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sweet-ann [11.9K]
3 years ago
15

Barry is trying to calculate the distance between point E(3, 1) and point F(4, 7). Which of the following expressions will he us

e? square root of the quantity of 7 minus 1 all squared plus 4 minus 3 all squared square root of the quantity of 7 minus 3 all squared plus 4 minus 1 all squared square root of the quantity of 7 minus 4 all squared plus 3 minus 1 all squared square root of the quantity of 4 minus 7 all squared plus 1 minus 3 all squared
Mathematics
2 answers:
Serga [27]3 years ago
8 0

sooooo messy dude D: but the answer is (7-1)^2 + (4-3)^2

Try to memorize the distance formula because in highschool you're going to use that A LOT.

Best of luck https://gyazo.com/150dc8a2f4905b4f8d0e94d8690e2b47

Alex777 [14]3 years ago
6 0

Answer:

Option (1) is correct.

Barry uses the expression " square root of the quantity of 7 minus 1 all squared plus 4 minus 3 all squared " to find the distance between point E(3, 1) and point F(4, 7).

Step-by-step explanation:

Given : Barry is trying to calculate the distance between point E(3, 1) and point F(4, 7).

Distance between two points can be calculate using distance formula,

Distance formula states given two points P(a,b) and Q(c,d)  the distance between P and Q can be calculated using the given expression ,

D=\sqrt{(c-a)^2+(d-b)^2}

Thus,  distance between point E(3, 1) and point F(4, 7) can be calculate using above formula as ,

Here, a= 3 , b= 1 , c = 4 and d = 7

D=\sqrt{(c-a)^2+(d-b)^2}

Substitute above values, we get,

D=\sqrt{(4-3)^2+(7-1)^2}

D=\sqrt{(1)^2+(6)^2}

D=\sqrt{37}

Thus, Barry uses the expression " square root of the quantity of 7 minus 1 all squared plus 4 minus 3 all squared " to find the distance between point E(3, 1) and point F(4, 7).

Thus, Option (1) is correct.


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George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his t
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a. B+S = 1

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Step-by-step explanation:

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In order to solve the first part of the problem we need to take into account that the problem wants us to determine the percentage that should be allocated to each of the possible investment alternatives. In that case, the sum of the percentages must be equal to 1 (which means that we will have 100 of the trust fund)

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0.06B+0.1S \geq 0.075

Next, the problem tells us that whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund, so that's where the last restriction comes from:

B \geq 0.3

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R=0.06B+0.1S

which represents the return on the investment.

b)

For part b we can start by graphing each of the restrictions:

B+S = 1

This will be a single line, you can draw the line by setting B=0 first so you get:

0+S=1

S=1

So the first point to plot will be (0,1)

next, we can set s=0 to get:

B+0=1

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so the second point to plot will be (1,0)

so you can plot the two points and connect them with a straight line. This is the green line on the uploaded graph.

Next we can graph the second restriction:

0.06B+0.1S \geq 0.075

we can use the same procedure we used for the previous graph, in this case the points would be:

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and again connect the two points with a straight line. Next we need to decide which region of the graph to shade for which we can pick two arbitrary points on each side of the line, for example we can pick:

(0,0) and (2,2) and see which one makes the inequality true:

for (0,0) we get:

0.06B+0.1S \geq 0.075

0.06(0)+0.1(0) \geq 0.075

0 \geq 0.075

Which is false, therefore we need to shade the other region of the graph:

for (2,2) we get:

0.06B+0.1S \geq 0.075

0.06(2)+0.1(2) \geq 0.075

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Which is true, so we shade the region of the graph that contains that point. (see red graph)

now we graph the third restriction:

B \geq 0.3

In order to graph this third restriction we just need to draw a vertical line at B=0.3 and shade everything to the right of that line. (Blue graph)

Now, we can analyze the graph, in this case we need to locate the points where the green line crosses the red and the blue line which gives us the following coordinates:

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these two points can be found by setting the first restriction equal to each of the other two restrictions if you are to do it algebraically. If you are using a graphing device, you can directly read them from the graphs.

So once we got those points, we can see which one gives us the greatest percentage of return.

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R=0.06B+0.1S

R=0.06(0.3)+0.1(0.7)

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(0.625, 0.375)

R=0.06B+0.1S

R=0.06(0.625)+0.1(0.375)

R=0.075

so this distribution gives us 7.5% in return.

In this case the best distribution for us is 30% in bonds and 70% in the stock fund to get a return of 8.8%

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