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3 years ago

Best explained and correct answer gets brainliest!

Mathematics

1 answer:

mezya [45]3 years ago

3 0

The answer is B because C and D are not true. Angle-Angle theorem does not prove congruency. Hypotenuse-Leg does because having a hypotenuse means that the triangle is a right angle triangle, which means that 2 sides and an angle are congruent in the triangles. By Side-Side-Angle Theorem, the triangles are congruent.

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Pls pls help<br> Show work :)

Natasha2012 [34]

9514 1404 393

Answer:

31.243 units

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between sides and angles in a right triangle. Using the attached figure, it is convenient to find the length of BE as an intermediate step in the solution.

Sin = Opposite/Hypotenuse

sin(30°) = BE/100

BE = 100·sin(30°)

Then ...

Tan = Opposite/Adjacent

tan(58°) = BE/x

x = BE/tan(58°) = 100·sin(30°)/tan(58°)

x ≈ 31.243 . . . . units

_____

<em>Comment on the figure</em>

The intermediate problem in creating the figure was to locate point D. That was accomplished by locating point C on a line at an angle of 58° CCW from the horizontal, using point B as a center. Then D is the intersection of BC with the x-axis. BE is drawn perpendicular to the x-axis.

5 0

3 years ago

6 times a number is 27 less then the square of that number find the positive soloution

ella [17]

Answer:

Step-by-step explanation:

n2-27=6n

Than n (exponet) 2 - 27 - 6n = 0

Now factor (n-9)(n+3)=0

5 0

3 years ago

Jack and Jill live 126 km apart. They want to leave their homes at the same time,

Digiron [165]

Answer:

Both will leave their homes to meet on time at 9 am

Step-by-step explanation:

Given as, Distance between Jack and Jill = 126 km

Speed of Jack rides = 18 kilometers per hours

Speed of Jill rides = 24 kilometers per hours

Let the distance travel by Jack = x km

And the distance travel by Jill = (126 - x ) km

Time taken by Jack and Jill = T hours

Now , Distance = Speed × Time

So, x = 18 × T

And 126 - x = 24 × T

Or, 126 - x = 24 × $\frac{x}{18}$

Or, 126 - x = x × $\frac{4}{3}$

Or, 378 - 3x = 4x

Or, 378 = 7x

i.e x = $\frac{378}{7}$ = 54 km

And distance travel by Jill = 126 - 54 = 72 km

So, time taken by Jack = $\frac{x}{18}$ = $\frac{54}{18}$

Or, Time taken by Jack = 3 hours

Similarly Time take by Jill = $\frac{72}{24}$ = 3 hours

∵ Both Jack and Jill will take 3 hours to meet at 12 : 00 pm

Hence, Both will leave their homes to meet on time at 9 am Answer

7 0

3 years ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

Please help fast <br>need it by today

KiRa [710]

6. It is asking you to find the surface area for this one:

1 litre = 0.001 cubic meters
15.4 litres = 0.0154 cubic meters

The volume of the cylinder has to be 0.0154m^3.

V = (pi(r)^2)h
0.0154 = (pi(r)^2)(1)
r^2 = 0.0154/pi
r = 0.07m

Surface Area of Circles on Bottom:
A = pi(r)^2
A = pi(0.07)^2
A = 0.0154
0.0154*2 = 0.0308m^2

Surface Area of Walls:
This will be the circumference of the circle times the height, since the walls are just like a big rectangle.

C = 2pi(r)
C = 2pi(0.07)
C = 0.44m
0.44*1 = 0.44m^2

Finally, add the two surface areas:
0.44 + 0.0308 = 0.47m^2

You will need 0.47m^2 of sheet metal to make this cylinder.

7. Find the volume of everything and just the graphite, and subtract the graphite’s volume from everything to get just the wood. The volume of a cylinder is pi((r)^2)h.

Everything:
Watch out for units, since the diameter is in mm and the length is in cm.

r = 3.5mm or 0.35cm
V = pi((0.35)^2)(14)
V = 5.34cm^3

Graphite:

r = 0.5mm or 0.05cm
V = pi((0.05)^2)(14)
V = 0.11cm^3

5.34 - 0.11 = 5.23cm^3

8. For this problem, it wants your answer in cm^3. Find the volume of one bowl and multiply it by 250:

r = 3.5cm
V = pi((3.5)^2)(4)
V = 153.94cm^3

153.94*250 = 38484.51cm^3 of soup needed.

I sure hope that I didn’t confuse you too much with all of my math gibberish (sorry). Please let me know if there is anything else that I can help with. Have a nice day

3 0

3 years ago