All Questions ⁺⁰237767 Questions

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118

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help

Find $x$ if $7^{4x + 10} = 7^{2x}.$

Guest May 21, 2023

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155

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system

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 41
2a + 3b + 4c + 5d + e = 15
3a + 4b + 5c + 1d + 2e = 34 read more ..

Guest May 21, 2023

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139

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coefficient

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.

Guest May 21, 2023

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144

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proof

Let ABC be a right triangle, and let H be the point on side AB so that CH is perpendicular to AB. Prove that (x + h)^2*(y + h)^2 = (a + b)^4.

Guest May 21, 2023

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141

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Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that CD = CE and angle DBE = \angle BAD. Show that triangle ACE is isosceles.
Diagram read more ..

Guest May 21, 2023

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129

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I NEED HELP

A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most $120$ hours available for each operation. A regular gadget requires $1$ hour of assembly and read more ..

Guest May 21, 2023

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143

2

+90

Help needed on Special Factorizations and Clever Manipulations

totalkoolnezz May 21, 2023

+1

107

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solve

A candy bar and a piece of bubble gum together cost 1.50. The candy bar costs a dollar more than the bubble gum. How much does the piece of bubble gum cost, in cents?

Guest May 21, 2023

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146

1

help

In triangle $ABC,$ $\angle A = p + 2q$ degrees, $\angle B = 6p - 5q$ degrees, and $\angle C = 11p + 3q$ degrees. Find $p$ (in degrees).

Guest May 21, 2023

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119

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Una pequeña empresa agroindustrial

Una pequeña empresa agroindustrial tiene una cisterna rectangular a 2m del suelo, con base 2m por 3m y una altura de 2m, la cual está llena de agua. Este tanque de agua se utiliza para el riego tecnificado de 4 parcelas de plantas de aguacate. Se solicita read more ..

Guest May 21, 2023

May 20, 2023

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92

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What is the value of 1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + ... + 24 + 96 + 25 + 100?

What is the value of 1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + ... + 24 + 96 + 25 + 100?

Guest May 20, 2023

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144

1

help geo

In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to line PR. If PQ = 9, QR = 9, and PR = 9, then compute the length of XY. read more ..

Guest May 20, 2023

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154

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Colin is having a birthday party. There are 7 party favors, and 4 people. How many favors does each person get? How many will be left over?

Colin is having a birthday party. There are 7 party favors, and 4 people. How many favors does each person get? How many will be left over?

Guest May 20, 2023

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146

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Altitudes

I need help with altitudes
Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = , and CF is a positive integer, then find the largest possible value of CF.

Guest May 20, 2023

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138

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plz help

This is some very hard geometry
Triangle XYZ is equilateral. Points Y and Z lie on a circle centered at O, such that X is the circumcenter of triangle OYZ, and X lies inside triangle OYZ. If the read more ..

Guest May 20, 2023

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153

2

system

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

Guest May 20, 2023

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127

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trapezoid

help i need help with this
Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, read more ..

Guest May 20, 2023

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156

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ratios

At a math convention, a poll is taken about cable news. It turns out that 7 out of every 12 people are bored by cable news. If there are 280 people at the convention who are bored by cable news, then how many people at the convention read more ..

Guest May 20, 2023

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