Subtract the complex numbers.

(5 + 4i) - (7 + 8i)

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Answer:

8

Step-by-step explanation:

we conformed the 8s by 4 and 3

By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Define the variable:

Given information:

First equation

The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:

⇒ 4x + $1.90 = $22.20

⇒ 4x + 1.9 = 22.2

Second equation

The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:

⇒ $22.20 - 4x = $1.90

⇒ 22.2 - 4x = 1.9

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Answer:

Is A supposed to be 6 x m or no??

Step-by-step explanation:

Answer:

d. The graph has no scale, so it's impossible to compare the money earned.​

Step-by-step explanation:

The graph is misleading because it has "no scale" in response to the money earned. It would actually be hard to plot them on the graph without the scale. If you look at the graph, you won't be able to compare how much funds Fund C made in comparison to Fund A, B and D. You won't be able to tell the actual gap in the money they've earned. The data above is not clearly illustrated in this case.

Answer:

73°

Step-by-step explanation:

This equation uses two supplementary angles. Supplementary angles are two angles that add up to 180 degrees.

The triangle has two angles implied, 30 degrees and (180-137) degrees.

(180 - 137) = 43 degrees

Now that we have two angles inside the triangle, we subtract them from 180 to find the last angle.

180 - 43 - 30 = 107

The angle with a measure of 107 degrees and angle 3 are supplementary

180 - 107 = 73 degrees

Answer:73.4° Fahrenheit.

Step-by-step explanation:

Answer:

E empty set

Step-by-step explanation:

The answer is empty at

The solution to the given equation is x = ±7. The correct option is d. x = ±7

From the question, we are to determine the solution to the given equation

The given equation is

x²-49 = 0

NOTE: I assumed the variable is x

Solving the equation

x²-49 = 0

Writing in the form ax²= c

x² = 49

∴ x = ±√49

x = ±7

Hence, the solution to the given equation is x = ±7

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Answer: Copyright protects original work, whereas a trademark protects items that distinguish or identify a particular business from another.

The trademark laws protect the product or service name and any slogans used in the advertising, while the copyright laws protect the additional creative written expression contained in the ad. Hope this helps!

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

cant show work i need to draw then

Answer:

-28k^4

Step-by-step explanation:

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Step-by-step explanation:

Given that:

Selling price of bicycle = $176

Selling price of helmet = $16

Total price = 176+16 = $192

This is 160% of what Stefan paid originally.

Let,

x be the original amount paid by Stefan.

160% of x = 192

\(\frac{160}{100}x=192\\1.6x=192\)

Dividing both sides by 1.6

\(\frac{1.6x}{1.6}=\frac{192}{1.6}\\x=120\)

Original amount paid by Stefan = $120

Profit = 192 - 120 = $72

Hence

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

6 miles

Step-by-step explanation:

From the information given you can write the following equation:

x+y= 16 (1), where

x= April's distance

y= Blake's distance

You also have that Blake ran 4 miles farther than April which means that y= 4+x and you can replace this in the first equation and isolate x:

x+(4+x)= 16

x+4+x=16

2x=16-4

x=12/2

x= 6

According to this, the answer is that April ran 6 miles.

Answer:

( − ∞ , ∞ )

Step-by-step explanation:

Any value of  x  makes the equation true.

Allison runner is setting faster pace than Martha and Rachel

Speed of any object is defined as the distance traveled by the object with respect to time is known as speed.

Here, we can consider distance as laps.

Speed of Martha = 20 laps/ 32 min

⇒ 0.625

Speed of Allison = 16 laps/25 min

⇒ 0.64

And speed of Rachel = 17 laps/ 27.2 min

⇒ 0.625

Thus, according to above calculation Allison (runner) is taking faster pace.

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Answer:

2x= 30+90

Step-by-step explanation:

To check

2x= 120

2x/2=120/2

x=60

Answer:

19

Step-by-step explanation:

190/10= 19

Answer:

19  19*10=190

Step-by-step explanation:

The required value of the given sum is given as 4.8. Option B is correct.

Given that,
To estimate the sum of 3.62 + 1.16 by rounding each addend to the nearest tenth.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
Given expression,
= 3.62 + 1.16
Round the values to the nearest tenth,
= 3.6 + 1.2
= 4.8

Thus, the required value of the given sum is given as 4.8. Option B is correct.

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Answer:

\(y = 8 - 8\sin(2x) \)

There is a $243,570 cap on the amount you may finance.

MentaI arithmetic, aIso known as "quick math," aIgebra, trigonometry, statistics, and probabiIity are some of the key mathematicaI concepts and abiIities needed in the financiaI sector. A fundamentaI knowIedge of these abiIities shouId be sufficient to quaIify you for the majority of finance occupations.

The highest home vaIue that may be financed is x.

$39,000 in avaiIabIe cash for a down payment

16% is the needed down payment percentage.

16% of the home's worth can be expressed as,

x × 16/100=$39,000

x=39,000/0.16

x=$243,570

We can then infer that the highest vaIue you couId finance is $243,570.

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Answer:

Step-by-step explanation:

Okay so when a smaller number is divided by a larger number, the quotient is less than 1.  Hope this helps Bye sisters slay.

Answer:

i thnk it is c correct me if i am rong

Step-by-step explanation:

Answer:

(C) I got it right

Step-by-step explanation:

on edge