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aleksandrvk [35]
2 years ago
7

Writing equations in standard form:

Mathematics
1 answer:
d1i1m1o1n [39]2 years ago
3 0
You have already done half of it. Now substitute for x1 = 4 and y = 5
y - 5 = 6/7(x - 4)
Multiply everything by 7 to remove fractions
7y - 35 = 6(x - 4)
7y - 35 = 6x - 24
-6x + 7y = -24 + 35
-6x + 7y = 11

Some people prefer a positive number in front of x so multiply by -1
6x - 7y = -11

You can check the answer by testing it works for both of the original points
6x4 - 7x5 = 24 - 35 = -11 true
6x-3 - 7x-1 = -18 - -7 = -11 true
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You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s
fredd [130]

Answer:

Time spent rowing down stream =100\ seconds

Speed of boat in still water =14\ ms^{-1}

Step-by-step explanation:

Let speed of boat in still water be = x\ ms^{-1}

Speed of current = 10\ ms^{-1}

Speed of boat down stream = \textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}

Distance rowed down stream = 2400 m

Time spent rowing down stream = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s = \frac{Distance}{Speed}=\frac{2400}{x+10}\ s

Speed of boat up stream = \textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}

Distance rowed up stream = \frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m

Time spent rowing up stream = \frac{Distance}{Speed}=\frac{400}{x-10}\ s

We know that,

\textrm{Time spent rowing down stream =Time spent rowing up stream}

So,

\frac{2400}{x+10}=\frac{400}{x-10}

Cross multiplying

2400(x-10)=400(x+10)

Dividing both sides by 400

\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}

6(x-10)=x+10

6x-60=x+10

Adding 60 to both sides.

6x-60+60=x+10+60

6x=x+70

Subtracting both sides by x

6x-x=x+70-x

5x=70

Dividing both sides by 5.

\frac{5x}{5}=\frac{70}{5}

∴ x=14

Speed of boat in still water =14\ ms^-1

Time spent rowing down stream =\frac{2400}{14+10}=\frac{2400}{24}=100\ s

3 0
3 years ago
1.6 × 10^6 ÷ 4.8 × 10^5. Give your answer as a mixed number​
Tasya [4]

Answer:

(10^11)/3

10^6 x 10^5 = 10^11

8/5 x 5/24 = 1/3

so multiply 10^11 and 1/3 together

6 0
2 years ago
1)The original price of concert is $100. They are on sale for 21% off. How much will the tickets cost after the discount? 2)Ms.B
mel-nik [20]
1.  79%  Take 100 x 21%=21, then subtract 21 from 100 = 79
2.  $138  Take 1200 x 11.5%= $138
3 0
3 years ago
If mABD​, what are mABC and m​DBC?
Sedbober [7]

Answer:

45

Step-by-step explanation:

8 0
3 years ago
If you have $2500 how many board feet can you buy if the cost per board foot is $3.21?
dexar [7]

Answer:

2500÷$3.21 =778.81

just round to the nearest whole number

6 0
3 years ago
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