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labwork [276]
3 years ago
7

line segment AB has endpoints A (7.5,4.2) and B (2.3,5.4). Find the coordinates of the point that divides the line segment direc

ted from A to B in the ratio of 1:3
Mathematics
1 answer:
Marrrta [24]3 years ago
5 0

9514 1404 393

Answer:

  (6.2, 4.5)

Step-by-step explanation:

We want, for some point P, ...

  (P -A) / (B -P) = 1 / 3

  3(P -A) = (B - P) . . . . . multiply by 3

  4P = B +3A . . . . . . . . add P+3A

  P = (B +3A)/4 . . . . . . .divide by 4

Filling in the coordinate values, we can find P to be ...

  P = ((2.3, 5.4) +3(7.5, 4.2))/4 = (2.3+22.5, 5.4+12.6)/4

  P = (6.2, 4.5)

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A family on vacation records the time in hours) and the distance (in miles) that they travel. The data are shown in the scatter
nata0808 [166]

Answer:

In the first 3.5 hours, the family travelled 175 miles.

Step-by-step explanation:

We have the table:

time (hours)              distance ( miles)

      0                                   0

      1                                   50

       2                                 100

      3                                  150

      4                                 200

      5                                 250

      6                                 300

      7                                 350

      8                                 400

      9                                 450

This seems like a linear relationship, let's write the general line:

y = a*x + b

That represents this situation, y is the distance in miles and x is the time in hours.

In the line equation, a represents the slope and b the y-intercept.

And if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we have a lot of points for the line, we can use any pair we want (we actually should use a few different pairs to see that the slope is always the same)

So if we use the first two (0, 0) and (1, 50)

the slope is:

a = (50 - 0)/(1 - 0) = 50

Now, if we use the third and fifth points (4, 200) and (5, 250) now the slope is:

a = (250 - 200)/(5 - 4) = 50/1 = 50

So we can conclude that the slope of the equation is a = 50

Then the equation is something like:

y = 50*x + b

To find the value of b, we can use any of the points of the line, for example (0, 0)

This means that when x = 0, y also must be 0, then:

0 = 50*0 + b

0 = b

Then the equation is:

y = 50*x

Now, to answer how many miles the family travelled in the first 3.5 hours, we just need to replace x by 3.5 in the equation:

y = 50*3.5 = 175

In the first 3.5 hours, the family travelled 175 miles.

6 0
3 years ago
Radio tower had a special on rechargeable batteries. It sold AA for $1 and AAA for $0.75. It sold 42 batteries on a single day a
PIT_PIT [208]
AA = $1
AAA= $0.75

AA + AAA = 42

$1AA + $0.75AAA= $37

AA + AAA = 42
AA + AAA-AAA= 42- AAA
AA = 42- AAA

$1(42- AAA) + $0.75AAA= $37
$42 - AAA +0.75AAA = $37
$42 -0.25AAA= $37
$42-$42 -0.25AAA= $37 -$42
-0.25AAA= -5
-0.25AAA/-0.25 = -5/-0.25
AAA= 20

AA + AAA= 42
AA + 20 = 42
AA +20 -20 = 42-20
AA= 22

Check
$1AA + $0.75AAA= $37
$1(22)+ $0.75(20)= $37
$22 + $15 =$37
$37 = $37


5 0
3 years ago
A construction worker has 1,032 nails. He needs to put them in containers with 12 in each container. How many containers will he
miv72 [106K]

Answer:

86

Step-by-step explanation:

1,032 ÷ 12 = 86

86 containers would be needed.

4 0
2 years ago
All ir rational numbers are rational numbers
patriot [66]

Answer:

no

Step-by-step explanation:

false

irrational numbers cannot be rational

8 0
3 years ago
Given a minimum usual value of 135.8 and a maximum usual value of 155.9, determine which (1 point) of the following values would
maxonik [38]

Answer:  b. 134

Step-by-step explanation:

Given : A minimum usual value of 135.8 and a maximum usual value of 155.9.

Let x denotes a usual value.

i.e.  135.8< x < 155.9

Therefore , the interval for the usual values is [135.8, 155.9] .

If interval for any usual value is [135.8, 155.9] , then any value should lie in this otherwise we call it unusual.

Let's check all options

a. 137  ,

since  135.8< 137 < 155.9

So , it is usual.

b. 134

since 134<135.8 (Minimum value)

So , it is unusual.

c. 146  

since  135.8< 146 < 155.9

So , it is usual.

d. 155  

since 135.8< 1155 < 155.9

So , it is usual.

Hence, the correct answer is b. 134 .

4 0
3 years ago
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