All Questions ⁺⁰234855 Questions

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+1481

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

parmen Oct 1, 2024, 2:26:21 AM

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+145

Algebra

Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
(a) Is the number 1/7 in the set S?
(b) Is the number 1/4 in the set S? read more ..

MEMEG0D Oct 1, 2024, 2:24:45 AM

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+836

Algebra

Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.

Hi6942O Oct 1, 2024, 2:19:40 AM

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+169

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
f(p) = f(q) = f(r) = f(s) = 1
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

BRAlNBOLT Oct 1, 2024, 2:18:40 AM

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+790

Algebra

The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

eramsby1O1O Oct 1, 2024, 2:17:52 AM

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+1348

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

blackpanther Oct 1, 2024, 2:17:14 AM

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+36

I'm backkk (was inactive) new question in need of help. HINTS ONLY. I AM ALSO BEHIND IN GEOMETRY SINCE OF STUFF.

1)An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.
2)A quadrilateral has angles of q,4q+12 degrees , 3q+21 read more ..

Answerscorrectly Oct 1, 2024, 2:02:45 AM

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+369

Geometry

All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co read more ..

cooIcooIcooI17 Oct 1, 2024, 1:47:21 AM

Sep 30, 2024

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+350

Number Theory

Find the first ten digits after the decimal point in the decimal expansion of \frac{13}{29}=0.abcdefghij\ldots without a calculator.
(Express your answer as a ten digit number.)

onyuIee Sep 30, 2024, 8:10:11 PM

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+350

Number Theory

Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

onyuIee Sep 30, 2024, 8:09:37 PM

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+4

Synthetic Division with Polynomials

Divide f(z) by d(z), and write a summary statement in polynomial form and fraction form.
f(z)=8z4-14z3+50z2-33z-26 ; d(z) = z2-z+6

pizzacat Sep 30, 2024

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+1220

Number Theory

Convert 3132_4 to base 3 without first converting to decimal.

Akhain1 Sep 30, 2024

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+1220

Number Theory

Find the smallest positive integer B so that when we express the decimal number 301 as a base B number, we still get a 2-digit number.

Akhain1 Sep 30, 2024

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+4

help this is due today and I don't know what it is?

a large community college has professors and lecturers.The total number of faculty members is 228 the school reported that they have 5 members for every 14 lecturers how mant type of faculty member does the community college employ

Victoriabo Sep 30, 2024

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+475

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 $XY.$

Pythagorearn Sep 30, 2024

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+582

Algebra

Fill in the blanks to make a true equation:
1/(n(n + 3)(n + 5)) = __/n + ___/(n + 3) + ___/(n + 5)

booboo44 Sep 30, 2024

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+582

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 12}

booboo44 Sep 30, 2024

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+582

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2}

booboo44 Sep 30, 2024

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+280

Geometry

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

Stanry Sep 30, 2024

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+280

Geometry

Let a be a real number such that 0 < a < \frac{\pi}{2}. Show that \left(\sin(a)\right)^7 + \left(\cos ( a)\right)^7< 2*sin(a)^4*cos(a)^4.

Stanry Sep 30, 2024

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+280

Geometry

Let $ABC$ be a triangle. Let $D$ be a point on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 30^\circ$, $\angle C = 90^\circ$, and $AC = 12$, then find the area of triangle $ABD$. Give your answer in exact read more ..

Stanry Sep 30, 2024

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