Solve each equation.
log₉3=x

An object that appears to be 4 inches on a scale illustration actually measures 32 feet.

A representation of a real thing with correct sizes that has been scaled back or blown up slightly (called the scale).

The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.

A measurement of 150 mm on the picture would be 1500 mm on the actual horse since this drawing has a scale of "1:10," meaning that everything represented with a size of "1" would have an the actual world, a size of "1" corresponds to a size of "10."

based on the facts provided;

4 in =1/4 in 2ft

= 16*2 ft

= 32 ft

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Answer:

i’m pretty sure it’s 6,039

Step-by-step explanation:

12,078 divided by 2

t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.

Now,

In ln ( t -1 )² = 3, by property of logarithm ( [tex]log_b(a)^m=m(log_b(a))[/tex]),

=> 2 ( ln (t -1) ) = 3

=> ln (t - 1) = [tex]\frac{3}{2}[/tex]

=> t - 1 = [tex]e^\frac{3}{2}[/tex]

=> t = [tex]e^\frac{3}{2}[/tex] + 1 = 4.48 + 1 = 5.48

Hence, t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.

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The simplest form of the expression is 4   .

We have given an expression √2 . √8 .

On multiplying , we get

√2 . √8 = √16

On simplifying , we get

√16  =  √ 4 × 4

           = 4

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Answer:

To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:

39375:    3 3     5 5 5 5 7  

779625:    3 3 3 3 5 5 5   7 11

GCF:    3 3     5 5 5   7  

The Greates Common Factor (GCF) is:   3 x 3 x 5 x 5 x 5 x 7 = 7875

Step-by-step explanation:

The simplified form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).

An algebraic expression (or variable expression) is a term that has been combined with operations like addition, subtraction, multiplication, and division.

To simplify an algebraic expression, we simply combine like terms. As a result, variables that are similar will be combined. The same abilities will now be combined from the similar variables.

The given expression is (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y).

As we know [tex]x^{a}[/tex] + [tex]x^{b}[/tex] = [tex]x^{a+b}[/tex]

So, (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (3×[tex]2^{3}[/tex])([tex]x^{2}[/tex]×[tex]x^{3}[/tex])([tex]y^{-1}[/tex]×y)

(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])([tex]y^{0}[/tex])

(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])

As a result, the abbreviated form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).

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The length of the segment when J is between H and K will be HJ = 21 and JK = 12.

From the information given, J is between H and K and we want to use the segment addition Postulate to solve for x.

It should be noted that:

HJ=4x+9,

Jk=3x+3,

HK=33

Therefore, we will equate the values. This will be:

4x + 9 + 3x + 3 = 33

7x + 12 = 33

Collect like terms

7x = 33 - 12

7x = 21

Divide

x = 21 / 7

x = 3

HJ=4x+9, = 4(3) + 9 = 21

Jk=3x+3 = 3(3) + 3 = 12

Therefore, the length of the segment when J is between H and K will be HJ = 21 and JK = 12.

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The logarithmic expression changed by the base formula is ㏒₁₀9/㏒₁₀4.

A number's logarithm is the exponent that a fixed value known as the base should be raised in order to generate that number. For example, because 1000 is 10 to a third power, the log of 1000 to base 10 is 3.

Some rule of the logarithmic functions are-

Now, as per the sated condition of the log function;

= log₄9

Now, use the Base Rule to re-write the expression;

= ㏒ₓ9/㏒ₓ4

or, for the base 10 this could be written as;

= ㏒₁₀9/㏒₁₀4

Therefore, the given logarithmic expression converted by the base formula is ㏒₁₀9/㏒₁₀4.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{14}~,~\stackrel{y_1}{21})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +14}{2}~~~ ,~~~ \cfrac{ y +21}{2} \right) ~~ = ~~\stackrel{midpoint}{(41~~,~~50)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +14}{2}=41\implies x+14=82\implies \boxed{x=68} \\\\\\ \cfrac{ y +21}{2}=50\implies y+21=100\implies \boxed{y=79}[/tex]

for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.

We are given the equation:

- 7 + 4 u = - 35

We need to solve the equation for u.

- 7 + 4 u = - 35

Add 7 to both the sides, we get that:

- 7 + 4 u + 7 = - 35 + 7
4 u = - 28

Divide both the sides by 4, we get that:

4 u / 4 = - 28 / 4

u = - 7

Therefore, for the equation - 7 + 4 u = - 35, we get the value of u after solving it as - 7.

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The measure of angle <3 is 105 degrees

The diagram that completes the question is added as an attachment

The angle is given as

<6 = 75

From the diagram, we have

<3 + <6 = 180 degrees

The above is true by the sum of internal angles between parallel lines

So, we have

<3 + 75 = 180

Subtract 75 from both sides of the equation

So, we have

<3 + 75 - 75 = 180 - 75

Evaluate the like terms

So, we have

<3 = 105

Hence, the measure of angle <3 is 105 degrees

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In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.

Now,

In  [tex]e^{2x}=12[/tex], taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(12)[/tex]

=> 2x = 2.48 (approx)

=> x = 1.24

Hence, In [tex]e^{2x}=12[/tex], x = 1.24, by the properties of logarithm.

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Answer:1 hour 30 minutes

Step-by-step explanation:8 kilometres are compete in an hour, plus another 4 kilometres (to make 12 total) is half of that, so adds another half an hour

The time it will take the man 1.5 hours to cover a distance of 12 km, travelling at the same speed.

Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.

The speed formula is speed = distance / time.

We are given that;

Distance = 12 km

Speed = 8 km/h

Now,

Plugging these values into the formula for time, you get:

time = 12 / 8

time = 1.5 hours

Therefore, by the given speed the answer will be 1.5 hours.

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The simplification of the given expression using laws of Indices is :

[tex]\frac{y^{14}}{z^{14}}[/tex]

How to use Laws of Indices?

We want to simplify the expression y raised to the negative second power times z raised to the third power end quantity over quantity z raised to the negative fourth power times y raised to the fifth power end quantity all raised to the negative second power.

The above can be expressed as :

[(y⁻² * z³)/(z⁻⁴ * y⁵)]^(-2)

Collecting like terms and When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence :

= [(y⁻² * z³)/(z⁻⁴ * y⁵)]²

= [(z⁻⁴ * y⁵)/(y⁻² * z³)]²

= [(z⁻⁴/z³) x (y⁵/y⁻²)]²

= [z^{-4-3} x y^{5+2}]²

= [z^{-7} x y^{7}]²

Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is :

= [tex][\frac{y^{7}}{z^{7}}]^{2} = \frac{y^{14}}{z^{14}}[/tex]

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Answer: C.

Step-by-step explanation:

Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.

It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.

In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.

Therefore, it should be noted that 8.33 will be:

= 8 + 1/3

It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...

Therefore, the appropriate fraction for 8.33 will be 8 1/3.

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Answer: 6

Step-by-step explanation:

4 9/10

explanation:

1: Simplify both sides of the equation.

x+−2/5=9/2

2: Add 2/5 to both sides.

x+−2/5+2/5=9/2+2/5

x=4 9/10

Answer to this question is:

Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,0)

Set-Builder Notation:{x|x<0}

The set of all valid y values constitutes the range.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (-∞,0),{x|x<0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is -1/2x²

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Step-by-step explanation:

the range of a function is the interval or set of all valid y (function result) values.

so, what values is this function creating ?

we see that y never gets larger than -4.

but it will clearly go and go and go ... further down without any limit.

so, the range is

-infinity < y <= -4

Answer: 6912

Step-by-step explanation:

96x12=1,152

1,152x6=6912

The elephant can move 53.2 meters if it is charged for 1 minute.

Given,

The time that the elephant charged = 15 seconds

The distance that the elephant can travel by this charge = 13.3 meters

We have to find the distance moved by the elephant if it is charged for 1 minute:

That is,

15 seconds = 13.3 meters

Then,

1 minute (60 seconds) = x

Therefore;

15 × x = 13.3 × 60

x = (13.3 x 60) / 15

x = 798 / 15

x = 53.2

That is, the elephant can move 53.2 meters if it is charged for 1 minute.

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The sun is [(1.974) * (10^1)] times farther from Neptune, than Mercury, mentioned in scientific notation.

As per the question statement, there is no information provided about the actual distance of the sun from Neptune, or from Mercury. Hence, let us consider that the actual distance of the sun from Neptune is [4.5 * (10^9)] kilometers, while that from Mercury is [2.28 * (10^8)] kilometers.

We are required to calculate the number of times, which the sun is times farther from Neptune, than Mercury, and express our desired answer in proper scientific notation.

Considering that, the sun is "x" times farther from Neptune, than Mercury, we can state that,

[{2.28 * (10^8)} * x] = {4.5 * (10^9)}

or, x = [{4.5 * (10^9)}/{2.28 * (10^8)}]

or, x = [{4.5 * 10 * (10^8)}/{2.28 * (10^8)}]

or, x = [{45 * (10^8)}/{2.28 * (10^8)}]

or, x = (45/2.28)

or, x = 19.7368

or, x = 19.74

or, x = [(1.974) * (10^1)]

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Answer: 6.30

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7

The sweets in jar B in the box with Amir will be 190 sweats.

From the information, Jar A contains 205 sweets. Jar c contains 175 sweet. Also, jar a has the most sweets and Jar c has the least of sweets.

The deets in jar B will be:

= (205 + 175) / 2

= 380 / 2

= 190

Therefore, the sweets in jar B in the box with Amir will be 190 sweats.

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Answer:  f(x) = | x |

Step-by-step explanation:

when transforming and translating a function, you use the form a | x - h | + k  

a= vertical shrink/stretch factor

h = horizontal movement ( right or left)  

k = vertical movement ( up or down )

So a = 1/2  h = 0 and k =2

g(x) = 1/2 | x-0 | + 2

g(x) = 1/2 | x | + 2    [which means vert shrink of 1/2 and up 2 units ]

Since no line segment or reference diagram is provided in the question statement, considering ourselves a line as shown in the picture attached hereby, another name of the line "l" is UM.

As per the question statement, we are required to determine another name of the line, but no no line segment or reference diagram is provided, on whose basis, we were supposed to answer. Hence, we consider a line ourselves, as shown in the picture attached hereby, and then try to answer as per the question statement,

From the picture attached hereby, we can clearly see that, although the line "l" is a ray, it has two points "U" and "M" at the extremes, i.e., points U and M lie on the line. Hence, line "l" can be referred to as "UM" also.

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The questions tests on indices. Write 27 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 27 = 3×3×3

27 = 3^3

(27^3)^(1/3) = 3^(3×1/3) = 3

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