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2 years ago

Find the distance between the point.(5,5) amd the line -3x-4y+10=0

Mathematics

1 answer:

gayaneshka [121]2 years ago

6 0

Answer:

Step-by-step explanation:

the formula of the distance between

the point (p, q) and the line ax + by +c = 0 =>

d = |p.a + q.b +c| / √(a²+b²)

d = |5(-3)+5(-4)+10| / √[(-3)²+(-4)²]

= |(-15-20+10)|/√25

= |-25|/ 5

= 25/5

= 5

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A restaurant sells burritos for $8.00 each. The cost of the meat is $1.50 and the cost of the other ingredients is $1.00 for eac

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Answer:

Profit for 100 burritos: $550

Cost to make one burrito: $2.50

Step-by-step explanation:

If a restaurant sells burritos for $8, that's a positive 8 dollars they earned. Then, we need to find what the cost was to make the burrito. If the meat is 1.50 and the cost for all the other ingredients is 1 dollar, then they lose 2.50 for every 8 dollars they make (for each burrito). So, to find the profit in one burrito, we would add -2.5+8, giving us an answer of 5.5. So, they earn 5 dollars and 50 cents each burrito and lose $2.50.

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6 0

1 year ago

Read 2 more answers

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

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3 years ago

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3 years ago