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3 years ago

Find three consecutive integers that have an average of 53

1 answer:

5 0

Consecutive intergers are 1 away from each other so
numbers are
x,x+1,x+2

average is found by adding the numbers up and dividng the total by the number of numbers you have
so we add x+x+1+x+2 up and divide it by 3 (3 numbers)
x+x+1+x+2=x+x+x+1+2=3x+3
(3x+3)/3=53
[3(1x+1)]/3=53
3/3 times 1x+1=52
1x+1=53
subtract 1 from both sides
x=52

subsitute
x+1 is the second
x+2 is the third
x+1=52+1=53
x+2=52+2=54

numbers are 52,53,54

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Bonsoir pour vais vous m'aider svp développer et réduire l'expression D=(2x+3)²-(x+4)² et factoriser D Svp aider moi

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Answer:

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3 years ago

Area of a triangle with points at (-9,5), (6,10), and (2,-10)

Ann [662]

First we are going to draw the triangle using the given coordinates.
Next, we are going to use the distance formula to find the sides of our triangle.
Distance formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Distance from point A to point B:
$d_{AB}= \sqrt{[6-(-9)]^2+(10-5)^2}$
$d_{AB}= \sqrt{(6+9)^2+(10-5)^2}$
$d_{AB}= \sqrt{(15)^2+(5)^2}$
$d_{AB}= \sqrt{225+25}$
$d_{AB}= \sqrt{250}$
$d_{AB}=15.81$

Distance from point A to point C:
$d_{AC}= \sqrt{[2-(-9)]^2+(-10-5)^2}$
$d_{AC}= \sqrt{(2+9)^2+(-10-5)^2}$
$d_{AC}= \sqrt{11^2+(-15)^2}$
$d_{AC}= \sqrt{121+225}$
$d_{AC}= \sqrt{346}$
$d_{AC}= 18.60$

Distance from point B from point C
$d_{BC}= \sqrt{(2-6)^2+(-10-10)^2}$
$d_{BC}= \sqrt{(-4)^2+(-20)^2}$
$d_{BC}= \sqrt{16+400}$
$d_{BC}= \sqrt{416}$
$d_{BC}=20.40$

Now, we are going to find the semi-perimeter of our triangle using the semi-perimeter formula:
$s= \frac{AB+AC+BC}{2}$
$s= \frac{15.81+18.60+20.40}{2}$
$s= \frac{54.81}{2}$
$s=27.41$

Finally, to find the area of our triangle, we are going to use Heron's formula:
$A= \sqrt{s(s-AB)(s-AC)(s-BC)}$
$A=\sqrt{27.41(27.41-15.81)(27.41-18.60)(27.41-20.40)}$
$A= \sqrt{27.41(11.6)(8.81)(7.01)}$
$A=140.13$

We can conclude that the perimeter of our triangle is 140.13 square units.

3 0

3 years ago

Ricardo bought 6 pounds of peanuts at the local wholesaler for $12. His friend Saniya bought 4 pounds of peanuts at the supermar

guapka [62]

Answer:

ricardo

he payed 2 per pound while she payed 2.50

7 0

3 years ago

Read 2 more answers

The function f is defined by the following rule.

Leno4ka [110]

X= -4; f(x)= -15
X= 2; f(x)= 3
X=5; f(x)= 12

6 0

3 years ago

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

dlinn [17]

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies \boxed{2=d}$

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3 years ago