f (8^9)p = 8^18, what is the value of p? (5 points)
A 2
B 9
C 10
D 18

Thus, the measure of the angle C for the given triangle using sine rule is found as: C = 51.64.

The law of sines, often known as the sine rule or sine formula, is a formula that links a triangle's sides to the sine of its diagonally opposed angles.

You must apply the form of the sine rule in which the lengths are the numerators in order to determine the length of a side:

The formula for sine rule:

a/sinA = b/sinB = c/sinC

where the side lengths perpendicular to angles A, B, and C, respectively, are a, b, and c.

Given data:

b = 17

c = 14

angle B = 56

angle C = ?

So,

b/sinB = c/sinC

sinC = c*sinB / b

Put the values:

sinC = 14* sin (56) / 17

Sin C = 0.725

C = 51.64

Thus, the measure of the angle C for the given triangle using sine rule is found as: C = 51.64.

Know more about the sine rule

https://brainly.com/question/27174058

#SPJ1

Complete question:

Find the value of angle C (using the law of sine).

Answer:

VZ = 72

FINDING VZ:

XW / VW = VZ / YZ

48 / 24 = VZ / 36

*Simplify:

*Multiply both sides by 36:

I don't know how's that even possible, but I did the same formula and solutions the pictures below show.

Answer:

16

Step-by-step explanation:

18-7=11 2+3=5. 11+5=16

according to BODMAS rule

18 - 7 × 5

18 - 35

-17

The divergence of the vector field F is positive for y > -1/3 and negative for y <  -1/3.

To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.

Here is a sample grid of points and their corresponding vectors:

(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)

(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)

(x, y) = (0, -2) -> F(0, -2) = (0, 2)

(x, y) = (1, -2) -> F(1, -2) = (0, 2)

(x, y) = (2, -2) -> F(2, -2) = (4, 2)

(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)

(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)

(x, y) = (0, -1) -> F(0, -1) = (0, 1)

(x, y) = (1, -1) -> F(1, -1) = (0, 1)

(x, y) = (2, -1) -> F(2, -1) = (2, 1)

... and so on for other values of y and for positive values of y.

To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.

F(x, y) = (xy, x + y^2)

∂F/∂x = y

∂F/∂y = 1 + 2y

divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1

Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).

For divF > 0:

If y > -1/3, then divF > 0.

For divF < 0:

If y < -1/3, then divF < 0.

Know more about vector field here;

https://brainly.com/question/102477

#SPJ11

The quotients and remainders and equations of the polynomials are;

Q. 1 (x + 3)

Q 2. 3·x² + 2

Q 3. The remainder is 4

Q 4. y ≈ 1.4705·(x+ 3)·(x + 1)·(x + 2.06)

Q 5. y ≈ (x - 1)·(x - 2²)·(x - 4)

Q. 6. The polynomial identity is the difference of two squares

8² - 2²

Q. 7. The key features includes; x-intercepts, y-intercepts, local minimum and maximum, points, and inflection points.

The quotient of a polynomial expression is the result obtained when one polynomial is divided by another polynomial.

Q1 To find the quotient (2·x² + 12·x + 18) ÷ (2·x + 6), the numerator and the denominator can be factored as follows;

(2·x² + 12·x + 18) ÷ (2·x + 6) = (2·(x² + 6·x + 9)) ÷ (2·(x + 3))

The common factor of 2 divide each other, so we get;

(x² + 6·x + 9)/(x + 3) = (x + 3)²/(x + 3) = x + 3

Therefore, the quotient of (2·x² + 12·x + 18) ÷ (2·x + 6) is (x + 3)

Q2 To find the quotient of (6·x⁴ -15·x³ + 10·x² - 10·x + 4)/(2·x² - 5·x + 2), the polynomial long division can be used to get;

\(\documentclass{}\usepackage{}\begin{document}\[\begin{array}{c|ccccc} & 3 \cdot x^2 & & +2 \\\cline{2-6}2 \cdot x^2-5 \cdot x+2 & 6 \cdot x^4 & -15 \cdot x^3 & +10 \cdot x^2 & -10 \cdot x & +4 \\ & 6 \cdot x^4 & -15 \cdot x^3 & + 6 \cdot x^2 & & \\\cline{2-4} & & & 4 \cdot x^2 & -10 \cdot x & 4 \\ & & & 4 \cdot x^2 & -10 \cdot x & 4 \\\cline{4-6} & & & & & 0 \\\end{array}\]\end{document}\)

The quotient of (6·x⁴ -15·x³ + 10·x² - 10·x + 4)/(2·x² - 5·x + 2) is 3·x² + 2

Q.3 To find the remainder when (3·x⁴ + 2·x³ - x² + 2·x - 20)/(x + 2), we can use polynomial long division

\(\begin{document}\[\begin{array}{cccccc} & 3x^3 & -4x^2 & +7x & -12 \\\cline{2-6}x+2 |& 3x^4 & +2x^3 & -x^2 & +2x & -20 \\ & 3x^4 & +6x^3 & & & \\\cline{2-3} & & -4x^3 &-x^2 & +2x & -20 \\ & & -4x^3 & -8x^2 & & \\\cline{2-4} & & & 7x^2 & +2x & -20 \\ & & & 7x^2 & 14x & \\\cline{3-5} & & & & -12x & -20 \\ & & & & -12x & -24\\ & & & & & 4\end{array}\]\end{document}\)

(In the above long division; 3x³ = 3·x³)

Therefore;

Q. 4. The shape of the graph and points on the graph; (-3, 0), local max at (-2.6, 0.4), local min at (-1.4, -0.4), (-1, 0), indicates that the graph is a cubic function.

The x-intercepts (-3, 0) and (-1, 0) indicates that the factors of the graph are; (x + 3) and (x + 1)

The equation of the graph is therefore of the form;

y = a·(x + 3)·(x + 1)·(x - r)

The point (-2.6, 0.4) indicates;

0.4 = a·((-2.6) + 3)·((-2.6) + 1)·((-2.6) - r) = 0.4 × (-1.6) × a × (-2.6 - r) = 0.64·a·(2.6 + r)

0.4 = 0.64·a·(2.6 + r)

2.6 + r = 0.4/(0.64·a) = 1/(1.6·a)

r = 1/(1.6·a) - 2.6

Similarly, for the point (-1.4, -0.4) we get;

-0.4 = a·((-1.4) + 3)·((-1.4) + 1)·((-1.4) - r) = 1.6×(-0.4) × a × (-1.4 - r)

-0.4 = 1.6×(-0.4) × a × (-1.4 - r)

1/(1.6·a) = (-1.4 - r)

r = -1.4 - 1/(1.6·a)

Therefore;

1/(1.6·a) - 2.6 = -1.4 - 1/(1.6·a)

a ≈ 1.14705

r = 1/(1.6 × 1.14705) - 2.6 ≈ -2.06

y = 1.14705·(x + 3)·(x + 1)·(x + 2.06)

Q5. The points in the graph which includes;

The x-intercepts of a graph are; (1, 0), (4, 0) (2, 0), the graph bounces at (2, 0). The multiplicity of the factor (x + 2) is therefore 2 The graph has two local mins at (3.4, -2.8), and (1.3, -0.4) The graph is w shaped. indicates;

y =a·(x - 1)·(x - 2)²·(x - 4)

The graph is U shaped indicating a even degree polynomial

The point (3.4, -2.8), indicates that we get;

-2.8 =a·(3.4 - 1)·(3.4 - 2)²·(3.4 - 4)

a = -2.8/((3.4 - 1)·(3.4 - 2)²·(3.4 - 4)) ≈ 1

The possible equation of the graph is therefore;

y =(x - 1)·(x - 2)²·(x - 4)

Q. 6 The polynomial identity that will prove that 64 - 4 = 60 is a difference of squares; a² - b² = (a + b)·(a - b). In this case, a = 8 and b = 2 so we have;

64 - 4 = (8² - 2²) = (8 + 2) × (8 - 2) = 10 × 6 = 60

Q. 7 - Some of the key features that can be identified from higher degree polynomial graphs includes;

The overall shape is determined by the degree of the polynomial

The leading coefficient determines the direction the graph opens to (down or up)

The x-intercept are the points the graph crosses the x-axis, which are the roots of the polynomial

The local maxima and minima

The inflection points, where the concavity of the graph changes.

Learn more on graphing polynomial functions here: https://brainly.com/question/18517998

#SPJ1

Answer:

4

Step-by-step explanation:

compare the coordinates of each point:

G: (1,2)    x4→   G': (4,8)

H: (3,0)   x4→   H': (12,0)

I:  (2,-2)   x4→    I':  (8,-8)

As you can see the scale factor is 4

Each x and each y coordinate of the small triangle GHI is multiplied by 4 to get the image triangle G'H'I'

Answer:

C. 50 degrees

Step-by-step explanation:

Angle EDG is 90 degrees

x = 10

5 multiplied by 10 is 50

4 multiplied by 10 is 40

40+50=90

Answer:

50 = EDH

Step-by-step explanation:

We know that angle EDG is a right triangle (measures 90°). We also know that angle EDH and angle HDG make up angle EDG which is 90°. So ultimately we can state that;

EDH + HDG = EDG

 5x  +   4x  =   90

      9x = 90

        x = 90/9

        x = 10

Now that we know that value of x, we can say that;

EDH = 5x

since x = 10

EDH = 5(10)

EDH = 50

Hope this helps!

Answer:

15/16

Step-by-step explanation:

Answer:

15/16

Step-by-step explanation:

The circulation of the vector field G = xy i + z j + 3y k around a square centered at the origin and lying in the yz-plane, with a counterclockwise orientation from the positive x-axis.the total circulation of G around the square is 3(s^2/8).

To evaluate the circulation, we need to compute the line integral of G along the boundary of the square. The square lies in the yz-plane and is centered at the origin, with side length s. Since the square is oriented counterclockwise from the positive x-axis, its boundary can be parametrized as follows:

Top side: r(t) = (0, t, s/2), for t ranging from -s/2 to s/2.

Right side: r(t) = (0, s/2, t), for t ranging from s/2 to -s/2.

Bottom side: r(t) = (0, t, -s/2), for t ranging from s/2 to -s/2.

Left side: r(t) = (0, -s/2, t), for t ranging from -s/2 to s/2.

Next, we calculate the dot product of G and the tangent vector along each side of the square, and then integrate over each side. The circulation is given by the sum of these line integrals. The dot product of G and the tangent vector along each side simplifies to the following:

Top and bottom sides: G · dr = (t)(dy) + (3y)(dz) = (t)(dt) + 3y(dy) = t dt + 3yt dy.

Right and left sides: G · dr = (3y)(dy) = 3y dy.

Integrating over each side, we find:

Circulation along the top and bottom sides = ∫(t dt + 3yt dy) = 0 (since the integral of t dt over a symmetric interval is zero, and y(dy) is zero at the endpoints).

Circulation along the right and left sides = ∫(3y dy) = 3 ∫(y dy) = 3(y^2/2) evaluated from -s/2 to s/2 = 3(s^2/8).

Hence, the total circulation of G around the square is 3(s^2/8).

Learn more about tangent here:

https://brainly.com/question/10053881

#SPJ11

Discouraging consumers from purchasing products from an insurer is referred to as "consumer dissuasion." It involves implementing strategies or tactics to dissuade potential customers from choosing a particular insurance company or its products.

Consumer dissuasion is a practice employed by insurers to discourage consumers from selecting their products or services. This strategy is often used to manage risk by discouraging individuals or groups that insurers perceive as having a higher likelihood of filing claims or incurring higher costs. Insurers may employ various techniques to dissuade potential customers, such as setting higher premiums, imposing strict eligibility criteria, or offering limited coverage options. The purpose of consumer dissuasion is to selectively attract customers who are deemed less risky or more profitable for the insurer, thereby ensuring a healthier portfolio and reducing potential losses. By implementing strategies that discourage certain segments of the market, insurers can manage their risk exposure and maintain profitability. It is important to note that consumer dissuasion practices should adhere to applicable laws and regulations governing the insurance industry, including fair and transparent practices. Insurers are expected to provide clear and accurate information to consumers, enabling them to make informed decisions about insurance coverage and products.

Learn more about insurance company here:

https://brainly.com/question/32110345

#SPJ11

Answer:

Last option: 4a³

Step-by-step explanation:

Adding up the terms in the a³ column we get

12a³ -6a³ -2a³ = B

B = 12a³ -6a³ -2a³

B = (12 - 6 -2)a³

B = 4a³ ANSWER

Last choice in the answer choices

Answer:

15 units

Step-by-step explanation:

The terms of an odd integer are given by 2n - 1. Since the sides of the triangle are three consecutive odd integers, let them be 2n - 1, 2(n + 1) - 1 and 2(n + 2) - 1 respectively, where 2n - 1 is the shortest side

Let P = perimeter of triangle = 2n - 1 + 2(n + 1) - 1 + 2(n + 2) - 1

= 2n - 1 + 2n + 2 - 1 + 2n + 4 - 1

= 2n - 1 + 2n + 1 + 2n + 3

= 2n + 2n + 2n - 1 + 1 + 3

= 6n + 3

Since the shortest side is 20% of the perimeter of the triangle, we have that

2n - 1 = 20%(6n + 3)

2n - 1 = 0.2(6n + 3)

expanding the bracket, we have

2n - 1 = 1.2n + 0.6

subtracting -1.2n and adding +1 to both sides, we have

2n - 1.2n = 1 + 0.6

0.8n = 1.6

dividing both sides by 0.8, we have

n = 1.6/0.8

n = 2

Since P = 6n + 3, substituting n = 2, we have

P = 6(2) + 3 = 12 + 3 = 15 units

Answer:

x=0.3

Step-by-step explanation:

-0.4x-4.15=x-1.6-2.97

-0.4x-x=-(1.6-2.97)+4.15

-1.4x=0.42

x=0.3

Answer:

x=0.3

Step-by-step explanation:

Answer:

3x+2=\frac{14}{3}

Step-by-step explanation:

Your answer: a. When you do not know the standard deviation of a normally distributed population.

a. When you do not know the standard deviation of a normally distributed population, you would use the t-distribution procedure to find the confidence interval for the population mean. This is because the t-distribution allows for the estimation of the population standard deviation based on the sample standard deviation.

In statistics, the standard deviation is a measure of the variability or spread of an outcome. [1] A low standard deviation indicates that the value is close to the mean of the cluster (also called the expected value), while a high standard deviation indicates that the results are very interesting.

The standard deviation of can be abbreviated as SD and is often used in mathematics and equations with the Greek letter σ (sigma) for population standard deviation or the Latin letter s for different sample sizes.

The standard deviation of a variable, such as a population, a data set, or a probability, is the basis of its variance. Algebraically it is easier than the mean absolute difference, but in practice, it means a lower absolute difference. The useful feature of standard deviation is that it is expressed in the same unit as the data, not the difference.

Learn more about standard deviation:

brainly.com/question/23907081

#SPJ11

Solution:

Given a table of data;

Where the total hours in 50 hours

The hours spent for jogging is 20 hours.

The sum of angles about a point or in a circle is, 360°

The portion for jogging in degrees is

Substitute into the formula above

Hence, the portion for jogging is 144°

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

To know more about abscissa visit:

brainly.com/question/32034993

#SPJ11

Answer:

D. 0

Step-by-step explanation:

A function must not have 2 or more first number or X that have the same value.

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

Know more about Standard deviation here,

https://brainly.com/question/29115611

#SPJ11

Answer:

The correct option is (D).

Step-by-step explanation:

A one-to-one function can be defined such the every value of x corresponds to exactly one value of y.

That is:

x₁ → y₁

x₂ → y₂

x₃ → y₃

.

.

.

and so on.

Consider the graph.

From the graph it can be seen that for y = 0 and y = 2 there are multiple x coordinates.

So, the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.

According to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Given :

Draw the graph of the three lines in order to determine the function is one-one function or not.

The equation of the line passing through (-5,6) and (-2,0) is given by:

\(\dfrac{y-6}{x+5}=\dfrac{0-6}{-2+5}\)

\(\dfrac{y-6}{x+5}=\dfrac{-6}{3}\)

\(y-6=-2(x+5)\)

y + 2x + 4 = 0    --- (1)

The equation of the line passing through (-2,0) and (2,2) is given by:

\(\dfrac{y-0}{x+2}=\dfrac{2-0}{2+2}\)

2y = x + 2   ---- (2)

The equation of the line passing through (2,2) and (4,-2) is given by:

\(\dfrac{y-2}{x-2}=\dfrac{-2-2}{4-2}\)

y - 2 = -2(x - 2)

y + 2x = 6   ---- (3)

Now, with the help of these three equations, the graph of the three lines can be plotted. The Graph is attached below.

So, according to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/12465796

Answer:

its to show data like rainfall how many people does the teacher get per year

Step-by-step explanation:

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

To learn more about Perpendicular bisector theorem refer to:

https://brainly.com/question/4137998

#SPJ4

The division gives the Quotient 180.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

Given:

We have to divide 1 thousand 8 hundreds divide by 10

So, 1800 ÷ 10

The Division is as follows:

                                        10 | 1800 | 180

                                               10

                                             ____

                                               80

                                               80

                                               ____

                                                  0

Thus, the Quotient is 180.

Learn more about Division here:

https://brainly.com/question/21416852

#SPJ9

Answer:

ig the answer is 245788675428

Step-by-step explanation:

but if u was talking about 139x12 then the answer is 1668

hope it helps

mark me brainliest pls

Answer:

y equals 4 because if you substitute solve and isolate you get that answer.

Answer:

2  addition

4 multiplication

Step-by-step explanation:

In step 2 we are adding 6 to each side so we use the  addition property of equality

In step 4 we are multiplying by -2 on each side so we use the multiplication property of equality

Answer:

2- addition

4- mult.

Step-by-step explanation:

The area of the rectangle should be written as 0.682 m². To determine the area of a rectangle, you multiply its length by its width. The length of the rectangle is 1.125 m, and the width is 0.606 m.

Area of rectangle = length x widthA = 1.125 m x 0.606 mA = 0.68175 m²Now, rounding the answer to the correct number of significant figures, which is 3. The digit after the third significant figure is 7 which is greater than 5, therefore the third digit should be rounded up. So the final answer will be 0.682 m².

Thus, the long answer to this question is: After multiplying the length and width of a rectangle of dimensions 1.125 m and 0.606 m respectively, the product obtained from the calculator is 0.68175. To find the area of the rectangle, we use the formula A = l × w, which gives A = 1.125 m × 0.606 m = 0.68175 m². Rounding this answer to 3 significant figures, we find that the third digit is 1 which is greater than 5. Therefore, we must round the third digit up to get the final answer of 0.682 m².

To know more about rectangle visit:

https://brainly.com/question/10834438

#SPJ11

The possible slope of the line is (c) 3

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

This means that the line is ascending from left to right in which case, the slope of the line is positive.

So, the possible values of the slope include the set of numbers greater than 0.

From the options, we have (c) 3

Read more about slope at;

brainly.com/question/534570

#SPJ1