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3 years ago

Consider the quadratic equations

2 answers:

6 0

Consider the two functions as
<span>y1(x) =3x^2 - 5x,
y2(x) = 2x^2 - x - c

The higher the value of c, father apart the two equations will be.
They will touch when the difference, i.e. y1(x)-y2(x)=x^2-4*x+c has a discriminant of 0.
This happens when D=((-4)^2-4c)=0, or when c=4.
(a)
So when c=4, the two equations will barely touch, giving a single solution, or coincident roots.
(b)
when c is greater than 4, the two curves are farther apart, thus there will be no (real) solution.
(c)
when c<4, then the two curves will cross at more than one location, giving two distinct solutions.

It will be more obvious if you plot the two curves in a graphics calculator using c=3,4, and 5.

</span>

laila [671]3 years ago

3 0

Can you please make this more clear

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Money is borrowed at 15% simple interest. After one year,$1181.05 pays off the loan. How much was originally borrowed?

marin [14]

Answer: $787 was originally borrowed.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

From the information given,

Total amount = $1181.05

Interest = total amount - principal

I = 1181.05 - P

R = 15%

T = 1 year

Therefore,

1181.05 - P

Therefore,

1181.05 - P = (P × 15 × 1)/100

1181.05 - P = 0.15P

P + 0.15P = 1181.0

1.5P = 1181.05

P = 1181.05/1.5

P = $787

5 0

2 years ago

If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?

ELEN [110]

Answer:

The total number of students in Toby's grade is 200.

3 0

2 years ago

Each container has a base of 4 1/4 yds by 1 2/3 yds. What is the area covered by all the containers?

svet-max [94.6K]

Answer:

See Explanation

Step-by-step explanation:

Given

Base Dimension

$Length = 4\frac{1}{4}yd$

$Width = 1\frac{2}{3}yd$

Required

The base area of all containers

First, calculate the base area of 1 container.

This is calculated as:

$Area = Length * Width$

$Area = 4\frac{1}{4}yd * 1\frac{2}{3}yd$

Express as improper fraction

$Area = \frac{17}{4}yd * \frac{5}{3}yd$

So, we have:

$Area = \frac{17*5}{4*3}yd^2$

$Area = \frac{85}{12}yd^2$

The number of containers is not given. So, I will use 'n' as the number of containers.

So, we have:

$Total = n * Area$

$Total= n * \frac{85}{12}yd^2$

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

Assume n is 3 (i.e. 3 containers)

The total area is:

$Total= 3 * \frac{85}{12}yd^2$

$Total= \frac{85}{4}yd^2$

$Total= 21\frac{1}{4}yd^2$

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

6 0

2 years ago

HELP ASAP WILL GIVE BRAINLIST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Question 4(Multiple Choice Worth 4 points) (02.05)The

OverLord2011 [107]

Answer:

A. D and E are similar but not congruent.

Step by step explanation :

The side lengths of D are 3 units and 1 unit. The side lengths of E are 2 units and 6 units. The sides are proportional, but are not congruent; this means that the quadrilaterals are similar but not congruent. Choice A is true and choice C is false.

The side lengths of E are 2 units and 6 units. The side lengths of F are 3 units and 1 unit. The sides are proportional, but are not congruent; this means that the quadrilaterals are similar but not congruent. Choice B is false.

The side lengths of D are 3 units and 1 unit. The side lengths of F are 3 units and 1 unit. The sides are congruent; this means that the quadrilaterals are congruent. Choice D is false.

6 0

2 years ago

Read 2 more answers

a box of colored pencils contain exactly 6 red pencils. The probability of choosing a red pencil from the box is 2/7. How many o

katrin [286]

Answer:

Step-by-step explanation:

You have to find the total number of crayons whcih will be 21.

Then you do 21-6 ( red pencil) to get 15

15 pencil not read.

7 0

2 years ago