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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If v=<4, 12> , and w=<4, -3> , find v+w .

Possible Answers:

v+w=<9,8>

v+w=<1,16>

v+w=<8,15>

v+w=<16,1>

v+w=<8,9>

Correct answer:

v+w=<8,9>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=4+4=8

y=12+(-3)=9

v+w=<8,9>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 9.05.46 am

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Example Question #42 : Vector & Matrix Quantities

If v=<1, 8> , and w=<-4, 6> , find v+w .

Possible Answers:

v+w=<9,2>

v+w=<-3,14>

v+w=<14,-3>

v+w=<7,4>

v+w=<2,9>

Correct answer:

v+w=<-3,14>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=1+(-4)=-3

y=8+6=14

v+w=<-3,14>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 9.49.05 am

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Example Question #11 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If v=<-4, -5> , and w=<2, -9> , find v+w .

Possible Answers:

v+w=<-9,-7>

v+w=<-14,-2>

v+w=<-2,-14>

v+w=<3,-13>

v+w=<13,3>

Correct answer:

v+w=<-2,-14>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=-4+2=-2

y=-5+(-9)=-14

v+w=<-2,-14>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 9.57.56 am

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Example Question #12 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

If v=<5, 10> , and w=<-5, -7> , find v+w .

Possible Answers:

v+w=<15,-12>

v+w=<0,3>

v+w=<-12,15>

v+w=<0,3>

v+w=<3,0>

Correct answer:

v+w=<0,3>

Explanation:

This problem is asking us to add vectors , and . To add vectors together, we need to sum up like components together. This means that we sum up the x's , and the y's .

x=5+(-5)=0

y=10+(-7)=3

v+w=<0,3>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 10.07.23 am

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Example Question #42 : Vector & Matrix Quantities

If $\left \| v\right \|=10$ , and $\left \| w\right \|=5$ , and the angle in between them is $60^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=\sqrt{75}$

$\left \| v+w\right \|=15$

$\left \| v+w\right \|=\sqrt{85}$

$\left \| v+w\right \|=7$

$\left \| v+w\right \|=\sqrt{65}$

Correct answer:

$\left \| v+w\right \|=\sqrt{75}$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=10 , b=5 , and $C=60^{\circ}$ , then

$c^2=10^2+5^2-2\cdot10\cdot5\cos(60^{\circ})$

$c^2=100+25-20\cdot5\cos(60^{\circ})$

$c^2=125-100\cos(60^{\circ})$

$c^2=125-100\cdot\frac{1}{2}$

c^2=125-50

c^2=75

$\sqrt{c^2}=\sqrt{75}$

$c=\sqrt{75}\approx8.66$

Here is a visual representation of what we just found.

Locs

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Example Question #145 : High School: Number And Quantity

If $\left \| v\right \|=11$ , and $\left \| w\right \|=21$ , and the angle in between them is $21^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=11.43$

$\left \| v+w\right \|=12$

$\left \| v+w\right \|=11.6$

$\left \| v+w\right \|=11.5$

$\left \| v+w\right \|=\sqrt{85}$

Correct answer:

$\left \| v+w\right \|=11.43$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=11 , b=21 , and $C=21^{\circ}$ , then

$c^2=11^2+21^2-2\cdot11\cdot21\cos(21^{\circ})$

$c^2=121+441-462\cos(21^{\circ})$

$c^2=562-462\cos(21^{\circ})$

$c^2=562-462\cdot0.9336$

c^2=562-431.3142

c^2=130.6858

$\sqrt{c^2}=\sqrt{130.6858}$

$c=\sqrt{130.6858}\approx11.43$

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Example Question #146 : High School: Number And Quantity

If $\left \| v\right \|=8$ , and $\left \| w\right \|=22$ , and the angle in between them is $103^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=21.04$

$\left \| v+w\right \|=24.04$

$\left \| v+w\right \|=22.04$

$\left \| v+w\right \|=25.04$

$\left \| v+w\right \|=23.04$

Correct answer:

$\left \| v+w\right \|=25.04$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=8 , b=22 , and $C=103^{\circ}$ , then

$c^2=8^2+22^2-2\cdot8\cdot22\cos(103^{\circ})$

$c^2=64+484-16\cdot22\cos(103^{\circ})$

$c^2=548-352\cos(103^{\circ})$

$c^2=548-352\cdot-0.2249511$

c^2=548+79.18277

c^2=627.1828

$\sqrt{c^2}=\sqrt{627.1828}$

$c=\sqrt{627.1828}\approx25.04$

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Example Question #147 : High School: Number And Quantity

If $\left \| v\right \|=1$ , and $\left \| w\right \|=38$ , and the angle in between them is $116^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=38.45$

$\left \| v+w\right \|=38.5$

$\left \| v+w\right \|=40.8$

$\left \| v+w\right \|=38.6$

$\left \| v+w\right \|=41.34$

Correct answer:

$\left \| v+w\right \|=38.45$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=1 , b=38 , and $C=116^{\circ}$ , then

$c^2=1^2+38^2-2\cdot1\cdot38\cos(116^{\circ})$

$c^2=1+1444-2\cdot38\cos(116^{\circ})$

$c^2=1445-76\cos(116^{\circ})$

$c^2=1445-76\cdot-.4383711$

c^2=1445+33.31621

c^2=1478.316

$\sqrt{c^2}=\sqrt{1478.316}$

$c=\sqrt{1478.316}\approx38.45$

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Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

If $\left \| v\right \|=18$ , and $\left \| w\right \|=16$ , and the angle in between them is $26^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=7.89$

$\left \| v+w\right \|=4.67$

$\left \| v+w\right \|=20.27$

$\left \| v+w\right \|=11.43$

$\left \| v+w\right \|=9.62$

Correct answer:

$\left \| v+w\right \|=7.89$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=10 , b=5 , and $C=60^{\circ}$ , then

$c^2=18^2+16^2-2\cdot18\cdot16\cos(26^{\circ})$

$c^2=324+256-36\cdot16\cos(26^{\circ})$

$c^2=580-576\cos(26^{\circ})$

c^2=580-517.7054

c^2=62.2946

$\sqrt{c^2}=\sqrt{62.2946}$

$c=\sqrt{62.2946}\approx7.89$

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Example Question #149 : High School: Number And Quantity

If $\left \| v\right \|=16$ , and $\left \| w\right \|=19$ , and the angle in between them is $150^{\circ}$ , find the magnitude of the resultant vector.

Possible Answers:

$\left \| v+w\right \|=31.42$

$\left \| v+w\right \|=36.87$

$\left \| v+w\right \|=40.58$

$\left \| v+w\right \|=33.82$

$\left \| v+w\right \|=30.8$

Correct answer:

$\left \| v+w\right \|=33.82$

Explanation:

In order to find the resultants magnitude, we need to use the law of cosines. The law of cosines is $c^2=a^2+b^2-2ab\cos(C)$ . Suppose that a=16 , b=19 , and $C=150^{\circ}$ , then

$c^2=16^2+19^2-2\cdot16\cdot19\cos(150^{\circ})$

$c^2=256+361-32\cdot19\cos(150^{\circ})$

$c^2=617-608\cos(150^{\circ})$

$c^2=617-608\cdot-0.8660254$

c^2=1143.543

$\sqrt{c^2}=\sqrt{1143.543}$

$c=\sqrt{1143.543}\approx33.82$

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

Example Question #42 : Vector & Matrix Quantities

Example Question #11 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

Example Question #12 : Add Vectors End To End, Component Wise, And By Parallelogram Rule: Ccss.Math.Content.Hsn Vm.B.4a

Example Question #42 : Vector & Matrix Quantities

Example Question #145 : High School: Number And Quantity

Example Question #146 : High School: Number And Quantity

Example Question #147 : High School: Number And Quantity

Example Question #1 : Magnitude And Direction Of A Vector Sum: Ccss.Math.Content.Hsn Vm.B.4b

Example Question #149 : High School: Number And Quantity

All Common Core: High School - Number and Quantity Resources

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