find the missing side length, n. ABC​

The value of the function at x = 4 is 8.79.

Tangent line approximation is the approximation of any function using a linear function. It is also called as linear approximation.

It allows us to approximate the value of a general function with a more simpler linear function.

Given that,

f(1) = 2

f'(x) = \(\sqrt{x^{2} +2cos x + 3}\)

We have the formula for linear approximation as,

f(x) = f(a) + f'(a) (x - a)

Here x = 4 and a = 1

f(a) = f(1) = 2

f'(a) = f'(1) = \(\sqrt{1^{2} +2cos 1 + 3}\) = 2.254

Substituting,

f(4) = 2 + (2.254) (4 - 1)

     = 8.762 ≈ 8.79

Hence the value of f(4) is 8.79.

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The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula \(A=\frac{1}{2}ap\) to find the area of the base, where a is the apothem and p is the perimeter, we get \(A=\frac{1}{2}(0.87)(6)=2.61\)

So, using the formula \(V=Bh\), we get the volume to be \(2.61(2)=5.22 \text{ m}^{3}\)

Answer:

*does

Step-by-step explanation:

Answer:

92?

Step-by-step explanation:

2x9=18 100-18+10=92

\(\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}\)

By simplifying answer is \(\frac{-3}{13}\) in decimals -0.230769

Here, we have done addition, subtraction, multiplication and division.

\(\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}\\\)

First, We will do Multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

\(\frac{-18}{91} +\frac{3}{13}-\frac{\frac{24}{13} }{7}\)

Now, We will do the division

Basically, dividing is the act of dividing anything into equal sections or groups.

\(\frac{-18}{91} +\frac{3}{13}-\frac{24 }{91}\)

Now, We will do the subtraction and Addition

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

The reverse of adding in mathematics is called subtraction. When a specific number of objects from a group are removed, subtraction is used to determine how many objects are still present in the group.

\(\frac{3}{13}-\frac{6 }{13}\\\frac{-3}{13} \\\)

Therefore, the simplified answer is  \(\frac{-3}{13}\) in decimals -0.230769.

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Given:

Then:

An equation is formed of two equal expressions. Your normal hourly rate is $9.8 per hour.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the normal hourly rate be represented by x, therefore, the work-over hourly rate is 1.2x.

Given that You work 46 hours this week and earn $462.56. Now, since you earn 1.2 times above 40 hours, therefore, we can write,

Total earnings = Earning for 40 hours + Earning for above 40 hours

462.56 = 40x + (46 - 40)(1.2x)

462.56 = 40x + 6(1.2x)

462.56 = 40x + 7.2x

462.56 = 47.2x

x = 462.56 / 47.2

x = 9.8

Hence, your normal hourly rate is $9.8 per hour.

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Answer:

\( \frac{7}{24} \)

Step-by-step explanation:

\( \frac{1}{4} < x < \frac{1}{3} \)

\( \frac{3}{12} < x < \frac{4}{12} \)

Let x = 3.5/12 = 7/24.

Answer: Each can of soda costed $1.50

Step-by-step explanation:

The total cost was $8

Xavier's bought 4 snacks; each $1.25

4 x 1.25 = $5

How much for 2 cans of soda?

Well we know how much the snacks were ($5) and the total cost was $8, so the 2 cans costed $3 because 5 + 3 = 8. But how much did each can cost? Each can costed $1.50 because if the 2 cans costed $3, and we wanted to know how much 2 costed, we would have to divide 3 by 2 which is 1.50. So each can costed $1.50

The value if T(290) is 330.6

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Given:

T(x) = x + 0.14x

T ( 290)= 290+ 0.14* 290

            = 290+ 40.6

           = 330.6

Hence, the value of T(290) is 330.6.

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Answer:

V≈18.63m³

Step-by-step explanation:

V=ABh

3=6.5·8.6

3≈18.63333m³

Answer:

[(5z+3 -3z)5z+3 - 3z

combine 5z and _3z to get 2z

(2z+3)x5z +3 - 3z

use the distributive property to multiply 2z + 3 by 5

(10z + 15)z + 3 - 3z

use the distributive property to multiply 10z+15 by z

10z2+15z+3-3z

combine 15z and -3z to get 12z

10z2+12z+3

Step-by-step explanation:

Answer:

When y = 84

X = 9

Step-by-step explanation:

\(\frac{6}{56} = \frac{x}{84} \\\)

To find x, cross multiply by doing (84 x 6) and (56 x X)

You should have 504 / 56x

Divide 504 by 56 to find x.

Answer:

my buttholw

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

10 minutes

Step-by-step explanation:

t × s = d

if they catch up distance is equal and time is except for 5 minute difference

therefore s × t = s × t

convert minutes to hours

(a+5)/60 and a/60

60 × (a+5)/60 = 90 ×a/60

times both sides by 60

60a+300=90a

300=30a

a=10

Answer:

y=145°, x=35°

Step-by-step explanation:

y = 145° (vertically opposite angles)

x + y = 180°(linear pair)

x + 145° = 180°

x = 180° - 145°

x = 35°

hope you understood!

Answer:

Step-by-step explanation:

xy + 2z = (-2)*4 + 2*(-5)

            = -8 + (-10)

            = -18

Answer:

The value is -18

Step-by-step explanation:

Numerical Value of Expressions

We are given the expression

xy + 2z

It's required to find its value for

x=-2

y=4

z=-5

Substituting:

(-2)(4) + 2(-5)

Operating:

-8 + (-10)

-8 - 10

-18

The value is -18

Answer:

Step-by-step explanation:

EXPLANATION

If we dilate the figure with a scale factor of 4 the answer is the option because when

As 4 is the scale factor, the distance of the image to the center must be 4*-2= -8 and 4*5= 20

Therefore, the image must be on the point (-8,20)

we know the radius has a diameter of 26 cm, so its radius must be half that, or 13 cm.

\(\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=13 \end{cases}\implies A=\pi (13)^2 \\\\\\ A=(3.14)(13)^2\implies A=530.66~cm^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=13 \end{cases}\implies C=2\pi 13 \\\\\\ C=2(3.14)(13)\implies C=81.64~cm\)

Check the picture below.

Answer:

t = ±2.179

Step-by-step explanation:

Given:

Regression equation = Y = 30 + 2.56X

Sample size, n = 14

Standard error, e = 0.97

Significance level, \( \alpha \) = 0.05

Required:

Find the critical value

At level of significance = 0.05

Degrees of freedom, df = n - 2 = 14 - 2= 12

Find critical value:

Using t table, two tailed, df = 12, we have:

\( t_\alpha_/_2_, _d_f = t_0_._0_2_5_,_1_3 = 2.179 \)

Therefore, the critical value,

t-critical = ±2.179

In this exercise we will use the knowledge of degrees of freedom and the data reported in the exercise to calculate the critical temperature of the system, so:

\(t-critical = +/- 2.179\)

Given in the exercise we have to:

in this exercise we want to find the critical value in this way, we will have that it will be:

Using t table, two tailed, df = 12, we have:

\(T_{\alpha /2} , df = t_{0.025,13)= 2.179\)

Therefore, the critical value corresponde to;

\(t-critical = +/- 2.179\)

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actually the answer is yellow

The number of oranges that  Carlos bought is n - 8. n is variable.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

Any alphabet from a to z can be used for these variables. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are used in equations.

Given that Frank bought n oranges. Carlos bought 8 fewer oranges than Frank.

The number of oranges that Frank bought is more than the number of oranges that Carlos.

The number of oranges that Carlos bought is n - 8.

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Answer:

b just took the test and i put c trust me it is b

Step-by-step explanation:

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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Answer:

The answer is C. 16.65 Hope that helps :)

45 percent of 37 is equal to 16.65. The correct answer is C) 16.65.

To find 45 percent of 37, we can multiply 37 by 0.45 since 45 percent is equivalent to 0.45 as a decimal.

37 * 0.45 = 16.65

Therefore, 45 percent of 37 is equal to 16.65.

The correct answer is C) 16.65.

The calculation represents taking 45 percent (or 0.45) of the value 37, resulting in the product 16.65. This means that if you were to take 45 percent of 37, you would obtain the value 16.65. It's essential to understand how to convert percentages to decimals to perform accurate calculations involving percentages.

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Answer:

No, Dale Isn't correct because 3:5 is greater than 2:10

Step-by-step explanation:

3:5 and 2:10 is the same as in \(\frac{3}{5}\)  and \(\frac{2}{10}\)

First Find the least common denominator or LCM of the two denominators:

LCM of 5 and 10 is 10

Next, find the equivalent fraction of both fractional numbers with denominator 10

For the 1st fraction, since 5 × 2 = 10,

\(\frac{3}{5} =\frac{3*2}{5*2} =\frac{6}{10}\)

Likewise, for the 2nd fraction, since 10 × 1 = 10,

\(\frac{2}{10} =\frac{2*1}{10*1} =\frac{2}{10}\)

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

\(\frac{6}{10} >\frac{2}{10} Or\frac{3}{5} >\frac{2}{10}\)

Hence, \(\frac{3}{5}\) is Greater than \(\frac{2}{10}\)

Hence, 3:5 is Greater than 2:10

Answer:

According to Charles' Law the order of arrangement of the location where the balloon has the smallest size to the location where the balloon has the largest size is given as follows;

A freezer < A cold refrigerator < A normal room temperature classroom < A warm cupboard

Step-by-step explanation:

The parameter of the balloon Katie blows are;

The amount of air in the balloon = Fixed (constant)

The initial size of the balloon = The length of the measured string

The locations in which the balloon can be placed = A freezer, a warm cupboard, a cold refrigerator, a normal temperature classroom

The size of the balloon is given by the volume of the balloon

according to Charles' Law, the volume of a given mass of gas is directly proportional to its temperature

Mathematically, Charles law can be expressed as follows;

V ∝ T

Therefore, as the temperature to which the balloon is subjected decreases, the volume decreases

The locations arranged in order of increasing temperature is given as follows;

Freezer < Cold refrigerator < Normal temperature classroom < Warm cupboard

Given that Katie blow's the balloon in a normal temperature classroom, according to Charles Law, we have;

The temperature of the air in the balloon decreases largely in a freezer, therefore, the size of the balloon largely decreases

The temperature of the air in the balloon increases in a warm cupboard, therefore, the size of the balloon increases

The temperature of the air in the balloon decreases slightly in a cold refrigerator, therefore, the size of the balloon decreases

The temperature of the air in the balloon remains the in a normal temperature classroom, therefore, the size of the balloon remains the same

The size of the balloon reduces the most in a freezer

The size of the balloon increases in a warm cupboard

The size of the balloon decreases slightly in a cold refrigerator

The size of the balloon remains the same in a normal temperature classroom.

25.42 marked down by 33 % is 17.0314.

This is a question of percentages.

Percentage

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Percentages have no dimension. Hence it is called a dimensionless number.

33 % of 25.42 is given by:-

(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886

25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.

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