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Slav-nsk [51]
3 years ago
5

a map that contains cities A and b is shown the map used it uses a scale of 1 inch:20 mi if you are making a map that uses a sca

le of 3 inch: 35 mi how far apart are cities A and b on your mat
Mathematics
1 answer:
OverLord2011 [107]3 years ago
3 0

Answer:

Step-by-step explanation:

Hi

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How would u do this need help
Lunna [17]
Standard form: y = x^2 + 10x + 21
Axis of symmetry: x = -5
X intercepts: (-3,0) (-7,0)
Y intercepts: (0,21)
Vertex: (-5,-4)
4 0
4 years ago
How are the x-axis and the y-axis related<br> on a coordinate grid?
seropon [69]

Answer:

they unite through the origin at (0,0)

6 0
4 years ago
Prove that a cubic equation x 3 + ax 2 + bx+ c = 0 has 3 roots by finding the roots.
evablogger [386]

That's a pretty tall order for Brainly homework.  Let's start with the depressed cubic, which is simpler.

Solve

y^3 + 3py = 2q

We'll put coefficients on the coefficients to avoid fractions down the road.

The key idea is called a split, which let's us turn the cubic equation in to a quadratic.  We split unknown y into two pieces:

y = s + t

Substituting,

(s+t)^3 + 3p(s+t) = 2q

Expanding it out,

s^3+3 s^2 t + 3 s t^2 + t^3 + 3p(s+t) = 2q

s^3+t^3 + 3 s t(s+t) + 3p(s+t) = 2q

s^3+t^3 + 3( s t + p)(s+t) = 2q

There a few moves we could make from here. The easiest is probably to try to solve the simultaneous equations:

s^3+t^3=2q, \qquad st+p=0

which would give us a solution to the cubic.

p=-st

t = -\dfrac p s

Substituting,

s^3 - \dfrac{p^3}{s^3} = 2q

(s^3)^2 - 2 q s^3 - p^3 = 0

By the quadratic formula (note the shortcut from the even linear term):

s^3 = q \pm \sqrt{p^3 + q^2}

By the symmetry of the problem (we can interchange s and t without changing anything) when s is one solution t is the other:

s^3 = q + \sqrt{p^3+q^2}

t^3 = q - \sqrt{p^3+q^2}

We've arrived at the solution for the depressed cubic:

y = s+t = \sqrt[3]{q + \sqrt{p^3+q^2}} + \sqrt[3]{ q - \sqrt{p^3+q^2} }

This is all three roots of the equation, given by the three cube roots (at least two complex), say for the left radical.  The two cubes aren't really independent, we need their product to be -p=st.

That's the three roots of the depressed cubic; let's solve the general cubic by reducing it to the depressed cubic.

x^3 + ax^2 + bx + c=0

We want to eliminate the squared term.  If substitute x = y + k we'll get a 3ky² from the cubic term and ay² from the squared term; we want these to cancel so 3k=-a.

Substitute x = y - a/3

(y - a/3)^3 + a(y - a/3)^2 + b(y - a/3) + c = 0

y^3 - ay^2 + a^2/3 y - a^3/27 + ay^2-2a^2y/3 + a^3/9 + by - ab/3 + c =0

y^3 + (b - a^2/3) y = -(2a^3+9ab) /27

Comparing that to

y^3 + 3py = 2q

we have p = (3b - a^2) /9, q =-(a^3+9ab)/54

which we can substitute in to the depressed cubic solution and subtract a/3  to get the three roots.  I won't write that out; it's a little ugly.

8 0
4 years ago
At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the slope, y-interc
LenKa [72]

Answer:-8

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Jim Lee received his bank statement from Bayne Bank indicating a balance of $7,980. Lee's checkbook showed a balance of $6,800.
bezimeni [28]
<span>Given:
Bayne Bank indicating a balance of $7,980.
Lee's checkbook showed a balance of $6,800.
checks outstanding were $1,330.
NSF check for $120 and a service charge of $30. 

Bank balance:                     7,980
less: outstanding checks <u>   (1,330)</u>
Bank balance, end              6,650

Jim's checkbook balance:   6,800
less: NSF check      120
         service charge 30    <u>   (150)</u>
Jim's balance, end              6,650

The reconciled balance is: $6,650.

In reconciling the bank balance, we need to add the deposits in transit and deduct the outstanding checks. This are all transactions reflected in the book but not yet reflected in the bank account.

In reconciling the book balance, we need to add the credits made in the bank account and deduct the debits like service charges.</span>
5 0
3 years ago
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