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3 years ago

2. 1

Mathematics

1 answer:

prohojiy [21]3 years ago

4 0

Answer:

Step-by-step explanation:

2.1 = A - 33 [Solve for A]

+ 33 . + 33

35.1 = A

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ΔABC ~ ΔDEC. ∠1 and ∠2 have the same measure. Find DC and DE. (Hint: Let DC=x and AC=x+3. Use the figure shown.)

Sveta_85 [38]

DC/AC=EC/BC
x/(x+3)=10/16
10(x+3)=16x
10x+30=16x
30=6x
x=5
DC=x=5
DC=5 units long

10/16=DE/AB, DE=y

10/16=y/10
16*y=10*10
y=6.25≈6.3
DE≈6.3

8 0

3 years ago

Let f(x)=√3x and g(x)=x-6 What's the smallest number that is in the domain of fog?

yaroslaw [1]

9514 1404 393

Answer:

Step-by-step explanation:

Maybe you have ...

f(x) = √(3x)

g(x) = x-6

Then ...

f(g(x)) = √(3(x -6))

The square root function is only defined for non-negative arguments, so we require ...

3(x -6) ≥ 0

x -6 ≥ 0 . . . . . divide by 3

x ≥ 6 . . . . . . . . add 6

The smallest number in the domain of f(g(x)) is x = 6.

4 0

3 years ago

Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).

Oduvanchick [21]

Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).

1. Find

$\overrightarrow{DE}=(1-1,-5-1,2-1)=(0,-6,1),\\ \\\overrightarrow{DF}=(-2-1,2-1,7-1)=(-3,1,6).$

Then

$\cos \angle D=\dfrac{0\cdot (-3)+(-6)\cdot 1+1\cdot 6}{\sqrt{0^2+(-6)^2+1^2}\cdot \sqrt{(-3)^2+1^2+6^2}}=\dfrac{0}{\sqrt{37} \cdot \sqrt{46} }=0.$

2. Find

$\overrightarrow{ED}=(1-1,1-(-5),1-2)=(0,6,-1),\\ \\\overrightarrow{EF}=(-2-1,2-(-5),7-2)=(-3,7,5).$

Then

$\cos \angle E=\dfrac{0\cdot (-2)+6\cdot 7+(-1)\cdot 5}{\sqrt{0^2+6^2+(-1)^2}\cdot \sqrt{(-3)^2+7^2+5^2}}=\dfrac{37}{\sqrt{37} \cdot \sqrt{83} }=\sqrt{\dfrac{37}{83}}.$

3. Find

$\overrightarrow{FE}=(1-(-2),-5-2,2-7)=(3,-7,-5),\\ \\\overrightarrow{FD}=(1-(-2),1-2,1-7)=(3,-1,-6).$

Then

$\cos \angle F=\dfrac{3\cdot 3+(-7)\cdot (-1)+(-5)\cdot (-6)}{\sqrt{3^2+(-7)^2+(-5)^2}\cdot \sqrt{3^2+(-1)^2+(-6)^2}}=\dfrac{46}{\sqrt{83} \cdot \sqrt{46} }=\sqrt{\dfrac{46}{83}}.$

$\angle E=\arccos0=\dfrac{\pi}{2},\\ \\
\angle D=\arccos\letf(\sqrt{\dfrac{37}{83}}\right)\approx 0.27\pi,\\ \\
\angle F=\arccos\letf(\sqrt{\dfrac{46}{83}}\right)\approx 0.23\pi.$

3 0

3 years ago

Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help

LenKa [72]

Answer:

Step-by-step explanation:

3.14(rs + r2)

3.14 (r= 2 x s= 3 + r =2 x 2)

3.14 ( 6+4)

3.14 (10)

3.14 x 10 = 31.4 units ² I guess

4 0

3 years ago

Data about cell phone usage was collected from 14 different people. The list shoes the number of incoming calls each person rece

Rudik [331]

Answer: 121

Step-by-step explanation:

I calculated, trust. Also took the test.

7 0

3 years ago