Find the conjugate and product of the following surds

1) i3 + i5
2) i3 + 9
3) - i2 + 1
4) - 3 + iy​

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

\(x = \sqrt{\frac{49}{2}}\)

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

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Answer:

Geometric mean = 6.71

Arithmetic mean = 9

Step-by-step explanation:

\(geometric \: mean \\ = \sqrt{3 \times 15} \\ = \sqrt{45} \\ = 6.70820393 \\ = 6.71 \\ \\ arithmetic \: mean \\ \\ = \frac{3 + 15}{2} \\ \\ = \frac{18}{2} \\ \\ = 9\)

We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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Answer:

Incline plane 4

Step-by-step explanation:

Determine the distance between two points.

So answer is 6.4 units.

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

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Answer:

9 is 3rd -- 8 is last -- 10 is first --

Step-by-step explanation:

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Step-by-step explanation:

-x + y = -5

Transform to slope-intercept form, y = mx + b:

-x + x + y = x - 5

y = x - 5 (Slope-intercept form where m = 1, b = -5).

Plot the y-intercept (0, -5) on the graph. Using the "rise over run" of the slope, m = 1, the next point will be: (1, -4).

I also plotted other points (please see the attached screenshot of the graph).

fever thermometer: decimeter

needle: decimeter

interstate highway:kilometer

fingernail: probably a centimeter

river: kilometer

tree trunk: meter

hope this helps.

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

Answer:

No

Step-by-step explanation:

Answer:

The first is 1:6 and the second one is 4

Step-by-step explanation:

The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.

On a coordinate plane, the graph of a hyperbola is shown.

In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.

The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.

The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.

A fraction with a denominator of zero cannot exist.

The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.

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The midpoint of a line segment is the point that is halfway between the two ends of the line segment. A midway separates a line segment into two equal parts.

This is further explained below.

Generally, In the field of geometry, a line segment is defined as the portion of a line that is enclosed by two unique points on the line.

Alternatively, we may say that a line segment is the portion of a line that is between two points. A line does not have any endpoints and may stretch endlessly in any direction, however, a line segment has two endpoints that are fixed or definite in some way.

In conclusion, The term "midpoint" refers to the point along a line segment that is situated exactly midway between the beginning and ending points. A midway separates a line segment into two equal parts.

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Answer:

  plot the points (0, 2) and (π, 4)

Step-by-step explanation:

To use your sine plotting tool, you need two points on the graph. The midline point is given for you. It is the y-intercept, (0, 2).

The maximum amplitude point is 1/4 of a period from this midline point. The frequency is 1/(4π), and the period is the inverse of frequency:

  T = 1/f = 4π

So, 1/4 of a period is ...

  T/4 = (4π)/4 = π

The peak value of the function is the amplitude added to the midline, so is 2+2 = 4.

The second point you need to plot is the peak value, (π, 4).

Your points are (0, 2) and (π, 4).

The decimal representation of the given sequence is 4,063.21.

The given sequence can be interpreted as follows: "63 ones, 21 hundredths, 4 thousand." To convert this sequence into decimal form, we need to understand the place value of each digit.

Starting from the left, we have "63 ones." This means we have 63 units, which can be represented as 63.

Next, we have "21 hundredths." Since there are two digits after the decimal point, the number becomes 0.21.

Finally, we have "4 thousand." Considering the place value, 4 thousand would be written as 4,000.

Putting it all together, we have 63 + 0.21 + 4,000, which equals 4,063.21. Therefore, the decimal representation of the given sequence is 4,063.21.

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Answer:

D

Step-by-step explanation:

The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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Answer:

Step-by-step explanation:

Given:

Find the speed:

\(\\ \sf\longmapsto Speed=\dfrac{Distance}{Time}\)

\(\\ \sf\longmapsto Speed=\dfrac{36}{0.5}\)

\(\\ \sf\longmapsto Speed=72mph\)

Answer:

The answer is 1.62 ounce

Step-by-step explanation:

Now,

3.6% of his 45 ounce

45 × 3.6 ÷ 100

162 ÷ 100 = 1.62

Thus, Jaydon has eaten 1.62 ounce block of chocolate fudge.

The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.

Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).

The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.

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Answer:

\(y=-\frac{4}{3}x +\frac{26}{3}\)

Step-by-step explanation:

1) if the point A has coordinates (-1;10) and the point B - (5;2), then it is possible to write common view of the required equation of the line:

\(\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};\)

2) if to substitute the coordinates of A&B into the common equation, then:

\(\frac{x+1}{5+1} =\frac{y-10}{2-10}; \ => \frac{x+1}{6}=\frac{y-10}{-8};\)

3) finally, in slope-intersection form:

3y= -4x+26; ⇔ y= -4/3 x +26/3.

P.S. the suggested way of the solution is not the only one.

The average speed of the car is 80 km per hour

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

Distance = 200 km

Time = 2 hours 30 minutes

using the above as a guide, we have the following:

Speed = Distance/Time

substitute the known values in the above equation, so, we have the following representation

Speed = 200/2.5

Evaluate

Speed = 80 km per hour

Hence, the average speed of the car is 80 km per hour

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Answer: The second image you attached (I also attached the picture of the right answer)

Step-by-step explanation:

In this equation A is negative so you know it is going downward.

the shift is down 5 units and to the right 2.

You can see this shift in the graph I attached

it is also 1 to 1

Answer:

b

Step-by-step explanation:

The method for computing a z-score is  \(\bold{z = \frac{(x-\mu)}{\sigma}}\), where x is the crude score, \(\bold{\mu}\) is the mean population, and \(\bold{\sigma}\) seems to be the standard population difference.

\(\bold{\bar{x}=150}\\\\ \bold{\sigma=25}\)

following are the calculation of the Z scores:

\(\to \ (a)\ 100:\ \text{Z score}=\frac{(100-150)}{25}= \frac{(-50)}{25} = -2\\\\\to \ (b)\ 120:\ \text{Z score}=\frac{(120-150)}{25}= \frac{(-30)}{25} = -1.2\\\\\to \ (c)\ 140:\ \text{Z score}=\frac{(140-150)}{25}= \frac{(-10)}{25} = -0.4\\\\\to \ (a)\ 160:\ \text{Z score}=\frac{(160-150)}{25}= \frac{(10)}{25} = 0.4\\\\\)

Using formula:

\(\to \text{Raw score = Mean(series) +Z score} \times \text{SD(series)}\)

Calculating the Raw scores:

\(\text{(e) -1: Raw score= 150 +(-1)} \times 25 = 125 \\\\\text{(f) -0.8: Raw score= 150 +(-0.8)} \times 25 = 130\\\\\text{(e) -0.2: Raw score= 150 +(-0.2)} \times 25 = 145\\\\\text{(e) 1.38: Raw score= 150 +(1.38)} \times 25 = 184.5\\\\\)

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Answer:

  0.042563 km

Step-by-step explanation:

You want the distance 4256.3 cm expressed in km.

The prefixes centi- and kilo- refer to 1/100 and 1000, respectively.

  4256.3 cm = 4256.3 (1/100 m) = 42.563 m

Then 1 km = 1000 m, so 1 m = 1/1000 km, and we have ...

  42.563 m = 42.563 (1/1000 km) = 0.042563 km

Answer:

0.042563 km

Step-by-step explanation:

To convert centimeters to kilometers, divide the number of centimeters by 100,000.

So, 4256.3 cm = 4256.3 cm / 100,000 cm/km = 0.042563 km.

Answer: 1.96

2

Step-by-step explanation:

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).