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3 years ago

Select the property of equality used to arrive at the conclusion.

Mathematics

1 answer:

artcher [175]3 years ago

5 0

Answer:

Step-by-step explanation:

The statement "If x = 3, then x^2 = 3x" was formed by multiplying x = 3 by x on both sides. Thus x = 3 becomes x*x=3*x. This simplifies to x^2 = 3x. This property is the multiplication property of equality.

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Twice a number plus twice a second number is 310. The difference between the numbers is 55

agasfer [191]

Answer:

x = 105

y = 50

Step-by-step explanation:

To solve this, try writing it out as an equation/expression first.

When you do, you should get something like this:

2x + 2y = 310

x - y = 55

This is a system of equations. To solve this, we're going to multiply the second equation [x - y = 55] by 2.

2(x - y = 55) = 2x - 2y = 110

Now, subtract your new equation from the first one [2x + 2y = 310]

2x + 2y = 310

-2x + 2y = -110

//If you're wondering why I changed the signs of the new equation, I multiplied our new equation [2x - 2y = 110] by -1 since we're subtracting//

When you're done subtracting, the "2x" and "-2x" cancel out, so you're left with:

4y = 200

Now, simply solve for "y" by dividing both sides by 4.

4y = 200

y = 50

Now that we know y's value, substitute it into one of our original equations to solve for x.

//I'm gonna plug y into the second equation [x - y = 55] just because it's easier, but you can plug it into the first one as well and get the same answer//

When we plug it in, we get:

x - (50) = 55

To solve for "x," we must get rid of "-50." To do this, add 50 to both sides.

x - 50 = 55

x = 105

So, x = 105 and y = 50

4 0

3 years ago

Rachel and Hugo sorted 265 crayons each box had 10 crayons how many crayons are left?

ryzh [129]

Answer:

Step-by-step explanation:

6 0

3 years ago

A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The

liubo4ka [24]

Answer:

The equation that represents the motion of the string is given by:

$y =Ae^{-kt}\cos(2\pi ft)$ .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

$y =0.6e^{-1.8t}\cos(2\pi 105t)$

$y =0.6e^{-1.8t}\cos(210\pi t)$

(a)

The trigonometric function that models the motion of the string is given by:

$y =0.6e^{-1.8t}\cos(210\pi t)$

(b)

Determine the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$

Using graphing calculator for the equation

$y =0.6e^{-1.8x}\cos(210\pi x)$

let x = t (time in sec)

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$ is, 0.5 sec

4 0

3 years ago

Which number is a solution of a² +4= 6a – 1? 07 6 7 8

LuckyWell [14K]

Answer:

a=1 or a=5

Step-by-step explanation:

$a^{2}$ +4=6a−1

Step 1: Subtract 6a-1 from both sides.

$a^{2}$ +4−(6a−1)=6a−1−(6a−1)

$a^{2}$ −6a+5=0

Step 2: Factor left side of equation.

(a−1)(a−5)=0

Step 3: Set factors equal to 0.

a−1=0 or a−5=0

a=1 or a=5

(is it helpful rate me according to that

Thank You:-)

6 0

3 years ago

Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant,

USPshnik [31]

By definition of tangent,

tan(2θ) = sin(2θ) / cos(2θ)

Recall the double angle identities:

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1

where the latter equality follows from the Pythagorean identity, cos²(θ) + sin²(θ) = 1. From this identity we can solve for the unknown value of sin(θ):

sin(θ) = ± √(1 - cos²(θ))

and the sign of sin(θ) is determined by the quadrant in which the angle terminates.

We're given that θ belongs to the third quadrant, for which both sin(θ) and cos(θ) are negative. So if cos(θ) = -4/5, we get

sin(θ) = - √(1 - (-4/5)²) = -3/5

Then

tan(2θ) = sin(2θ) / cos(2θ)

tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)

tan(2θ) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2θ) = 24/7

4 0

3 years ago