All Questions ⁺⁰236052 Questions

0

18

1

+1557

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 read more ..

parmen Jul 10, 2024

0

8

5

+40

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 read more ..

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onyulee Jul 10, 2024

0

20

1

+478

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

ChiIIBill Jul 10, 2024

0

22

1

+478

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).

ChiIIBill Jul 10, 2024

0

20

1

+478

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

ChiIIBill Jul 10, 2024

0

11

1

+1310

Number Theory

For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

learnmgcat Jul 10, 2024

-1

17

0

+1310

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

13

0

+1310

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 read more ..

learnmgcat Jul 10, 2024

0

12

2

+54

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?

RedDragon1 Jul 10, 2024

0

7

2

+606

Algebra

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

cooIcooIcooI17 Jul 10, 2024

-1

8

3

+606

Algebra

Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.

cooIcooIcooI17 Jul 10, 2024

0

22

1

+606

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 read more ..

cooIcooIcooI17 Jul 10, 2024

0

17

1

+606

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 $a+b$.

cooIcooIcooI17 Jul 10, 2024

0

12

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 read more ..

bookworm Jul 10, 2024

Jul 9, 2024

0

13

0

+862

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

15

1

+862

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 $AB.$ read more ..

magenta Jul 9, 2024

0

14

0

+862

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

13

0

+862

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 read more ..

magenta Jul 9, 2024

0

15

1

+478

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 ..

ChiIIBill Jul 9, 2024

0

16

1

+478

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 ..

ChiIIBill Jul 9, 2024

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