Very confused how to do this please help

In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.

Now,

In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.

=>  [tex]log_e(e^{2x})=log_e(10)[/tex]

By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]

=> [tex]2x(log_e(e))=ln(10)[/tex]

Also, as [tex]log_e(e)[/tex] = 1,

=> 2x (1) = ln(10)

=> 2x = 2.302 (approx)

=> x = 1.151

Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.

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An equation for the likelihood that Gordon does not win, in the form of such a combined single fraction:

= [tex]$\frac{4}{n+4}$[/tex]

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 as well as 1, where 0 denotes the event's impossibility and 1 represents certainty.

The addition rule, the multiplication rule, and indeed the complement rule are the three main rules related with basic probability.

Formulate based on the provided conditions:

[tex]$1-\frac{n}{n+4}$[/tex]

Look for the common denominator as well as write additional numerators above it denominator:

[tex]$\frac{n+4-n}{n+4}$[/tex]

Rearrange and collect related terms:

[tex]$\frac{(n-n)+4}{n+4}$[/tex]

Gather coefficients for similar terms:

[tex]$: \frac{(1-1) \times n+4}{n+4}$[/tex]

The product of two polar opposites is 0:

[tex]$: \frac{0 n+4}{n+4}$[/tex]

Use the Multiplication Zero Property:

[tex]$\frac{4}{n+4}$[/tex]

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Answer:

1/243

Step-by-step explanation:

The value of the expression sec (-π) is equal to -1 if the given expression is undefined.

As given in the question,

Given expression: sec (-π)

Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)

Hypotenuse = √ (-1)² + 0²

                     = 1

Value of the expression is given by

sec α = Hypotenuse / Base (x-coordinate)

⇒sec(-π) = 1 / -1

⇒sec(-π) = -1

Therefore, the value of the expression sec (-π) is equal to -1.

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Answer:

350

Step-by-step explanation:

Okay, so we have a total of 639 tickets that they were sold. Using both students and adults tickets.

And also we know that the students r 61 fewer than the adults. So X minus 61.

X -61 = 289.

350 -61= 289

It's gonna be a total of 289. And we can check our results, X plus Y. So 350 plus 289. It's gonna be a total of 639.

The measured angle ABD=24° and ABC=71°

The figure in the question is either a triangle or a quadrilateral, but this has not been stated. It is possible to solve this regardless of shape. The accompanying graphic shows the two potential shapes and angles.

Now, based on the information provided, we may deduce that line BD divides angle ABC into two parts: Angle ABC is equal to angle ABD plus angle DBC.

Additionally, we know that angle DBC is 47 degrees and angle ABC is 1 degree less than 3 times angle ABD.

Angle ABC Equals 3x-1 if angle ABD is x.

Angle ABC also equals Angle ABD plus Angle DBC.

Changing the values in the equations above 3x-1 = x+47 ⇒ 2x = 48⇒ x = 24

Angle ABD thus equals 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree

∴∠ABD=24° and ∠ABC=71°

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Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. x<3 is the inequality describes all the solutions to 11(3 - x) < -2x + 6

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The given inequality is 11(3 - x) < -2x + 6

We need to separate the variable x.

11(3 - x) < -2x + 6

33-11x<-2x+6

Let us shift -2x from RHS to LHS and 33 from LHS to RHS

2x-11x<6-33

Divide both sides by -9

-9x<-27

x<3

Therefore the solution to inequality 11(3 - x) < -2x + 6 is x<3.

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Simplify the expression by applying the index rule: a^mx a^n = a^m+n.

y¹/₂ . y³/₁₀

y¹/₂ . y³/₁₀ = y¹/₂ +³/₁₀

¹/₂ +³/₁₀ = 4/5

y¹/₂ +³/₁₀ = y^ 4/5

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Answer:

For 2 more panes of glass it will cost $5.70.  

Step-by-step explanation:

To find the price of each pane of glass you take the total price/ total panes of glass.  

25.65/ 9 = $2.85.

If he wanted one more pane of glass it would be $2.85 but since you asked for two you multiply by 2 and get $5.70.  Hope this helps!

Exponential Form

We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.

So, we use the following method to write the given expression in exponential.

Expression 1 = ⁴√x³

Expression 2 = ⁵√y⁴

Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)

similarly, we can write the second equation as

Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)

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Answer:

LCD = 30

Equivalent Fractions with the LCD

1/10 = 3/30

1/6 = 5/30

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/10, 1/6

For the denominators (10, 6) the least common multiple (LCM) is 30.

LCM(10, 6)

Therefore, the least common denominator (LCD) is 30.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/10 = 1/10 × 3/3 = 3/30

1/6 = 1/6 × 5/5 = 5/30

Answer:

the answer is 4 hundreds because starting from the decimal point is hundreds

The side of square is (B) 5.7m

We are given the formula relating side and area of square. Using the mentioned formula to find the value of side of square.

Side² = Area

Rewriting the equation according to side of the square -

Side = √Area

Keep the values in formula to find the value of side of square

Side = √32

Finding square root of the number to find the value of side of square

Side = √(8×4)

Side = √(4×2×4)

Side = 4√2

Side = 4×1.414

Performing multiplication  to find the value of side of square

Side = 5.66

Side = 5.7 meters

Hence, the side of square is (B) 5.7m

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if the point I is between points H and J, then the numerical length of hj is 14 units

The given parameters are

IJ= 3x + 3

HI = 3x - 1

HJ = 3x  + 8

The above implies that the point I is between points H and J

So, we have

HJ = HI + IJ

Substitute the known values

3x + 8 = 3x + 3 + 3x - 1

Evaluate the like terms

3x = 6

Divide by 3

x = 2

Substitute x = 2 in HJ = 3x  + 8

HJ = 3 x 2 + 8

Evaluate

HJ = 14

Hence, the numerical length of hj is 14 units

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The constant term of this polynomial function with real coefficients will be - 240.

We are given the zeroes of the equation as:

16 and 1 - 2i

Now, we know that, the imaginary root are always in a pair, so the third root will be:

1 + 2i

This means that the factors of the cubic polynomial will be:

(x - 16)

(x - [1 - 2i])

(x - [1 + 2i])

The leading coefficient is 3, so the polynomial function will be:

y = 3 (x - 16) (x - [1 - 2i]) (x - [1 + 2i])

Now, the constant term will be:

3 (- 16) (1 + 2i) (1 - 2i)

( - 48) (1 - 4i²)

= ( - 48) (5)

= - 240

Therefore, the constant term of this polynomial function with real coefficients will be - 240.

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a. 3.5 x 4.1 (3.5 ×2.8) = -0.7

b.  2.5+ (-4.1) + [(−2.3) × (-1.1)] = 4.29

c. [-5.5 (-6.5) ÷ 2.4]+ (-1.1) = -0.5

Hence the required parentheses are added to make the statement true.

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Answer:

I'm assuming you inserting the variable x was a mistake.

Step-by-step explanation:

The least common multiple of 18 and 42 is 126.

[tex]\bold{Step-by-step}[/tex]

[tex]\mathrm{"LCM"}[/tex]

[tex]18 \times 7 = 126\\42 \times 3 = 126[/tex]

Any concerns, let me know, have a great day!

The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

The complete question is added as an attachment

The coordinates of the triangle are given as

R = (-4, 1)

S = (-4, 4)

T = (-2, 1)

The transformation is given as

The rule of the transformations is

(x, y) = 3(x, y)

So, we have

R' = 3 * (-4, 1) = (-12, 3)

S' = 3 * (-4, 4) = (-12, 12)

T' = 3 * (-2, 1)= (-6, 3)

Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)

See attachment for the image of the transformation

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Two or more expressions with equal sign is called as Equation. If mWVY = 70 is an angle then mYVX =165 we get by solving the equation x-13=70.

Two or more expressions with equal sign is called as Equation.

mWVY = 70

From the figure we can observe that mWVY =x-13

By this we form an equation

x-13=70

x-13=70

x=70+13

x=83.

So value of x is 83.

Now mYVX=2x-1

2(83)-1

166-1

=165

Therefore mYVX is 165 degree when  mWVY = 70.

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Answer:1314 or 13.14%

Step-by-step explanation:yes

Answer: 90 miles.

Step-by-step explanation:

Since 12 is 1/5 of an hour, you can simply multiply 18 by 5 to get 90.

Answer:  x  ≤ 4.5

Step-by-step explanation:

Since there is a closed circle on 4.5 and the ray is going left we know that x is ≤ 4.5

The value of x for the equation log₇343=x will be 3.

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties.

These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

For log₇343=x

It can be expressed in the form of -

343 = 7ˣ

It can be further expressed as -

7³ = 7ˣ

As base is same,

x = 3

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Answer:

A

Step-by-step explanation:

if it is meant literally as stated (lead AND nickel), then the check was only for both to be present.

and then A is the correct answer (L n N : intersection of both sets).

if it would have the typical meaning (we say we check for L and A, but mean inclusive "or" : either L or N or both), then B would be correct.

The fact that $45 is enough to make bracelets for 10.44 persons means that the we can make bracelets for 10 friends

What is the total necklace cost function?

The total cost of necklaces that can be made within the total budget of $45 can be modeled using a straight-line equation, which considers the fixed cost of necklace supplies of $21.50 and the total variable cost of supplies, the cost per necklace multiplied by the total number of necklaces possible, defined as x

45=21.50+2.25x

let solve for x to determine whether we can make bracelets for 10 friends

45-21.50=2.25x

23.50=2.25x

x=23.50/2.25

x=10.44

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Based on the information, it should be noted that there's an increase in percentage of 30%.

Based on the information, it should be noted that the following can be illustrated:

Original amount = 30

New amount = 39

Therefore, it should be noted that the change in percentage will be:

= Change in amount / Old amount × 100

= (39 - 30) / 30 × 100

= 9/30 × 100

= 30%

Therefore, there's a increase in percentage of 30%.

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The slope of the line is 1 / 3

The slope of a line is a measure of its steepness.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

Mathematically, the slope of a line can be described as follows;

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Let's take two points from the graph

(0, 2)(3, 3)

where

x₁ = 0

x₂ = 3

y₁ = 2

y₂ = 3

Hence,

slope = 3 - 2 / 3 - 0

slope = 1 / 3

Therefore, the slope of the line is 1 / 3

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