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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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Example Questions

Example Question #191 : High School: Number And Quantity

Calculate $\left \| -10v\right \|$ , where v=<-6,7> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| -10\:v\right \|=-\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=-10\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is the same as .

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from .

$\left \| -10\:v\right \|=\sqrt{85}$ , Direction is the same as .

Correct answer:

$\left \| -10\:v\right \|=10\sqrt{85}$ , Direction is away from .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=10\cdot\sqrt{(-6)^2+7^2}=10\cdot\sqrt{36+49}=10\sqrt{85}$

As for the direction of the vector, since c<0 , the resulting vector will be against the original vector .

See below for a picture.

Screen shot 2016 03 07 at 12.02.14 pm

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Example Question #192 : High School: Number And Quantity

Calculate $\left \| 7v\right \|$ , where v=<8,6> . Also determine the direction of the resulting vector.

Possible Answers:

$\left \| 7\:v\right \|=70$ , Direction is away from .

$\left \| 7\:v\right \|=7$ , Direction is the same as .

$\left \| 7\:v\right \|=-7$ , Direction is away from .

$\left \| 7\:v\right \|=-70$ , Direction is away from .

$\left \| 7\:v\right \|=70$ , Direction is the same as .

Correct answer:

$\left \| 7\:v\right \|=70$ , Direction is the same as .

Explanation:

In order to solve the first part of the problem, we need to remember how to take the magnitude of a vector and scalar.

Now lets calculate this.

$=7\cdot\sqrt{8^2+6^2}=7\cdot\sqrt{64+36}=7\sqrt{100}=7\cdot10=70$

As for the direction of the vector, since c>0 , the resulting vector will be in the same direction as the original vector .

See below for a picture.

Screen shot 2016 03 07 at 12.10.09 pm

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Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:10x-4y=7 , and 2:-7x+5y=-10 ?

Possible Answers:

$\begin{bmatrix} 10 & 5 &-10 \\ -7& -4& 7 \end{bmatrix}$

$\begin{bmatrix} 10 & -7 &7 \\ -7& 5& -10 \end{bmatrix}$

$\begin{bmatrix} 10 & -4 &7 \\ -7& 5& -10 \end{bmatrix}$

$\begin{bmatrix} -10 & 5 &7 \\ -7& -4& 10 \end{bmatrix}$

$\begin{bmatrix} 10 & 5 &7 \\ -7& -4& -10 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 10 & -4 &7 \\ -7& 5& -10 \end{bmatrix}$

Explanation:

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

where x_1,y_1 , x_2,y_2 are coefficients of and in the first and second equation respectively. c_1, c_2 refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} 10 & -4 &7 \\ -7& 5& -10 \end{bmatrix}$

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Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:-20x-8y=9 , and 2:-13x+18y=14 ?

Possible Answers:

$\begin{bmatrix} 20 & -18 &9 \\ -13& 18& 14 \end{bmatrix}$

$\begin{bmatrix} -20 & -9 &18 \\ -13& 8& 14 \end{bmatrix}$

$\begin{bmatrix} -20 & -8 &9 \\ -18& 13& 14 \end{bmatrix}$

$\begin{bmatrix} 20 & -8 &9 \\ 13& 18& 14 \end{bmatrix}$

$\begin{bmatrix} -20 & -8 &9 \\ -13& 18& 14 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -20 & -8 &9 \\ -13& 18& 14 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -20 & -8 &9 \\ -13& 18& 14 \end{bmatrix}$

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Example Question #194 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-15x-3y=-1 , and 2:7x-8y=0 ?

Possible Answers:

$\begin{bmatrix} 15 & -3 &1 \\ 7& -8& 0 \end{bmatrix}$

$\begin{bmatrix} 15 & 3 &1 \\ 7& 8& 0 \end{bmatrix}$

$\begin{bmatrix} -15 & 3 &1 \\ 7& 8& 0 \end{bmatrix}$

$\begin{bmatrix} -15 & -3 &0 \\ 7& -8& 0 \end{bmatrix}$

$\begin{bmatrix} -15 & -3 &-1 \\ 7& -8& 0 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -15 & -3 &-1 \\ 7& -8& 0 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -15 & -3 &-1 \\ 7& -8& 0 \end{bmatrix}$

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Example Question #195 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:16x+9y=11 , and 2:11x-18y=17 ?

Possible Answers:

$\begin{bmatrix} 16 & -18 &11 \\ 11& 11& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &11 \\ 11& 18& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & -9 &11 \\ -11& -18& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &11 \\ 11& -18& 17 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &17 \\ 11& -18& 11 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 16 & 9 &11 \\ 11& -18& 17 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 16 & 9 &11 \\ 11& -18& 17 \end{bmatrix}$

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Example Question #196 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-18x-6y=4 , and 2:-4x-7y=15 ?

Possible Answers:

$\begin{bmatrix} -18 & -7 &4 \\ -4& -6& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -6 &-4 \\ -4& -7& -15\end{bmatrix}$

$\begin{bmatrix} 18 & 6 &4 \\ 4& 7& 15\end{bmatrix}$

$\begin{bmatrix} 18 & -6 &4 \\ -4& 7& 15\end{bmatrix}$

Correct answer:

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

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Example Question #197 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-18x+8y=-9 , and 2:8x+6y=11 ?

Possible Answers:

$\begin{bmatrix} 18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} 18 & 8 &9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 6 &-9 \\ 8& 8& 11 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

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Example Question #198 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:11x-15y=16 , and 2:-14x+20y=-18 ?

Possible Answers:

$\begin{bmatrix} 11 & 15 &16 \\ 14& 20& -18\end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& 18\end{bmatrix}$

$\begin{bmatrix} 11 & 15 &16 \\ 14& 20& 18\end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

$\begin{bmatrix} -11 & -15 &-16 \\ -14& -20& -18\end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

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Example Question #199 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:19x-8y=-20 , and 2:17x+4y=20 ?

Possible Answers:

$\begin{bmatrix} 19 & -8 &-20 \\ -17& 4& -20 \end{bmatrix}$

$\begin{bmatrix} -19 & -8 &-20 \\ 17& -4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ -17& -4& -20 \end{bmatrix}$

$\begin{bmatrix} -19 & 8 &20 \\ 17& -4& 20 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

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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 #191 : High School: Number And Quantity

Example Question #192 : High School: Number And Quantity

Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #194 : High School: Number And Quantity

Example Question #195 : High School: Number And Quantity

Example Question #196 : High School: Number And Quantity

Example Question #197 : High School: Number And Quantity

Example Question #198 : High School: Number And Quantity

Example Question #199 : High School: Number And Quantity

All Common Core: High School - Number and Quantity Resources

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