Please help me out please please please

The logarithmic form is 2log₁₀6

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

loga where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logabc where a is the base is given as logab+logc

loga b/c where a is the base is given as logab-logac

Now it is given to us to find the logarithmic form of 36=6^2

Let us consider the base of the logarithm to be 10

thus log₁₀36=log₁₀[tex]6^{2}[/tex]

log₁₀36=2 log 6

Hence the expression becomes 2log6

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Answer:

∠ ABC = 52° , ∠ CBD = 38°

Step-by-step explanation:

the 2 angles form a right angle and sum to 90° , that is

∠ ABC + ∠ CBD = 90

4x + 4 + 5x - 22 = 90

9x - 18 = 90 ( add 18 to both sides )

9x = 108 ( divide both sides by 9 )

x = 12

then

∠ ABC = 4x + 4 = 4(12) + 4 = 48 + 4 = 52°

∠ CBD = 5x - 22 = 5(12) - 22 = 60 - 22 = 38°

Answer:

[tex]\textsf{a)} \quad g'(x)=2x-4[/tex]

[tex]\textsf{b)} \quad y=2x[/tex]

[tex]\textsf{c)} \quad x=5[/tex]

Step-by-step explanation:

Given function:

[tex]g(x) = x^2-4x+9[/tex]

Differentiate the given function with respect to x:

[tex]\begin{aligned}g(x) & = x^2-4x+9\\\implies g'(x) & = 2 \cdot x^{2-1}-1 \cdot 4x^{1-1}+0\\& = 2x^{1}-4x^{0}\\& = 2x-4(1)\\& = 2x-4 \end{aligned}[/tex]

The y-value of the function at x = 3:

[tex]\begin{aligned}\implies g(3) & = (3)^2-4(3)+9\\& = 9-12+9\\& = -3+9\\& = 6\end{aligned}[/tex]

Therefore: (3, 6).

To find the slope of the function at x = 3, substitute x = 3 into the differentiated function:

[tex]\begin{aligned}\implies g'(x) & = 2(3)-4\\& = 6-4\\& = 2\end{aligned}[/tex]

Therefore, the slope of the function at x = 3 is 2.

Substitute the found slope and point (3, 6) into the point-slope form of linear equation to find the equation of the tangent line of g(x) at x = 3:

[tex]\begin{aligned} y-y_1 & =m(x-x_1)\\\implies y-6 & = 2(x-3)\\y-6 & = 2-6\\y & = 2x-6+6\\y&=2x\end{aligned}[/tex]

To find the value of x for which the slope of the graph is equal to 6, set the differentiated function to 6 and solve for x:

[tex]\begin{aligned}g'(x) & = 6\\\implies 2x-4 & = 6\\2x & = 6+4\\2x & = 10\\x & = \dfrac{10}{2}\\x & = 5\end{aligned}[/tex]

After solving the given inequality the answer is x∈(5/6, ∞).

So,

Given: 3(2) x¹>5

Then,

Therefore, after solving the given inequality the answer is x∈(5/6, ∞).

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The simplified form of given number is 16

We are given the number 64 with exponent ²/₃

Now, as per the known fact, cube of 4 is equal to 64. As, 4 multiplied with 4 gives 16. Further multiplying 16 and 4 gives 64. So, rewriting the number using 4 as follows -

Number = [tex]4^{3(2/3) }[/tex]

Cancelling 3 from exponent as it is present in both numerator and denominator. Rewriting the number with remaining exponent to find the simplified form of the number-

Number =  4²  

Taking square of the number to find the simplified form of the number given in question

Number = 16

Hence, the simplified form of the number is 16

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The total required cost of downloading books and videos is $57.92

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are:

Cost of downloading a book = $5.99

Cost of downloading a video = $7.99

The number of books and videos downlaoded are

Books = 3

Videos = 5

So, the total cost of downloading books and videos is

Total cost = Cost of downloading a book * x + Cost of downloading a video *  y

This gives

Total cost = Cost of downloading a book * Books + Cost of downloading a video *  Videos.

This gives

Total cost = 5.99 * 3 + 7.99 * 5

Evaluate

Total cost = 57.92

So, the total cost of downloading books and videos is $57.92

Hence, the total required cost of downloading books and videos is $57.92

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Applying the definition of a midpoint, the value of x is calculated as: x = 10.

The midpoint of a segment, for example, point M, is a point that bisects a segment into two equal parts with the same measurement.

Thus, this means that:

PM = MQ

PM = 9x + 3

MQ = 11x - 17

Substitute

9x + 3 = 11x - 17

Combine like terms

9x + 3 - 11x = 11x - 17 - 11x

-2x + 3 = -17

-2x + 3 - 3 = -17 - 3

-2x = -20

-2x/-2 = -20/-2

x = 10

Thus, applying the definition of a midpoint, the value of x is calculated as: x = 10.

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The questions tests on indices. Write 125 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 125 = 5×5×5

125 = 5^3

(125^3)^(1/3) = 5^(3×1/3) = 5

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Value of the given function as a piecewise-defined function is equal to

f(x) =    -5x -10 , x ≤ -2

            5x +10 , x > -2

As given in the question,

Function as a piecewise-defined function

y = |x| = x , x≥0

            -x , x<0

Given function: f(x) = |-5x-10|

-5x -10≥0 ⇒ -5x ≥ 10 ⇒x ≤ -2

 -5x -10 <0 ⇒ -5x < 10 ⇒ x> -2

Therefore, value of the given function as a piecewise-defined function is equal to

f(x) =    -5x -10 , x ≤ -2

            5x +10 , x > -2

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The height in feet that the water from the hose hits the wall is; 7x + 12 ft

Let the height where the spray from a fire extinguisher hits the wall be denoted as x.

Now, we are told that Water from their firetruck hose hits the wall 12 feet

higher than 7 times where the spray from a fire extinguisher hits the wall.

Thus, the algebraic equation that expresses this statement is;

7x + 12

Thus, the height in feet that the water from the hose hits the wall is; 7x + 12 ft

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When he wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up is 1/4.

It should be noted that from the information, in the art class, Mr. Jacobs compared the amount of glitter left on students' plates and the dot plot shows this data

It should be noted that the least two plates of glitters will be:

= 1/4 + 2/4

= 3/4

Therefore, when e wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up will be:

= 3/4 ÷ 3

= 3/4 × 1/3

= 1/3

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Explanation:

The regression equation is in the form y = mx+b

The slope tells us how much the value of y changes each time x goes up by 1. In this case, the scores decrease by 0.624 percentage points each time x goes up by 1

You can think of it like saying

This is why the answer is 0.624. We don't type the negative sign because that is part of the term "decrease".

The heat of the sun penetrates the atmosphere and warms the Earth's surface. The warmed rEarth Radiates and this heat back into the atmosphere.The gases the surround the atmosphere such as carbon dioxide , methane , nitrous oxide and water vapour absorb some of the radiated heat and send it back to the Earth . This trapping of heat from the Sun by excess carbon dioxide and other gases present in the atmosphere is known as the greenhouse effect. The gases involved in the phenomenon are called greenhouse gases.

The 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.

The formula of the potential energy of each driver:

Replace the value of PE for driver 1 with the driver 2 formula.

Now, solve for (h) height:

Therefore, the 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.

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Answer:14.12

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

answer: they spend $27.92 on goodie bags

the hourly rate is $37.5

they spend $177.92 in total

The value of  f(x) . g(x) is [tex]2x^2+28x[/tex] by using multiplication of functions.

By considering the given functions

f(x)=4 x

g(x)=1/2 x+7

f(x) . g(x)

=4 x (1/2 x+7 )

[tex]=2x^2+28x[/tex]

A y-intercept, a horizontal asymptote, a domain (the range of x values at which the function exists), and a constant growth factor, b, are the four main characteristics of exponential functions.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.

Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

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After direct variation y = 10 when x = -3.

So,

The initial statement is y = kx

Then to find y when x = -3.

When x = -3:

Therefore, y = 10 when x = -3.

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Answer:

I think its 34 feet

Step-by-step explanation:

If you subtract 20 to get to 0 its 20, minus another 14 to get to zero is 14. Add them and you get 34 feet. Hope it helps! =)

The difference in their positions on the number line is 34 feet

from the question, we have the following parameters that can be used in our computation:

Bird = 20 feet above sea level

Fish = 14 feet below sea level

using the above as a guide, we have the following:

Bird = 20 feet

Fish = -14 feet

So, we have

Difference = 20 feet - -14 feet

Evaluate

Difference = 34 feet

Hence, the difference on the number line is 34 feet

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Answer: because if you have a argument you have all.

Step-by-step explanation:

The best estimate for the total Aisha spent organizing is; 1/2 hour

We are told that Aisha organized her books for 1/6 and her coin collection for 3/7.

Now, normally when we want to find the total, we just add both fractions in this manner;

1/6 + 3/7 = 25/42

Now, since we want to find the best estimate, we will just approximate each fraction individually to get;

1/6 hour is closer to 0 hours than 1/2 hour. Thus;

1/6 hr ≈ 0 hour

3/7 hour is closer to 1/2 hour than 0 hours. Thus;

3/7 hr ≈ 1/2 hour

Thus;

Best estimate for total spent = 0 + 1/2 = 1/2 hour

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Let [tex]n[/tex] be an integer such that

[tex]\begin{cases} n \equiv 1 \pmod 3 \\ n \equiv 3 \pmod 4 \\ n \equiv 1 \pmod 5 \end{cases}[/tex]

Note that (3, 4, 5) are mutually coprime, so we can use the Chinese remainder theorem.

Starting with

[tex]n = 1 + 3 + 1[/tex]

we adjust to

[tex]n = (1\cdot4\cdot5) + (3\cdot3\cdot5) + (1\cdot3\cdot4)[/tex]

to make computing the residues a bit easier.

• Taken modulo 3, we have

[tex]n \equiv 20 + 0 + 0 \equiv 2 \not\equiv 1 \pmod 3[/tex]

so we need to further adjust the first term by introducing the inverse of 2 modulo 3. We have

[tex]2\cdot2 \equiv 4 \equiv 1 \pmod 3 \implies 2^{-1} \equiv 2 \pmod 3[/tex]

Then

[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5) + (1\cdot3\cdot4)[/tex]

• Taken modulo 4, we have

[tex]n \equiv 0 + 45 + 0 \equiv 1 \not\equiv 3 \pmod 4[/tex]

We need another inverse; we have

[tex]3\cdot3 \equiv 9 \equiv 1 \pmod 4 \implies 3^{-1} \equiv 3 \pmod 4[/tex]

and so

[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5\cdot3) + (1\cdot3\cdot4)[/tex]

• Taken modulo 5, we have

[tex]n \equiv 0 + 0 + 12 \equiv 2 \not\equiv 1 \pmod 5[/tex]

One more inverse:

[tex]2\cdot3 \equiv 6 \equiv 1 \pmod 5 \implies 2^{-1} \equiv 3 \pmod 5[/tex]

and so

[tex]n = (1\cdot4\cdot5\cdot2) + (3\cdot3\cdot5\cdot3) + (1\cdot3\cdot4\cdot3)[/tex]

Simplifying, we have [tex]n = 211[/tex], and by the CRT we have

[tex]n \equiv 211 \pmod{3\cdot4\cdot5} \implies n \equiv 31 \pmod{60}[/tex]

which is to say [tex]n=60k + 31[/tex] where [tex]k[/tex] is an integer.

The two integers that fall between 1 and 100 occur for [tex]k\in\{0,1\}[/tex]; they are 31 and 31 + 60 = 91, and their sum is 31 + 91 = 122.

It is untrue to claim that words like grid, linear, quadrant, zone, and spiral are frequently used to refer to datum points.

A location that acts as a base or reference for the measurement of other quantities is known as a datum point. It can be located at any reference point where known or guessed coordinates can be used to make calculations or measurements.

Datum references, which the maker can choose, are used when marking out an object as a reference point from which all measurements are obtained. Accuracy can be increased and maintained by measuring from a limited selection of fixed points.

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If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.

The volume of the cone can be described as the measure of a 3-D space occupied by matter.

The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,

v = πr²h / 3

As the radius of the cone = 7 inches

Height of the cone = 28 inches

v = π(7)²28 / 3

v = (π)(49)(28) / 3

v = (π)(1372) / 3

As π = 3.14

v = (3.14)(1372) / 3

v = 4308.08 / 3

v = 1436.02 ≈ 1436 cubic inches

Hence, 1436 cubic inches of sand is calculated to fit inside the cone.

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The area of a parallelogram when the dimensions are a base of 440 miles and a height of 120 miles is 52800 miles²

It should be noted that the area of a parallelogram is calculated by multiplying the base by the height.

The dimensions are a base of 440 miles and a height of 120 miles.

The area of the parallelogram will be:

= Base × Height

= 440 × 120

= 52800 miles²

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The given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.

Notice that the given conjecture does not necessarily be always true.

To be precise; there are no reasons as to why A, B and C must be noncollinear.

1.  we are given If AB, BC, and AC are congruent, then A, B, and C and colllinear.

A,B ,C are not collinear so it will be false

Therefore, the given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.

A Counter- example of the given statement is that  A, B, C are three points that lie on the same line and so they are collinear.

2. We are given If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.

It may be true.

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