Solve for x: √(32^0 + 2/3)=(0.6)^2-3x​

Answers

Answer 1

Step-by-step explanation:

Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

Asked: Find the value of x = ?

Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

⇛√{1 + (2/3)} = (0.6)²⁻³ˣ

⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ

⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ

⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ

⇛√(5/3) = (0.6)²⁻³ˣ

Squaring on both sides then

⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²

⇛√(5²/3²) = {0.6}(²⁻³ˣ)²

⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²

⇛5/3 = {0.6}(²⁻³ˣ)²

[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]

⇛5/3 = (0.6)²*²⁻³ˣ*²

⇛5/3 = (0.6)⁴⁻⁶ˣ

⇛5/3 = (6/10)⁴⁻⁶ˣ

⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ

⇛5/3 = (3/5)⁴⁻⁶ˣ

⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ

[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]

Base are the same, so the exponents must be equal.

[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x

Shift the number 4 from RHS to LHS, changing it's sign.

⇛-1 - 4 = -6x

⇛-5 = -6x

⇛x = {(-5)/(-6)}

[tex]\mathsf{\therefore}[/tex] x = 5/6

Answer: Hence, the value of x for the given problem is 5/6.

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Related Questions

How much of a radioactive substance must be presented to decay to 80 grams in 12 years if the half-life of the substance is 7.6 years?

Answers

Answer:

Radioactive in half life is 51gram

Step-by-step explanation:

80grams:12years

X :7.6years

12x÷x=x

7.6×80÷12=51gram

Answer:

239 grams.

Step-by-step explanation:

Half life t(1/2) = ln 2 / k

So 7.6 = ln 2 / k

k = ln 2 / 7.6 = 0 0901204

N = No e^-kt

So after 12 years

80 = No / e^(-0.0901204*12)

No = 80 / e^(-0.0901204*12)

= 239.

four triangles are shown

Answers

Answer:

G

Step-by-step explanation:

The answer is statement G

If each of these runners travels the indicated number of spaces in the same amount of time, at which numbered spot will all of the runners be next to one another?

Answers

Answer:

Step-by-step explanation:

This is kinda confusing give me a second

Which of the following is a defined term?
Angle
Line
Point
Plane

Answers

Answer:

C. Point is a defined term

Step-by-step explanation:

kleann

Label the probabilities in the tree diagram below and determine what is the probability of wearing a red shirt and black jeans?

Answers

The probability of wearing a red shirt and a black jean is the likelihood of the shirt and jean

The probability of wearing a red shirt and a black jean is is 1/6

How to determine the probability?

From the tree diagrams, we have the following parameters

Total combination = 6

Red shirt and Black Jean = 1

The probability of wearing a red shirt and a black jean is calculated as:

P = n(Red shirt and Black Jean)/Total combination

This gives

P = 1/6

Hence, the probability of wearing a red shirt and a black jean is is 1/6

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17
What percent does 20
8%
850%
85%

Answers

Answer:

=0

Step-by-step explanation:becase I got it right on a test

Is 3822 divisible by three or nine

Answers

Answer:

The number 3,822 is divisible by 3 and is not divisible by 9, because the sum of the digits is 3 + 8 + 2 + 2, which equals 15, and 15 is divisible by 3 but not by 9.

On Thursday the cows at the Putnam Dairy produced 70 bottles of milk. Friday, the cows produced 5/8 as much milk as on Thursday. How many bottles of milk did the cows produce on Friday?

Answers

the answer is a on edge

Write the equation of the line that passes through the points (-9,-9)(−9,−9) and (6,-7)(6,−7). Please help me

Answers

Answer:

y = (2/15) x -(117/15)

Step-by-step explanation:

To write the equation we should know the slope m and the y-intercept b .

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

For points (x1 = -9, y1 = -9) and (x2 = 6, y2 = -7)

m = (-7 - - 9)/(6 - - 9) = (-7 + 9)/(6 +9) = 2 / 15

The general equation of a line is

y= mx + b

Our equation is

y = (2/15) x +b

To find b, substitute one of the two points, we know are on the line, in our equation. For example, we can substitute point (-9,-9)

-9 = (2/15) (-9) +b , multiply -9 by 2/15

-9 = - (18/15) +b, add -18/15 on both sides

-9 + (18/15) = b, find common denominator and add

[(-9 ·15) +18]/15 = b , simplify

-117/15 = b

So our equation is:

y = (2/15) x -(117/15)

23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
24. The speed of a skidding car is directly proportional to the
square root of the length of the skid. On a snowy road, a car
with good brakes traveling at 40 mph would skid approxi-
mately 178 ft. If the skid marks of a similar car on a similar
road were 400 ft, how fast would this car be traveling?
24. If the skid marks of a similar car on a similar road were 400 ft, how fast would this car be
traveling?

Answers

The direct variation that of the speed to the skid length implies that the speed increases as the length increases

The car would be traveling at 59.96 mph

How to determine the speed of the skidding car?

A direct variation that illustrates the speed of the skidding car is:

s = k√l

Where:

s represents the speed of the carl represents the length of the skidk represents the proportionality constant

Make k the subject in s = k√l

k = s /√l

Rewrite as:

s₁ /√l₁ = s₂ /√l₂

Substitute known values

40 /√178 = s₂ /√400

Evaluate the square root of 40

40 /√178 = s₂ /20

Multiply both sides by 20

800 /√178 = s₂

Evaluate the quotient

s₂ = 59.96

Hence, the car would be traveling at 59.96 mph

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30 feet is equivalent to how many inches?

Answers

Answer:

  360 inches

Step-by-step explanation:

Each foot is 12 inches. The number of inches in 30 feet is found by multiplying the number of inches in 1 foot by 30.

  30 × (12 inches) = 360 inches

Which interval on the graph could be described as linear constant?

A
B
C
D

Answers

What graph? You need to upload a picture..

A swimsuit is on sale for $29.75. If the original price of the swimsuit is $35, what is the percent of the discount?

A. 2%
B. 5%
C. 15%
D. 17%

Answers

Answer:

C. 15%

Step-by-step explanation:

35 * 0.15 = 5.25

35 - 5.25 = 29.75

A percentage is a way to describe a part of a whole. The percentage of discount on the swimsuit is 15%.

What is the Percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

We know that the cost of the swimsuit is $29.75, while the original cost of the swimsuit is $35. Now, after the discount the price will be a percentage of the original, therefore, the discounted price can be written as,

Discounted Price = x% of Original Value

[tex]29.75 = \dfrac{x}{100} \times 35\\\\x = 85[/tex]

Now, as we know that the discounted price is 85% of the original price, therefore, the price will have a 15% discount(100%-85%).

Hence, the percentage of discount on the swimsuit is 15%.

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If the slope of a line is zero the line must be a
line.

Answers

Answer:

Straight along the horizontal axis

Step-by-step explanation:

Hope this helped :)

12. You have $10 to spend on charms and stickers. The equation
0.5x + 0.25y = 10 represents this situation, where x is the number
of charms and y is the number of stickers. How many stickers can
you buy when you do not buy any charms?

Answers

Answer:

40

Step-by-step explanation:

the easiest way to solve this equation is to divide 10 by .25 since, in this situation, all that is being bought are stickers

10/.25=40

hope this helps

HELP PLEASE URGENT, ASAP. THIS IS GRADE 11 TRIGONOMETRY ILL GIVE THE BRAINLIEST!!!!!!!!!!!!

Answers

Answer:

1. [tex] \theta = 61.9^\circ [/tex]

2. [tex] x = 23.7~cm [/tex]

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex] \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} [/tex]

[tex] \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} [/tex]

[tex] \sin \theta = 0.88176 [/tex]

[tex] \theta = \sin^{-1} 0.88176 [/tex]

[tex] \theta = 61.9^\circ [/tex]

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex]\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}[/tex]

[tex]x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}[/tex]

[tex] x = 23.7~cm [/tex]

Find the value of 9u-2 given that -7u-7=7 ?

Answers

Answer:

-20

Step-by-step explanation:

when you solve:  -7u-7=7, you get u= -2 and when you plug it in you get this equation 9(-2)-2=?

then you get -20

Hey there!

-7u - 7 = 7

ADD 7 to BOTH SIDES

-7u - 7 + 7 = 7 + 7

CANCEL out: -7 + 7 because it give you 0

KEEPs 7 + 7 because it help solve for the u-value

NEW EQUATION: -7u = 7 + 7

SIMPLIFY IT!

-7u = 14

DIVIDE -7 to BOTH SIDES

-7u/-7 = 14/-7

CANCEL out: -7/-7 because it give you 0

KEEP: 14/-7 because it give you the

u-value

NEW EQUATION: u = 14/-7

SIMPLIFY IT!

u = -2


SOLVING FOR : 9u - 2

9u - 2

= 9(-2) - 2

= -18 - 2

= -20


Therefore, your answer is: -20

Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

Jasmine is trying to replace the flooring in her rectangular bedroom. When she measured the width and length of the floor, she found that the length is 5 ft. longer than the width. If the perimeter of the room is 50 ft., how much flooring will she need to replace the existing flooring in her room?

Answers

Answer:

150ft^2

Step-by-step explanation:

FINDING THE LENGTHS

50 = x + 5 + x + x + 5 + x

50 = 4x + 10

50 - 10 = 4x

40 = 4x

40/4 = x

10ft = x

AMOUNT OF FLOORING

area = l x b

= (10 + 5) x 10

= 15 x 10

= 150ft^2

A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $300 each, and the laptop computers cost $350 each. How much would it cost to buy 18 notebooks and 12 desktop computers? How much would it cost to buy nn notebooks and dd desktop computers?

Answers

Answer:

$9,600

Step-by-step explanation:

notebook computer : $300

laptop computer : $350

18 x 300 = 5,400

12 x 350 = 4,200

4,200 + 5,400 = 9,600

Please help ASAP!!! Thank you!

Answers

Answer: 58 1/3 in^3.

Step-by-step explanation: To find the volume of a pyramid, you need to multiply the length, width, and height and divide it by 3.  The length and width are both 5 and the height is 7, so the equation is 5 x 5 x 7.  The answer to that is 175.  Now, you have to divide 175 by 3, which is 58.33, or 58 1/3, which is your answer.

Let me know if this is right! :)

What is an equation of the line perpendicular to y=-x-2 and through (-2, 4)?

I would really appreciate the help, I've been stuck on this problem for awhile.​

Answers

Answer: y = x + 6

Step-by-step explanation:

[tex]\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:perpendicular\:to\:}y=-x-2\mathrm{\:that\:passes\:through\:}\left(-2,\:4\right)[/tex]

[tex]\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}[/tex]

[tex]m=-1[/tex]

[tex]\mathrm{The\:perpendicular\:slope\:is\:the\:negative\:reciprocal\:of\:the\:given\:slope}[/tex]

[tex]\left(-1\right)m_p=-1[/tex]

[tex]\frac{\left(-1\right)m_p}{-1}=\frac{-1}{-1}[/tex]

[tex]m_p=1[/tex]

[tex]\mathrm{Compute\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:for\:slope\:m=}1\mathrm{\:and\:passing\:through\:}\left(-2,\:4\right)[/tex][tex]\mathrm{Plug\:the\:slope\:}1\mathrm{\:into\:}y=mx+b[/tex]

[tex]y=x+b[/tex]

[tex]\mathrm{Plug\:in\:}\left(-2,\:4\right)\mathrm{:\:}\quad \:x=-2,\:y=4[/tex]

[tex]4=\left(-2\right)+b[/tex]

[tex]-2+b=4[/tex]

[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]

[tex]-2+b+2=4+2[/tex]

[tex]\text{Simplify}[/tex]

[tex]b=6[/tex]

[tex]\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=1\mathrm{\:and\:}\mathbf{b}=6[/tex]

[tex]y=x+6[/tex]

Find the volume of the prism in terms of y.

Answers

is there a value to y? if not, this is what I got:

Y^2 + 2y + 3

pls help
Triangle MNP with the vertices M(-6,-8) M(-1,-6) and P(-2,-8) in the line y= -5

Answers

Triangle MNP with the vertices M(-6,-8) N(-1,-6) and P(-2,-8) is reflected across the line y= -5 to give M'(-6, -2), N'(-1, -4) and P'(-2, -2)  

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Triangle MNP with the vertices M(-6,-8) N(-1,-6) and P(-2,-8) is reflected across the line y= -5 to give M'(-6, -2), N'(-1, -4) and P'(-2, -2)  

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What is the median age of a group of employees
whose ages are 32, 37, 30, 43, 29 and 31?

Answers

To get the median of a set, simply arrange the numbers or elements in either ascending order or descending order then get the middle number. If there are two middle numbers, add them together and divide by two. The quotient is the median.
36, 38, 28, 30, 26 and 25
{25, 26, 28, 30, 36, 38}
The two middle numbers are 28 and 30.
28 + 30 = 58
58/2 = 29
The median is 29.

10. To calculate the area of a rectangle, you multiply the length by the width. If the
length of a rectangle is (2x + 1) and the width is (x - 1), what is the area of the
) -
rectangle?
A. 3x
B. 3x2 - 1
C. 2x2 - x - 1
D. X - 1

Answers

Answer:

Multiply those side lengths using the F.O.I.L method (first-outer-inner-last). Write it longhand then simplify if that’s what is needed.

(x+5)(x-5) = x^2 -5x + 5x -25

the -5x and + 5x cancel each other so it simplifies to x^2 - 25 units squared.

The number of students taking algebra increased 20% in one year. If
60 students are taking algebra this year, how many took algebra last
year?

Answers

Answer: 50 students

Step-by-step explanation:

You know that the number of students last year plus 20% of that number equals the number of students this year, which can be written as: x + 0.2x = 60 →

1.2x = 60 → x = 50 students :)

Answer: 50 students

Step-by-step explanation:

x + .2x = 60

1.2x = 60

x = 60/1.2

x = 50

Tony is flying from Los Angeles to Boston. His plane ticket costs $605 and the total flight distance is 3,052 miles. What is the cost per mile?

Answers

Answer:

AROUND $0.20 per mile

Step-by-step explanation:

605/3052 is around 0.198, which rounds to 0.20.

These cones are similar. find the surface

area of the smaller cone. round to the

nearest tenth.

2 cm

3 cm

surface area = [? ] cm2

surface area = 75 cm?

Answers

Answer:

33.3 is your answer

Step-by-step explanation:

The surface area of the smaller cone A₁ is approximately 33.3 cm² when rounded to the nearest tenth.

What is a cone?

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Two cones A₁ and A₂ are similar.

The radius of A₁ = 2 cm

radius of A₂ = 3 cm

The surface area of A₁ = ? cm²

surface area of A₂ = 75 cm²

Since the cones A₁ and A₂ are similar, their corresponding sides are proportional.

Specifically, the ratio of their radii is the same as the ratio of their surface areas. That is,

(radius of A₁) / (radius of A₂) = (surface area of A₁) / (surface area of A₂)

We can use this relationship to solve for the surface area of A₁:

(surface area of A₁) = (radius of A₁ / radius of A₂)^2 × (surface area of A₂)

Substituting the given values, we get:

(surface area of A₁) = (2/3)² × 75

(surface area of A₁) = 4/9 × 75

(surface area of A₁) ≈ 33.3 cm²

Therefore, (surface area of A₁) ≈ 33.3 cm²

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I WILL GIVE BRAINLEIST(I NEED THIS RIGHT OR I HAVE TO START OVER)

Answers

Answer:

It’s irrational hope this is correct

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

Convert both to decimals

[tex]\\ \rm\Rrightarrow x=0.147147\dots [/tex]

[tex]\\ \rm\Rrightarrow 1000x=147.147..[/tex]

Hence..

999x=147x=147/99

On similar way we can get second one

So if

p/q and r/s [tex]\in [/tex]Q

Then

pr/qs also rational

When you use a (___________________ ), the money you spend is deducted
A credit card
B debit card
C deposit
D credit score

Answers

Answer:

B  Debit Card

Step-by-step explanation:

When you use a debit card money comes out of your checking account

Answer:

a credit card

Step-by-step explanation:

because I think it makes sense

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