Sophia bought 2 jars of pickles for $65. What is the unit price?

June's flower bed has a length of 8 feet and a width of seven eighths feet. Is the area of the flower bed larger, smaller, or eq

xxTIMURxx [149]

Area = length x width

Because the width is less than 1 foot the area would be less than 8 square feet.

Answer: smaller than

7 0

3 years ago

What is the arc length if Θ = 2 pi over 7 and the radius is 3 cm? A. 7 pi over 12

hodyreva [135]

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

$\theta=\frac{2\pi}{7} \\\\r=3\ cm$

An arc is a part of total circumference of circle and length of that arc is the measurement of linear distance.

Since we know the formula for "Length of an arc " , we get

$L=r\times \theta\\\\L=\frac{2\pi}{7}\times 3\\\\L=\frac{6\pi}{7}$

Hence, Option 'C' is correct.

6 0

3 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

3 years ago

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Describe the relationship between the values of the independent and dependent variables (plz help)

Vadim26 [7]

Dependent variable is the variable that changes due to the independent variable, independent variable is the variable that scientists change on purpose.

5 0

3 years ago

Sarah started with $150 of credit card debt. Each month, she paid $50 of her bill, but by the next month the interest made her r

frosja888 [35]

D. Is the correct answer

4 0

3 years ago

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