5 more than three times a number is -7

Answer:

slope = -4

Step-by-step explanation:

slope formula is

slope = y2-y1/x2-x1

as we know that from the question x1 = 3 , y1 = 0

and x2 = 2 , y2 = 4

then put these equation in the slope formula and we get slope which is equal to (-4)

(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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Answer:

x=6

Step-by-step explanation:

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

Are not

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

To see what multiple y is of x, divide y by x:

  y/x = 3/1 = 3

  y/x = 5/2 = 2.5

  y/x = 6/3 = 2

The values 3, 2.5, and 2 are not all the same, so you must conclude y is not a constant multiple of x.

If the multiple is not constant, the relationship is not proportional.

Answer:

it would be 0.4 to the power (exponent) of 3

Step-by-step explanation:

should the answer be 0.4^3

(hope this helps can i plz have brainlist :D hehe)

Answer:

1,2,4,8,16,32,64,128

Step-by-step explanation:

You just multiply the number by two to get the next number in the pattern

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Answer:

it eqals 2

Step-by-step explanation:

Answer:

x+4

Step-by-step explanation:

Answer:

\(125 \degree\)

Step-by-step explanation:

Let the unknown angle be x

As the interior angles in a triangle are added up to 180°

\(x + 25 + 30 = 180 \\ x + 55 = 180 \\ x = 180 - 55 \\ x = 125 \degree\)

Hope this helps you.

Let me know if you have any other questions :-)

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

They are collinear if they are on the same line

The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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By estimating the angle with quadrants it is within ± 10° it is about 150°.

We have I, II, III, IV quadrants.

In quadrant I the referece angle Ф is Ф.

In quadrant II the referece angle Ф is (π - Ф).

In quadrant III the referece angle Ф is (π + Ф).

In quadrant IV the referece angle Ф is (2π - Ф).

We know each quadrant is of 90°.

By observing the given angle it is in the second quadrant so must be n between 90° and 180°.

Now, half of 90° is 45°.

Therefore, (90 + 45)°.

= 135° which is in between 90° and 180°.

Again observing the angle it is closer to 180° than 90° so we estimate the angle to be about 150°.

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The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

False

Step-by-step explanation:

The angles are different degrees

Answer: false

Step-by-step explanation: dont really have an explenantion

Answer: 1. is 20.2 and 2. is 92.1 and 3 is 22.12 and 4 is 43.5 and 5 is 78.12 and 6 is 94.11 and 7 is 47.19 and 8 is 99.31 and 9 is 29.4

Step-by-step explanation: those are the answer for all your questions you welcome!

This is a probability question. Let's take note first of the important parts that we will be needing to write the probability for the problem.

Mr. Griese only chooses the sophomore class. The sophomore class has 17 males and 17 females, which means that he has a total of 34 students in the sophomore class.

To compute for the probability, we have:

For this problem, the total sample space is the total number of students of Mr. Griese in the sophomore class, which is 34 students. The number of objects is the number of female students that he has since we are looking for the probability that a female will be picked up to collect yesterday's work. He has 17 females in his class. We now substitute these numbers on the probability equation, having:

Therefore, the probability of choosing a female to collect yesterday's work in sophomore class will be P = 1/2 or 0.50.

Answer: P = 1/2 or 0.50

The solution is the point (0, 1/6) y = 1/6

Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.

In this case, the equation is in slope-intercept form (y = mx + b),

where m represents the slope (-3/4) and b represents the y-intercept (1/6).

The slope-intercept form allows us to determine various properties of the equation.

Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.

Each pair of x and y values that satisfy the equation represents a solution.

For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:

y = (-3/4)(0) + 1/6

y = 1/6

Therefore, the solution is the point (0, 1/6).

In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.

Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.

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The value of n that satisfies the given polynomial expression is 10

From the question, we are to determine determine the corresponding value of n in the simplified expression.

The given expression is

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

First, we will simplify this expression

(12x⁵ + 6x³ + x) - (x + 26)(2nx² + 1)

(12x⁵ + 6x³ + x) - (2nx³ + x + 52nx² + 26)

(12x⁵ + 6x³ + x - 2nx³ - x - 52nx² - 26)

Simplify further

(12x⁵ + 6x³ - 2nx³ - 52nx² - 26)

(12x⁵ + (6 - 2n)x³ - 52nx² - 26)

By comparison with (12x⁵ - 14x³ - 520x² - 26)

(6 - 2n)x³ = - 14x³

and

- 52nx² = - 520x²

Solve (6 - 2n)x³ = - 14x³ for n

(6 - 2n)x³ = - 14x³

6 - 2n = - 14

6 + 14 = 2n

20 = 2n

n = 20/2

n = 10

Similarly,

Solve - 52nx² = - 520x² for n

52n = 520

n = 520/52

n = 10

Hence, the value of n is 10

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Answer:

Explanation:

a) From the information given,

68 F = 20 C

212 F = 100C

Let F be the dependent variable and C be the independent variable. F would be on the y axis of the graph while C would be on the x axis. Recall, the equation of a line in the slope intercept form is expressed as

y = mx + b

where

m represents slope

b represents y intercept

The formula for calculating slope is expressed as

m = (y2 - y1)/(x2 - x1)

Considering the given values,

y1 = 68, x1 = 20

y2 = 212, x2 = 100

Thus,

m = (212 - 68) /(100 - 20)= 144/80

m = 1.8

We would find the y intercept, b by substituting m = 1.8, x = 20 and y = 68 into the slope intercept equation. We have

68 = 1.8 * 20 + b

68 = 36 + b

b = 68 - 36

b = 32

The linear model would be

y = 1.8x + 32

Replacing y with F and x with C, the linear model becomes

F = 1.8C + 32

b) The gradient is 1.8. It means that the rate of change of C with respect to F is 1.8.

c) The F intercept is the value of F when C is zero. Thus,

F = 1.8 * 0 + 32

F = 32

F intercept = 32

The F intercept is the temperature in degrees fahrenheit equal to 0 degrees celsius.

d) The C intercept is the value of C when F is zero. Thus,

0 = 1.8C + 32

1.8C = 0 - 32 = - 32

C = - 32/1.8 = - 17.78

C intercept = - 17.78

e) To convert 10 degrees to F, we would substitute C = 10 into the linear model. We have

F = 1.8 * 10 + 32

F = 18 + 32

F = 50

10 degrees celsius = 50 degrees fahrenheit

Answer:

50

Step-by-step explanation:

7850/3.14

Square root 2500

50

Answer:

DH

Step-by-step explanation:

this is just to comment to tell everyone this is multiple choice meaning it could be ad or ij togethe.

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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Answer:

d . 49

Step-by-step explanation:

180-131 ( supplementary angle)

= 49°

Answer:

=D 49

.......................

Answer:

Three to the second power

Step-by-step explanation:

Hey there!

3 square

Can be written as the following,

Three to the second power

Hope this helps :)