The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?
The complex numbers have equal imaginary coefficients.
The complex numbers have equal real numbers.
The complex numbers have opposite imaginary coefficients.
The complex numbers have opposite real numbers.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{b}\\ a=\stackrel{adjacent}{3}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ b=\sqrt{ 3^2 + 3^2}\implies b=\sqrt{ 9 + 9 } \implies b=\sqrt{ 18 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{7}\\ a=\stackrel{adjacent}{\sqrt{18}}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 7^2 - (\sqrt{18})^2}\implies h=\sqrt{ 49 - 18 } \implies h=\sqrt{ 31 }\implies h\approx 6[/tex]

Answer:

6 ft

Step-by-step explanation:

In the right triangle ABC connect points A and B

BC=3ft

AC=3ft

AB² =BC² + AC²=9+9=18ft²

In the right triangle ABD, AB²=18ft

BD=7ft

AB²+AD²=BD²

18+AD²=7²

AD²= 49-18

AD=[tex]\sqrt{31\\[/tex]    =5.6

the length of AD is a whole number, round it

AD=6ft {the shortest height}

The solutions are where the graphs of the functions intersect at x = 1 and the value at x ≈ 3.642

Given data ,

Let the first function be f ( x )

Now , the value of f ( x ) = log ( x - 1 )

Let the second function be g ( x )

g ( x ) = ( 1/3 )x² - 4

On simplifying the equation , we get

f ( x ) = g ( x )

On plotting the graph , we get the point of intersection at x = 1 and x = 3.642

Hence , the solution of equations are x = 1 and x = 3.642

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Answer:

x = 1 and x = 3.642

Step-by-step explanation:

Plato/Edmentum

Answer and explanation:

a) To find the average speed of Miss Lim for the whole journey, we need to use the formula:

Average speed = Total distance ÷ Total time

Let's first calculate the total distance traveled by both Miss Wan and Miss Lim. We know that Miss Wan drove at an average speed of 60 km/h and reached Orchard Road 30 minutes later. So, the total distance traveled by her would be:

Distance = Speed × Time

Distance = 60 km/h × (30/60) h

Distance = 30 km

Now, we also know that Miss Lim was still 5 km away from Orchard Road when Miss Wan reached there. Therefore, the total distance traveled by both of them would be:

Total distance = Distance covered by Miss Wan + Distance left for Miss Lim

Total distance = 30 km + 5 km

Total distance = 35 km

Next, let's calculate the total time taken by both of them. We know that Miss Wan took 30 minutes less than Miss Lim to reach Orchard Road. So, if we assume that Miss Lim took t hours to reach Orchard Road, then Miss Wan took (t - 0.5) hours. Therefore, the total time taken by both of them would be:

Total time = Time taken by Miss Wan + Time taken by Miss Lim

Total time = (t - 0.5) h + t h

Total time = 2t - 0.5 h

Now, we can use the formula to find the average speed of Miss Lim:

Average speed = Total distance ÷ Total time

Average speed = 35 km ÷ (2t - 0.5) h

Therefore, the average speed of Miss Lim for the whole journey is 35/(2t-0.5) km/h.

b) To find out what time Miss Lim would reach Orchard Road, we can use the formula:

Time taken = Distance ÷ Speed

We know that Miss Lim was 5 km away from Orchard Road when Miss Wan reached there. Therefore, the distance left for Miss Lim to cover would be:

Distance = 5 km

We also know that Miss Lim's average speed for the whole journey is 35/(2t-0.5) km/h. Therefore, the time taken by her to cover the remaining distance of 5 km would be:

Time taken = Distance ÷ Speed

Time taken = 5 km ÷ 35/(2t-0.5) km/h

Time taken = (2t - 0.5) ÷ 7 h

Now, we need to add this time to the time when Miss Wan reached Orchard Road, which was 30 minutes past 2.50 p.m. So, the time when Miss Lim would reach Orchard Road would be:

Time = Time when Miss Wan reached Orchard Road + Time taken by Miss Lim

Time = 2.50 p.m. + 30 min + (2t - 0.5) ÷ 7 h

Simplifying this equation, we get:

Time = (14t + 11) ÷ 14 p.m.

Therefore, Miss Lim would reach Orchard Road at (14t + 11) ÷ 14 p.m.

Answer:

  a) 50 km/h

  b) 3:26 p.m.

Step-by-step explanation:

You want to know Miss Lim's average speed and arrival time at Orchard Road if Miss Wan gets there in 30 minutes at 60 km/h, starting at 2:50 pm.

The distance Miss Wan traveled is ...

  distance = speed × time

  distance = (60 km/h) × (1/2 h) = 30 km

In the same 30 minutes that Miss Wan traveled 30 km, Miss Lim traveled 5 km less, so 30 -5 = 25 km. Miss Lim's speed was ...

  speed = distance/time

  speed = (25 km)/(1/2 h) = 50 km/h

Assuming Miss Lim maintained that speed for the remaining 5 km, her average speed for the journey was 50 km/h.

Miss Lim's travel time is ...

  time = distance/speed

  time = (30 km)/(50 km/h) = 3/5 h = 36 min

The clock time 36 minutes after 2:50 pm is 3:26 pm.

Miss Lim reached Orchard Road at 3:26 p.m..

The ratios as a fractions without reducing are:

a. 6/13

b. 7/40

c. 45/36

d. 37/43

To express a ratio as a fraction, we simply write the first number (the antecedent) as the numerator and the second number (the consequent) as the denominator. We do not reduce the fraction to its lowest terms because it changes the value of the ratio. For example, the ratio 6:13 cannot be reduced to 3:7 because they are not equal.

By expressing the ratios as fractions, we can easily compare and calculate with them, especially in mathematical operations such as multiplication and division. It is also a common practice in statistics to represent ratios as fractions, which can be useful in interpreting data and making comparisons between groups.

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The remaining zeros of h based on the function will be 9 and -5.

A function in math represents the correlation between two groups of numerical data, known as domain and range. The input value is drawn from the first set or domain, while the resulting output value belongs to the second set or range.

It should be noted that to specify, a formal breakdown states that a function f operates from X into Y whereby each component x of X possesses an exclusive element y in Y referred to by the mentioning of f(x) = y. Here, it's clear that 'x' applies to input with its respective contribution being labeled as 'y', which denotes the result of the equation belonging to set Y.

In this case, the remaining zeros of h based on the function will be 9 and -5.

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10√15 + 2 is a simplified expression of the given expression.

We need to use the distributive property of multiplication to simplify the expression:

√6(5)√10 + 2

= 5√6√10 + 2

Since √6 and √10 cannot be simplified any further, we can multiply them together to get:

√6√10 = √(6 × 10) = √60

Now, we need to simplify the expression using this result:

5√6√10 + 2

= 5(√60) + 2

= 5(√4 × √15) + 2

= 5(2√15) + 2

= 10√15 + 2

Therefore, √6(5)√10+2 simplifies to 10√15 + 2.

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Answer:

x = 8.1

Step-by-step explanation:

According to Euclidean theorem:

10² = 12 × (2x - 8)

10² = 24x - 96

100 = 24x - 96

100 + 96 = 24x

196 = 24x

8.1 = x approximately

Answer:

None is obtuse

Step-by-step explanation:

An obtuse is something more than 180°and less than 360°

A.35°+65°+80°=180° Not obtuse

B.30°+40°+110°=180° Not obtuse

60°+60°+60°=180° Not obtuse

C.30°+60°+90°=180° Not obtuse

Answer:

B. a triangle with angles that measure 30°, 40°, and 110°

Step-by-step explanation:

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

The surface area of the footrest is 1018 inches squared.

1 yard square of fabric will completely cover the footrest.

Alicia wants to cover a footrest in the shape of a rectangular prism with cotton fabric . The footrest is 19 inches, 11 inches and 10 inches.

She has only 1 square yard of fabrics.

Hence, let's check if she can cover the footrest completely.

Therefore,

surface area of the rectangular prism = 2(lw + hw + lh)

Hence,

surface area of the rectangular prism = 2(19 × 11 + 19 × 10 + 10 × 11)

surface area of the rectangular prism = 2(209 + 190 + 110)

surface area of the rectangular prism = 2(509)

surface area of the rectangular prism = 1018 inches squared

Therefore, the footrest has a surface area of  1018 inches squared.

1296 inches² = 1 yard²

1018 inches² = ?

surface area of the footrest in yards squared = 1018 / 1296

surface area of the footrest in yards squared = 0.79 yard²

Therefore, the fabric will completely cover the footrest.

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Answer: 4224.413805 miles

Step-by-step explanation:

First, we use The Pythagorean Theorem equation to find the distance between California and Florida

Equation: [tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]

[tex]3186^{2}[/tex]+[tex]2774^{2}[/tex]=[tex]c^{2}[/tex]

So, we are trying to solve for c.

The first thing we do is evaluate the expression.

10,150,596+7,695,076=[tex]c^{2}[/tex]

Add like terms

17,845,672=[tex]c^{2}[/tex]

Then, do inverse operations and square root 17,845,672

You would then get 4224.413805 miles.

The angle relationships are as follows:

Corresponding angles → ∠5 and ∠13  and ∠3 and ∠11

Alternate interior angles → ∠4 and ∠9 and ∠7 and ∠14

Alternate exterior angles → ∠5 and ∠16

Consecutive interior angles → ∠3 and ∠9

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

Therefore, let's classify the angle relationships in the diagram.

Hence,

∠5 and ∠13  and ∠3 and ∠11 are corresponding angles

∠4 and ∠9 and ∠7 and ∠14 are alternate interior angles.

∠5 and ∠16 are alternate exterior angles.

∠3 and ∠9 are consecutive interior angles.

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Check the picture below.

Answer :

Step-by-step explanation:

It's given that, Area of square is 595.36 square feet.

As we know that area of square is calculated by,

Area = side²

Substituting the values,

595.36 = side

side =√595.36

side = 24.4 feet

Hence, the side of the square is 24.4 feet.

Now,

Perimeter (square) = 4 × side

Perimeter = 4 × 24.4

Perimeter = 97.6 feet

Therefore, The perimeter of the square is 97.6 feet

The calculated value of the solution to the system of equations  (- 1, - 1)

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

The graph

The solution to the system of equations is the point of intersection between the lines on the graph

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

Intersection point =  (- 1, - 1)

This means that the solution to the system of equations  (- 1, - 1)

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Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

An equation that shows how to find the pounds of seed, p, needed for h hectares of land is p = 20h.

An equation that shows how many hectares, h, Harper can plant with p pounds of seed is h = p/20.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this table;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (300 - 200)/(15 - 10)

Slope (m) = 100/5

Slope (m) = 20

At data point (10, 200) and a slope of 20, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 200 = 20(x - 10)  

y = 20x - 200 + 200

y = 20x ≡ p = 20h

Making h the subject of formula, we have:

h = p/20

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The surface area of the cone is 763.02 cm²

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex.

The surface area of a cone is expressed as;

SA = πr( r+l)

where l is the slant height and r is the radius

Incase l is not given ;

l = √h²+r²

The radius of this cone = diameter/2

= 18/2 = 9cm

SA = 3.14 × 9( 9+18)

SA = 28.26 × 27

SA = 763.02 cm²

therefore the surface area of the cone is 763.02 cm²

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The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

t = 9.79 years

Given that;

The number of miles m (in billions) traveled by vehicles in City A can be modeled by,

m = 2.86t + 112

where t is the number of years since 1994.

Hence, We can formulate;

The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

m = 2.86t + 112

140 = 2.86t + 112

140 - 112 = 2.86t

28 = 2.86t

t = 28/2.86

t = 9.79 years

Thus, The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

t = 9.79 years

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The probability of picking a 7 and then picking a number greater than 7 is 1/3.

Now, given that we have already picked three cards. So, 7, 8, and 9.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

The number of possible outcomes is 3.

Probability of picking 7 = 1/3

Now, as card seven is already picked up cards 8 and 9 are the only card left.

therefore, the sample size(possible outcomes) was reduced to 2 only.

Also, cards 8 and 9 both are greater than 7, thus the desired outcome is also 2.

Further the probability of the number greater than 7 occurring,

Probability (n>7) = 2/2 =1

Probability picking a number greater than 7

The probability of picking a 7 and then picking a number greater than 7

= Probability of card 7 occuring x probability of card 8 and 9 occurring

= 1/3 ×1

= 1/3

Hence, the probability of picking a 7 and then picking a number greater than 7 is 1/3.

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"Your question is incomplete, probably the complete question/missing part is:"

You pick a card at random. Without putting the first card back, you pick a second card at random. There're 3 cards. One is 7, one is 8, and the other is a nine. What is the probability of picking a 7 and then picking a number greater than 7? (Write the probability as a fraction or whole number.)

After considering the given data we come to the conclusion that the evaluated angle of 20 1/2° can be placed in degrees and minutes as 20° 30'.

Angles are generally measured in degrees, also known as a unit of measurement for angles, arcs, and circles, in geometry and trigonometry. A degree is 1/360th of a full circle's revolution, and it is typically designated by the sign.

Angles can be gradually divided into minutes and seconds, which are smaller units of measurement when they are presented in degrees. One degree has 60 minutes, and one minute has 60 seconds. Then, 360 degrees, 0 minutes, and 0 seconds can be used to express a full circle.

For instance 20 1/2°, we first apply the entire number (20) to represent the number of degrees before multiplying the fraction (1/2) by 60 to represent the number of minutes.

The angle may be exposed as 20 degrees and 30 minutes since this provides us with 30 minutes. It should be helpful to express angles in degrees and minutes (or seconds) in a variety of contexts, including engineering, astronomy, and navigation.

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The calculated value of the weight in kilograms is 60 kg

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

He stepped on a scale and he weighed 132 pounds

This means that

Weight = 132 pounds

By the metric units of conversion, we have

1 pound = 0.453592 kg

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

Weight = 132 * 0.453592 kg

Evaluate

Weight = 59.87 kg

Approximate

Weight = 60 kg

Hence, the weight is 60 kg

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The collusive outcome is better for both firms than the Bertrand outcome.

Setting the price equal to marginal cost gives us:

P = $100

Substituting into the demand function, we get:

Q = 140 - (100/0.5) = 40

Therefore, each firm will sell 20 units of service, for a total of 40 units sold. The market price will be $100, and each firm will earn zero profit

The market demand function is:

P = 70 - 0.5Q

Total revenue for the monopoly is:

TR = P*Q = (70 - 0.5Q)*Q = 70Q - 0.5Q^2

The marginal revenue function is:

MR = dTR/dQ = 70 - Q

Setting marginal revenue equal to marginal cost (which is still $100), we get:

70 - Q = 100

Q = 30

Therefore, the monopoly will sell 30 units of service. Each firm will sell half of this quantity, or 15 units. The market price will be:

P = 70 - 0.5Q = $55

Each firm's total revenue will be:

TR = P*Q = $1,650

Each firm's total cost will be:

TC = 100*15 = $1,500

Therefore, each firm will earn a profit of:

π = TR - TC = $150

Note that this collusive outcome is better for both firms than the Bertrand outcome,

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Answer:

$400

Step-by-step explanation:

80% = 80/100 = 8/10 = 0.8

0.8(500)=400

Note that the area of the shaded region is 0.4129. See how it was derived.

Using the standard normal distribution table, the area to the left of

z = 0.22 is 0.5871.

Therefore,  the area of the shaded region to the right of z = 0.22 is

1 - 0.5871 = 0.4129

  Rounding to 4 decimal places, the area of the shaded region is 0.4129.

The shaded region's area is the difference between the area of the complete polygon and the area of the polygon's unshaded portion.

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The calculated value of the surface area of the cylinder is 1056π

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

Slant height, l = 40 mm

Height, h = 32 mm

Calculate the radius r using

(2r)² = 40² - 32²

So, we have

(2r)² = 576

r = 12

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

SA = 2πr(r + h)

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

SA = 2π * 12(12 + 32)

Evaluate

SA = 1056π

Hence, the surface area of the cylinder is 1056π

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a) For equation y = x

x and y are directly proportional and the constant of proportionality k = 1

b) For equation y = -52x

x and y are directly proportional and the constant of proportionality k is -52

A) Consider equation y = x

For x = 1, y = 1

For x = -1, y = -1

And for x = 1/2 the value of y is 1/2

This means that y is directly proportional to x.

And the  constant of proportionality k would be,

k = y/x

k = 1

B) Consider equation y = -52x

For x = 1 the value of y is -52

For x = -1,  the value of y is y = 52

And for x = 0 the value of y is 0

This means that y is directly proportional to x.

And the  constant of proportionality k would be,

k = y/x

k = -52

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The equation of the line that passes through the points (-2, -1) and (2, 11) will be y = 3x + 5.

Given that:

Points, (-2, -1) and (2, 11)

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The equation that passes through (-2, -1) and (2, 11) is calculated as,

(y + 1) = [(11 + 1) / (2 + 2)](x + 2)

y + 1 = 3x + 6

y = 3x + 5

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Step-by-step explanation:

to[tex]3w - 7 = \sqrt{8w - 7} \\ {(3w - 7)}^{2} = ({ \sqrt{8w - 7} })^{2} \\ 9 {w}^{2} - 42w + 49 = 8w - 7 \\ 9 { w}^{2} - 42w - 8w + 49 + 7 = 0 \\ 9 {w}^{2} - 50w + 56 = 0 \\ (9w - 14)(w - 4) = 0 \\ w = \frac{14}{9} \: or \: w = 4[/tex]

to make sure the answer

substitute w = 14/9 and w = 4 to the equation.

if w = 14/9

[tex]3w - 7 = \sqrt{8 w - 7} \\ 3 \times \frac{14}{9} - 7 = \sqrt{8 \times \frac{14}{9} - 7} \\ - \frac{ 7}{3} = \frac{7}{3} [/tex]

we know that if we substitute w = 14/9, the answer is not the same.

if w = 4

[tex]3w - 7 = \sqrt{ 8 w - 7 } \\ 3 \times 4 - 7 = \sqrt{8 \times 4 - 7} \\ 5 = 5[/tex]

if we substitute w = 4 the answer is the same.. we can conclude the the answer of 3w - 7 = √8w - 4 is 4