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
const2013 [10]
3 years ago
6

Is x^2+13x-4=0 a quatratic function? Why?

Mathematics
1 answer:
zysi [14]3 years ago
8 0
Yes it is a quadratic function. A quadratic function contains the term x^2 and x^2 has the highest exponent in the whole function of a quadratic function. What I mean by this is for example x^3 + x^2 + 2x + 3 is not a quadratic. It includes x^2 but x^3 has the largest exponent. That makes that equation a cubic. Just for more info the largest exponent is referred to as the degree of the function so the degree of a quadratic function is always 2. Hope this helps!
You might be interested in
Decide if the following statement is valid or invalid. If two sides of a triangle are congruent then the triangle is isosceles.
Naya [18.7K]

Answer:

Step-by-step explanation:

Properties of an Isosceles Triangle

(Most of this can be found in Chapter 1 of B&B.)

Definition: A triangle is isosceles if two if its sides are equal.

We want to prove the following properties of isosceles triangles.

Theorem: Let ABC be an isosceles triangle with AB = AC.  Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC).  Then

a)      Triangle ABM is congruent to triangle ACM.

b)      Angle ABC = Angle ACB (base angles are equal)

c)      Angle AMB = Angle AMC = right angle.

d)      Angle BAM = angle CAM

Corollary: Consequently, from these facts and the definitions:

Ray AM is the angle bisector of angle BAC.

Line AM is the altitude of triangle ABC through A.

Line AM is the perpendicular bisector of B

Segment AM is the median of triangle ABC through A.

Proof #1 of Theorem (after B&B)

Let the angle bisector of BAC intersect segment BC at point D.  

Since ray AD is the angle bisector, angle BAD = angle CAD.  

The segment AD = AD = itself.

Also, AB = AC since the triangle is isosceles.

Thus, triangle BAD is congruent to CAD by SAS (side-angle-side).

This means that triangle BAD = triangle CAD, and corresponding sides and angles are equal, namely:

DB = DC,

angle ABD = angle ACD,

angle ADB = angle ADC.

(Proof of a).  Since DB = DC, this means D = M by definition of the midpoint.  Thus triangle ABM = triangle ACM.

(Proof of b) Since angle ABD = angle ABC (same angle) and also angle ACD = angle ACB, this implies angle ABC = angle ACB.

(Proof of c) From congruence of triangles, angle AMB = angle AMC.  But by addition of angles, angle AMB + angle AMC = straight angle = 180 degrees.  Thus 2 angle AMB = straight angle and angle AMB = right angle.

(Proof of d) Since D = M, the congruence angle BAM = angle CAM follows from the definition of D.  (These are also corresponding angles in congruent triangles ABM and ACM.)

QED*

*Note:  There is one point of this proof that needs a more careful “protractor axiom”.  When we constructed the angle bisector of BAC, we assumed that this ray intersects segment BC.  This can’t be quite deduced from the B&B form of the axioms.  One of the axioms needs a little strengthening.

The other statements are immediate consequence of these relations and the definitions of angle bisector, altitude, perpendicular bisector, and median.  (Look them up!)

Definition:  We will call the special line AM the line of symmetry of the isosceles triangle.  Thus we can construct AM as the line through A and the midpoint, or the angle bisector, or altitude or perpendicular bisector of BC. Shortly we will give a general definition of line of symmetry that applies to many kinds of figure.

Proof #2 (This is a slick use of SAS, not presented Monday.  We may discuss in class Wednesday.)

The hypothesis of the theorem is that AB = AC.  Also, AC = AB (!) and angle BAC = angle CAB (same angle).  Thus triangle BAC is congruent to triangle BAC by SAS.

The corresponding angles and sides are equal, so the base angle ABC = angle ACB.

Let M be the midpoint of BC.  By definition of midpoint, MB = MC. Also the equality of base angles gives angle ABM = angle ABC = angle ACB = angle ACM.  Since we already are given BA = CA, this means that triangle ABM = triangle ACM by SAS.

From these congruent triangles then we conclude as before:

Angle BAM = angle CAM (so ray AM is the bisector of angle BAC)

Angle AMB = angle AMC = right angle (so line MA is the perpendicular bisector of  BC and also the altitude of ABC through A)

QED

Faulty Proof #3.  Can you find the hole in this proof?)

In triangle ABC, AB = AC.  Let M be the midpoint and MA be the perpendicular bisector of BC.

Then angle BMA = angle CMA = right angle, since MA is perpendicular bisector.  

MB = MC by definition of midpoint. (M is midpoint since MA is perpendicular bisector.)

AM = AM (self).

So triangle AMB = triangle AMC by SAS.

Then the other equal angles ABC = ACB and angle BAM = angle CAM follow from corresponding parts of congruent triangles.  And the rest is as before.

QED??

8 0
2 years ago
My cousin needs help on all the questions. Please help him he is failing math
Solnce55 [7]

Answer:

  (a) more

  (b) less

  (c) more

  (d) greater

  (e) Left to right: Susan, George, Antonio, Maria

Step-by-step explanation:

When a point total is lower, more points are needed to stay in the game.

__

(a) Maria's total is less than -30, so she needs more than 30 to stay in the game. Phone #4 is the only one indicating a need of more than 30, so it is Maria's.

__

(b) Susan's total is greater than -25, so she needs less than 25* to stay in the game. Phone #1 is the only one indicating a need of less than 25, so it is Susan's.

__

(c) George's point total is lower than Susan's, so he needs more points than Susan. Susan's phone indicates she needs 20 points. Since George needs 5 more points, his is phone #2.

__

(d) Antonio needs 15 fewer points than Maria, so his total is more than Maria's total. Maria's phone indicates she needs 45 points, so Antonio only needs 30 points. His is phone #3.

__

(e) Susan needs 20, George needs 25, Antonio needs 30, Maria needs 45.

_____

* If we assume whole numbers of points, a total of "greater than -25" might be a total of -24. To bring the score to a positive value (1), <em>exactly 25 points</em> might be needed. That is, there is some ambiguity in part (b) in that Susan might need <em>less than or equal to 25 points</em>. Susan's phone could be either the first or the second.

The problem is poorly worded. The answer choices above are consistent with the problem statement overall.

6 0
3 years ago
The price of a computer component is decreasing at a rate of 15​% per year. State whether this decrease is linear or exponential
Margaret [11]

Answer:

Since the price is given by an exponential function, the decline in price is exponential.

The component will cost $36.8475 in three years.

Step-by-step explanation:

The equation for the price of a component has the following format:

P(t) = P(0)(1-r)^{t}

In which P(t) is the price after t years, P(0) is the initial price, and r is the rate that the price decreases.

Since the price is given by an exponential function, the decline in price is exponential.

The price of a computer component is decreasing at a rate of 15​% per year.

This means that r = 0.15

Component costs ​$60 ​today

So P(0) = 60. Then

P(t) = P(0)(1-r)^{t}

P(t) = 60(1-0.15)^{t}

P(t) = 60(0.85)^{t}

What will it cost in three​ years?

This is P(3).

P(t) = 60(0.85)^{t}

P(3) = 60(0.85)^{3} = 36.8475

The component will cost $36.8475 in three years.

6 0
3 years ago
How to solve the problem
Dima020 [189]
A=1 B=2 C=3 Yes it would work for all because its using the commutative property.
5 0
3 years ago
Can y’all plz help me
ziro4ka [17]

I think the answer would be C to this problem

7 0
3 years ago
Other questions:
  • What is the quotient and remainder of 6 divided by 15
    7·2 answers
  • What is the answer for 12 over 75 (fraction)
    7·1 answer
  • X y
    5·1 answer
  • 1. Write the following polynomial in factored form. Show your work.
    13·1 answer
  • M+ 38 &gt;50 <br> M - 50 &gt;38<br> M - 50 &lt; 38 <br> M + 38 &lt; 50
    7·2 answers
  • 15. A bag contains 8 blue chips, 7 green chips, and 2 white chips. If three chips are drawn
    5·1 answer
  • 10 minutes left unit test PLEASE HELPP
    9·2 answers
  • Lol please help :))))).
    11·1 answer
  • Find the midpoint of PQ
    13·1 answer
  • What is the solution to the system of equations represented by these two lines?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!