Consider the equation:
0 = x^2 - 10x + 10
1) Rewrite the equation by completing the square.
Your equation should look like (x + a)2 = b or (x - c)2 = d.

Answers

Answer 1
x² - 10x + 10 = 0

Isolate the constant term

x² - 10x = -10

Complete the square
• coefficient of the x term: -10
• divide in half: -5
• square it: (-5)² = 5²
• add 5² to both sides, to complete the square and keep the equation balanced:
x² - 10x + 5² = -10 + 5²
(x-5)² = 15
Answer 2

Answer:

1) We can rewrite the equation as 15=(x-5)^2

2) The solutions to the equation are x=5±15


Related Questions

Suppose I randomly choose 4 distinct integers between 1 and 60. Is it true, or is it not true, that at least 2 of them must differ by no more than 19.

Answers

Answer:

It’s true

Step-by-step explanation:

Proof by induction

Let the four chosen numbers be x_1, … x_4 and, without loss of generality, let x_1 < x_2, … < x_4.

For x_1 = 1, the smallest possible choice, let x_2 = x_1 + 20 = 21 be the smallest possible choice that has a difference larger than 19. Likewise, x_3 = x_2 + 20 = x_1 + 40 = 41. Then x_4 has to be at least x_3 + 20 = x_1 + 60 = 61 which is out of range.

For the induction, suppose that x_4(n) = x_1(n) + 60 > 60 and therefore x_4(n) can’t be chosen for a given x_1(n). Then incrementing x_1(n+1) = x_1(n) + 1 would require x_4(n+1) to be at least x_1(n) + 1 + 60 = x_4(n) + 1 > 61, so this is out of range as well.

For another induction, suppose that x_4(n) = x_2(n) + 40 > 60 and therefore x_4(n) can’t be chosen for a given x_2(n). Then incrementing x_2(n+1) = x_2(n) + 1 would require x_4(n+1) to be at least x_2(n+1) + 40 = x_4(n) + 1 > 61, so this is out of range as well.

Likewise, for the induction, suppose that x_4(n) = x_3(n) + 20 > 60 and therefore x_4(n) can’t be chosen for a given x_3(n). Then incrementing x_3(n+1) = x_3(n) + 1 would require x_4(n+1) to be at least x_3(n+1) + 20 = x_4(n) + 1 > 61, so this is out of range as well.

Therefore all choices of x_1, x_2, x_3 with differences greater than 19 leaves no choice of x_4 within range with x_4 > x_3 + 19.

40 is 20 of what number

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{40 is 20\% of what time number?}\\\\\\\bullet \large\bold{We\ are\ looking\ for\ your\ UNKNOWN\ number; we\ can\ the\ value}\\\large\bold{is\ \underline{a}\ for\ our\ answer!}\\\bullet\large\bold{REMEMBER: Percentages\ are\ out\ 100\ \& the\ word\ \underline{of}\ means\ \underline{multiply}}[/tex]

[tex]\huge\text{NOW LETS SOLVE FOR YOUR ANSWER!}[/tex]

[tex]\bold{Equation: 20\%\ \times \ a\ =\ 40}\\\\\bold{a = \dfrac{40}{20\%}}}\\\\\bold{20\% = \dfrac{20}{100}\rightarrow 0.2}}}\\\\\bold{Equation: a = \dfrac{40}{0.2}}\\\\\bold{\dfrac{40}{0.2}=200}\\\\\bold{a=200}\\\\\boxed{\boxed{\bold{Answer: 200}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Ben has $19 to spend. He spent $7.25, including tax, to buy a notebook. He needs to save $2.75 but he wants to buy a snack. If pretzels cost $0.50 per package including tax, what inequality would show the maximum number of packages that Ben can buy?
PLS HELP ASAP:
- what is the INEQUALITY FOR THIS PROBLEM. THAT'S ALL IM ASKING. DON'T SOLVE IT.

Answers

Answer:

($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19

Step-by-step explanation:

First, let's define the variable:

p = pretzel packages

Let's first find out how much money Ben has after buying the notebook.

$19 - $7.25 = $11.75

So, we know that Ben has $11.75 left.

The inequality would be: ($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19

Evaluate expression below if t=3
2t+7-t+1

Answers

Answer:

doo doo fart

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Evaluate: ab+a^2, if a=937 and b=63

Answers

i think it’s 937,000

The value of expression ab + a² is,  9,37,000

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ ab + a²

And, a = 937, b = 63

Now, Substitute the value of a and b in expression as,

⇒ ab + a²

⇒ 937 × 63 + 937²

⇒ 937 (63 + 937)

⇒ 937 × 1,000

⇒ 9,37,000

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

What is the conjugate of the product (2 - i)(1+2i)?

Answers

Answer:

4-3i is the answer.......

Explanation

Product

(2-i)(1+2i) = 2+4i-i-2i²

= 2+4i-i+2

= 4+3i

conjugate of 4+3i is 4-3i

Help me I’ll mark brainliest please

Answers

Answer:

I don't know sorry but I really want brainliest

Work out the size of angle x
Next to 164 and 90

Answers

Answer:

x=106 degrees

Step-by-step explanation:

I'm going to assume that this is a circle since you didn't give it to me

So you want to add 164 and 90 together and subtract the sum by 360

360-(164+90)=106

So you want to use PEMDAS (order of operations) to solve this

so do what's in the perenthesis first so 164+90=254Then you want to subtract 254 from 360 so 360-254=106

x=106 degrees

Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery County tax rate is 9.5%.

Answers

Answer:

$68.24

Step-by-step explanation:

Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery County tax rate is 9.5%.

Given data

The total bill was $76.25

tip

=20/100*76.25

=0.2*76.25

=15.25

Tax

=9.5/100*76.25

= 0.095*76.25

=$7.24375

In all the bills is 76.25-15.25+7.24375

=61+7.24375

=$68.24

13. Find AC. PLEASEE I NEED HELP!!!!!

Answers

AC should equal to 14.

5r + 2(3r - 1) = -46

please show the work

Answers

Answer:

R = - 4

Step-by-step explanation:

5 r + 6r - 2 = - 46

11 r - 2 = - 46

11 r = - 46 + 2

11 r = - 44

r = - 4

Help Needed! What is the value of x in the triangle? A. 21 B. 10 C. 7 D. 7√3

Answers

Answer:

21

Step-by-step explanation:


HELP PLEASE PLEASE PLEASE

1. A lawncare worker charges $45 per hour of work.
additional fee of $20 for equipment transportation.
A. Write an equation in slope-intercept form for this
situation
B. Il your total bill was S155, how long did the worker fix
your yard?
C. If the lawncare worker works a full 8-hour shift, how
much does he make

Answers

A.Slope- intercept form is y= Mx+b so y= 45x + 20

B. 3 hours;
155=45x+20
155 -20 = 135
135/45 = 3

C. $380
y= 45(8)+ 20
45*8= 360
360+20= 380

Decide which item is the better purchase in each scenario below. In addition, state how much you will save per item. Brayden was looking to purchase apples; 5 lbs for $2.89 or 7 lbs for $3.25

Answers

Answer:

7 pounds for 3.25

Step-by-step explanation:

7 pounds of apples is alot for a cheap price like 3.25

5lbs for $2.89 because 5x2.89=14.15 and 7x3.25=22.75, and $14.15 is cheaper than $22.75

Can someone help me please :)

Answers

Step-by-step explanation:

the answer is in the attachment.

Three coins are tossed simultaneously 350 times. The distribution of various outcomes is listed below :Outcome3 Tails2 Tails1 TailNo TailsNo. Of times65 95 110 80 respevtove;y Compute the probability of getting:(i)At least 1tail(ii) Exactly 3 heads

Answers

Answer:

(i) [tex]\frac{27}{35}[/tex]

(ii) [tex]\frac{8}{35}[/tex]

Step-by-step explanation:

Probability refers to chances of occurrence of any event.

Probability is calculated by dividing number of favorable outcomes by total number of possible outcomes.

Total number possible of outcomes = 350

(i)

Number of favorable outcomes = [tex]65+95+110=270[/tex]

Probability [tex]=\frac{270}{350}=\frac{27}{35}[/tex]

(ii)

Exactly 3 heads is equivalent to no tails.

Number of favorable outcomes = [tex]80[/tex]

Probability [tex]=\frac{80}{350}=\frac{8}{35}[/tex]

Evaluate (c^-2)^0 where c=4

Answers

Answer:

1

Step-by-step explanation:

Any value to the power of 0 is equal to 1.

[tex](c^-^2)^0=(4^-^2)^0=(\frac{1}{16} )^0= 1[/tex]

plssssssssssssssssss hellllllllllp meeeee

Answers

Answer:4b+5=1+5b

Step-by-step explanation: b= 14b I HOPE THIS HELPS AND HAVE A GOOD DAY!!!! And i really do hope this did help.

Name the property of addition modeled here. If a = b, then a + c = b + c. A. Addition Property of Equality B. Commutative Property of Addition C. Associative Property of Addition D. None of the above I think it is either B or C

Answers

Answer: I'm pretty sure it's B

Step-by-step explanation:

Answer:

Do you still need an answer? If so, B!

Step-by-step explanation:

Just by looking at the equation you can see the addition symbols. Since there are also letters, you can use that information to help you solve the answer using the key word: Commutative.

For Example: If Lily needs $40 and she already has $30 how many more dollars does she need?

Answer: m-$30=$40 m=$10

If g(x)=5/4x-7 what is the value of g(12)

Answers

Answer:

g(12) = 8

Step-by-step explanation:

g(x) = 5/4(12) - 7

g(x) = 5 × 3 - 7

g(x) = 15 - 7

g(x) = 8

i hope this helps :)

N/-3 - 2 = 8 n=___ help

Answers

Answer:

-30

Step-by-step explanation:

[tex]\frac{N}{-3} -2 =8[/tex] ( Add 2 on both sides)

[tex]\frac{N}{-3} = 10[/tex] ( Multiply by -3 on both sides)

[tex]N = -30[/tex]

Verify:

[tex]\frac{-30}{-3} =10[/tex] (Correct)

Answer:

[tex] \frac{n}{ - 3} - 2 = 8 \\ \frac{n}{ - 3} = 8 + 2 \\ = 10 \\ n = 10 \times - 3 \\ n = - 30[/tex]

The budget for a school dance is 370.00. The band charges $65.00 per hour. What is the maximum number of hours the school can have the band play at the dance?

Answers

C. 4 hours I think hope this helps :)
I think it’s C but the amount of hours is 5

cell phone provider offers a plan that costs ​$40 per month plus ​$0.20 per text message sent or received. A comparable plan costs ​$70 per month but offers unlimited text messaging.

Answers

Answer:

the second one is the better deal

Step-by-step explanation:

Ursula likes to kayak. She uses the equation y=4x to calculate how far she has traveled, where y represents the number of miles traveled, and x represents the number of hours spent kayaking.

How many hours must Ursula kayak to travel 10.4 miles?

Answers

Hopefully this helps you get how to set up these types of problems
Answer: 2.6 hours

Y = 4x

Given: y = 10.4

10.4 = 4x

Rearrange

4x = 10.4

x = 10.4/4 = 2.6 hours

(The below part might not be needed)

0.6 x 60 = 36 min

2 hr 36 min

Find the 3rd term in the sequence​

Answers

c₂ = c₁ - 16 = 6 - 16 = -10
c₃ = c₂ - 16 = -10 - 16 = -26

A worker on the production line is paid a base salary of ​$170 per week plus ​$1.21 for each unit produced. Write an equation to represent his earnings of ​$491.86 for a week when he produced x units. How many units did he ​produce? Use pencil and paper. If the worker had produced twice that number of​ units, what would his earnings have​ been? Show your work.

Answers

Answer:

Part 1)

$170 + $1.21x = $491.86

Part 2)

170 + 1.21x + 491.86

1.21x = 491.86 - 170

1.21 x = 321.86

1.21x/ 1.21 = 321.86/ 1.21

x = 266 units produced

Part 3)

Twice that number of units = 266 x 2 = 532

$170 + ($1.21 x 532) =

$170 + $643.72 = $813.72

Cards in a pack are black or red in the ratio
black: red = 2:5
What fraction of the cards are red?
Ovo

Answers

I’m pretty sure it’s 5/7 .

Please give brainliest !

Factor the algebraic expression. 9a+21

Answers

Step-by-step explanation:

1. factor 3 out of 9a + 21

answer: 3(3a + 7)

2v+7=3

Help me out


I’m dating vinnie hacker

Answers

2v=3-7
2v=-4 divide both sides
v=-2

Answer:

v= -2

Step-by-step explanation:

2v+7=3 ------> 2v = 3 - 7 ----------> 2v = -4 ( divide by 2)

v = -2

A car is parked 80 feet from the base of a 120-foot building. What is the angle of depression from the top of the building to the car? Round your answer to the nearest degree.


A 48° degrees


B 34° degrees


C 42° degrees


D 56° degrees

Answers

The angle of depression should be the inverse tangent of 80/120, which is about 34 degrees.
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