All Questions ⁺⁰237293 Questions

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Coefficient

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

ChiIIBill Jan 16, 2024

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57

1

+478

Real numbers

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

ChiIIBill Jan 16, 2024

0

59

1

+478

Constant Term

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

ChiIIBill Jan 16, 2024

0

41

1

+1678

Equation of line

A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

wiseowl Jan 16, 2024

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51

1

+1678

Coordinates

Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 8x - 3y$.

wiseowl Jan 16, 2024

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61

2

+39

math quesiton

All seven smaller circles are tangent to each other, and the larger circle is tangent to the six outer smaller circles. the radius of each of the smaller circles is 3 cm. In cm^2, the sum of the areas marked "a" is. read more ..

hi1234 Jan 16, 2024

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35

1

+1678

Coordinates

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

wiseowl Jan 16, 2024

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56

1

+1678

Coordinates

A line has a slope of $m,$ and its $y$-intercept is $(0,b)$. If $m = 8$ and $b = 14,$ then what is the $x$-intercept of the line?

wiseowl Jan 16, 2024

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56

1

+1776

Trapezoid

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 90^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle XZW$, in degrees.

bader Jan 16, 2024

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42

0

+1776

Quadrilateral

Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EBF$ is $5,$ and the area of triangle $EAD$ is $5.$ Find the area of parallelogram read more ..

bader Jan 16, 2024

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38

1

+1776

Trapezoid

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

bader Jan 16, 2024

Jan 15, 2024

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59

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+1776

Parallelogram

In parallelogram $EFGH,$ let $M$ be the point on $\overline{EF}$ such that $FM:ME = 3:5,$ and let $N$ be the point on $\overline{EH}$ such that $HN:NE = 2:5.$ Line segments $\overline{FH}$ and GM intersect at P, and line segments FH and GN intersect at read more ..

bader Jan 15, 2024

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44

1

+1776

Trapezoid

The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the perimeter of the trapezoid.

bader Jan 15, 2024

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48

1

+1776

Trapezoid

In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.

bader Jan 15, 2024

+1

70

1

+344

cool problem

The symbol n! is pronounced "n factorial" and it is shorthand for the product n x (n-1) x (n-2) x ... x 2 x 1. How many zeros does 2017! end in?

hipie Jan 15, 2024

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67

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+1926

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 5x + 12. Compute 1/(a^2 - 4) + 1/(b^2 - 4).

tomtom Jan 15, 2024

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61

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+1926

Algebra

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 5x - 19. Find \frac{u^2}{v} + \frac{v^2}{u}.

tomtom Jan 15, 2024

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56

1

+1926

Algebra

Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 + 11x + 13. Find \frac{1}{a^3} + \frac{1}{b^3}.

tomtom Jan 15, 2024

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39

1

+1556

Triangle Inequality

All the sides of a triangle have integer length. The perimeter of the triangle is 5 and the triangle is isosceles. How many such non-congruent triangles are there?

kittykat Jan 15, 2024

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56

0

+1776

Dilation

Let G be the center of equilateral triangle ABC A dilation centered at G with scale factor -1/5 is applied to triangle ABC to obtain triangle A'B'C' Let K be the area of the region that is contained in both triangles ABC and A'B'C' Find K/[ABC] read more ..

bader Jan 15, 2024

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65

1

+1776

Geometry

The vertices of triangle $ABC$ lie on the sides of equilateral triangle $DEF$, as shown. If $CD = 5$, $CE = BD = 4$, and $\angle ACB = 60^\circ$, then find $AE$.

bader Jan 15, 2024

0

53

1

+1556

Coordinates

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
Point A is (5,7), and the line is y = x.

kittykat Jan 15, 2024

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35

1

+1556

Coordinates

Line $\ell$ is drawn in the coordinate plane below. If the slope of line $\ell$ is $2,$ then find the area of the triangle determined by the line and the coordinate axes.

kittykat Jan 15, 2024

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