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DanielleElmas [232]
2 years ago
15

Which equations are equivalent to ? Check all that apply. X 4 = 64 60 = x.

Mathematics
1 answer:
hram777 [196]2 years ago
5 0

You can use the fact that equivalent equations are such that one equation can be obtained by performing some operations(which doesn't break equality) on the other equation and vice versa.

The equivalent equation to x + 4 = 64 is x = 60

<h3>What are equivalent equations?</h3>

Equivalent equations are such that one equation can be obtained by performing some operations(which doesn't break equality) on the other equation and vice versa.

<h3>How to get the equivalent equation of the given equation?</h3>

The given equation is

x + 4 = 64

Subtracting 4 from both sides, we get

x + 4 - 4 = 64 - 4\\x = 60

Thus, one equivalent equation to the given equation is x = 60

The equivalent equation to x + 4 = 64 is x = 60

Learn more cases of equivalent equations here:

brainly.com/question/14332869

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-------100 POINTS------<br> Complete the proof of the Pythagorean theorem.
KIM [24]

Step-by-step explanation:

Complete the proof of the Pythagorean theorem is given below.

         Statement                                              Reason

1. ΔABC is a right triangle, with a     1. Given

right angle at ∠C

2. Draw an altitude from point C     2. From a point not on a line, exactly                    

to AB               one perpendicular can be drawn through the point to the line

3. ∠CDB and ∠CDA are right          3. Definition of altitude

angles

4. ∠BCA  ≅ ∠BDC                            4. All right angles are congruent

5. ∠B  ≅ ∠B                                      5. Reflexive\:Property

6. ΔCBA ~ ΔDBC                             6. AA Similarity Postulate                                                                                                                                                                                                                                      

7. \frac{a}{x}\:=\:\frac{c}{a}                                           7. Polygon\:Similarity\:Postulate\:\:\:

8. a^{2}  = cx                                          8. Cross\:Multiply\:and\:Simplify

9. ∠CDA  ≅ ∠BCA                           9. All\:Right\:Angles\:are\:Congruent

10. ∠A  ≅ ∠A                                    10. Reflexive\:Property

11. ΔCBA ~ ΔDBA                             11. AA Similarity Postulate

12. \frac{b}{y}\:=\:\frac{c}{b}=                                      12. Polygon\:Similarity\:Postulate

13. b^2\:=\:cy                                       13. Cross\:Multiply\:and\:Simplify

14. a^2\:+\:b^2\:=\:cx\:+cy                    14. Addition\:Property\:of\:Equality

15. \left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)  15. Distributive Property

16. x + y = c                                    16. Segment\:Addition\:Postulate

17. a^2\:+\:b^2\:=\:c^2                             18. Substitution\:Property

7 0
3 years ago
Read 2 more answers
Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
djverab [1.8K]

I'll assume the ODE is

y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}

Solve the homogeneous ODE,

y'' - 3y' + 2y = 0

The characteristic equation

r^2 - 3r + 2 = (r - 1) (r - 2) = 0

has roots at r=1 and r=2. Then the characteristic solution is

y = C_1 e^x + C_2 e^{2x}

For nonhomogeneous ODE (1),

y'' - 3y' + 2y = e^x

consider the ansatz particular solution

y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x

Substituting this into (1) gives

a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1

For the nonhomogeneous ODE (2),

y'' - 3y' + 2y = e^{2x}

take the ansatz

y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}

Substitute (2) into the ODE to get

b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1

Lastly, for the nonhomogeneous ODE (3)

y'' - 3y' + 2y = e^{-x}

take the ansatz

y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}

and solve for c.

ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16

Then the general solution to the ODE is

\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}

6 0
1 year ago
Suppose f(x)=x^2-1find the graph of f(3x)
RideAnS [48]
The answer would be f(x)=9 because when you substitue the 3 in for 'x' you then square the 3.
Hope this helps!
7 0
3 years ago
Betty took a doll she inherited from her grandmother to the antique store. The dolls original price tag says $6.80. The antique
mariarad [96]
There was a 12.35% increase in the price.
5 0
3 years ago
What is the factored form of x^2-x-2
lisov135 [29]

Answer:

(x-2),(x+1)

Step-by-step explanation:

5 0
2 years ago
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