All categories

3 years ago

Polynomials with the same roots can have different graphs. True? Or false?

1 answer:

8 0

True.

E.g. (x-1)(x-2) versus 100(x-1)(x-2)

They have same roots of x= 1 or 2, but the second equation is 100 times stretching of the first one vertically

You might be interested in

The sum of 5 times a larger number and twice a smaller is 5. The difference of 4 times the larger and the smaller number is 4. F

Gemiola [76]

Answer:

1 and 0

Step-by-step explanation:

Let's call the smaller number x and the larger number y.

This means 5y+2x=5.

Also, 4y-x=4.

This is a system of equations. There are two main ways two solve this.

Method 1: Substitution

5y+2x=5

4y-x=4

Solve for one of the variables, then substitute it back into one of the equations to solve for the other variable.

I will take 4y-x=4 and solve for x.

4y=4+x

x=4y-4

Then substitute for x in the other equation and solve for y.

5y+2x=5

5y+2(4y-4)=5

5y+8y-8=5

13y=13

y=1

Now we can go back to our equation for x and substitute for y.

x=4y-4

x=4(1)-4=0

y, the larger number, is 1 and

x, the smaller number, is 0

Method 2: Elimination

5y+2x=5

4y-x=4

Change the equations so that the coefficient of one of the variables in an equation is opposite the one in the other equation. Then add the equations and solve for each variable.

If I multiply both sides of the second equation, 4y-x=4, by 2, the coefficient of x will become -2. In the first equation, the coefficient is 2, so they will become opposites.

4y-x=4

becomes

8y-2x=8

Now we have 5y+2x=5 and 8y-2x=8.

Add the sides of both equations to cancel the x values.

5y+2x+8y-2x=5+8

13y=13

y=1

like last time, we can substitute for y in any of the original equations to get x.

5y+2x=5

5(1)+2x=5

5+2x=5

2x=0

x=0

y, the larger number, is 1 and

x, the smaller number, is 0

6 0

3 years ago

One pound of swordfish costs as much as 1.5 pounds of salmon. Mrs. O pays $39 for 2 pounds of salmon and 3 pounds of swordfish.

Dimas [21]

Answer:

The ratio of the amount for swordfish to the amount of salmon is 6:4

Step-by-step explanation:

Given as :

The price for 1 pound of swordfish = The price of 1.5 pound of salmon

So, On this relation

The price for ( 1 × 2 ) pound of swordfish = The price of ( 1.5× 2 ) pound of salmon

i.e The price for 2 pound of swordfish = The price of 3 pound of salmon

Now According to question

Mrs. O pay the total money for 2 pounds of swordfish and 3 pound of salmon = $ 39

Let the money she pay for swordfish = 2 sw

And The money she pay for salmon = 3 sa

∵, The total money she pay for both = $ 39

I.e 2 sw + 3 sa = 39

As 2 sw = 3 sa

So, 3 sa + 3 sa = 39

Or, 6 sa = 39

or, sa = $\frac{39}{6}$ = $\frac{13}{2}$

∴ sw = $\frac{13}{2}$ × $\frac{3}{2}$

or, sw = $\frac{39}{4}$

Now, the ratio of the amount for swordfish to the amount of salmon = $\frac{\frac{39}{4}}{\frac{13}{2}}$

I.e The ratio = $\frac{6}{4}$

Hence The ratio of the amount for swordfish to the amount of salmon is 6:4

Answer

3 0

3 years ago

Determine the function that represents the relationship.

soldier1979 [14.2K]

Answer:

Option B

Step-by-step explanation:

To solve these kind of question we just simply keep on inserting the values of x and if we get the required value of y that is in the table that equation is our answer, For example lets take Option A,

y = 8x

If we insert x = 0 we get,

y = 8(0)

y=0

but in the table it says we get 14 so option A is incorrect

Like this we keep checking for more values and all the values of x satisfy our equation in Option B like this,

$y=8x+14\\y=8(0)+14\\y= 14\\\\y=8x+14\\y=8(1)+14\\y=8+14\\y=22\\\\y=8x+14\\y=8(2)+14\\y=16+14\\y=30\\$

and so on so Option B is the answer

8 0

3 years ago

Read 2 more answers

Someone please help ASAP will give brainliest

Svetach [21]

Answer:

Step-by-step explanation:

The degree is cubic (3) and there are 3 terms X^3, X^2, X

7 0

3 years ago

F equals to 2 f - 20

ICE Princess25 [194]

Answer:

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

7 0

3 years ago