MATHEMATICS HIGH SCHOOL

What are the solutions of x^2 - 5x+7 = 0 ?

Answers

Answer 1

Answer:

Answer:

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=(-b\pm√(b^2-4ac) )/(2a)$

Algebra II

Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define

x² - 5x + 7 = 0

Step 2: Identify Variables

a = 1

b = -5

c = 7

Step 3: Find solutions

Substitute [Quad Formula]: $x=(5\pm√((-5)^2-4(1)(7)) )/(2(1))$
Evaluate Exponents: $x=(5\pm√(25-4(1)(7)) )/(2(1))$
Evaluate Multiplication: $x=(5\pm√(25-28) )/(2)$
Evaluate Subtraction: $x=(5\pm√(-3) )/(2)$
Factor: $x=(5\pm√(-1) √(3) )/(2)$
Simplify: $x=(5\pm i√(3) )/(2)$

Answer 2

Answer:

The solutions to the equation x² - 5x + 7 = 0 are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Option C is the correct answer.

We have,

To find the solutions of the quadraticequation x² - 5x + 7 = 0, we can use the quadraticformula:

x = (-b ± √(b² - 4ac)) / (2a)

For the given equation, the coefficients are:

a = 1

b = -5

c = 7

Substituting these values into the quadraticformula,

x = (-(-5) ± √((-5)² - 4(1)(7))) / (2(1))

Simplifying further:

x = (5 ± √(25 - 28)) / 2

x = (5 ± √(-3)) / 2

Since the discriminant (the value inside the square root) is negative, √(-3) is imaginary, meaning there are norealsolutions to this quadratic equation.

The solutions exist in the complex number system.

So,

√-1 = i

x = (5 ± i√3) / 2

This can be written as,

x = (5 + i√3) / 2

and

x = (5 - i√3) / 2

Thus,

The solutions to the equation x² - 5x + 7 = 0 are:

x = (5 + i√3) / 2 or x = (5 - i√3) / 2

Learn more about solutionsofequations here:

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Yh plss I need an answer to this question plss

Answers

Question:

A boy makes a cone of diameter 28 cm without a base. He then cuts a smaller cone of diameter 20 cm from the cone. He used the bottom part as a lampshade. If the height of the lampshade is 11cm,

(a) find the volume of the whole cone.

(b) find in cm2, the area of the material used to make the lampshade.

Answer:

(a) V ≈ 16420.1

(b) A ≈ 2690.1 cm²

Step-by-step explanation:

Solution for (a)

Formula: The formula for the volume of a cone is V = 1/3 hπr².

V= πr² h/3 = π × 28/ 2 × 20/ 3 ≈ 16420.0576

16420.0576 in nearest tenths is 16420.1

Therefore, the volume of the whole cone is 16420.1 cm²

Solution for (b)

Formula: A = πrl + πr2.

l = r² + h²

Solving for A

A = πr (r + h²+ r²) = π × 20 × (20 + 112 + 202) ≈ 2690.80077

2690.80077 In nearest tenths, is 2690.1

Therefore, the area of the material used to make the lampshade is 2690.1 cm²

What is the value of x in the following proportion? 7/x-5 = 15/x+4

Answers

For this question you should first add -15/x on both sides of the equation and then add +5 on both sides:
7/x - 15/x = 5 + 4
-8/x = 9
so now you can multiply both sides by x:
-8 = 9x
now you should divide both sides by 9:
-8/9 = x :)))
I hope this is helpful
have a nice day

Tickets at the theater or $9 for adults seniors receive a discount and only have to pay $6 but capicity of the theater is 80 people. If the theater was at full capacity and made $675, then how many seniors bought tickets for the movies? And how did you get that answer

Answers

so $9 for adults and $6 for seniors

so number of adults is represented by x
number of seinors is represented by y

9x+6y=675 since every adult pays 9 and seinors pay 6

x+y=80 since adults+seinors=80

multiply x+y=80 by -6
-6x-6y=-480
add this to 9x+6y=675
9x-6x+6y-6y=675-480
3x+0=195
divide both sides by 3
x=65
there were 65 adults

subsitute 65 for x in x+y=80
65+y=80
subtract 65 from both sides
y=15

there were 15 seinors at the event

What is the range of 22,44,66,88

Answers

the range is 66 u subtract 88 to 22

Tom Slick buys a set of tires for his car. The price, including tax, is $950.00. Tom finances the tires over 12 months after making a $50 down payment. The true annual interest rate is 18%. What are his monthly payments (principal plus interest)?

Answers

The price of the car is 950 dollars.
he paid 50 dollars for downpayment
=> 950 dollars - 50 dollars = 900 dollars to be paid for 12 months
=> 12 months = 1 year which have 18% annual interest.
=> 900 dollars * .18 = 162 dollars
=> 900 + 162 = 1062 dollars
=> 1062 / 12 = 88.5 dollars is his monthly

Hey guys! I would be thankful if anyone could help me answer this question. A can manufacturing company needs to purchase labels for the cans they produce. They are planning to produce 200,000 cans that will have a height of 20cm and a radius of 5 cm. If the labels cover the entire curved surface of each can, how many square metres of material will be required to label all the cans?

Answers

In order to not get confused, start by converting cm to m
h=20 cm = 0.2m and r=5cm = 0.05m

The cans are cylinders and we only need the rectangular shape, which is equal to the height x the circumference of the circle (2r(pi)), which you'll have to multiply by 200,000 for the number of cans necessary

your equation is therefore:
A=200,000h(2pi(r))
A=200,000(0.2)(2)(0.05)(pi)
A=4000pi m^2

Surface area for a cylinder = 2πrh

r = 5cm, h= 20cm

Surface area for one can = 2πrh = 2*π*5*20 = 200π = 200* 3.14

Surface area ≈ 628 cm²

For the 200, 000 cans, Total area = 200 000 * 628 = 125 600 000 cm²

But 1 000 000 cm² = 1m²

125 600 000 cm² = 125 600 000 / 1 000 000 = 125.6 m²

Total surface area ≈ 125.6 m²

What are the solutions of x^2 - 5x+7 = 0 ?​

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What are the solutions of x^2 - 5x+7 = 0 ?