Please Help! In which of the following intervals does the trigonometric inequality sec(x)

Considering the definition of parallel and perpendicular line:

A linear equation o line can be expressed in the form y = mx + b.

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 9x+8y=-2. Expressed in the form y = mx + b, you get:

8y= -2 - 9x

y= (-9x -2)÷ 8

y= -\(\frac{9}{8}\)x - \(\frac{1}{4}\)

Two lines are parallel if they have the same slope. So, in this case, the parallel line has a slope of  -\(\frac{9}{8}\) and has a form of: y= -\(\frac{9}{8}\)x + b

The line passes through the point (-3, 2). Replacing in the expression for parallel line:

2= -\(\frac{9}{8}\)× (-3) + b

2= \(\frac{27}{8}\) + b

2- \(\frac{27}{8}\)= b

- \(\frac{11}{8}\)= b

Finally, the equation of parallel line is y= -\(\frac{9}{8}\)x - \(\frac{11}{8}\).

The line is y= -\(\frac{9}{8}\)x - \(\frac{1}{4}\).

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -\(\frac{9}{8}\). So:

-\(\frac{9}{8}\)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-\(\frac{9}{8}\))

slope perpendicular line= \(\frac{8}{9}\)

So, the perpendicular line has a form of: y= \(\frac{8}{9}\)x + b

The line passes through the point (-3, 2). Replacing in the expression for parallel line:

2= \(\frac{8}{9}\)× (-3) + b

2= -\(\frac{8}{3}\) + b

2+ \(\frac{8}{3}\)= b

\(\frac{14}{3}\)= b

Finally, the equation of of perpendicular line is y= \(\frac{8}{9}\)x + \(\frac{14}{3}\).

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Answer:

Dear User

Answer to your query is provided below

X = 2/7 or X = -3/2

Step-by-step explanation:

Explanation for the same is attached in image

Step-by-step explanation:

The last option 45 and 46

Answer:

its 4-5 not 45-46 \

Step-by-step explanation:

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

900

Step-by-step explanation:

Given that :

Enrollment declined by 20% from between September 1991 to September 1994

This means there was a reduction in enrollment ;

Enrollment in September 1994 = 720

Enrollment in September 1991 = x

Hence,

Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991

720 = (1 - 20%) * x

720 = (1 - 0.2) * x

720 = 0.8x

720 / 0.8 = 0.8x/0.8

900 = x

Hence, Enrollment in September 1991 = 900 enrollments

Answer:

g= - 27

Step-by-step explanation:

Answer: 16590

Step-by-step explanation:

Let p be the population proportion of high school students in the area who attend their home basketball games.

As per given,

prior p = 0.5

Margin of error E= 0.01

Criticfor z-value for 99% confidence = 2.576

Sample size will be computed as

\(n=p(1-p)(\frac{z^*}{E})^2\\\\ n= 0.5(1-0.5)(\frac{2.576}{0.01})^2\\\\=0.25(257.6)^2\\\\=0.25 (66357.76)\approx16590\)

Hence, required sample size = 16590

1) the supply and demand schedule for Blue-ray movie "Frozen is attached accordingly.

Equilibrium price and quantity are $20 and 40 units respectively.

2) At a price of $30, quantity demand  and supplied are 20 and 60 units respectively

This is an example of supply surplus.

To get the price back to equilibrium, they have to setthe price at $20 /unit

3) at $10 the quantity demand and supplied are 60 units and 20 units respectively.

This is an example of supply shortage.

increasing the price to $20 per unit will help achieve equilibrium.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

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The equation that represents a linear function is D 4x - 2 = 6.

A linear function is a function whose graph is a straight line. In general, the equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Option A (x = 1) represents a vertical line passing through x = 1. Since the slope of a vertical line is undefined

Option B (y = 12²) represents a horizontal line passing through y = 144. Since the slope of a horizontal line is zero

Option C (y = 12-1) represents a horizontal line passing through y = 11. Since the slope of a horizontal line is zero

Option D (4x - 2 = 6) can be rewritten as 4x = 8 or x = 2. This is the equation of a vertical line passing through x = 2.

Therefore, the only equation that represents a linear function is D 4x - 2 = 6.

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The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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Remember that

(mxn)*(nxk)=(mxk)

In this problem

This product is not defined

(3x2)*(3x2) is not defined

their dimensions are not compatible

The measure of angle W in the kite WXYZ is 115°

A kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides.

Given that, In kite WXYZ, m ∠ x = 90° and m ∠ z =40°.

Please refer to figure attached,

We know that, in a kite, it has two opposite and equal angles.

According to figure, here,

m ∠ W = m ∠ Y

Let m ∠ W = m ∠ Y = x

Also, the sum of interior angles of quadrilateral = 360°

Therefore,

x + x + 90° + 40° = 360°

2x = 360° - 130°

2x = 230°

x = 115°

Thus, m ∠ W = m ∠ Y = 115°  

Hence, the measure of angle W in the kite WXYZ is 115°

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Option A is correct. The value of function (f/g)(x) is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = \(\sqrt[3]{3x}\)

g(x) = 3x + 2

(f/g)(x) =  \(\sqrt[3]{3x}\)/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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The solution to the multiplication of the decimals is; 39.15

One of the ways to multiply decimals is as follows;

To multiply decimals, first multiply as if there is no decimal.

Second step is to count the number of digits after the decimal in each factor.

Last step is to put the same number of digits behind the decimal in the product.

Now, we want to multiply the decimals given as;

8.7 × 0.45

Converting them to fractions gives us;

(87/10) × (45/10)

= 3915/100

= 39.15

Thus, that is the solution to the multiplication of the decimals.

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If the given integer is positive, then it is plotted to the right of zero on the number line. If the given integer negative, then it is plotted to the left of zero on the number line.

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

17690

Step-by-step explanation:

The amount Michael owes is given by :

y = - 290x +18,560

x = number of months ; y = amount owed

Amount owed after 3 months :

Put x = 3 in the equation :

y= - 290(3) +18,560

y = - 870 + 18560

y = 17690

According to the general form of a linear equation :

y = mx + c

Where, m = slope ; c = intercept

The slope = - 290 ; Intercept = 18560

Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month

The intercept shows that the original amount borrowed is 18560

Amount Michael owes his father decreases by 290 per month.

Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer:

7 to the power of negative 8

Answer:

  7^-8 = 1/5764801

Step-by-step explanation:

The appropriate rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

So, ...

  7^-6/7^2 = 7^(-6-2) = 7^-8 = 1/5764801

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming \(a\neq o\)

First, subtract c from both the sides to get:

\(y-c=ax^{2}\)

then, divide both sides by \(a\) and transpose to get:

\(x^{2} =\frac{y-c}{a}\)

So, \(x\) must be a square root of \(\frac{y-c}{a}\)  and we can deduce:

\(x=\) ± \(\sqrt \frac{y-c}{a}\)

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Answer:

8 lions

Step-by-step explanation:

We need to subtract!!

14 - 6 = 8

Have an amazing day!!

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Step-by-step explanation:

let the number of penguins be X and the number of lions be Y. then X=14 and since there are more penguins than lions the equation will be X=Y+6

Substitute 14 instead of X. 14=Y+6

and now shift 6 to the left 14-6=Y

then the answer should be 8lions

Answer:

Tuna = 39 pounds

Red Snapper 13 pounds

Sailfish = 156 pounds

Step-by-step explanation:

T = 3x

RS = x

S = 12x

3x + x + 12x = 208

16x = 208

x = 208/16

x = 13

Tuna = 3(13)=39

Red Snapper = 13

Sailfish = (12)(13) = 156

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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Answer:

the angle between the diagonal is 0.6155 RADIANS

Step-by-step explanation:

Given the data in the question

as illustrated in the image below;

O is [0,0,0]

B is [15,0,15]

E is [15,15,15]

Now to find angle BOE

vector OB = [15,0,15]

vector OE = [15,15,15]

OB.OE = [15,0,15].[15,15,15] = 15 × 15 + 15 × 15 = 450 = |OB||OE|cos[angleBOE]

|OB| = √(15² + 15²) = √(225 + 225) = √450

|OE| = √(15² + 15² + 15²) = √(225 + 225 + 225) = √675

so

Angle BOE = cos⁻¹ (  450 / ( √450 × √675 )

Angle BOE = cos⁻¹ ( 0.81649 )

Angle BOE = 35.265°

Angle BOE = 0.6155 RADIANS

Therefore, the angle between the diagonal is 0.6155 RADIANS  

Answer:

B......................

There is no change in the y dimension