What is the simplified form of the expression?

omeli [17]

-4 < -12 and 9 > -35

Hope this helps!

5 0

3 years ago

determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y

grandymaker [24]

Answer:

(x, y) = (3, 5)
(x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

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The usual methods of solving a system of equations involve elimination or substitution.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to elimination. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

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1. In standard form, your equations are ...

2x -3y = -9
5x +2y = 25

Then the solution is ...

$x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)$

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2. In standard form, your equations are ...

3x +2y = 7
2x +5y = 12

Then the solution is ...

$x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)$

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Note on Cramer's Rule

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

7 0

4 years ago

Help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!

SVEN [57.7K]

82.2

Add all of them up and then divide by 10.

5 0

3 years ago

Read 2 more answers

What are the asymptotes of the graph of f(x) ?

Ad libitum [116K]

When in doubt, graph it.

The 3rd and 4th choices are appropriate.

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This is what is known as a "logistic function." It is used to model population growth when there is a resource limit. It starts out exponential, but then slows as it reaches the "carrying capacity" of the environment. The lower asymptote is zero; the upper one is the carrying capacity of the resource--here 15/1 = 15.

6 0

3 years ago

In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║ AB. Find the measures of the angles of ΔABC, if m∠ADE: m∠ADB = 2

drek231 [11]

Answer: ∠A=48°,∠B=48°,∠C=84°.

Step by-step explanation:

Given: AD and BE are the angle bisectors of ∠A and ∠B

i.e ∠6=∠7 ( ∵ Angles formed after AD bisected ∠A)

∠4=∠5 ( ∵ Angles formed after BE bisected ∠B)

Also, DE║AB

⇒ ∠2=∠7 (∵ Alternate interior angles)

∠3=∠6 (∵ Alternate interior angles)

And ∠ADE : ∠ADB =∠2:∠3= 2:9 =2x : 9x ..(1)

To Find: ∠A,∠B,∠C.

Solution: ∠2=∠7 (∵ Given) ...(2)

∠2=∠4 (∵ angles on the same segment) ...(3)

∠4=∠5 =∠B/2 (∵ Given) ...(4)

∴ In Δ ABD

∠3+∠4+∠5+∠7 = 180 (∵ Sum of interior angles of a triangle)

From equation 2,3,4,5, Put values

9x+2x+2x+2x =180°

⇒15x = 180°

⇒x=12°

Putting values in equation (4) ⇒ ∠ B =2*(2*12) = 48°

Also, ∠B=∠A=48°

Now,in Δ ABC

∠C+∠B+∠A= 180°

⇒48°+48°+∠C= 180°

⇒∠C=84°

6 0

4 years ago