So basically what you have to do is subtract the above ground level (1) with ground level (4) and you’ll get 3 which is negative bc it counts as below ground level . Now that the car rises 13 meters subtract 13-3= 10 and add it with the other ground level 6 meters . 10-6=4

The value of the expression log₃9 is 2.

The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.

Log a to the base b can be written as- log a/ log b.

Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a

Here, we are given a logarithmic expression- log₃9

We can expand this as-

log₃9 = log 9/ log 3

= log [tex]3^{2}[/tex]/ log 3

= 2 log 3/ log 3

= 2

Thus, the value of log₃9 is 2.

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The value of the x is 1 in the linear equation. Thus, option C is correct.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is:

4x−3=−12x+13

Then

we have to solve it

4x−3=−12x+13

4x+12x = 3+13

16x = 16

x = 16/16

x =1.

When we put x =1 in the given equation and then i satisfy the equation and give same values after calculation.

So, The value of the x is 1 in the linear equation. Thus, option C is correct.

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Answer: 96%

How to Solve

Formula:

y ÷ x *100
Substitute
=> 24 ÷ 25 * 100

Lets Multiply 24 * 100 (or you can divde 24 and 25 then multiply with 100. do as you're convenience, answer will remain)
Answer 2400

Now As our formula says divide 2400 by 25
Answer  96

Hence 96%

So, 24/25

as a percentage is 96%

All done!

Answer:

96%

Step-by-step explanation:

First, divide 100 but 25 (the denominator) and you get 4. This means that to get a number over 100, which is a percentage you need to multiply the initial fraction by 4. You get 96/100, and you can remove the 100 to get 96%

Solution of this polynomial equation is x = 4

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

2x = 8

=> 2x / 2 = 8 /2

=> x = 4

Thus solution for given equation is x = 4.

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For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25

Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.

Step 2: balance the arguments.

Step 3: Solve the resultant equation.

Step 4: Double-check your answers.

Given,

1/2 log x + log 4 = 2

log x^(1/2) + log 4 = 2

using logₐ(m.n) = logₐ(m) + logₐ(n)

log e (4 (x^1/2)) = 2

e² = 4x^(1/2)

7.38 = 4√x

Squaring on both sides -

54.4644 = 16x

x = 54.4644 / 16

x = 34,040.25

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The exponential model for the given data set is [tex]y(x) = 70 + (110)e^{-0.135x}[/tex].

Given that cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F and the table shows temperature readings for the cake and the room temperature is 70°F.

Temperature at time = 0 min, y₀= 180° F

Ambient (room) tempertaure = y₁ = 70° F

Using Newton's cooling method,

y(x) = y₁ + (y₀ - y₁)e⁻ⁿˣ

y(x) = 70 + (180-70)e⁻ⁿˣ

y(x) = 70 + (110)e⁻ⁿˣ

Given, at x=5 min, y(5) = 126,

y(5) = 70 + (110)e⁻⁵ⁿ  = 126

Solving,  e⁻⁵ⁿ  = (126-70)/110 = 0.5091

Taking and log and solving for n,

- 5n = log(0.5091)

-5n= -0.67511

n = 0.135

Thus, the exponential model is [tex]y(x)=70+(110)e^{-0.135x}[/tex]

Hence, an exponential model for given data set when a room temperature  of 70°F is [tex]y(x)=70+(110)^{-0.135x}[/tex].

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Answer:

5 and -5

This is because these 2 spots are exactly 5 spaces from 0.

Answer:

p = - 12

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] p - 11 = [tex]\frac{1}{3}[/tex] p - 15

multiply through by 3 to clear the fractions

2p - 33 = p - 45 ( subtract p from both sides )

p - 33 = - 45 ( add 33 to both sides )

p = - 12

Answer:

-12

Step-by-step explanation:

(sorry its a bit messy - hope it helps though!)

Answer:

see explanation

Step-by-step explanation:

a rational number has the form

[tex]\frac{a}{b}[/tex] , where a and b are integers

given

0.3596 ← with 6 in the [tex]\frac{1}{10000}[/tex] place

= [tex]\frac{3596}{10000}[/tex] = [tex]\frac{899}{2500}[/tex] ← a rational number

Answer:

12

Step-by-step explanation:

[tex]\sqrt{8} * \sqrt{18} =12[/tex]

Answer:

codec log 8x + y =15

Step-by-step explanation:

have a good day!

The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.

Given that

To find

So, according to the question

we have,

                                                     = (9 ×5)/10

                                                     = 4.5 miles.

Now, from question

So, Total laps walk by your friend

             = ( Total distance walk by you)/(Total length of your friends track)

             = [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]

             = [tex]\frac{4.5\times 2}{3}[/tex]

             = 9/3 = 3

Answer:

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Answer:

Step-by-step explanation:

1/2÷4 = 1/8 = 0.125.

[tex]\cfrac{1}{2}\div -4\implies \cfrac{1}{2}\div \cfrac{-4}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{-4}\implies {\LARGE \begin{array}{llll} -\cfrac{1}{8} \end{array}}[/tex]

Answer:

is 7 more than 4 or 4 more than 7?

Step-by-step explanation:

JUST USE YOUR BRAIN!

Answer:

no

Step-by-step explanation:

of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no

The correct option is (b) square root 112 units

By using Pythagoras theorem,

where a & b = legs of triangle and c = hypotenuse

Hence:

Answer:

Step-by-step explanation:

30 and 20

The missing numbers are 17,66,13, 9 3 and 15 respectively .

The rules given to us are-

first row consist of a number which is the sum of two numbers of middle row

Third row consist of a number which is the product of two numbers of middle row

The first part

The sum of 6 and 11 is 17 and the product of 6 and 11 is 66

       17

6                11

       66

The second part

To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13

       13

4               9

       36

The third part

To find the numbers of middle row we need to find the factors of 45 that sum up to 18

The factors of 45 are 3*3*5

The factor 15 and 3 satisfy both the requirements

       18

3                15

       45

Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively

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We have expression ln a-2 ln b+1/3 ln c as a single natural logarithm

㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to express ln a-2 ln b+1/3 ln c as a single natural logarithm.

⇒ ln a-2 ln b+1/3

⇒ ㏑ (a) - ㏑ (b²) + ㏑ [tex]c^{\frac{1}{3} }[/tex]

Use the quotient property of logarithms for ln a-2 ln b

⇒ ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]

Use the quotient property of logarithms for ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]

⇒ ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

Finally, we have expressed ln a-2 ln b+1/3 ln c as a single natural logarithm ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

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The actual area of the care park in hectares is 18.75

As per the known fact, ratio of measurement on scale is equal to the ratio of measurement in real. So, writing the equation first -

Area of car park = 3 cm²

Keep the value of 1 cm in the above mentioned equation.

Area of car park = 3 × (250)²

Taking square

Area of car park = 3 × 62,500

Performing multiplication

Area of car park = 1,87,500 m²

Converting the area in hectares

10,000 m² = 1 hectare

1,87,500 m² = (1 ÷ 10,000) × 1,87,500

1,87,500 m² = 18.75 hectares.

Therefore, the actual area of the care park is 18.75 hectares.

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Decimal value                                     Scientific Notation

987,650,000                                       9.8765 × 108

Answer:Tenths

Step-by-step explanation:Hope it helps

Answer: 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

f(x) = x - 8

Step-by-step explanation:

Answer: The problem asks to solve for x. Equation B gives you the value of y, y = 2, so you can substitute 2 into Equation A for y.

Step-by-step explanation:

The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.

From the information given, the product of two factors is 1 and one of the factors is 1.

Let the other number = y

The other number will be:

1 × y = 1

y = 1

Therefore, the other number is 1

In conclusion, the correct option is B.

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We need to know about linear and proportional relationship to solve this problem. Statement 2 is true, the description shows a linear relationship and a proportional relationship.

Linear relationship is a relationship between two variables where if one increases the other increases or if one decreases the other decreases. The varibales in a linear relationship form a straight line on graph. Proportional relationship is the relationship between two variables where the ratio between pairs of different data always remains constant. In the given question, a 12 ounce cup costs $1.97, a 16 ounce cup costs $2.62 and a 20 ounce cup costs $3.27. The price of each cup increases with increase in capacity of the cup, so we can say that the cup capacity and price have a linear relationship. The ratio between each pair can be given by

12/1.97=6.10

16/2.62=6.10

20/3.27=6.10

The ratios between every pair is same, so it is a proportional relationship.

Thus we found that the description shows a linear relationship and a proportional relationship between the cup capacity and it's price, statement 2 is the right option.

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Answer:x=6 x=-3

Step-by-step explanation:

3x(x^2-3x-18)=0

   (X-6)(x+3)=0

X-6=0.      X+3=0

 +6=+6.       -3=-3

X=6.             X= -3

Answer:

75 degree

Step-by-step explanation:

35+70+75=180 degree