Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b

Answer:

cost of producing the 501st item = $9.92

Step-by-step explanation:

The function representing the cost is given by;

C(x) = 10000 + 90x - 0.08x²

To get the cost of producing the 501st item, we have to first find the cost of producing 500 items and then do the same for 501 items then subtract the values gotten.

Thus;

C(500) = 10000 + 90(500) - 0.08(500)²

C(500) = 10000 + 45000 - 20000

C(500) = $35000

Similarly;

C(501) = 10000 + 90(501) - 0.08(501)²

C(501) = 10000 + 45090 - 20080.08

C(501) = $35009.92

cost of producing the 501st item = C(501) - C(500) = 35009.92 - 35000 = $9.92

Answer:

y = -3/4x - 6

Step-by-step explanation:

( x − 1 + i ) ( x − 1 − i )

Step-by-step explanation:

_____________ (x-1+i)(x-1-i)

Since you asked how to solve this, I will put the answer at the bottom.

You might not think the same way as I but I think in steps.

The bacteria divide every 20 minutes, and will therefore divide three times every hour, 60/20 = 3.

If the bacteria grow for eleven hours, each bacterium will divide 3 times per hour × 11 hours = 33 times.

(This part is edited)

(orginial size)*2^number of divisions

10*[tex]2^{33\\}[/tex]

=85899345920

Answer:

81.88 is the answer

Step-by-step explanation:

Answer:

1. x >/= -1

2. x < 4

3. x </= -1

4. x >/= -2

5. x < -3

6. x </= 7

Step-by-step explanation:

Answer:

y = -1/4x + 2

Step-by-step explanation:

slope = rise over run

-1 rise for 4 run

y intercept = 2

y = -1/4x + 2

Answer:28604 in total

Step-by-step explanation:

just copy and paste hope this helps

Answer:

28604 miles

Step-by-step explanation:

Just add the two numbers to get the total number of miles:

  14735

+ 13869=

  28604

Problem 1

We're given that angle A = angle B. Also that angle B = angle C.

By the transitive property, we can say angle A = angle C.

So basically all three angles are equal to one another. Let's call that unknown angle x.

For any triangle, the three angles always add to 180, so,

x+x+x = 180

3x = 180

x = 180/3

x = 60

That proves angles A,B, and C are each 60 degrees. This triangle is considered equiangular since all angles are the same. Furthermore, the triangle is also considered equilateral meaning all sides are the same. The term equilateral is more widely used, so I'd go with that term if you could only pick one.

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Problem 2

As mentioned in problem 1, the three angles of a triangle add to 180

A+B+C = 180

A+B+90 = 180

A+B+90-90 = 180-90

A+B = 90

This shows A and B are complementary angles. Complementary angles by definition add to 90 degrees.

Answer: y= -2/7x-2

Step-by-step explanation:

To be parrell they have to have the same slope but different y intercepts.

so just put -2 so it will cross that point

Answer:

Step-by-step explanation:

14

Answer:

1/2

Step-by-step explanation:

Answer:

y÷x 1÷2=1/2 This is the answer.

Answer:

Fill the blank with [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]9xy * (\frac{2}{3}x)^3 = (--/--)x^4y[/tex]

Required

Fill in the gaps

[tex]9xy * (\frac{2}{3}x)^3 = (--/--)x^4y[/tex]

Open Brackets

[tex]9xy * \frac{2^3}{3^3}x^3 = (--/--)x^4y[/tex]

[tex]9xy * \frac{8}{27}x^3 = (--/--)x^4y[/tex]

Multiply xy and x^3

[tex]9 * \frac{8}{27}x^4y = (--/--)x^4y[/tex]

[tex]\frac{9 * 8}{27}x^4y = (--/--)x^4y[/tex]

Divide fraction by 9/9

[tex]\frac{8}{3}x^4y = (--/--)x^4y[/tex]

By comparison, the blank will be filled with:

[tex]\frac{8}{3}[/tex]

Hence, the solution to the question is: [tex]9xy * (\frac{2}{3}x)^3 = \frac{8}{3}x^4y[/tex]

Answer:

115.462

Step-by-step explanation:

Answer: 115.462

Step-by-step explanation:

To start, the first thing we can observe is two negative signs, which we know turns into a positive sign.

Therefore, we now have:

112.212 + 3.25

115.462

Hope this helps!

Answer:

131,040

Step-by-step explaination:

There is around 29-31 days in a month, so if you just round it's around 30 days a month.

30×6= 180 (days)

180×728= 131,040 ounces

jasons dog would drink 131,040 in 6 months.

Answer:

-7 degrees celsius

Step-by-step explanation:

12-19=-7

Answer:

-7

Step-by-step explanation:

12 - 19 = -7

Answer:

In trigonometry, the tangent of an angle in a right-angled triangle is equal to the ratio of opposite side and the adjacent side of the angle. Tan 30 degrees is also represented by tan π/6 in terms of radians. The exact value of tan 30° is 0.57735.

Answer:

None, They are Both Equal

Step-by-step explanation:

7 2/5 = 7.4

7.4 = 7.4

So, 7.4 = 7.4

Hence, none of them are bigger

Answer:

At 5% , $300 was invested

At 15%, $4,700 was invested

Step-by-step explanation:

Let the amount invested at 5% be $x and the amount invested at 15% be $y

x + y = 5000 ••••••(i)

Let’s work with the interest;

5% of x + 15% of y = 720

0.05x + 0.15y = 720 •••••(ii)

From i;

x = 5000-y

Insert this into ii

0.05(5000-y) + 0.15y = 720

= 250 - 0.05y + 0.15y = 720

250 + 0.1y = 720

0.1y = 720-250

0.1y = 470

y = 470/0.1

y = $4700

x = 5000-y

x = 5000-4700 = $300

Answer:

3-gallon container of laundry detergent for $34.56

Step-by-step explanation:

48-fluid-ounce container of laundry detergent for  $5.28

5.28 : 48 = 0.11

check your work:  0.11 x 48 = 5.28

so for the first offer you will be paying $0.11 per ounce of laundry detergent.

3-gallon container of laundry detergent for $34.56

1 gallon = 128 ounces

3 gallons = 384 ounces

34.56 : 384 = 0.09

check your work:  0.09 x 384 = 34.56

for the second offer you will be paying $0.09 per ounce of laundry detergent. 3-gallon container of laundry detergent for $34.56 is a better buy because you will be paying less for each ounce of detergent.

hope this helps!

Answer:

f⁻¹(y) = y^(-7/17)

Step-by-step explanation:

f(x) = x^(-17/7)

To find the inverse, switch x and y, and solve for y.

x = y^(-17/7)

x^(-7/17) = y

Therefore, f⁻¹(y) = y^(-7/17).

Answer: 5 days

Step-by-step explanation:

5*7=35 - means the total amount of the days to complete the job by 1 worker is 35 days

So 7 workers can do this job in

35:7=5 days

Answer:

[tex]\boxed {d = 15}[/tex]

Step-by-step explanation:

Use the Distance Formula to help determine the distance between two given points:

[tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]

First point: [tex](x_{1}, y_{1})[/tex]

Second point: [tex](x_{2}, y_{2})[/tex]

-Substitute both given points:

[tex](x_{1}, y_{1}) = (6, 4)[/tex]

[tex](x_{2}, y_{2}) = (-6, -5)[/tex]

[tex]d = \sqrt{(-6 - 6)^{2} + (-5 - 4)^{2}}[/tex]

-Solve for the distance:

[tex]d = \sqrt{(-6 - 6)^{2} + (-5 - 4)^{2}}[/tex]

[tex]d = \sqrt{(-12)^{2} + (-9)^{2}}[/tex]

[tex]d = \sqrt{144 + 81}[/tex]

[tex]d = \sqrt{225}[/tex]

[tex]\boxed {d = 15}[/tex]

Therefore, the distance is [tex]15[/tex].

Answer:

That would be;

+52-20

Step-by-step explanation:

From the first part, he gained/earned 52 points

This is a positive so we have + 52

In the second round , he lost 20

This is a negative so we have - 20

Writing this as an addition problem, it will be;

+52-20

Answer:

Step-by-step explanation:

Answer:

3 and 12

Step-by-step explanation:

3*5=15 and 15-3=12. The product of 3 and 12 is 36.

The integers are 3 and 12.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

let the one integer be x.

Another integer = 5x - 3

According to question,

x *(5x-3 ) =36

5x ² -3 x =36

5x² -3 x - 36 = 0

5x² -15 x +12 x - 36 =0

5x( x-3) + 12 ( x -3) =0

(5x +12)( x- 3)=0

x= -12/5 or 3

So, the integers are 3 and 12.

Learn more about this concept here:

https://brainly.com/question/17023448

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