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3 years ago

Please help me find out what k is.

Mathematics

1 answer:

Ghella [55]3 years ago

7 0

Answer: a) k=8

b) The area of the addition = $30\text{ square feet}$

The area of the entire patio after addition $=80\ \text{square feet}$

Step-by-step explanation:

Given: The area of the patio before addition = 50 square feet

The area of the addition portion is given by $k^2-3k-10$

We can see that dimension of the total portion is $k\times(k+2)$

therefore, the area of the patio with the addition portion = $k\times(k+2)=k^2+2k$

According to the question we have,

$k^2-3k-10+50=k^2+2k\\\Rightarrow-3k+40=2k\\\Rightarrow\ 5k=40\\\Rightarrow\ k=8$

Therefore, The area of the addition = $8^2-3(8)-10=64-24-10=30\text{ square feet}$

The area of the entire patio after addition = $30+50=80\ \text{square feet}$

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8 0

4 years ago

The number -3 can be classified as which of the following?

sp2606 [1]

Answer:

-3 is an integer, rational number and real number , so correct option id D) that is all of the above.

Explanation:

Integer is all natural number that a 1 , 2 , 3 , 4 ……. And zero and negative of natural numbers like -1 , -2 , -3 , - 4 ……. So -3 is an integer.

Rational number is the number which can be represented in the form of p/q where p and q are integers and q ≠ 0 . As -3 can be represented as (-3)/1 . hence -3 is also a rational number.

Real number is all number which can be represented on number line. All integers and rational numbers are real numbers . so -3 is also a real number.

Hence as -3 is an integer, rational number and real number , so correct option id D) that is all of the above.

5 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. He

dezoksy [38]

Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

Learn more about volumes at

brainly.com/question/12398192

#SPJ4

For the complete question, refer to the attachment.