1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tresset [83]
3 years ago
13

Solve the following quadratic by completing the square. y = x2 + 10x + 10

Mathematics
1 answer:
IgorC [24]3 years ago
3 0

Answer:

<h2>         x = -5 - √15    or   x = -5 + √15</h2>

Step-by-step explanation:

y = x^2+10x+10\\\\y=x^2+10x+25-25+10\\\\y=(x+5)^2-15\\\\y=0\quad\iff\quad (x+5)^2-15=0\\\\(x+5)^2=15\\\\x+5=\pm\sqrt{15}\\\\x=-5-\sqrt{15}\quad or\quad x= -5+\sqrt{15}

You might be interested in
Can someone please help me with this question I don’t understand. Thanks
Ghella [55]
I'm assuming your teacher meant to say "line segment AB" and not "line segment AD". Point D is not given at all. If that assumption holds up, then you can proceed with the rest of the solution below. If not, then you'll have to talk to your teacher. I think its a typo but its possible that there's more context somewhere that I'm not seeing (a diagram maybe?)

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

We're given the two points (2,7) and (5,1). The first thing we need to do is find the slope of the line through those points. Lets assign them to be equal to (x1,y1) and (x2,y2), so,

(x1,y1) = (2,7) and (x2,y2) = (5,1)

which further breaks down into these four items:
x1=2
y1=7
x2=5
y2=1

Plug each of those into the slope formula and simplify
m = (y2 - y1)/(x2 - x1)
m = (1 - 7)/(5 - 2)
m = (-6)/(3)
m = -2

The slope is -2. We'll use this to find the y intercept. We'll also use one of the points given to us, say the point (2,7)

(x,y) = (2,7) ---> x = 2 and y = 7

Plug m = -2, x = 2, and y = 7 into the equation below and solve for b
y = m*x + b
7 = -2*2 + b
7 = -4 + b
7 + 4 = -4 + b + 4
11 = b
b = 11

So we figured out that m = -2 is the slope and b = 11 is the y intercept

Therefore, the equation y = mx+b turns into y = -2x+11

Final Answer: y = -2x+11

-------------------------------------------------
Checking the answer:
plug in x = 2 and we get...
y = -2*x + 11
y = -2*2 + 11
y = -4 + 11
y = 7 
so that proves (x,y) = (2,7) is on the line y = -2x+11

Plug in x = 5 and we get...
y = -2*x + 11
y = -2*5 + 11
y = -10 + 11
y = 1
so that proves (x,y) = (5,1) is on the line y = -2x+11

Both points are on the same line y = -2x+11 so the answer is confirmed
7 0
3 years ago
The solution to 2 x 27 will be what kind of number
SCORPION-xisa [38]

2*27= 54


54 is a rational number


I hope that's help :)

5 0
2 years ago
The last time Dior made tacos for her family,she spent $5.33 on 1 1/2 pounds of ground beef. She's heading back to the store aga
Gwar [14]
$5.33=1.5lbs
.5lbs = $1.78
2.5lbs = $8.90
4 0
3 years ago
Does anyone know the answers to this algebra question? Will give brainiest
MaRussiya [10]
Option 1 : -22

using formula

(a + b )(a - b ) = a^2 - b^2

(√10 + 2√8) (√10 - 2√8)

= (√10)^2 - (2√8)^2

= 10 - 2×2×8=10-32

= -22

2nd question answer is option 3
3 0
2 years ago
If you are given odds of 6 to 7 in favor of winning a​ bet, what is the probability of winning the​ bet?
maxonik [38]

Answer: 6/13

Step-by-step explanation: a/a+b = 6/6+7 = 6/13

7 0
3 years ago
Other questions:
  • Choose the expression that represents a quadratic expression.
    11·2 answers
  • What is the solution to the following equation? 1/3 (p+9)=3+2(p-6)
    5·1 answer
  • A local hamburger shop sold a combined total of 695 hamburgers and cheeseburgers on Sunday. There were 55 fewer cheeseburgers so
    11·1 answer
  • Mr. Laing and Mr. Cho we’re having a shoot out during lunch. Mr. Laing scored 8 times and missed 13. Mr. Cho scored 7 goals of h
    13·1 answer
  • Find the difference between the cash price and the payment plan and calculate the interest rate for the following questions.
    7·1 answer
  • What is 8 divided by 9045
    10·2 answers
  • Line segment BA¯¯¯¯¯¯¯¯ has endpoints B(−3,0) and A(5,4). What are the coordinates of the point located 14 of the way from B to
    12·1 answer
  • Help Asap!!!! Giving brainliest
    15·1 answer
  • How do “near facts” help you solve division problems?
    12·1 answer
  • Parallel lines
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!