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3 years ago

Points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k

1 answer:

8 0

Slope equation: y2-y1 over x2-x1
3-0 over 3-0 = 1
to get the perpendicular slope of a line, you must use the negative reciprocal therefore, the slope of a line that is perpendicular to k is equal to -1

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If 2x - 3 = 3x - 7, what is the value of x?

icang [17]

Answer:

x=4

Step-by-step explanation:

2x-3=3x-7

Subtract 2x from both sides of the equation

-3=x-7

Add 7 to both sides of the equation to isolate x

7 0

3 years ago

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"

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

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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"

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

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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."

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

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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.

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

8 0

3 years ago

Read 2 more answers

A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inch

daser333 [38]

Total lot - house -other side
=(56 ft 9 in) - (34 ft 10 in) - (5 ft 5 in)
=(55 ft 21 in) - (34 ft 10 in) - (5 ft 5 in)
=16 ft 6 in
Convert to inches: 16 ft x 12 in/ft)+ 6 in= Total in inches192 in + 6 in= Total in inches
198 in= Total in inches
Check: One side + house + other side = Lot width
(5 ft 5 in)+(34 ft 10 in)+(16 ft 6 in)=Lot width
56 ft 9 in=Lot width, which equals the given.

8 0

2 years ago

Last week Karen spent $121.35 on food for her family. She only has $200 to spend every two weeks. How much does hse have left to

yan [13]

Answer:

$78.65

Step-by-step explanation:

take 200-121.35=78.65

$78.65

5 0

3 years ago

Read 2 more answers