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3 years ago

Keelie has a triangular-shaped card. The lengths of its sides are 3.9 cm, 5.2 cm, and 6.5 cm. Is the card a right triangle?

Mathematics

1 answer:

alexdok [17]3 years ago

3 0

Answer:

Yes

Step-by-step explanation:

Since the longest side is 6.5 cm, so let it be hypotenuse c.

Verifying by right angle formula

c^2=a^2+b^2

(6.5)^2=(3.9)^2+(5.2)^2

42.25=15.21+27.04

42.25=42.25

Hence the given triangle is a right angles triangle

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hree vertices of a rectangle are given. Find the coordinates of the fourth vertex. (–2, 4), (4, 0), (2, –3)

zhannawk [14.2K]

V1=(-2,4)=(x1,y1)→x1=-2, y1=4
V2=(4,0)=(x2,y2)→x2=4, y2=0
V3=(2,-3)=(x3,y3)→x3=2, y3=-3
V4=(x4,y4)→x4=?, y4=?

V1-V2
dx=x2-x1=4-(-2)=4+2→dx=6
dy=y2-y1=0-4→dy=-4

V4-V3
dx=x3-x4→6=2-x4
Solving for x4:
6=2-x4→6-2=2-x4-2→4=-x4→(-1)(4=-x4)→-4=x4→x4=-4

dy=y3-y4→-4=-3-y4
Solving for y4:
-4=-3-y4→-4+3=-3-y4+3→-1=-y4→(-1)(-1=-y4)→1=y4→y4=1

V4=(x4, y4)→V4=(-4, 1)

Answer: The coordinates of the fourth vertex are (-4,1)

5 0

3 years ago

X + 16 = 25 What is the value of x?

Paraphin [41]

Answer:

x = 9

Step-by-step explanation:

Isolate x first by moving 16 to the other side

x = 25 - 16

x = 9

5 0

3 years ago

adiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the

Zigmanuir [339]

Answer:

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$ and $\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661$

Step-by-step explanation:

The equation of the isotope decay is:

$\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }$

14-Carbon has a half-life of 5568 years, the time constant of the isotope is:

$\tau = \frac{5568\,years}{\ln 2}$

$\tau \approx 8032.926\,years$

The decay time is:

$t = 1315\,years + 2007\,years \pm 13\,years$ (There is no a year 0 in chronology).

$t = 3335 \pm 13\,years$

Lastly, the relative amount is estimated by direct substitution:

$\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$

$\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661$

4 0

2 years ago

What is the exact solution of cos (17pi/6)?

kolbaska11 [484]

<span>The exact solution of cos (17</span>π<span>/6) is as follows:

First change the angle into degrees.

17(</span>π/6) (180°/π) = 510°

Then we calculate the cosine of the angle above and it as follows:

cos 510° = -(√3)/2

Hope this answers the question. Have a nice day.

4 0

3 years ago

Erica uses 9 gallons of gas to drive 198 miles. How many miles can he drive using 1 gallon of gas?

lara31 [8.8K]

Answer:

198 / 9 = 22

Step-by-step explanation:

3 0

3 years ago