The point (5,2) is on the terminal side of angle theta find sec theta

The Solution of the 9x⁴ – 2x² – 7 = 0 is x = ±1, ±i √(7/9)

What are the quadratic equations?

A quadratic equation is a type of polynomial equation with degree 2 (the highest power of the variable is 2). Quadratic equations have the general form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

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Answer:

Yes. All real numbers are either rational or irrational.

Step-by-step explanation:

The set of all irrational numbers is commonly defined as the set of all real numbers that are not rational.

Let \(\mathbb{R}\) denote the set of all real numbers. Let \(\mathbb{Q}\) denote the set of all rational numbers.

For any given real number \(x\) (\(x \in \mathbb{R}\),) either \(x\!\) is rational (\(x \in \mathbb{Q}\)) or \(x\!\!\) isn't rational (\(\lnot (x \in \mathbb{Q})\), such that \(x \not\in \mathbb{Q}\) and thus \(x \in (\mathbb{R} \backslash \mathbb{Q})\).)

Assume that \(x\) isn't a rational number. By the definition of rational numbers, since \(x\!\!\) is a real number but not a rational number (\(x \in (\mathbb{R} \backslash \mathbb{Q})\),) \(x\!\) would be an irrational number.

Therefore, either \(x\) is rational or \(x\!\) is irrational. Every real number would either be rational or irrational.

The volume of the blue triangular prism is 216 cubic centimeters.

We assume that the two figures are similar, if the scale factor between the two is K, then the volume of the blue prism will be K³ times the volume of the green one.

To find the value of K, we can compare the two known sides:

4cm*K = 6cm

K = 6cm/4cm = 3/2

Then the volume of the blue prism is:

(3/2)³*64cm³ = 216 cm³

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Answer: 35 square units.

Step-by-step explanation:

- In this question you need to substitute in the given values to the triangle to fulfill the equation for the area of triangle.

Area of a triangle = \(\frac{1}{2}\) x base x height.

The base was 'x', which was 14 units.

The height was 'h', which was given as 5 units.

Substitute these into the equation.

Answer:

54 square inches

Step-by-step explanation:

\(area \: of \: kite \: = \frac{1}{2} \times product \: of \: diagonals \\ \\ = \frac{1}{2} \times 9 \times 12 \\ \\ = 54 \: {in}^{2} \)

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Answer:

-60

Step-by-step explanation:

-46-14=-60

Answer:

-46-14=-60

Step-by-step explanation:

Answer:

y = 1

x = 3

Step-by-step explanation:

First, try to eliminate one of the variables.

Steps:

1)  3x - 2y = -5

 -

   2x - 4y = 2

2)  (3x - 2y = -5)*2

    -

     (2x + 4y = 2)*3

3)   6x - 4y = -10

     -

      6x + 12y = 6

#subtract and you will get -16y = -16

4)  -16y = -16

   = y = -16/-16

   = y = 1

5) substitute the value of y...

2x - 4y = 2

2x - 4*1 = 2

2x - 4 =2

2x = 2 + 4

2x = 6

x = 6/2

x = 3

Hope you find it helpful...

please vote and mark brainliest.

To determine whether the vectors (-2,1,-1) and (0,3,1) are parallel, we need to compare their direction. If they have different directions, they are not parallel. the correct answer is option c) Not parallel.

To check if two vectors are parallel, we can compare their direction vectors. The direction vector of a vector can be obtained by dividing each component of the vector by its magnitude. In this case, let's calculate the direction vectors of the given vectors.

The direction vector of (-2,1,-1) is obtained by dividing each component by the magnitude:

Direction vector of (-2,1,-1) = (-2/√6, 1/√6, -1/√6)

The direction vector of (0,3,1) is obtained by dividing each component by the magnitude:

Direction vector of (0,3,1) = (0, 3/√10, 1/√10)

Comparing the direction vectors, we can see that they are not equal. Therefore, the vectors (-2,1,-1) and (0,3,1) are not parallel. Hence, the correct answer is option c) Not parallel.

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Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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As R² with the given operations satisfies all the vector space axioms, it is indeed a vector space.

To determine whether the set R² with the given operations is a vector space, we need to verify if it satisfies all the vector space axioms.

1. Closure under addition: (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2), which is of the same form as the original elements in R². Thus, addition is closed.

2. Commutativity of addition: (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) = (x2 + x1, y2 + y1) = (x2, y2) + (x1, y1). Thus, addition is commutative.

3. Associativity of addition: ((x1, y1) + (x2, y2)) + (x3, y3) = (x1 + x2, y1 + y2) + (x3, y3) = (x1 + x2 + x3, y1 + y2 + y3) = (x1, y1) + (x2 + x3, y2 + y3) = (x1, y1) + ((x2, y2) + (x3, y3)). Thus, addition is associative.

4. Identity element of addition: The additive identity is (0, 0), since (x, y) + (0, 0) = (x + 0, y + 0) = (x, y) for any (x, y) in R².

5. Inverse elements of addition: The additive inverse of (x, y) is (-x, -y), since (x, y) + (-x, -y) = (x - x, y - y) = (0, 0).

6. Closure under scalar multiplication: c(x, y) = (cx, cy), which is of the same form as the original elements in R². Thus, scalar multiplication is closed.

7. Distributivity of scalar multiplication over vector addition: c((x1, y1) + (x2, y2)) = c(x1 + x2, y1 + y2) = (c(x1 + x2), c(y1 + y2)) = (cx1 + cx2, cy1 + cy2) = (cx1, cy1) + (cx2, cy2) = c(x1, y1) + c(x2, y2). Thus, scalar multiplication is distributive over vector addition.

8. Distributivity of scalar multiplication over scalar addition: (c1 + c2)(x, y) = ((c1 + c2)x, (c1 + c2)y) = (c1x + c2x, c1y + c2y) = c1(x, y) + c2(x, y). Thus, scalar multiplication is distributive over scalar addition.

9. Associativity of scalar multiplication: c1(c2(x, y)) = c1(c2x, c2y) = (c1c2x, c1c2y) = (c1c2)(x, y). Thus, scalar multiplication is associative.

10. Identity element of scalar multiplication: The multiplicative identity is 1, since 1(x, y) = (1x, 1y) = (x, y) for any (x, y) in R².

Since R² with the given operations satisfies all the vector space axioms, it is indeed a vector space.

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Answer:

\(y = -2x + 4\)

Have a fantastic day!^^

For example, if the base of a parallelogram is 10 cm and the height is 5 cm, the area of the parallelogram would be 10 x 5 = 50 square cm.

The area of a parallelogram is the amount of space that it occupies in two-dimensional space. To find the area of a parallelogram, you can use the base and height of the parallelogram. The base is one of the parallel sides of the parallelogram, and the height is the distance between the base and the opposite side.

To find the area of a parallelogram without using a calculator, you can use the formula:

Area = base x height

Another way to find the area of a parallelogram without a calculator is to use the properties of parallelograms. A parallelogram can also be divided into two congruent triangles, and the area of a triangle can be found using the formula:

Area = (base x height) / 2

So, to find the area of a parallelogram without a calculator, you can divide it into two congruent triangles, find the area of one of the triangles, and then double that value to find the area of the parallelogram.

In summary, you can use the base and height of a parallelogram to find its area using the formula base x height, or you can divide the parallelogram into two congruent triangles and find the area of one of the triangles and double it to find the area of the parallelogram.

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The light will be concentrated at the focal point, which is located at a distance of (22 in) / 4 = 5.5 inches from the vertex of the paraboloid.

A reflecting telescope contains a mirror shaped like a paraboloid of revolution. The mirror in the telescope is designed to focus the incoming light at a single point called the focus.

We can use the equation of a paraboloid to find the location of the focus. The equation of a paraboloid of revolution is: z = x^2/(4f) + y^2/(4f), where f is the focal length.

We can rearrange this equation to solve for f: f = x^2/(4z) + y^2/(4z). Plugging in the given values for x, y, and z, we get: f = (22/2)^2/(4*3) + (22/2)^2/(4*3) = 121/12 + 121/12 = 242/12 = 20.17 inches. Therefore, the light will be concentrated at a point 20.17 inches from the vertex of the paraboloid.

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Answer: 430,203,663,510?

Step-by-step explanation:

four hundred thirty billion, two hundred three million, six hundred sixty-three thousand five hundred ten, into number form is :

= 430,203,663,510.

Hope this helps?

Answer:

430 ,202 ,663 ,510 this is the answer

As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

Given that it consists of sides and three vertices, a triangle qualifies as a polygon. It connects to the fundamental geometric shapes. Triangle ABC is the term used to refer to such a triangle with the points A, B, and C. When the three points are not collinear, a unique plane and triangle in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the four structures of the triangle converge are referenced to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

given

Find the smallest angle by finding the angle opposite the smallest side, then the medium-sized angle by finding the angle opposite the medium-sized side .

Then the greatest angle by finding the angle opposite the largest side when there are three side lengths available.

As side FG is the smallest side at 7, and the smallest angle is the one across from it, ∠ E.

The opposing angle,  ∠G, is the medium-sized angle, just as side EF is a medium-sized side as measured by 12.39.

As side EG is the largest side at 15, and the greatest angle is the opposite side's angle,  ∠F.

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The complete question is :-

a) Order the angle measures m∠E , m∠F and m∠EGF from least to greatest ad well as side length .

Answer:214.29

Step-by-step explanation:600 divided by 2.8

possibly the answer

Answer:

this copy and paste is to hard to read making it impossible to solve sorry.

Step-by-step explanation:

The value of the expression is 256.

Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.

For the given situation,

The expression is  $x^{6} + (y^{2} \div z^3)\cdot w^3$

⇒ \(x^{6}(\frac{y^{2} }{z^{3} } )(w^{3} )\)

Substitute $x=2$, $y=3^2$ = 9$, $z=3$, and $w=4$,

⇒ \(2^{6}(\frac{9^{2} }{3^{3} } )(4^{3} )\)

⇒ \(64+(\frac{81}{27} )(64)\)

⇒ \(64+(3)(64)\)

⇒ \(64+192\)

⇒ \(256\)

Hence we can conclude that the value of the expression is 256.

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The probability that exactly two will have this mild side effect is

\(P(X=2)=0.1229\)

Probability is defined as the likelihood that a trial will succeed or fail. The ratio of positive events to all possible outcomes is known as probability. The probability scale ranges from 0 to 1.

Given data:

The probability of all patients that will have the mild side effect is p=5%=0.05

The number of people selected is n=14

The expression for the probability that exactly two will have this mild side effect is given as,

\(P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}\)

Substituting the values in the above equation as

\(P(X=x)=^{n}C _{x} p^{x} (1-p)^{n-x}\\P(X=2)=^{14}C _{2} 0.05^{2} (1-0.05)^{14-2}\\P(X=2)=91*0.0025*0.54036\\P(X=2)=0.1229\)

Thus the probability that exactly two will have this mild side effect is

\(P(X=2)=0.1229\)

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To practice adding mixed numbers with like denominators, you can use worksheets that include problems with varying variables.

Adding mixed numbers with like denominators. Since you mentioned worksheets, I'll explain the process step-by-step, and you can apply these steps to any worksheet problems you have.

Step 1: Identify the mixed numbers and their like denominators.
In a given problem, you'll be given mixed numbers (a whole number and a fraction combined) with like denominators (same number in the denominator).

Example: 2 1/4 + 3 3/4 (Both fractions have the denominator 4)

Step 2: Add the whole numbers.
Add the whole numbers of the mixed numbers together.

Example: 2 + 3 = 5

Step 3: Add the fractions with like denominators.
Add the numerators (top numbers) of the fractions and keep the denominators the same.

Example: 1/4 + 3/4 = (1+3)/4 = 4/4

Step 4: Simplify the fraction, if needed.
If the fraction is improper (numerator is equal to or greater than the denominator), simplify it to a mixed number.

Example: 4/4 = 1

Step 5: Combine the whole numbers and simplified fractions.
Add the whole numbers from Step 2 and the simplified fraction from Step 4.

Example: 5 (whole number) + 1 (simplified fraction) = 6

Final Answer: 2 1/4 + 3 3/4 = 6

Now, you can apply these steps to any problem in your adding mixed numbers with like denominators worksheets. Good luck!

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The location of point D on the number line is -5.15625

The given parameters are:

A = 5

B = -10

AC : CB = 1 : 3

This means that

C = AC/(AC + AB) * (A - B)

This gives

C = 1/4 * (5 + 10)

Evaluate

C = 3.75

Also, we have:

BD : DC = 3 : 5

So, we have:

D = BD/(BD + DC) * (B - C)

This gives

D = 3/8 * (-10 - 3.75)

Evaluate

D = -5.15625

Hence, the location of point D on the number line is -5.15625

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a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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There are 205,379 possible 3-letter "words" when repetitions are allowed and 195,822 possible 3-letter "words" when no repetitions are allowed in an alphabet of 59 letters.

For the first case, since we are allowed to use letters more than once in a word, we have 59 choices for each of the three positions in the word. Therefore, the number of possible 3-letter "words" is simply:

59 x 59 x 59 = 59^3 = 205,379

For the second case, we can no longer use the same letter more than once in a word. For the first letter, we have 59 choices, for the second letter we only have 58 choices left, and for the last letter we only have 57 choices left. Therefore, the number of possible 3-letter "words" with no repeated letters is:

59 x 58 x 57 = 195,822

So, there are 205,379 possible 3-letter "words" when repetitions are allowed and 195,822 possible 3-letter "words" when no repetitions are allowed in an alphabet of 59 letters.

In this problem, we are asked to determine the number of different 3-letter "words" that can be formed using an alphabet of 59 letters, with and without the restriction of not being able to use a letter more than once in a word.

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Add the numbers

It can be deduced that the addition of 5 and (-5) will be;

= 5+(-5)

= 0

It can be deduced that the addition of −15 and −13 will be;

=-15-13

=-28

It can be deduced that the addition of 25 and 40 will be;

=25+40

=65

Subtract the numbers

It can be deduced that the subtraction  of  2 and  4 will be;

=2-4

=2

Divide the numbers

It can be deduced that the division  of  ÷2 and ( 4 ) will be;

=÷2  ( 4 )

=-8

By solving the above equations we get,

The answer to the given equation is

-12990

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Answer: 40

Step-by-step explanation: k12 unit test

The equation in slope-intercept form is y = x - 3

The points are drawn on the graph

The line is drawn

The solution area is shaded

The point (0, 0) is a point in the solution area

From the question, we have the following parameters that can be used in our computation:

y > x - 3

The above expression is an inequality

In a slope-intercept form, we have

y = x - 3

So, y = x - 3 is the slope-intercept form

We have

x = -1, 0 and 1

So, we have

y = -1 - 3 = -4

y = 0 - 3 = -3

y = 1 - 3 = -2

So, the table of values is

x   -1     0     1

y   -4     -3   -2

From the table, we have the points

(-1, -4), (0, -3) and (1, -2)

The points are on the graph and the line is also drawn

Also, the solution area is shaded

We have

y > x - 3

Set x = 0 and y = 0

So, we have

0 > 0 - 3

Evaluate

0 > -3

This is true

So, (0, 0) is a point in the solution area

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The graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points.

The answer is (C) Three.To determine the number of points where the graph of the equation y = x(x² - 2)(x² + x + 1) intersects the x-axis, we need to find the x-values that make the equation equal to zero.

Setting y = 0, we have:

0 = x(x² - 2)(x² + x + 1)

Since the product of three factors is zero, at least one of the factors must be zero.

1. Setting x = 0:

0 = 0(x² - 2)(x² + x + 1)

This gives us one solution: x = 0.

2. Setting x² - 2 = 0:

x² = 2

Taking the square root of both sides:

x = ±√2

This gives us two additional solutions: x = √2 and x = -√2.

3. Setting x² + x + 1 = 0:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, there are no real solutions for this quadratic equation.

In summary, we have found three different x-values where the equation intersects the x-axis: x = 0, x = √2, and x = -√2.

Therefore, the graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points. The answer is (C) Three.

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Answer:

------------------------------------------

Find prime factors of 1265.

We see it is divisible by 5 since ends with 5:

253 is not divisible by 3 or 9 since the sum of digits is not divisible by 3 or 9. It is not divisible by 7 (since 25 - 3*2 = 19 is not divisible by 7) but divisible by 11, since the sum of digits in odd places is same as the digit in the even place (recall divisibility by 11):

23 is a prime number so no more factors.

Hence the prime factorization of 1265 is: