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stepan [7]
3 years ago
8

4. In one semester, Doug and Laura spent a combined 230 hours in the tutoring lab. If Doug

Mathematics
2 answers:
ANEK [815]3 years ago
7 0
The correct Answer is 80 hours
IRISSAK [1]3 years ago
6 0

Answer:

80 hours

Step-by-step explanation:

let d represent doug, let l represent laura

first, set up a system of equations representing the problem:

since doug spent 10 less than twice the hours laura did, and we know that the total amount of hours they spent together is 230:

l=2d+10

d+l=230

then solve:

*first i rearranged the equations so i can solve this system of equations using elimination method*

l-2d=10

l+d=230

*subtract*

3d=240

d=80

so, doug spent 80 hours in the lab

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If the scale is 1 : x, then multiply the map distance by x to calculate the actual distance.

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3 years ago
In the given figure find the value of x and y?<br>Show you works - Thank you!​
Vaselesa [24]

<u>EXPLANATION</u><u>:</u>

In ∆ ABC , ∠ABC = 40°

  • ∠CAB = x°
  • & ∠ACD = 50°

∠ACD is an exterior angle formed by extending BC to D

We know that

The exterior angle of a triangle formed by extending one side is equal to the sum of the opposite interior angles.

∠ACD = ∠CAB + ∠ABC

⇛50° = x° + 40°

⇛x° = 50°-40°

<h3>⇛x° = 10°</h3>

and

In ∆ ACD , AC = CD

⇛ ∠CDA = ∠CAD

Since the angles opposite to equal sides are equal.

Let ∠CDA = ∠CAD = A°

We know that

The sum of all angles in a triangle is 180°

In ∆ ACD,

∠CDA +∠CAD + ∠ACD = 180°

A°+A°+50° = 180°

⇛2A°+50° = 180°

⇛2A° = 180°-50°

⇛2A° = 130°

⇛A° = 130°/2

⇛A° = 65°

now,

∠CDA = ∠CAD = 65°

∠BAC + ∠CAD+y = 180°

Since angles in the same line

10°+65°+y = 180°

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<u>Answer</u><u>:</u> Hence, the value of “x” & “y” will be 10° and 105° respectively.

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2 years ago
-4 is less than or equal to a, and 9 is greater or equal to w
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Step-by-step explanation:

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Read 2 more answers
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Nonamiya [84]

128

This question requires us to solve an infinite GP

As we can see the first unit is 16 wide, then 8, then 4 and so on; this can be written as  

64(1,0.5,0.25,0.125,....\infinity∞)  (64 used as 16*4 = 64 is the area of the first rectangle)

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