1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena55 [62]
3 years ago
5

When solving the equation x2 – 8x - 7 = 0 by completing the square, which equation

Mathematics
1 answer:
IgorLugansk [536]3 years ago
4 0
<h3><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u>:</u><u>-</u></h3>

Lets Solve

\\  \rm \longmapsto \:  {x}^{2}  - 8x - 7 = 0 \\  \\  \rm \longmapsto \:  {x}^{2}  - 8 {}^{}x = 7 \\  \\  \rm \longmapsto \: 4( {x}^{2}  - 8x) = 4 \times 7 \\  \\  \rm \longmapsto \:  {4x}^{2}  - 32x = 28 \\  \\  \rm \longmapsto \:  {(2x)}^{2}  - 2 \times 2x \times 8 = 28 \\  \\  \rm \longmapsto \: (2x) {}^{2}  - 2 \times 2x \times 8 +  {8}^{2}  = 28 +  {8}^{2}  \\  \\  \rm \longmapsto \:  {(2x - 8)}^{2}  = 64 + 28 \\  \\  \rm \longmapsto \:  {(2x - 8)}^{2}  = 92 \\  \\  \rm \longmapsto \: 2x - 8 =  \underline{ + }9.3 \\ \\  \rm \longmapsto \:2x =  8 + 9.3  \: or \: 8 - 9.3 \\ \\  \rm \longmapsto \:2x = 17.3 \:or \:  - 1.3 \\ \\  \rm \longmapsto \:2x = 17.3 \\ \\  \rm \longmapsto \:x =  \frac{17.3}{2}  \\ \\  \rm \longmapsto x = \:8.6

  • Ignore negative value
You might be interested in
HELP WITH SOME GEOMETRY. 20 POINTS
AnnyKZ [126]
1. The triangle is translated 3 right and 2 down

2. I don't know

3. False

4. True

5. Translation

6. (1, 1)

7. The last option

8-10. You didn't provide the images

I hope this helped somewhat
3 0
3 years ago
Read 2 more answers
Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut
frozen [14]

Answer:

a)\sqrt{144-288t+208t^2} b.) -12knots, 8 knots c) No e)4\sqrt{13}

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved 12\dot t (n.m) and ship B has moved 8\dot t (n.m). We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}

b)

We want to find \frac{ds}{dt} for t=0 and t=1

\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0

Since function f(x)=199-288x+208x^2 is quadratic, concave up and has no real roots, we know that 199-288x+208x^2>0 for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

                                                \lim_{t \to \infty} \frac{ds}{dt}

So, lets check this limit:

\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}

Notice that:

4\sqrt{13}=\sqrt{12^2+5^2}=√(speed of ship A² + speed of ship B²)

5 0
3 years ago
Which expression represents B is decreased by 25%?
emmasim [6.3K]

b is decreased by 25% which means there will be (-ve) sign.

<h3>So,</h3>

b - 0.25b

  • <em>Option 5 is correct!!~</em>
3 0
2 years ago
If the sum of the measure of two angles in a triangle is 101, then the measure
LiRa [457]

Answer:

79 degrees.

Step-by-step explanation:

It is just a rule of trigonometry that all the angles inside ANY triangle will add up to 180 degrees.

There's only 3 possible angles in a triangle, so if you know what the sum of 2 are, its easy to find the last one.

All you have to do is 180 - 101, which equals 79 degrees.

Hope this helped : )

5 0
3 years ago
Read 2 more answers
In the diagram below DE is parallel to XY. What is the value of y?
kirza4 [7]

this would be 94 hope it helps

3 0
3 years ago
Read 2 more answers
Other questions:
  • What's the difference between a factor and a multiple?
    14·2 answers
  • What is the logarithmic function modeled by the following table?
    11·2 answers
  • Henri surveys his 20 classmates about the number of times they go swimming per week during the summer. He finds that 6 of his cl
    10·1 answer
  • The measures of the angles of LMN are in ratio 2:4:6 what are the measures of the angle
    12·1 answer
  • Find the solution x = 3 + y 21x + 8y = -24
    5·2 answers
  • Find the LCM of x2 + x,x2-1,x2-x
    11·1 answer
  • Asa spent $165.20 on 5 video games. If the video games each cost the same amount, how much did one video game cost?
    5·1 answer
  • Which function in vertex form is equivalent to f(x) = x2 + x +1?
    5·1 answer
  • PLEASE ASAP I NEED HELP
    9·1 answer
  • Any one help with math pls I really need this today
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!