find the x value of the point of intersection

The required modulus is 41 .

A real and imaginary number combo with the formula a + bi , where

a and b are real numbers, and

i is the "unit imaginary number" √(−1)

a and b may also have zero values.

We are aware that complex numbers are made up of both actual and fictitious numbers.

The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.

Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]

Here, 9 and 40 are substituted for x and y.

i.e. 9+40i

We square the coefficients, add them, and then find the square root to obtain the modulus.

|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]

By long division method we find that

|9+40i| =41

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Answer:

-1/2

Step-by-step explanation:

cos(-360+60)=-1/2

[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]

The slope of the line in graph 2 is equal to 1.

The slope of the line in graph 3 is equal to 1/2.

The slope of the line in graph 4 is equal to 3/4.

The slope of the line in graph 5 is equal to 3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (7 - 2)/(7 - 2)

Slope, m = 5/5

Slope, m = 1.

For the line in graph 3 with the given data points, we have:

Slope, m = (3 + 2)/(6 + 4)

Slope, m = 5/10

Slope, m = 1/2.

For the line in graph 4 with the given data points, we have:

Slope, m = (6 - 0)/(8 - 0)

Slope, m = 6/8

Slope, m = 3/4.

For the line in graph 5 with the given data points, we have:

Slope, m = (6 - 0)/(2 - 0)

Slope, m = 6/2

Slope, m = 3.

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√55 and √40 are the irrational numbers.

A number system is defined as a system of writing to express numbers.

A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.

But an irrational number cannot be written in the form of simple fractions.

√55 is an irrational number

√40 is an irrational number

√49 value is 7 which is a natural number

Hence, √55 and √40 are the irrational numbers.

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The answer is B. 18

When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.

33/44 = x/24

Once finished solving the proportion, you are left with 18

The missing length of triangle is 18.

What exactly is a triangle?

Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.

A triangle is categorised into three categories based on its sides, namely:

A triangle is categorised into three categories based on its angles, namely:

Now,

As these triangles are similar that means

we can find the proportion of sides from given sides and

from that find x.

So, here  AC/AM=AL/AB

44/33=24/x

AL=24*33/44

AL=18

Hence,

            The missing length AL of triangle is 18.

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Answer:

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.

Step-by-step explanation:

Let the number of fit men is x.

Now,

we know

x = 12% of 200 men

x =  [tex]\frac{12}{100}[/tex]   ×200

x = 0.12 × 200

   = 24 men.

Given,

The 60 people are fit to climb the Mount Shasta ,24 of them are men,

so there must be

60 - 24 = 36 women who are fit to climb the mountain.

The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,

P(male or fit) = P(male and fit) + P(female and fit)

P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)

P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])

                     =.4 × .12 + .6 × .12

                     = 0.048 + 0.072

                     =.12

So,

P(male or fit) ≈ 0.12

As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.

Answer:

The correct answer is c. 750

Step-by-step explanation:

if the shops makes 25 dozen in two days that makes it 300 cupcakes In two days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know he/she is going to make half of the 25 dozen on the 5th day so you will take half of 300 which is 150 and add it all together, so will get 300+300+150= 750 as your answer.

Answer:

  (a)  24%

Step-by-step explanation:

You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.

The fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.

  96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%

The Decades slice of the circle would be 24%, choice A.

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Answer:why not

Step-by-step explanation:that sa prrety nice ask

Answer: 5/8

Step-by-step explanation:

The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.

Answer:

48ft²

Step-by-step explanation:

Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.

Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.

Area of left triangle = 0.5*3*4 = 6ft²

Area of square = 4*9 = 36ft²

Area of right triangle = 0.5*3*4 = 6ft²

Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²

Answer:

48ft?

Visualize the trapezoid as consisting of

a rectangle with two triangles on either

side. To find its total area, find the area of

each and add them up.

The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.

Height of Sami in feet and inches is equal to 5 feet 8 inches

Height of Sami's younger sister is equal to 4 feet 11 inches

Convert all height into inches we get,

1 feet = 12inches

5 feet = 5 × 12 inches

          = 60 inches

4 feet = 4 × 12 inches

          = 48 inches

Number of inches Sami's is taller than his younger sister is equal to

= ( 5 feet 8 inches ) - ( 4 feet 11 inches )

= ( 60 + 8 ) inches - ( 48 + 11 ) inches

= 68 inches - 59 inches

= 9 inches

Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.

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Answer: approximately 40lbs.

Step-by-step explanation:

First, you multiply 20kg to 10%, or 0.10.

20(0.10)=2kg

Then you minus the 2kg from the initial weight

20kg

-2kg

18kg

1 kg is approximately 2.20462262 lbs., so you need to convert your kg to lbs

18kg * 2.20462262 lb/kg = 39.68320716 which is rounded up to approximately 40lbs

Hope that helps!

Answer:

[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]

You can choose the level of precision as desired from the above

Step-by-step explanation:

The area of an equilateral triangle of side a

is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]

We are given A = 243

Plugging in values we get

[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]

Switch sides so [tex]a^2[/tex] term is on the left

[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]

Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]

Divide by [tex]\sqrt{3}[/tex]  both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]

Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]

The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420

This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:

(12+2w)(16+2w) = 420

Expanding and simplifying, we get:

4w² + 56w - 204 = 0

Dividing by 4, we get:

w² + 14w - 51 = 0

Factoring, we get:

(w+17)(w-3) = 0

Since the width of the path cannot be negative, the only valid solution is w = 3.

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Complete question is in the image attached

The required overall translation is T<−9,−5>(ABC). The correct answer would be option B.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

Starting with triangle ABC, we first apply the transformation T<−5,−3>, which means each vertex of the triangle is shifted 5 units to the left and 3 units down. So the triangle becomes A'B'C'.

Next, we apply the transformation T<−4,−2> to triangle A'B'C', meaning that each vertex is shifted 4 units to the left and 2 units down.

To find the overall effect of these two transformations, we can think of the second transformation as shifting the entire triangle produced by the first transformation.

In other words, we're combining the effects of the two transformations by adding the translations together.

So, the overall translation is T<−5 + −4, −3 + −2> = T<−9,−5>,

Thus, the correct answer would be option B: T<−9,−5>(ABC).

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Explanation:

Points B and D are midpoints of segments AC and CE respectively. This is because of the tickmarks indicating congruent segment pieces (AB = BC and CD = DE)

Joining the midpoints together forms a midsegment. The midsegment is half as long as the side parallel to it. This means BD is half as long as AE. Flip things around to say that AE is twice as long as BD.

Answer: Looks like a positive correlation with an outlier in the lower left.

Step-by-step explanation:

Answer:

5x(8-1)=(5x10)-(5x4)

The value for the variable x in the parallelogram is equal to 7.

The parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.

We shall evaluate for variable x as follows:

5x + 9 = x + 37

5x - x = 37 - 9 {collect like terms}

4x = 28

x = 28/4 {divide through by 4}

x = 7

Therefore, the value for the variable x in the parallelogram is equal to 7.

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The value of the variable x is 7

It is important to note that the opposite sides of a parallelogram are congruent or equal in length.

Then, for the parallelogram LMNO

NM is parallel to OL

Now, substitute the values, we get;

NM = OL

x + 37 = 5x + 9

collect like terms

x - 5x = 9 - 37

subtract the like terms

-4x = -28

Make 'x' the subject

x = 7

Hence, the value is 7

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Answer:

B)32000

Step-by-step explanation:

Out of 300, 172 are in favor, and 142/300 is simplfieid as 43/75

43/75 is equal to 43,000/75000

Subtract 75000 by 43000

The difference is 32,000.

32,000 voters are against the Issue.

The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.

The system of equations that represents the question is:

f + s = 168 equation 1

2.41f + 1.57s = (1.66 x 168)

2.41f + 1.57s = 278.88 equation 2

Where:

The elimination method would be used to determine the required values

Multiply equation 1 by 2.41

2.41f + 2.41s = 404.88 equation 3

Subtract equation 2 from equation 3

126 = 0.84s

s = 126 / 0.84

s = 150

Substitute for s in equation 1

f + 150 = 168

f = 168 - 150

f - 118 gallons

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Answer:

C

Step-by-step explanation:

consider the coordinates of the same points on both figures

top left vertex of figure P (- 8, 8 )

top left vertex of figure Q (- 4, 4 )

note that both coordinates from Q are half the coordinates of P

then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is

(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )

The concept of exponential growth function is discussed below.

An exponential function is of the form -

y = A(B)ˣ

Given is to explain exponential growth.

Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -

y = A(B)ˣ

More specifically -

[tex]$f(x)=a(1+r)^{x}[/tex]

where -

f(x) = exponential growth function

{a} = initial amount

{r} = growth rate

{x} = number of time intervals

Therefore, the concept of exponential growth function is discussed above.

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{Question in english -

What is exponential growth?}

Answer:

For the nearest 10th of a centimeter, the value of h is 460 cm

Step-by-step explanation:

To find length of h we can use Law of Sines  . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:

a/sin A = b/sin B = c/sin C

In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.

Now:

h/sin 122° = i/sin 26°

We can find h by cross multiplying:

h = i * sin 122° / sin 26°

  =459.9

Here,

h = 459.9 cm

By taking approximation we get 460 cm

Answer:

This answer is actually 1280.3

Step-by-step explanation:

The investments are $ 4000 and $ 3000 in the respective accounts

The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

In the given question,

x = amount invested at 10 %

( 7000 - x ) = amount invested at 11 %

The total interest was $730 :

.10 (x) + .11 (7000-x) = 730

0.1 x + 770 - 0.11 x = 730

0.01 x = 40

x = 4000

Therefore, the amount invested in an account that pays 10 % per year is $ 4000.

Hence ,  the amount invested in an account that pays 11 % per year is

= ( 7000 - x ) = 7000 - 4000 = $ 3000.

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The graph is not a function because it fails the vertical line test

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

The graph (added as an attachment)

The given graph when represented as an equation, is a circle equation

As a general rule, we have

Circle equations are not functions and they do not represent a function on a graph

This is so because they do not pass the vertical line test

Hence, the graph is not a function

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If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.

What is Function?

In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.

They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.

If x and y vary inversely, we can write their relationship as:

x * y = k

where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:

10 * 8 = k

k = 80

Therefore, the function that models the inverse variation is:

x * y = 80

or

y = 80/x

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The lowest common denominator of the fraction is 6

The lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.

The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.

In the fraction given;

x / 3 + x / 2 = 20

The lowest common denominator is 6

Using 6, we can divide through each of the fraction.

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Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.

The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.

Company                    Cost ($)

Shipping Central        3x+3.50

Globe Delivery          2x + 2.99

To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.

The difference between the two cost functions is:

3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x

This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.

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