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2 years ago

How many $10 bills are the same as ten $1 bills

Mathematics

2 answers:

andrey2020 [161]2 years ago

4 0

10 * $1 = $ 10
$10 / 10 = 1
one 10$ bill
pretty simple

Ilia_Sergeevich [38]2 years ago

3 0

1 $10 bill is the same as ten $1 bills

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What is the domain of y = log Subscript 4 Baseline (x + 3)?

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Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

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Sails come in many shapes and sizes. The sail on the right is a triangle. Is it a right triangle? Explain your reasoning.

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Answer:

not a right triangle

Step-by-step explanation:

you can use the pythagorean theorem to prove whether not this is a right triangle

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1 year ago

The equation y = 5.5x represents a proportional relationship. What is the constant of proportionality?

lara31 [8.8K]

Y = 5.5x
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2 years ago

Each batch of Mrs. Crawley’s Toffee makes 14 pieces of toffee. If sandy needs 8 dozen pieces of toffee, how many batches does sh

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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

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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.

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

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