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castortr0y [4]
3 years ago
14

Find the VERTEX of the parabola f(x) = x^2 - 16x + 63

Mathematics
1 answer:
Eva8 [605]3 years ago
6 0

Answer:

vertex = (8, - 1 )

Step-by-step explanation:

Given a parabola in standard form, f(x) = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

x_{vertex} = - \frac{b}{2a}

f(x) = x² - 16x + 63 ← is in standard form

with a = 1 and b = - 16, thus

x_{vertex} = - \frac{-16}{2} = 8

Substitute x = 8 into f(x)

f(8) = 8² - 16(8) + 63 = 64 - 128 + 63 = - 1

vertex = (8, - 1 )

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Consider the sequence:<br> 1536,768, 384, 192,96, ---<br> Determine the 11th term of the sequence.
Naya [18.7K]

Answer:

1.5

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

768 ÷ 1536 = 0.5

384 ÷ 768 = 0.5

192 ÷ 384 = 0.5

96 ÷ 192 = 0.5

This indicates that the terms form a geometric sequence with

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

Here a = 1536 and r = 0.5, thus

a_{11} = 1536 × (0.5)^{10} = 1.5

7 0
3 years ago
Read 2 more answers
I would like to purchase 20 products at a cost of $65 per product. What would be my total with 3.5 sales tax
alexandr402 [8]

Answer:

Answer:

The total is: $ 1345.5

Step-by-step explanation:

It is given that:

I would like to purchase 20 products at a cost 65.00 per product.

This means that the cost of 20 products will be:

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

i.e. he need to pay 3/5% on $ 1300

This means that the amount of tax he need to pay is: 3.5% of 1300

                                                                             =  3.5%×1300

                                                                            = 0.035×1300

                                                                           = $ 45.5.

Hence, the total cost is: $ 1300+$ 45.5

This means that the total cost is: $ 134.5

8 0
3 years ago
A contractor is building a pool labeled ABCD on the plans. If AC = 5y + 6 and BD = 8y-3, what value of y ensures the pool is a r
KIM [24]

The value of y that ensures the pool is a rectangle is 3. Option D

<h3>How to determine the value</h3>

The formula for perimeter of a rectangle is expressed as;

Perimeter = 2 ( length + width)

It is important to note that parallel sides of a rectangle are congruent, that is, they are equal.

Given the sides as;

  • AC = 5y + 6
  • BD = 8y-3

5y + 6 = 8y -3

collect like terms

5y - 8y = -3 - 6

-3y = -9

Make 'y' the subject

y = 3

Thus, the value of y that ensures the pool is a rectangle is 3. Option D

Learn more about rectangles here:

brainly.com/question/25292087

#SPJ1

3 0
2 years ago
Find the residual if you know the actual number is 3 and the predicted value is 1.6
IgorC [24]

Answer:

The correct option is A.

Step-by-step explanation:

The difference between actual value and predicted value is called residual.

Formula of residual is

e=y-\hat{y}

Where, y is observed value or actual value and \hat{y} is predicted value.

e=3-1.6

e=1.4

The value of residual is 1.4 and option A is correct.

5 0
3 years ago
If there are x teams in a sports​ league, and all the teams play each other​ twice, a total of​ n(x) games are​ played, where ​n
EleoNora [17]
1.
Consider a group of n objects. Assume we want to form groups of r, from these n objects.

There are in total C(n, r)= \frac{n!}{r!(n-r)!} many ways of doing so.

where, r! is "r factorial", calculated as 1*2*3*...*(r-1)*r

2.

C(x, 2) is the total number of pairs out of x objects, that we can form.

so let the x objects represent the x teams, and 2, represent a group of 2, which means a game.

The total number of games is:

n(x)=2*C(x, 2) = 2*  \frac{x!}{2!(x-2)!}= \frac{x!}{(x-2)!}= \frac{x(x-1)(x-2)!}{(x-2)!}=x(x-1)= x^{2} -x

Remark, we multiplied by 2, since there will be 2 matches for each pair of teams.


Answer: x^{2} -x

6 0
3 years ago
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