All categories

2 years ago

The sum od the squares of two consecutive even integers is 164. Find the integers.

1 answer:

7 0

Let x be the smaller integer, then x+2 is the larger integer.
We're given
x^2+(x+2)^2=164
Expand and simplify
2x^2+4x+4=164
x^2+2x-80=0
(x-8)(x+10)=0
=> x=-10 or x=8.

Therefore the integers are{8,10} or {-10,-8}.
Note: question asks for integers, so negative integers count.

You might be interested in

WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing

Svetradugi [14.3K]

Answer:

Step-by-step explanation:

Given a system of equations graphically, then the solution is at the point of intersection of the 2 equations.

As can be seen from the graph there is only 1 point of intersection, thus only one solution,

7 0

2 years ago

Read 2 more answers

Peter spent 3/5 of his money and was left with $60. 1. How much money did he have at first2. Express what he remained with as a

german

60 / 2 = 30

30 * 5 = 150

he had $150 at first

60, the amount he was left with was 2/5 or 40% of his original amount

4 0

2 years ago

12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5

Murljashka [212]

Answer:

$\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}$

Step-by-step explanation:

$\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/$

$\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}$

$\text{Despite this, let's check the ratios}$

$\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5$

$\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}$

8 0

3 years ago

Write and solve an equation to represent the following situation: an electrician earns an hourly wage of $13.50 plus a $75 bonus

Bingel [31]

149.25=13.5h+75
(149.25-75)/13.5=5.5=h

8 0

3 years ago

Tyrone paid $2,800 plus 7% sales tax on mountain bikes for a bike club.How much did Tyrone pay in total for the mountain bikes?

timurjin [86]

2800 x 0.07 = 196
2800 + 196 = 2996
Total paid = $2996

8 0

3 years ago