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All Questions
^{+0}
234151 Questions
0
4
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+1443
Algebra
At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does
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parmen
Jul 10, 2024
0
1
5
+36
ratios?
At Central Middle School the 108 students who take the AMC meet in the evening to talk about problems and eat an average of two cookies apiece. Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe, which makes a pan of 15
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onyulee
Jul 10, 2024
0
3
1
+463
Algebra
Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.
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ChiIIBill
Jul 10, 2024
0
4
1
+463
Algebra
The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).
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ChiIIBill
Jul 10, 2024
0
4
1
+463
Algebra
Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___
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ChiIIBill
Jul 10, 2024
0
4
1
+961
Number Theory
For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$
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learnmgcat
Jul 10, 2024
-1
3
0
+961
Number Theory
For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does $n$ leave when divided by $23$?
learnmgcat
Jul 10, 2024
0
5
0
+961
Number Theory
Let N be a positive integer. The number N has three digits when expressed in base 7. When the number N is expressed in base 18, it has the same three digits, in reverse order. What is N? (Express your answer in decimal
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learnmgcat
Jul 10, 2024
0
3
2
+46
Help Please
Suppose that all four of the numbers
2-sqrt(5), 4+sqrt(10),14-2sqrt(7), -sqrt(2)
are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?
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RedDragon1
Jul 10, 2024
0
2
2
+242
Algebra
Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$
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cooIcooIcooI17
Jul 10, 2024
-1
2
3
+242
Algebra
Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.
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cooIcooIcooI17
Jul 10, 2024
0
3
1
+242
Algebra
I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 600 pounds more than each of her trucks, but no more than 1/2 of the total load her four trucks combined can carry. Based on these
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cooIcooIcooI17
Jul 10, 2024
0
3
1
+242
Algebra
The product $(3-\sqrt{5})(4+\sqrt{5})(1+6\sqrt{5})$ can be expressed in the form $a+b\sqrt{5}$, where $a$ and $b$ are integers. Find $a+b$.
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cooIcooIcooI17
Jul 10, 2024
0
3
1
+4
Algebra
At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and two muffins, which comes out to $4.85. Larry orders a piece of toast, two bagels, and a muffin, which comes out to $5.25. How many
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bookworm
Jul 10, 2024
Jul 9, 2024
0
5
0
+629
geometry
We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?
magenta
Jul 9, 2024
0
4
1
+629
Geometry
Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$
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magenta
Jul 9, 2024
0
3
0
+629
Geometry
Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.
magenta
Jul 9, 2024
0
5
0
+629
Geometry
A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table (as shown below) has a distance of 6 from one wall, and a distance of 6 from the other wall. Find the radius of the
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magenta
Jul 9, 2024
0
2
1
+463
Algebra
I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons
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ChiIIBill
Jul 9, 2024
0
4
1
+463
Algebra
I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons
read more ..
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ChiIIBill
Jul 9, 2024
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