All Questions ⁺⁰236343 Questions

-1

30

0

+2653

quadratic

For what values of $j$ does the equation $(2x+7)(3x-15) = -43 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

LiIIiam0216 Mar 16, 2024

0

49

0

+2653

Algebra

Find $d$ such that the equation $(d-1)x^2-4dx+(d + 10) = 0$ only has one real solution.

LiIIiam0216 Mar 16, 2024

0

27

0

+2653

quadratic

Let $m$ be a real number. If the quadratic equation $2x^2+mx+8 = x^2-11x-17$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

LiIIiam0216 Mar 16, 2024

0

50

0

+2653

Algebra

Find the product of all positive integer values of $c$ such that the quadratic equation $x^2+5x+c=-8x$ has two real roots.

LiIIiam0216 Mar 16, 2024

0

32

0

+2653

need help

Find the largest real number $c$ such that $10$ is in the range of $f(x)=x^2-5x+12x+c$.

LiIIiam0216 Mar 16, 2024

0

25

0

+2653

help quadratic

The quadratic equation x^2+4mx+m = 2x - 7x + 11 has exactly one real root. Find the positive value of $m$.

LiIIiam0216 Mar 16, 2024

0

45

0

+2653

Algebra

Solve for x: (\sqrt{12x}+12)(\sqrt{8x}+4)=2(x+3)+x

LiIIiam0216 Mar 16, 2024

0

50

0

+2653

Equation

What is the greatest possible value of $x$ for the equation $$\left(\frac{4x-16}{3x-4}\right)^2=12?$$

LiIIiam0216 Mar 16, 2024

0

41

0

+2653

quadratic

If $n$ is a constant and if there exists a unique value of $m$ for which the quadratic equation $x^2 + 5mx + (7m-n+1) = 0$ has one real solution, then find $n$.

LiIIiam0216 Mar 16, 2024

0

28

0

+2653

Algebra

Find the product of the $y$-coordinates of all the distinct solutions $(x,y)$ for the two equations $y=x^2-8$ and $y^2=-15x+12$.

LiIIiam0216 Mar 16, 2024

0

25

0

+2653

Quadratic

Let $m$ be an integer. If the quadratic equation $x^2 + mx + 3m = 120$ has one or more integer roots, then find the sum of all possible values of $m$.

LiIIiam0216 Mar 16, 2024

0

35

0

+2653

help algebra

The real numbers x and y satisfy the equation $x^2+y^2=14x+48-10x+2y$. What is the minimum value of $y$?

LiIIiam0216 Mar 16, 2024

0

28

2

+355

One solution of is twice the other solution. Find k.

One solution of is twice the other solution. Find k.

Lilliam0216 Mar 16, 2024

0

29

2

+355

What is the sum of the squares of the roots of ?

What is the sum of the squares of the roots of ?

Lilliam0216 Mar 16, 2024

0

35

0

+355

Surface area help

The surface area of a box is 160 square inches. The length of the box is twice its width, and is 4 inches less than its height. What is the height of the box, in inches?

Lilliam0216 Mar 16, 2024

0

25

1

+1577

Algebra

Let a and b be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are a^4 and b^4.

parmen Mar 16, 2024

0

28

1

+1577

help algebra

Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

parmen Mar 16, 2024

0

29

1

+478

Expand

Expand (a + 2)(3a^2 - 2a - 12)(a^2 - 2a + 1).

ChiIIBill Mar 16, 2024

0

34

1

+478

Roots

Fill in the blanks to make a quadratic whose roots are $5$ and $-5.$
x^2 + ___ x + ___

ChiIIBill Mar 16, 2024

0

32

1

+478

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

ChiIIBill Mar 16, 2024

0

30

1

+478

Integers

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

ChiIIBill Mar 16, 2024

-1

42

0

+2653

Triangles

As shown in the diagram $\angle BAC=90^\circ$. Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$, $\overline{AY}$ be the bisector of $\angle BAC$, and $\overline{AZ}$ be the median of $\triangle ABC$. If $\angle BAY = 16^\circ$, then read more ..

LiIIiam0216 Mar 16, 2024

-1

41

0

+2653

Quadrilateral

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.

LiIIiam0216 Mar 16, 2024

-1

28

1

+2653

Rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

LiIIiam0216 Mar 16, 2024

-1

31

1

+2653

Rectangle

Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 3$. Find $DX$.

LiIIiam0216 Mar 16, 2024

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