Jean, Pierre and Rachel are friends. Pierre is 8 years older than Rachel, while Jean is 15 years younger
than double the age of Peter. In addition, the sum of Peter's age and a quarter of Rachel's age is
John's age minus 5. Find out what each person's ages are.

AYO CAN ANYONE HELP ???

Another accepted answer is -5-i, but if your teacher wants only one answer, then I'd go for 5+i

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Work Shown:

[tex]\sqrt{24+10i} = a+bi\\\\\left(\sqrt{24+10i}\right)^2 = (a+bi)^2\\\\24+10i = a^2+2abi+b^2i^2\\\\24+10i = a^2+2abi+b^2(-1)\\\\24+10i = a^2+2abi-b^2\\\\24+10i = (a^2-b^2)+(2ab)i\\\\[/tex]

Equating terms, we have this system

[tex]\begin{cases}24 = a^2-b^2\ \text{.... real terms}\\10 = 2ab\ \text{.... imaginary terms}\end{cases}[/tex]

Solve the second equation for b to get b = 5/a

Plug that into the first equation to solve for 'a'

[tex]24 = a^2-b^2\\\\24 = a^2-\left(\frac{5}{a}\right)^2\\\\24 = a^2-\frac{25}{a^2}\\\\24a^2 = a^4-25\\\\0 = a^4-24a^2-25\\\\a^4-24a^2-25 = 0\\\\(a^2-25)(a^2+1) = 0\\\\(a-5)(a+5)(a^2+1) = 0\\\\[/tex]

Setting each factor equal to zero would lead to...

We're told that 'a' is a real number, so we ignore the solutions "a = i and a = -i". The only possible solutions are a = 5 and a = -5

If a = 5, then,

b = 5/a = 5/5 = 1

So

[tex]\sqrt{24+10i} = a+bi = 5+1i = 5+i[/tex]

or in short,

[tex]\sqrt{24+10i} = 5+i[/tex]

-----------------

If a = -5, then b = 5/a = 5/(-5) = -1

So it's very possible that we could also say

[tex]\sqrt{24+10i} = -5-i\\\\[/tex]

If you wanted to combine the two we would use the plus/minus notation like so

[tex]\sqrt{24+10i} = \pm(5+i)\\\\[/tex]

This is due to (5+i)^2 and (-5-i)^2 both having the same result of 24+10i. Hence the plus/minus. If your teacher wants one answer only, then I'd go for 5+i, as we could consider it a "principal" square root in a sense.

Answer:

Step-by-step explanation:

convert 1 day into hours

1 day=24 hour

2/24

=1/12

1 day = 24 hours

So,

Answer:

Step-by-step explanation:

use the idea of similar triangles.

6/3 = 3/x

2x = 3

x = 3/2

Answer:

B. x = 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

check by substituting each given value of x into the function

x = 0 ⇒ y =  × 0² = 0

hence (0, 0) is correct

x = 2 ⇒ y =  × 4 = 3

hence (2, 4 ) is incorrect

x = 3 ⇒ y =  × 9 = 6  

hence (3, 6 ) is correct

x = 5 ⇒ y =  × 25 = 18  

hence (5, 18 ) is correct

Answer:

I think it is the $4.20 because if you do the math technically the 4.20 is less for more

Step-by-step explanation:

Answer:

2 °F

Step-by-step explanation:

Overnight temperature = -7 °F

Total Noon temperature = 9 °F

What was the temperature in Chicago that afternoon?

Temperature in Chicago that afternoon = Total Noon temperature + Overnight temperature

= 9 °F + (-7 °F)

= 9 °F - 7 °F

= 2 °F

Temperature in Chicago that afternoon = 2 °F

Answer:

6in

Step-by-step explanation:

Using the pythagerous thereom,

10^2 = 8^2 + b^2

b^2 = 10^2-8^2

b^2 = 100-64

b^2 = 36

b = 6

Feel free to mark this as brainliest :D

Answer:

6

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

?^2 + 8^2 = 10^2

?^2 +64 = 100

?^2 = 100-64

?^2 = 36

Take the square root of each side

? = sqrt(36)

?= 6

Answer:

$3.60

Step-by-step explanation:

8 apples × 150 grams

1200 grams

1 kilogram = 1000 grams

x. = 1200 grams

X = 1.2 kg

1kg = $3.00

1.2kg =$3.6

The cost of 8 apples that have weight 1.2 kilograms is,

⇒ $3.60

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Amy buys eight apples that each weigh 150 grams.

And, She notices that they are on sale for $3.00 per kilogram.

Now,

Total weight of the apples is,

⇒ 8 × 150 grams

⇒ 1200 grams

⇒ 1.2 kilograms

Since, She notices that they are on sale for $3.00 per kilogram.

Hence, The cost of 8 apples that have weight 1.2 kilograms is,

⇒ $3.00 × 1.2

⇒ $3.60

Thus, The cost of 8 apples that have weight 1.2 kilograms is,

⇒ $3.60

Learn more about the multiplication visit:

https://brainly.com/question/10873737

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Answer:

The zeros the polynomial :

X=(1/2 , –5)

Answer:

It is not a function because as seen through the mapping diagram, 14 is paired with more than one output. Hence, it is not a function because a function occurs when an input is paired with one, and only one output.

Step-by-step explanation:

hope this helps and is right. p.s i really need brainliest :)

Answer:

33464.25

Step-by-step explanation:

Using BODMAS : brackets, division, multiplication, addition

[tex]177\times ((177+(9-4+7)) +\frac{90}{8}\\\\177\times (177+12) +\frac{90}{8}\\\\177\times 189 +\frac{90}{8}\\\\\\177 \times 189 + 11.25\\\\33453 + 11.25\\\\33464.25[/tex]

Answer:

35444.25

Step-by-step explanation:

OFC by computing them

Answer:

I say A or B but in favor A

Step-by-step explanation:

Answer:

$11838.7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + r)^t[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

P = 9500

r = 4.5% = 0.045

t = 5

Step 2: Find A

Answer:

7^5 (7 to the fifth power)

Step-by-step explanation:

those sevens can be represented by 7^5 because there are five sevens to multiply together

you can check the answer by doing 7 x 7 x 7 x 7 x 7=16807

and making sure that 7^5 is also equal to 16807, which it is.

Hope this helps! :)

Answer:

Step-by-step explanation:

C

The area of the circular shaped pizza is A = 254.5 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the pizza be r = 9 cm

The area A of a circle with radius r is given by the formula:

A = πr²

Substituting the given radius of 9 cm, we get:

A = π(9 cm)²

A = π(81 cm²)

A ≈ 254.47 cm²

Rounding to one decimal place, we get:

A ≈ 254.5 cm²

Hence , the area of the circular pizza with a radius of 9 cm is approximately 254.5 cm²

To learn more about circle click :

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Answer:

Step-by-step explanation:

2/3*x=20

2x=20*3

x=60/2

x=30

i need points srry

Step-by-step explanation:

Answer:

C. 600 m²

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides and four angles) with two pairs of parallel sides. Opposite sides and angles of a parallelogram are equal to each other. Also, the diagonals are equal.

The area of a parallelogram is the product of its base and its height. It is given by the formula:

Area = base * height

We can see that for this parallelogram, the height = 15 m, the base = 40 m, hence:

Area = base * height = 40 m * 15 m = 600 m²

5dgji

Step-by-step explanation:

how???? ... hope it is good

Answer:

It would be 17 feet.

Step-by-step explanation:

So to do this, there is a right triangle being made with the height of the water slide and its base (length). With this, the Pythagorean Theorem can be used to find the hypotenuse of these lengths by the equation:

a^2 + b^2 = c^2

So by plugging in the given legs of the triangle, the answer can be found.

15^2 + 8^2 = c^2

225 + 64 = c^2

289 = c^2

c = 17

Answer:

did u try looking it up lol?

Step-by-step explanation:

Answer:

i, 1.875 ft

ii. Since the volume of water is the same when resting on either the smallest or largest face, we we equate the expression for their volume and solve for the depth of water when the closed rectangular box is resting on its largest face.

Step-by-step explanation:

i. How deep will the water be if the box is resting on its largest face?

Since the smallest face is 5 feet by 3 feet (since they are the smallest dimensions), the volume of the 5 feet deep water is V = Ah where A = area of smallest face and h = depth of water.

V = Ah = 5 ft × 3 ft × 5 ft = 75 ft³

This is also the volume of the water when it is resting on its largest face.

Since the dimensions of the largest face are 8 feet by 5 feet (since they are the largest dimensions), then V = A'h' where A' = area of largest face and h' = depth of water when rectangular box is resting on its largest face

So, h' = V/A'

= 75 ft³/ (8 ft × 5 ft)

= 15/8 ft

= 1.875 ft

ii, Explain your reasoning.

Since the volume of the water in the closed rectangular box is always the same, which ever side we turn it to, its volume V = area of face × height. If we write this expression for both the smallest and largest face and equate them, we solve for the depth of the water when it is resting on its largest face, since, we already know the depth of water when it is resting on its smallest face.

Answer:

28

Step-by-step explanation:

Diagonals of a rectangle are congruent and bisects each other. So, using this property and By exterior angle theorem:

2x° = 56°

2x = 56

x = 56/2

x = 28

Answer: x=28

Step-by-step explanation:

A line has to be 180 degrees

You have 56, so 180-55=124 degrees

Angles are parallel because of the two double curve line.

Now you have that one triangle with the angle of 124degrees and x degrees and the third angle is unknown.

You know that a triangle is 180 degrees

So 180-124=56 degrees

So the unknown angle and the x angle together have to equal 56 degrees.

Since both angles are the same all you do is 56/2.

Now x= 28degrees

Answer:

OA. 81

Step-by-step explanation:

A composite number is a positive integer that can be formed by multiplying two smaller positive integers.

81 = 9 x 9

81 = 3 x 27

Answer:

79

Step-by-step explanation:

79, 85, 89, 68 have a mean of 80.25 according to calculator.net. the number itself Is close to the number you want, in this case 80, i input 80, but it gave me a score of 80.2, so i tried again with 81, it gave me a score of 80.4, so the third attempt was successful with 79 being the input and 80 the output

calculator.net is approved on my school computer so there is a chance it is on yours as well.

Answer:

B. -11

Step-by-step explanation:

ascending order means least to greatest.

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,...

3, -1, [tex]\sqrt{5}[/tex], 13, -11

-11 is the least number because it is the greatest negative number

Answer:

Around 140

Step-by-step explanation:

It's over 90 degree angle