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2 years ago

5

Review your answers to Question 4. What happens to the coordinates of a shape when the shape reflects about the line y = x? Expl

ain

1 answer:

Contact [7]2 years ago

6 0

Answer:

When the shape reflects about the line y = x, the x-coordinate and the y-coordinate of each point are swapped.

Step-by-step explanation:

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The area of Norway is 24% more than the area of Colorado so Norway's area is-------% of Colorado's area

zhenek [66]

Possibly 124%.........

8 0

2 years ago

Jake made a total of 7 copies at a copy shop, with some being black-and-white copies and some being color copies. Black-and-whit

Arada [10]

Jake spent a total of 70 cents.
b = black-and-white = 8 cents
c = color = 15 cents

70 = 8b + 15c

he made a total of 7 copies
b + c = 7

system of equation:
70 = 8b + 15c
b + c = 7

--------------------------

b + c = 7
b + c (-c) = 7 (-c)
b = 7 - c

plug in 7 - c for b

70 = 8(7 - c) + 15c
Distribute the 8 to both 7 and - c (distributive property)

70 = 56 - 8c + 15c
Simplify like terms

70 = 56 - 8c + 15c
70 = 56 + 7c

Isolate the c, do the opposite of PEMDAS: Subtract 56 from both sides

70 (-56) = 56 (-56) + 7c
14 = 7c

divide 7 from both sides to isolate the c

14 = 7c
14/7 = 7c/7
c = 14/7
c = 2

c = 2
---------------

Now that you know what c equals (c = 2), plug in 2 for c in one of the equations.
b + c = 7
c = 2
<em>b + (2) = 7
</em><em />Find b by isolating it. subtract 2 from both sides
b + 2 = 7
b + 2 (-2) = 7 (-2)
b = 7 - 2
b = 5

Jake made 5 black-and-white copies, and 2 color copies

hope this helps

8 0

2 years 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

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

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

------

<u>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"</u>

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

------

<u>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."</u>

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

------

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

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

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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2 years ago

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Gary used landscape timbers to create a border around a garden shaped like a right triangle. The longest two timbers he used are

Cloud [144]

Answer:

9 feet

Step-by-step explanation:

Given:

The border of the garden is a right angled triangle.

Two lengths are given as 12 ft and 15 ft.

Let the length of the shortest timber be 'x' feet.

Now, in a right angled triangle, the longest length is called the hypotenuse.

As 15 feet is the largest length, it is the hypotenuse of the triangle. Now, applying Pythagoras theorem, we get:

$(Leg1)^2+(Leg2)^2=(Hypotenuse)^2\\x^2+12^2=15^2\\x^2+144=225\\x^2=225-144\\x^2=81\\x=\pm \sqrt{81}=\pm 9$

The negative value is neglected as length can never be negative.

Therefore, the length of the shortest timber is 9 feet.

8 0

2 years ago

In a recent local taste contest testing Coke against Pepsi it was found that 3/5 of all people surveyed preferred to taste the C

goldenfox [79]

3/5 of 7500 is 4500. That means 4500 chose coke. Now all u need to do is subtract 4500 from 7500 to get the amount of people that chose Pepsi. The answer would be 3000

5 0

2 years ago

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