What is the relationship between 23 and 26?

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 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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5x-12-6x=-10x+7-1

=5x-6x+10x=7-1+12

= 9x=18

=9x/9=18/9

=x=2

Step-by-step explanation:

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Answer: Your answer is 6.

Step-by-step explanation:

You need to divide 42 from 294.

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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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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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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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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Answer:

85%

Step-by-step explanation:

[tex]\frac{17}{20} * 100 = 85[/tex]

Answer:

85%

Step-by-step explanation:

See attachment for answers.

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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Using the distance between two points, it is found that she cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.

The coordinates are given as follows:

It asks if the distance that he cycles from her house to the library is at least 2/3 of 12 miles = 8 miles.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the distance between her house and the library is:

[tex]D = \sqrt{(9 - 4)^2 + (2 - 9)^2}[/tex]

D = 8.6 miles.

She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.

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

Step-by-step explanation:

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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Answer:

1.2 x. 100000

3. x. 100

=120000

300

=400

Answer:

w=17.613

l=15.613

Step-by-step explanation:

w×l=area

l=w-2

therefore w×(w-2)=575

rearrange the equation to make a quadratic

(w^2)-2w-575=0

w=-(b+ or - sqrt (b^2-4ac))/2a

a=1

b=-2

c=-575

using quadraric formula to solve

w=17.613 or -15.613

cant be -15.613

l=w-2

=15.613

Answer:

2/-9

Step-by-step explanation:

When e>1, the base - e exponential function is an increasing function.

f(x) = aˣ

Here,

So,

Therefore, when e>1, the base - e exponential function is an increasing function.

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Answer:

0.1152

Step-by-step explanation:

multiply 0.96 by 0.12 to get 0.1152.

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.

Answer:

y = -1/3x + 2

Step-by-step explanation:

The slope of a line that is perpendicular has an opposite inverse of the slope of the line given.

The slope of the line given is 3.  The opposite inverse is -1/3.

Use the slope (-1/3), the x(3) and the y(1) to find the y-intercept (b) and to write the equation of the line.

y =mx + b

1 = -1/3(3) + b

1 = -1 + b  Add 1 to both sides

2 = b

y = -1/3x + 2

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°

The rationalization of the given expression is x√3 .

We have to rationalize the denominator of the expression √36 x³/√12x ,

where x is positive.

√36 x³/√12x

= √36 x³/√12x × √12x ×√12x

= 6√(x³ × 12x)/√(12x × 12x)

= 6√(x⁴12)/12x

= √(12x⁴)/2x

= √(2 × 2 × 3 × x × x × x × x)/2x

= 2x²√(3)/2x

= x√3

The answer is x√3

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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.

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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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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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".

Answer:

115

Step-by-step explanation:

The total collection is 33408

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total = 800 seats

On Monday 2/5

So, seats= 800*2/5 = 1600/5

=320 seats

On Tuesday

seats = 800 * 4/5

=3200/5

= 640

On Wednesday

seats = 800 * 4/5

=3200/5

= 640

On Thursday

seats = 800 * 1/5

=800/5

= 160

On Friday

seats = 800 * 3/5

=2400/5

= 480

As, the ticket price is €8.7

Hence, the total collection  = 33408

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The translation of the complete question is

I need urgent help

A cinema has 800 seats: during the week the attendance was: on Monday

2/5, Tuesday 4/5, Wednesday 4/5, Thursday 1/5, Friday 3/5, Saturday and Sunday complete. The ticket price is €8.7. What was the collection of all

week?