All Questions ⁺⁰235282 Questions

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Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

AUnVerifedTaxPayer Oct 18, 2024

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+120

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the largest number of primes that could divide a terrific positive integer?

AUnVerifedTaxPayer Oct 18, 2024

0

1

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+120

Number Theory

A positive integer is called terrific if it has exactly 5 positive divisors. What is the smallest terrific positive integer?

AUnVerifedTaxPayer Oct 18, 2024

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+81

Function Notation

A function is a relation where each input value is assigned to ?
one output value.
The ?
of a function is the set of read more ..

Alyssiaca Oct 18, 2024

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+81

Function Notation

Find the value of h(45) for the function below.
h(x)= 1/9 (90-x)
A.
15 read more ..

Alyssiaca Oct 18, 2024

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+81

Function Notation

Which of the following shows a function written in equation notation that is equivalent to the function below?
f(x) = 3(x + 10)
A.
y = 3x + 10 read more ..

Alyssiaca Oct 18, 2024

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+81

Function Notation

Find the value of h(-67) for the function below.
h(x) = -49x − 125

Alyssiaca Oct 18, 2024

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+1186

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. How many prime numbers are divisors of $n?$

learnmgcat Oct 18, 2024

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+1186

Number Theory

A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. What is the smallest possible value of $n$?

learnmgcat Oct 18, 2024

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+1186

Number Theory

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

learnmgcat Oct 18, 2024

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+1186

Number Theory

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

learnmgcat Oct 18, 2024

Oct 17, 2024

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+744

Geometry

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

AnswerscorrectIy Oct 17, 2024

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+744

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 8$ and $WX = 8,$ find $XY.$

AnswerscorrectIy Oct 17, 2024

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+744

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

AnswerscorrectIy Oct 17, 2024

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+744

Geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

AnswerscorrectIy Oct 17, 2024

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+1186

Algebra

At a store, you are interested in purchasing a candy bar and a piece of bubble gum. Together, they cost $2.00. The candy bar costs a dollar more than the bubble gum. How much does the piece of bubble gum cost, in cents?

learnmgcat Oct 17, 2024

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+1186

Algebra

If I give my brother $8$ dollars, then we will have the same amount of money. If instead he gives me $19$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

learnmgcat Oct 17, 2024

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+1186

Algebra

What is the smallest positive integer n such that \sqrt[4]{1323*n*84*779*5*3*441} is an integer?

learnmgcat Oct 17, 2024

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+190

Counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?

jaekg Oct 17, 2024

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+190

Counting

At a meeting, $4$ scientists, $3$ mathematicians, and $2$ journalists are to be seated around a circular table. How many different arrangements are possible if every mathematician must sit next to a journalist? (Two seatings are considered read more ..

jaekg Oct 17, 2024

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