4x²+8x=1 by completing the square

Answers

Answer 1

Answer: First thing you do is subtract both sides by 1.
Then divide everything by 4, to remove the 4x².
After completing the square, you multiply the 4 back in.

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I’m having a hard time understanding substitution. Please help!

Answers

$b_1=(2A)/(h)-b_2$

Step-by-step explanation:

Given expression is;

$A=(h(b_1+b_2))/(2)$

Solving for $b_1$

Multiplying both sides by 2

$2*A=(h(b_1+b_2))/(2)*2\n2A=h(b_1+b_2)$

Dividing both sides by h

$(2A)/(h)=(h(b_1+b_2))/(h)\n(2A)/(h)=b_1+b_2$

Subtracting $b_2$ from both sides

$(2A)/(h)-b_2=b_1+b_2-b_2\n(2A)/(h)-b_2=b_1\nb_1=(2A)/(h)-b_2$

$b_1=(2A)/(h)-b_2$

Keywords: division, subtraction

Learn more about subtraction at:

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Michael drives 143 km from town A to town B in 2 hours 36 minutes. He then drives from town B to town C at the same speed and it takes 21 minutes. (a) Work out Michael’s average speed from town A to town B.urgent plzzzzzzzzzzzz

Answers

To town b. Urban dictionary is a good way to add

Which box is greater a 1.5 pound box of raisins or a 650 gram box of raisins?

Answers

The 1.5 pound box of raisins
Convert the 650 grams to pounds and you will get 1.433 pounds which we would round to 1.4

1.5 is definitely greater than 1.4

1.5 gram= 680 grams
it means 1.5 gram box is greater than 650 gram box

hope u understand

Curt just drank a cup of coffee to help him stay awake. The coffee had 130 milligrams of caffeine in it. If his body processes 7% of the caffeine every hour, how much will be left in 4 hours?

Answers

Answer: 97.25 milligrams

Step-by-step explanation:

Given: Curt just drank a cup of coffee to help him stay awake.

The initial amour of caffeine in coffee= 130 milligrams

The rate of decay of caffeine in body = 7%= 0.07

We know that the exponential decay equation with rate r and and time t is given by :-

$f(x)=A(1-r)^t$ , where A is the initial value.

Now, the amount of caffeine left in body after 4 hours is given by :-

$f(4)=130(1-0.07)^4\n\n\Rightarrow\ f(4)=97.2467613\approx97.25\text{ milligrams}$

Hence, after 4 hours 97.25 milligrams will be left.

After 4 hours, his body will have processed 28% because 7*4 = 28. But, you're trying to find what's left (so, subtract that % from 100)

100%-28% = 72%

Then multiply the percent left by the total number of milligrams of caffeine

130*.72 = 93.6 mg

Describe this pattern. Then see if you can think of another Pythagorean triple that doesn't follow the pattern you just described and that can't be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings. x-value Pythagorean Triple 7 (14,48,50) 8 (16,63,65) 9 (18,80,82) 10 (20,99,101)

Answers

Answer:

See explanation

Step-by-step explanation:

A Pythagorean triple is a set of 3 positive integer numbers, a, b, and c which satisfies the Pythagorean theorem: $c^2=a^2+b^2$

Given the identity: $(x^2 - 1)^2 + (2x)^2 = (x^2 + 1)^2.$

We verify that the numbers given table are Pythagorean triples.

$14^2+48^2=2500=50^2\n16^2+63^2=4225=65^2\n18^2+80^2=6724=82^2\n20^2+99^2=10201=101^2$

Next, we examine the pattern:

$\left|\begin{array}{c|c|c|c|c}x-value&x^2-1&2x&x^2 + 1&$Triple\n--&--&--&--&----\n7&48&14&50&(14,48,50)\n8&63&16&65&(16,63,65)\n9&80&18&82&(18,80,82)\n10&99&20&101&(20,99,101)\end{array}\right|$

From the pattern, our first number is 2x, the second number is x² - 1, and the third number(hypotenuse) is x² + 1

Next, we show that (x² - 1)² + (2x)² = (x² + 1)² is an identity

$LHS: (x^2 - 1)^2 + (2x)^2 \n= (x^2-1)(x^2-1)+2x^2\n=x^4-2x^2+1+4x^2\n=x^4+2x^2+1$

$RHS: (x^2+1)^2\n= (x^2+1) (x^2+1)\n=x^4+2x^2+1$

Since Left Hand Side=Right hand Side. For all x, the equation is always true.

Therefore, the pattern is true for any Pythagorean triple.

Find the distance between the given pair of points. (a, a) and (b, b)_____

Answers

To find the distance between the points (a, a) and (b, b), we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

In this case, since the points are (a, a) and (b, b), we substitute a for both x1 and y1, and b for both x2 and y2:

Distance = √((b - a)² + (b - a)²)

Simplifying this expression further:

Distance = √((b - a)² + (b - a)²) = √(b² - 2ab + a² + b² - 2ab + a²) = √(2a² + 2b² - 4ab)

Therefore, the distance between the points (a, a) and (b, b) is √(2a² + 2b² - 4ab).

Other Questions

An asprin tablet in a shape of a right circular cylinder has the height of 2/5 cm and the raidus of 1/2cm. the manufacturer also wishes to market the asprin in capsule form. The capsule is to be 5/3cm in total length, in the shape of a right cylinder with hemispheres attached to both ends . find a function that represents the volume of the capsule. fund the radius of the capsule so that it is the same volume of the tablet.

A rotating light on top of a lighthouse sends outrays of light in opposite directions. As the beacon rotates, the ray at an angle 8 makes a spot of light that moves along the shore. The lighthouse is located 500 m from the shoreline and makes one complete rotation every 2 min. Determine the equation that expresses the distance, d, in metres, as a function of time, t, in minutes.

PLEASE HURRY 3/14 < x < 3/130.2030.2130.2230.233

Which sentence can represent the inequality x+2254?.