MATHEMATICS HIGH SCHOOL

A line goes through{2,-3)and (-1, 0).slope =
Equation in point -slope form or equation in slope-intercept form

Answers

Answer 1
Answer: (2,-3)(-1,0)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (0 - (-3) / (-1 - 2) = 3/-3 = -1

y = mx + b
slope(m) = -1
use either of ur points (2,-3)...x = 2 and y = -3
now we sub and find b, the y int
-3 = -1(2) + b
-3 = -2 + b
-3 + 2 = b
- 1 = b

so ur equation is : y = - x - 1 (slope intercept form)

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Determine the discriminant for the quadratic equation 0=-2x^2+3 Based on the discriminant value, how many real numbersolutions does the equation have?

Answers

Answer:

This problem has two number solutions. The solutions are x = ±√ 1.500 = ± 1.22474.

Step-bystepexplanation:

Step 1 :

Equation at the end of step 1 :

0 - ((0 - 2x2) + 3) = 0

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 2x2-3

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step 2 :

2x2 - 3 = 0

Step 3 :

Solving a Single Variable Equation :

3.1 Solve : 2x2-3 = 0

Add 3 to both sides of the equation :

2x2 = 3

Divide both sides of the equation by 2:

x2 = 3/2 = 1.500

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 3/2

The equation has two real solutions

These solutions are x = ±√ 1.500 = ± 1.22474

The sum of two consecutive odd integers is 236. What is smaller integers

Answers

I'll say the first integer is x.  The next consecutive odd number would be x+2.  If the sum of the odd integers is 236, the equation would be
x + (x + 2) = 236
solve for x
2x + 2 = 236    
subtract 2 from each side of the equation
2x = 234
divide both sides by 2
x = 117
117 is the first odd integer.  to find the other integer (x + 2), substitute 117 for x, and you have 117 + 2, which equals 119
The two consecutive odd integers that add up to 236 are 117 and 119.

Cheyanne plans to put $150 into a savings account. she can place her money into an account represented by f(x)=5x+150, or into another account represented by g(x)=150(1.03)^x. which account has the highest value in 3 years? which account has the highest value in 10 years?1. f(x) has the highest value in 3 years; g(x) has the highest value in 10 years

2. g(x) has the highest value in 3 years; f(x) has the highest value in 10 years

3. f(x) has the highest value in 3 years; f(x) has the highest value in 10 years

4.g(x) has the highest value in 3 years; g(x) has the highest value in 10 years

Answers

Answer: 1. f(x) has the highest value in 3 years; g(x) has the highest value in 10 years


Step-by-step explanation:

Given:- Principal amount= $150

First account represented by the function=f(x)=5x+150→Linear function

Second account represented by the function=g(x)=150(1.03)^x→Exponential function

where x is the time period in years.

When x=3 years

f(3)=5(3)+150=15+150=\$165

g(3)=150(1.03)^3=\$163.90

here, f(x) has the highest value .

When x=10 years

f(10)=5(10)+150=50+150=\$200

g(10)=150(1.03)^(10)=\$201.58

g(x) has the highest value.

Therefore, f(x) has the highest value in 3 years; g(x) has the highest value in 10 years

1. A polyhedron has 6 vertices and 9 edges. How many faces does it have? a. 3
b. 5
c. 7
d. 9
2. A polyhedron has 25 faces and 36 edges. How many vertices does it have?
a. 11
b. 12
c. 13
d. 14

Answers

V - number of vertices,
E - number of edges,
F - number of faces:
Euler`s polyhedron formula:
V - E + F = 2
1.  F = E - V + 2
F = 9 - 6 + 2 = 5
Answer: A ) 5
2. V = E - F + 2
V = 36 - 25 + 2 = 13
Answer: C ) 13 
 

Answer: 1. B. 2. C. 3. D. 4. A. 5. A.

For the whole practice test :)

A box of dried fruit has 60 calories in 5 servings. How many calories are there per​ serving?

Answers

There are 12 calories per serving. This can be known if you divide 60 by 5
I think 12 calories

Solve ry + s = tx - m for y. Explain each step in your solution?A. Would there be any limitations for the value of each variable? If so, explain the limitation?

Answers

Let's solve for mry+s=tx-mstep 1: Flip the equationstx-m=ry+sstep 2: Add -tx to both sidestx-m+(-tx)=ry+s+(-tx)-m=ry-tx+sstep 3 :Divide both sides by -1-m-1=ry-tx+s-1m=-ry+tx-sI hoped i help :)
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