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4 years ago

Solve for the variable in the following proportion. 1/4 is to 1 1/4 as 2 is to b b = 1

Mathematics

2 answers:

zavuch27 [327]4 years ago

7 0

the answer is 10 i just did this one!!!!!!!!

Kisachek [45]4 years ago

5 0

2.5=b at least that is what I think

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Plz help with this question

Dennis_Churaev [7]

Answer:

y = -2x+4

Step-by-step explanation:

the equation of the line there is: y = -2x+8

The parallel line to this one should have the same slope as the first one(-2x)

Parallel lines always have the same slopes

7 0

3 years ago

Simplify. 49\43 A) 45 B) 46 C) 412 D) 427

melisa1 [442]

If that is 49/43 then none of the answers fit

8 0

3 years ago

Read 2 more answers

Match each statement to the reasons for the geometric proof. Part 3

jarptica [38.1K]

9514 1404 393

Answer:

4 1 5 3 6 2

Step-by-step explanation:

The general approach to this proof is to show the triangles created by the diagonal are congruent. Then, parts of those triangles (opposite sides) are congruent. The congruence of the triangles is shown by making use of the fact that alternate interior angles are congruent, and the diagonal is congruent to itself. Thus, you have two angles and the side between shown as congruent, and can invoke the ASA postulate.

The steps of the proof (1 to 6) are already in order. The task is to find the geometric relation the step is describing from the list on the left.

Statements A to F on the left match with numbered statements 1 to 6 on the right as follows:

A - 4 (reflexive prop)

B - 1 (given)

C - 5 (ASA)

D - 3 (alt int angle)

E - 6 (the end point of the proof)

F - 2 (definition)

8 0

3 years ago

Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

3 years ago

Mrs. Kelley is driving 540 miles to visit Niagra Falls. She drives at an average rate of 60 miles per hour. Using the formula d

uranmaximum [27]

It will take Kelley 9 hours because 540 miles (distance) divided by 60 mph (rate) will give you 9 hrs

7 0

3 years ago

Read 2 more answers