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tangare [24]
3 years ago
5

The coordinate plane represents a map. Each grid unit represents 20 miles. A retail company has a warehouse at N(40, 60). A stor

e is located at P(40, −30). How long will it take a truck driving at 50 miles per hour to drive from warehouse N to this store?
Mathematics
1 answer:
pentagon [3]3 years ago
8 0
90*20= total distance between points
1800= 
1800/x=50/1
1800=50x
1800/50=x
36=x
it would take 36 hours

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In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
Kitty [74]
So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100  so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
5 0
3 years ago
Given the graph of log y=log(2)x. Find the area of the three inscribed rectangles
evablogger [386]

Answer: 6+2log_{2} 6

Step-by-step explanation:

S=s_{1} +s_{2} +s_{3} = 2(h_{1} +h_{2} +h_{3} )

h_{1} = log_{2}2=1

h_{2} = log_{2}4=2

h_{3} = log_{2}6

S = 2(1+2+log_{2}6) = 6+2log_{2}6

8 0
3 years ago
Could I get some help in here​
IgorC [24]

Answer:

  98 ft²

Step-by-step explanation:

There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...

  A = (1/2)(14 ft)(14 ft) = 98 ft²

Of course the area of the square from which it is cut is ...

  A = (14 ft)² = 196 ft²

So, the net area of the two triangles shown is ...

  A = (196 ft²) - (98 ft²) = 98 ft²

_____

Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...

  A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)

We can factor out 7 ft to get ...

  A = (7 ft)(x ft + (14 -x) ft)

  A = (7 ft)(14 ft) = 98 ft²

3 0
3 years ago
Which of the following is a point-slope equation of a line that passes through
Helen [10]
A

i need to put 20 characters in here so imma tell you, just use desmos.com. if you type in the equations, it’ll show you the graph
6 0
3 years ago
Find the equation of a line that passes through the points (1,2) and (5,6). Leave your answer in the form y=mx+c
Ainat [17]

Answer:

y=x+1

Step-by-step explanation:

first find the slope using the two coordinates:

use the slope formula- m=y^2-y^1/x^2-x^1

6-2/5-1

=4/4

=1

y=mx+b

now plug in one of the coordinates, and the slope we just found into the slope intercept formula

2=1(1)+b

2=1+b

subtract 1 from both sides

1=b

1=b; m=1,

y=x+1

5 0
3 years ago
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