a = 17, b = 8

Answers

The value of a and b given that the opposite side are equal are 17 and 6 respectively

Properties of a kite

The kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;

2a - 4 = 30
2a = 34

a = 17

Similarly

3b+6 = 24

3b = 18
b = 6

Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively

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a) What percentage of 5³ is 5?
b) What percentage of 5³ is 5²?​

Answers

Step-by-step explanation:

a) 5³= 5*5*5 = 125

5/125*100%

4%

b) 5²=5*5=25

25/125*100%

20%

Help with this question please

Answers

Answer:

See below

Step-by-step explanation:

(a)

[tex]\angle A\cong \boxed{\angle Z}[/tex]

[tex]\angle B\cong \boxed{\angle Y}[/tex]

[tex]\angle C\cong \boxed{\angle X}[/tex]

(b)

[tex]\overline{AB}\cong \boxed{\overline{ZY}}[/tex]

[tex]\overline{AC}\cong \boxed{\overline{ZX}}[/tex]

[tex]\overline{BC}\cong \boxed{\overline{YX}}[/tex]

(c)

[tex]\triangle CAB \cong \triangle \boxed{XZY}[/tex]

Work out
m
and
c
for the line:
y
=
x
+
4

Answers

Answer:

m = 1

c = 4

Step-by-step explanation:

First let's review what a slope-intercept form is.

Slope-intercept form is a specific form of linear equations. It always has y on one side and all the other terms on the other. Its structure is:

[tex]y = mx + c[/tex],

where m is the slope and c is the y-intercept.

You can easily read slope (m) and intercept (c) in your equation.

[tex]y = mx + c\\y = x + 4[/tex]

You can see that m in front of x is 1, because x = 1x. Multiplying with 1 perserves the number.

So:

[tex]m = 1\\c = 4[/tex]

please answer asap! 20 points!!
A new car is purchased for 23,900 dollars. The value of the car depreciates at a rate of 6.4% per year. Which equation represents the value of the car after 4 years?

1) V= 23,900(0.936)(0.936)(0.936)(0.936)
2) V=23,900(1+0.064)⁴
3) V= 23,900(1−0.064)(1−0.064)
4) V= 23,900(0.064)⁴

Answers

Answer:

  1) V= 23,900(0.936)(0.936)(0.936)(0.936)

Step-by-step explanation:

Each year, the car depreciates to 1 -0.064 = 0.936 of its previous value. After 4 years, the original value has been multiplied by this factor 4 times:

__

  depreciated value = 23,900(0.936)(0.936)(0.936)(0.936)

_____

This could be represented by ...

  V = 23,900(1 -0.064)⁴ . . . . . . not an answer choice


The length of AB is four times the length of BC.
AC = 75 cm.
=

Answers

Let length of bc be x cm
Thus, ab=4x
ab+bc=ac
4x+x=75
5x=75
x=75/5
x=15
Therefore, ab=x=15cm
bc=4x=60cm

A can has a height of 11cm and a volume of 486cm^3 . Find the radius of each can . Correct to two decimal places

Answers

If the height is 11 cm and the volume is486 cubic cm. Then the radius of the can will be 3.75 cm.

What is a cylinder?

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A can has a height of 11 cm and a volume of 486 cubic cm.

Then the radius of the can will be

We know that the volume is given as

Volume = πr²h

     486 = π r² x 11

         r² = 14.06

           r = 3.75 cm

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A date is picked at random on the calendar for april. what is the probability that the date chosen will be on a two digit odd number

Answers

Answer:

1/3

Step-by-step explanation:

That is the simplified version of the number of all the double-digit odd days (11,13,15,17,21,23,25,27,29), 10, over the total number of days in April, 30

10/30=1/3

Someone help me find the length of ST please!

Answers

Answer:

10

Step-by-step explanation:

I calculated and it's 10 I'm in car so I can't give the whole explanation

Tim tried to use Cavalieri's principle to show that the two figures have the same volume.
"The base areas are the same. Therefore, corresponding cross-sections have the same area. So the volumes must be the same."
What is the first mistake Tim made?

Answers

Answer:

The base areas aren't same

Step-by-step explanation:

The base areas arent same

Answer:

He did not establish that heights are the same.

Students must purchase a ticket to attend the show. the committee wants to
have $500 remaining from ticket sales, after paying for equipment, lighting,
and costumes.

the tickets will cost $5.60 for each ticket, and the committee expects to sell
as many tickets as there are seats available.

what is the greatest amount of money, in dollars, the committee can spend
on equipment and costumes?

Answers

Answer:

The total number of seats is also needed to answer the question.

Step-by-step explanation:

For example, if there were 100 seats the committee would make $560 in all, therefore having $60 to spend on equipment and costumes.

How far does the unicycle move if the wheel turns once?

Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?

Answers

The unicycle moves a distance of 251.20cm if the wheel turn once and the wheel must rotate 32 times to cover a distance of 100m

Circumference of a circle

The formula for calculating the circumference of a circle is given as:

C = 2pi r

r is the radius of the circle

a) r = 80/2 = 40cm

C = 2(3.14)(40)
C = 251.20 cm

Hence the unicycle moves a distance of 251.20cm if the wheel turn once

b) Number of revolution * 2pi r = distance covered

n * 2(3.14)(50) = 10000
314n = 10000
n = 10000/314

n =32

Hence the wheel must rotate 32 times to cover a distance of 100m

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Help pls!!!!!!


A family sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2x8x9 inches costs $4.50. What is the difference in price per cubic inch?

Answers

Answer:

$0.01

Step-by-step explanation:

Family size rate (per cubic inch)

Volume of box = 3 x 9 x 12 = 324 in³Cost = $6Rate = 6/324 = 1/54 = $0.02 per cubic inch

Regular size rate

Volume of box = 2 x 8 x 9 = 144 in³Cost = $4.50Rate = 4.50/144 = 1/32 = $0.03 per cubic inch

Difference in price

$0.03 - $0.02$0.01

Volume of family sized box

LBH3(9)(12)27(12)324in³

Price per inch

6/324=0.02$/in

Volume of regular size

2(8)(9)144in³

Price per in

4.5/144=0.03$/in

Difference:-

|0.02-0.03|=0.01$

For any positive numbers a,b, and d, with b=1, logb a+logb d=

Answers

Answer the right answer is a

Find a function y of x such that 2yy′=x and y(2)=6

Answers

Answer:

[tex]y=\sqrt{\frac{x^{2}}{2} +34}[/tex]

Step-by-step explanation:

[tex]2y\left( x\right) y^{\prime }\left( x\right) =x[/tex]

[tex]\Longrightarrow \int 2y\left( x\right) y^{\prime }\left( x\right) dx=\int x\ dx[/tex]

[tex]\Longrightarrow y^{2}\left( x\right) =\frac{x^{2}}{2} +c\ \text{(c is a constant)}[/tex]

[tex]y\left( 2\right) =6\Longleftrightarrow y^{2}\left( 2\right) =36[/tex]

[tex]y^{2}\left( 2\right) =36\Longleftrightarrow \frac{\left( 2\right)^{2} }{2} +c=36\ \Longleftrightarrow c=34[/tex]

[tex]\Longrightarrow y\left( x\right) =\pm\sqrt{\frac{x^{2}}{2} +34}[/tex]

Solve 6^x+2 = 10 for x using the change of base formula

Answers

Answer:

[tex]x\approx-0.7149[/tex]

Step-by-step explanation:

[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]

Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]

need help with this one geometry problem asap

Answers

Answer:

Step-by-step explanation:


pls help with this question asap

Answers

Answer:

30 ft

Step-by-step explanation:

Perimeter

= 3 + 4 + 4 + 7 + 4 + 4 + 4

=  30 ft.

Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)

Answers

The expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³

How to determine the volume of the empty space?

The cube box has a side length of 9.

So, the volume of the box is:

V = 9³

The sphere has a radius of 4.5.

So, the volume of the sphere is:

v = 4/3π(4.5)³

Calculate the difference between both volumes:

d = 9³ - 4/3π(4.5)³

Hence, the expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³

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Answer: that is answer d

Step-by-step explanation:

2023 edge

PLEASE HELP WILL MARK BRAINLIEST WITH 100 POINTS
What is the best way to describe the center of the data represented in this line plot?

Select from the drop-down menus to correctly complete the statement.

The
median
mean
is
1 inch
1.5 inch
1.8 inch
2 inches

Line plot titled Daily Rainfall. The number line is labeled Number of inches. There are 3 dots above 0, 3 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, and 1 dot above 6.
.

Answers

Answer:

Mean = 1.8 in

Step-by-step explanation:

Median

The Median is the middle value when all data values are placed in order of size.

Ordered data values:  0, 0, 0, 1, 1, 1, 2, 3, 4, 6

As there is an even number of data values, the middle value is the mean of the middle two data values.  Therefore, the Median = 1 in

Mean

The Mean is the sum of all data values divided by the total number of data values.

[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]

Therefore, the Mean = 1.8 in

Conclusion

The Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers.  As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.

Therefore, the Mean = 1.8 in

Write in scientific notation:
0,007 832

Answers

Answer:

The scientific notation for this will be

[tex]7.832 \times {10}^{ - 3} [/tex]

As there are three zero in expression

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

A right circular cone has a base radius of 4 and a height of 6. A right circular cylinder also has a base radius of 4 and a height of 6. Let A be the lateral surface area of the cone, and let B be the lateral surface area of the cylinder. Find A/B.

Answers

Answer:

A/B = 0.6

Step-by-step explanation:

Given dimensions of

Right circular cone: r = 4 and h = 6Right circular cylinder: r = 4 and h = 6

Find the lateral surface area of both figures

The cone[tex]A= \pi r\sqrt{h^2+r^2}=3.14*4\sqrt{6^2+4^2}= 90.57[/tex]The cylinder[tex]B=2\pi rh=2*3.14*4*6 = 150.72[/tex]

Find the ratio A/B

A/B = 90.57/150.72 = 0.6 (rounded0


An object is fired from a cannon. Its height after t seconds is given by the function
h(t)= 16t² + 128t + 140 feet. How high was the object after 2 seconds?
=
The object was
feet high.

Answers

Answer:

332 feet

Step-by-step explanation:

Height = h(2) = - 16(2^2) + 128t + 140   ( NOTE: I added the minus sign)

                      = 332 feet

The maximum height  is 908 feet.For a parabola, h = ax^2 + bx + c, the vertex at point (h,t), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.

What is more about the problem?

For a parabola, h = ax^2 + bx + c, the vertex at point (h,k), is first found by the equation t = b / 2a, and then plugging that point into the equation to find h.

Given the equation h = 16t^2 + 128t + 140, we know a = 16, b = 128, c = 140.

t = -b/2a

t = -(128) / 2(16)

t = -128 / 32

t = 4 seconds

let's plug in t=4 to our equation:

h = 16t^2 + 128t + 140

h = 16*(4)^2 + 128*(4)+ 140

h =  908ft

h = 908 feet

answer is that the maximum height  is 908 feet.

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( i will give brainlist ) please help is the following equation linear, quadratic, exponential or none of these?

Answers

Answer:

exponential

Step-by-step explanation:

It is exponential because the variable is in the exponent

Whats the product 72x0.45

Answers

Answer:

72 times 0.45 is equal to 33.75

Step-by-step explanation:

You can use a calculator to find this out.

Answer:

32.4

Step-by-step explanation:

After repeatedly adding 0.45 a total of 72 times. You end up getting 32.5

To check the answer you divide 32.5 by 72 and receive 0.45. Checking the answer

PLEASE HELP SUPER EASY bottom question please!!

Answers

Answers:  

The histogram is shown below.7/10 of the class passed the assignment.

============================================================

Explanation:

Part 1

Sort the data values to get

51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100

Now let's say we had these intervals

51-6061-7071-8081-9091-100

Notice each interval is 9 units wide.

The 5 scores 51,54,58,60,60 are in the interval 51-60, which means the first interval has a bar that's 5 units tall.

The scores 62,70 are in the interval 61-70, which means the second bar is 2 units high.

Keep this process going to create the histogram shown below.

It looks like you have the right idea, but your class interval widths aren't the same each time.

Because the class interval widths can change, this means other histograms are possible. Just be sure to stick to one interval width.

-----------------------------------

Part 2

Set A = set of scores that are 70 or larger, i.e. those who passed

Set A = {70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}

Set B = set of all scores in the class

Set B = {51, 54, 58, 60, 60, 62, 70, 72, 72, 75, 76, 80, 85, 88, 90, 90, 95, 100, 100, 100}

There are 14 items in set A and 20 in set B

This means 14/20 = 7/10 of the students passed.

Leah bought a bicycle for $118 that was originally priced at $472. What is the discount
percentage?
Write your answer using a percent sign (%).

Answers

Answer:

75%

Step-by-step explanation:

the discount percentage :

[tex]\frac{472-118}{472} \times100 = 75 \%[/tex]

Given:Bought price= $118Original price= $472To find:

The percentage decrease ( discount percentage ).

Solution:

[tex]\large\boxed{\sf{formula = 100 \times \frac{(final - initial)}{initial} }}[/tex]

We'll have to subtract 472 ( initial value ) from 118 ( final value).

[tex]472 - 118[/tex]

[tex] = 354[/tex]

Now, we'll have to divide 354 ( difference ) by 118 ( initial value ) and multiply by 100.

[tex] 100 \times \frac{354}{118} [/tex]

[tex]\large\boxed{\sf{ = 75\% }}[/tex]

Hence, the discount percentage is 75.

Amelia's car used 16 gallons to travel 656 miles. How many gallons of gas would she need to travel 533 miles?

Answers

Answer:

13 gallons of gas.

Step-by-step explanation:

If amelia used 16 gallons of gas for 656 miles, she is traveling 41 miles per gallon. (656 divided by 16). So we take the amount she needs to travel which is 533, and divide it by 41 because 41 miles is equal to one pound of gas, so, 533 divided by 41 is 13, she needs 13 gallons of gas to travel 533 miles.

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