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3 years ago

Which congruence theorem can be used to prove △ABR ≅ △RCA?

2 answers:

7 0

If all three pairs of corresponding sides are congruent, the triangles are congruent. This congruence shortcut is known as side-side-side<span> (SSS). Another shortcut is side-angle-side (SAS), where two pairs of sides and the angle between them are known to be congruent.</span>

klio [65]3 years ago

7 0

Answer:

A: HL on edge

Step-by-step explanation:

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A ball is launched upward at 14 m/s from a platform 30 m high.Find the maximum height the ball will reach and how long it will t

BartSMP [9]

Answer:

The ball will reach a maximum height of 39.993 meters after 1.428 seconds.

Step-by-step explanation:

Let suppose that no non-conservative forces acts on the ball during its motion, then we can determine the maximum height reached by the Principle of Energy Conservation, which states that:

$K_{1}+U_{g,1} = K_{2}+U_{g,2}$ (1)

Where:

$K_{1}$ , $K_{2}$ - Initial and final translational kinetic energies, measured in joules.

$U_{g,1}$ , $U_{g,2}$ - Initial and final gravitational potential energies, measured in joules.

By definition of translational kinetic energy and gravitational potential energy we expand and simplify the expression above:

$\frac{1}{2}\cdot m\cdot v_{2}^{2}+m\cdot g\cdot y_{2}= \frac{1}{2}\cdot m\cdot v_{1}^{2}+m\cdot g\cdot y_{1}$ (2)

Where:

$m$ - Mass of the ball, measured in kilograms.

$g$ - Gravitational acceleration, measured in meters per square second.

$v_{1}$ , $v_{2}$ - Initial and final speed of the ball, measured in meters per second.

$y_{1}$ , $y_{2}$ - Initial and final heights of the ball, measured in meters.

The final height of the ball is determined by the following formula:

$v_{2}^{2}+2\cdot g\cdot y_{2} = v_{1}^{2}+2\cdot g\cdot y_{1}$

$v_{1}^{2}-v_{2}^{2}+2\cdot g \cdot y_{1}=2\cdot g\cdot y_{2}$

$y_{2} = y_{1}+\frac{v_{1}^{2}-v_{2}^{2}}{2\cdot g}$ (3)

If we know that $y_{1} = 30\,m$ , $v_{1} = 14\,\frac{m}{s}$ , $v_{2} = 0\,\frac{m}{s}$ and $g = 9.807\,\frac{m}{s^{2}}$ , the maximum height that the ball will reach is:

$y_{2} = 30\,m + \frac{\left(14\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}}{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)}$

$y_{2} = 39.993\,m$

The ball will reach a maximum height of 39.993 meters.

Given the absence of non-conservative forces, the ball exhibits a free fall. The time needed for the ball to reach its maximum height is computed from the following kinematic formula:

$t = \frac{v_{2}-v_{1}}{-g}$ (4)

If we know that $v_{1} = 14\,\frac{m}{s}$ , $v_{2} = 0\,\frac{m}{s}$ and $g = 9.807\,\frac{m}{s^{2}}$ , then:

$t = \frac{0\,\frac{m}{s}-14\,\frac{m}{s} }{-9.807\,\frac{m}{s^{2}} }$

$t = 1.428\,s$

The ball will take 1.428 seconds to reach its maximum height.

6 0

3 years ago

The interest paid on a $8,000 loan is $600, a rate of 4%

weeeeeb [17]

It took 1.9 years to pay back the loan.

<h3>What is Interest ?</h3>

Interest is the amount of money given or received when a certain sum of amount is received as a loan or given or deposited for investment.

It is given that

Principal amount of loan = $ 8000

Interest paid = $ 600

Rate = 4%

Time Period = ?

Assuming Simple Interest has been applied

I = ( P* R* T) /100

600 = ( 8000 * 4 * T ) / 100

60000 = 8000 * 4 * T

T = 1.875 years

T = 1.9 years rounded to 1 decimal

T = 22.5 months

Therefore it took 1.9 years to pay back the loan.

To know more about Interest

brainly.com/question/13324776

#SPJ1

7 0

3 years ago

How many solutions does 0.5(x−3)=3x−2.5 have?

Yanka [14]

Answer:

Step-by-step explanation:

mark brainliest pls

6 0

3 years ago

Simplify 3(x+2=5).Explain how you found your answer

Simora [160]

Answer:

3(x+2=5)

=3(x=5-2)

=3(x=3)

=3(3)

=3×3

3 0

3 years ago

HELP ASAP WILL MARK THE BRAINLIEST!

kap26 [50]

Answer:

y = 3x² + 54x + 240

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 9, - 3), thus

y = a(x + 9)² - 3

To find a substitute either of the roots into the equation

Using (- 8, 0), then

0 = a(- 8 + 9)² - 3

0 = a - 3 ( add 3 to both sides )

a = 3

y = 3(x + 9)² - 3 ← in vertex form

Expand factor and simplify

y = 3(x² + 18x + 81) - 3

= 3x² + 54x + 243 - 3

= 3x² + 54x + 240 ← in standard form

3 0

3 years ago