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3 years ago

I need help with problem #7 please

Mathematics

1 answer:

Papessa [141]3 years ago

3 0

The ratio of the given legs of ΔFGH is 3:4, so we know this is a 3:4:5 triangle and the hypotenuse is 5/3 times the shortest leg. Then in similar ΔJKL, the hypotenuse will be (5/3)*2.4 m = 4 m. (selection B)

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two planes leave atlanta at 3 pm EST. one flies east and travels at a speed of 75 kilo. per hour slower than the other plane wit

Tom [10]

Let us start with the plane flying east at a slower speed. Let us assume that its speed is x kilometers per hour. After 4 hours, it will have traveled 4*x = 4x kilometers. Now let us calculate the speed of the plane flying west. It is faster by 75 kilometers per hour than the other plane. So its speed per hour is x+75 kilometers per hour. After 4 hours, it will have traveled 4( x+75) = 4x+300 kilometers. The total distance traveled by both the planes is 5460 kilometers. In other words, 4x+4x+300 =5460 kilometers. Now simplify the equation: 8x + 300 = 5460 8x = 5460 - 300 8x = 5160 x = 5160/8 645. x is the speed of the plane flying east. It is 645 kilometers. x + 75 is the speed of the plane flying west. It is 645 + 75 = 720 kilometers.

8 0

3 years ago

I can't figure out how to do (i + j) x (i x j)for vector calc

Vinil7 [7]

In three dimensions, the cross product of two vectors is defined as shown below

$\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}$

Then, solving the determinant

$\Rightarrow\vec{A}\times\vec{B}=(a_2b_3-b_2a_3)\hat{i}+(b_1a_3+a_1b_3)\hat{j}+(a_1b_2-b_1a_2)\hat{k}$

In our case,

$\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}$

Where we used the formula for AxB to calculate ixj.

Finally,

$\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}$

Thus, (i+j)x(ixj)=i-j

8 0

1 year ago

Does the point (–9, 8) satisfy the equation y = –x + 1?

Darina [25.2K]

Answer:

1. 3x+3y=9 since it is a coinciding line.It is equivalent because all the terms are multiplied by 3 from the original equation.

2. x-4=3x+4

x=3x+8

-2x=8

x=-4

y=-4-4

y=-8

please mark me brainlyest

8 0

2 years ago

A cooler contains 5 bottle of lemonade, 4 bottles of water, and 3 bottles of juice. Each type is equally likely to be chosen. Ba

lord [1]

I think the answer is 4

5 0

3 years ago

Instructions in picture

Kipish [7]

Answer:

12)

(9y +7)=(2y +98)( Because vertically opposite angle is always equal)

9y - 2y = 98-7

9y - 2y = 98-7

7y= 91

y =13

therfore y = 13

(9y + 7)

9*13+7

117+7

124

(2y +98)

2*13+98

26+98

124

5 0

3 years ago