MATHEMATICS HIGH SCHOOL

Solve the equation by completing the square. Round to the nearest tenth.x^2 + 8x = 10

A. 1.1, 9.1
B. 1.1, -9.1
c. -1.1, 9.1
D. -1.1, -9.1

Answers

Answer 1
Answer: B.
1.1, -9.1

x^(2) +8x=10
Answer 2
Answer:

Answer:  The correct option is (B) 1.1, -9.1.

Step-by-step explanation:  We are given to solve the following quadratic equation by the method of completing the square.

x^2+8x=10~~~~~~~~~~~~~~~~(i)

In completing the square method, we need to make left hand side of the above given equation as a perfect square trinomial.

From equation (i), we have

x^2+8x=10\n\n\Rightarrow x^2+2* x* 4+4^2=10+4^2\n\n\Rightarrow (x+4)^2=10+16\n\n\Rightarrow (x+4)^2=26\n\n\Rightarrow x+4=\pm√(26)\n\n\Rightarrow x=-4\pm √(26)\n\n\Rightarrow x=-4\pm 5.09\n\n\Rightarrow x=-4+5.09,~~~~~x=-4-5.09\n\n\Rightarrow x=1.09,~~~~~~~~~\Rightarrow x=-9.09.

Rounding to the nearest tenth, we get

x=1.1,~~-9.1.

Thus, the required solution is x = 1.1, -9.1.

Option (B) is CORRECT.

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The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62.The probability that any postcard posted in Portugal on Friday is delivered to the UK within a week is 0.41.
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Answers

Answer:

You can expect at least 9 of her postcards to arrive within a week

To find that, we multiply the number of postcards by the probability

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Hope this helps

Good Luck

Let f(x) = -5x - 4 and g(x) = 6x - 7. Find f(x) + g(x)

Answers

f(x) + g(x)
(-5x - 4) + (6x - 7)
Combine similar terms:
(6x - 5x) + (-4 + -7)
x + (-11) or x - 11


Brainiest would be nice.

What is the square root property of:

​

Answers

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

Answer: x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

------

x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

Answer: x = 2 or x = -8

A rectangular prism is 6 inches long, 3 inches wide, and 2 inches high. What is its surface area?

Answers

Area of a rectangular prism=2(long * wide) + 2(long* high)+2(wide* high)
Data:
long=6 in
wide=3 in
high=2 in-

Area of this rectangular prism=2(6 in* 3in)+2(6 in * 2 in)+2(3 in * 2 in)=
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answer: the surface area of this rectangular prism is 72 in².

Zoya has to earn at least $300 to meet her fundraising goal. She has only 100 bracelets that she plans to sell at $5 each. Which inequality shows the number of bracelets, x, Zoya can sell to meet her goal?

Answers

Call the number of bracelets sold x. Gvien that there are 100 bracelets: x < or equal than 100 Earnings = 5x => 5x > or equal than 300 => x > or equal than 300 / 5 => x > or equal than 60. Then, you obtain 60 < or equal than x < or equal than 300.

Answer:

Amount needed by Zoya to meet her fundraising goal ≥ $ 300

Number of Bracelets possessed by Zoya = 100

Cost of single bracelet = $ 5

To meet her goal , we need to convert these statement into equation

Let number of Bracelets sold = x

1. x≤ 100

2. 5 x ≥ 300

Dividing both sides by 5, we get

x ≥ 60

The two inequality are : x ≤  100 and x ≥ 60

So the inequality is : 60 ≤ x≤ 100.

Can someone please help me with this? Please explain

Answers

Do you remember that the circumference of every circle is

    Circumference  =  (pi) times (the circle's diameter)                ?

Well, before we get to work on the problem, let's take this big hairy
gigantic complicated formula, and divide each side by (pi):

     the circle's diameter = (circumference) / (pi)  .

In the problem, you're given the circumference, you're told to use 3.14 for (pi),
and you're asked to find the diameter.

I'm pretty sure that you can handle it from this point.
circumference of the garden (circle): 2\pir = 81.64

r = 81.64 / (2x3.14)

diameter = 2 x radius: 
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d= 2(81.64)/(2x3.14)
d= 81.64/3.14
d= 26
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