Name a pair of fractions that use the least common denominator and are equivalent to 9/10 and 5/6

a parabola has its vertex at 1,1 and passes through the point -2,-2. Find the equation of this parabola

Jet001 [13]

Answer:

The vertex form of the equation is $y = -\frac{1}{3}( x-1)^{2} +1$ .

Step-by-step explanation:

You will use the equation $y=a(x-h)^{2} +k$ to solve this parabola. (h, k) is the vertex. So, we plug this into the equation to get $y= a(x - 1)^{2} +1$ .

Then, we substitute the point as our x and y to get $-2 = 9a+1$ (a lot of simplifying was done here). Then, add 2 to the right side of the equation and isolate the $9a$ to get $9a = 3$ . Finally, divide by 9 on both sides to get $a=\frac{1}{3}$ .

Now, substitute your $a$ back into the equation to get y = $-\frac{1}{3}(x-1)^{2}+1$ .

This is in vertex form. If the answer is needed in standard form, simply distribute and simplify to get $y = -\frac{1}{3} x^{2} +\frac{2}{3} x+\frac{2}{3}$ .

5 0

3 years ago

#10) Mrs. Sommer states that angle I is 65 degrees. Is she correct? why or why not

Minchanka [31]

Answer: Mrs. Somner is correct.

Step-by-step explanation: In a triangle, the angles add up to 180 degrees. Since we know that Triangle ABC is equal to Triangle RST, we can assume that their angle values are equal as well. Angle A is 41 degrees, and Angle B is 74 degrees. This adds up to 115 degrees. If we subtract 115 from 180, we get 65. Therefore, Mrs. Somner is correct.

6 0

2 years ago

Could somebody please help me with this?

BARSIC [14]

For this problem, we are going to use the Remainder Theorem. This says that for $x - n$ to be a factor of a polynomial $p(x)$ , then $p(n) = 0$ . Essentially, it says that $x - n$ is a factor if when you substitute $n$ into the polynomial you get a result of 0.

Thus, in our case, when we substitute $x = 2$ into the polynomial, we should get an answer of 0 if $x - 2$ is a factor of the polynomial. Given this information, we can solve for $c$ :

$p(2) = 2^3 - 4(2^2) + 2c + 2 = 0$

$8 - 16 + 2c + 2 = 0$

$2c - 6 = 0$

$2c = 6$

$c = 3$

The solution is c = 3.

7 0

2 years ago

Read 2 more answers

Could I get some help?

balandron [24]

Answer:

#adult tickets sold = 346

#student tickets sold = 812

Step-by-step explanation:

let 'x' = # adult tickets sold

let 'y' = # students tickets sold

System of Equations:

x + y = 1158

5x + y = 2542

I used the elimination method and multiplied the first equation by -1

-x - y = -1158

+<u> 5x + y = 2542</u>

4x = 1384

x = 346

346 + y = 1158

y = 812

4 0

2 years ago

Batteries come in packs of 4. Last month, Joe used 58 batteries in his remote control drone. How many packs of batteries did he

vovangra [49]

It is given that batteries come in a packs of 4. It means in each pack there are 4 batteries.

Joe used 58 batteries . So to find the total number of packets of batteries joe has to open is

Number of batteries used / Total number of batteries in each packet

= 58 / 4

= 14.5

The number of battery can not be in decimal. So we will round the answer to integer. If we round it to 14 it means 14 packets. But in 14 packets there are 14*4 = 56 batteries .

But we know that Joe used 58 batteries. So we will round the final answer to 15.

It means Joe has to open 15 packets of batteries.

8 0

2 years ago