Simplify aaa^3bxa^2b^3abx^4

Carolyn is using the table to find 360% of 15. What values do X and Y represent in her table? Percent Total 100% 100% 100% 20% 2

asambeis [7]

Answer: c

Step-by-step explanation:

Based on the percent breakdown of 360%.

100% 100% 100% 20%20%20%

15. 15. 15. 3. 3. 3.

100% is all of it, so 15. This is x.

20% of it would be calculated as 0.2 x 15 or 3. This is y.

7 0

2 years ago

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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

2 years ago

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During his science experiment, Yuri measured the temperature of a water sample as 24 degrees Celsius. To determine the temperatu

mr Goodwill [35]

Answer:

75.2 degrees Fahrenheit

Step-by-step explanation:

F = StartFraction 9 Over 5 EndFraction C + 32

Substitute 24 for C.

Multiply the value of C by StartFraction 9 Over 5 EndFraction before adding 32.

24 Degrees Celsius is 75.2 Degrees Fahrenheit.

8 0

2 years ago

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Which shows how to solve the equation Three-fourths x = negative 6 for x in one step?

My name is Ann [436]

option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

Step-by-step explanation:

We have , The given expression as Three-fourths x = negative 6 , which can be written as $\frac{3}{4} (x) = -6$ . Now in order to solve this equation in one step , we must notice that coefficient of x must be 1 but it's $\frac{3}{4}$ , Let's make coefficient of x as 1 by multiplying both side of equations by 4/3:

$\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4}(\frac{4}{3} ) (x) = -6(\frac{4}{3} )$

⇒ $x = -6(\frac{4}{3} )$

⇒ $x = -2(4)$

⇒ $x = -8$

Therefore, x= -8 & correct option to solve the equation Three-fourths x = negative 6 for x in one step is option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

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2 years ago

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A hot air balloon descends to the ground. The function h(t) = 210 – 15t can be used to describe the altitude of the balloon as i

Olin [163]

It is D if its correct i will explain why

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2 years ago

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