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Salsk061 [2.6K]
3 years ago
11

How do you simplify the expression (y-15)5

Mathematics
1 answer:
Irina-Kira [14]3 years ago
8 0

Answer:

5y - 75

Step-by-step explanation:

(y-15)5

Distribute

y*5 -15*5

5y - 75

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What is the equation for a circle with a center at (-2,-4) that passes through the point (3,8)?
Margarita [4]
Check the picture below.

so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{ x_2 +  x_1}{2}\quad ,\quad \cfrac{ y_2 +  y_1}{2} \right)
\\\\\\
\left( \cfrac{3-2}{2}~~,~~\cfrac{8-4}{2} \right)\implies \left( \frac{1}{2}~,~2 \right)\impliedby center

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}~~~ 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[3-(-2)]^2+[8-(-4)]^2}\implies d=\sqrt{(3+2)^2+(8+4)^2}
\\\\\\
d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13\qquad\qquad \qquad  \stackrel{radius}{\frac{13}{2}}

\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{\frac{1}{2}}{ h},\stackrel{2}{ k})\qquad \qquad 
radius=\stackrel{\frac{13}{2}}{ r}
\\\\\\
\left( x-\frac{1}{2} \right)^2+(y-2)^2=\left( \frac{13}{2} \right)^2\implies \left( x-\frac{1}{2} \right)^2+(y-2)^2=\frac{169}{4}

3 0
3 years ago
Read 2 more answers
Convert 3/5 to a decimal using long division
NISA [10]

Step-by-step explanation:

5✓3

0.6

put a zero in 3and put a zero above put a decimal point and 6 because of 30

8 0
2 years ago
The person who answers the question with the mathematical explanation and answer gets 65 points in total if answers correctly an
liubo4ka [24]

Answer:

10.5 squared centimetres.

Step-by-step explanation:

First, find the area of that sector. We are already given that the circle is 154 squared centimetres.

We are given 90 degrees (or one fourth of the circle). Thus, divide 154 by 4 to get the area of the sector (the white area).

The area of the sector is 154/4 or 38.5

We then need to find the area of the square. After that, we can subtract the sector area (the white area) from the area of the square (the total area) to find the area of the shaded section.

The area of the square is 7*7 or 49.

Thus, the shaded portion will be 49-38.5 or 10.5 squared centimetres.

8 0
3 years ago
Read 2 more answers
Both Need To Be Checked :-)
Tems11 [23]
I think u should check the first one again u made a mistake but the second one is correct if u need any more help ask me
6 0
2 years ago
Read 2 more answers
4. The population of Bay Village is 35,000 today. Every year the
frosja888 [35]

Answer:

Linear Model:   y(x)=35,000+750x

Step-by-step explanation:

In principle <em>Linear Models </em>are employed when we want to define a relationship between an independent and a dependent variable. <em>Linear Models</em> are also known as<em> Functions </em>, where one variable is expressed as a function of <em>at least one</em> other variable. The most common example would be a dependent variable y that is directly linked as a response to any changes of an independent variable x. The most common expression of such relationship would be y=ax where a is the relationship factor between y and x and is also known as the <em>slope </em>of the function (representing a rate of change of that function).

In this question we are told that the population of Bay Village today is 35,000. So we know this is our constant variable, lets call it  b.

Next we know that every year the population is increased by 750 people. So we know that our variable and thus our independent variable is every year which we shall call x and our fixed factor is the 750 increment which we will call a.  

From that we can conclude that:

<em>Year 1 Population: 35,000</em>

<em>Year 2 Population: 35,000 + 750 = 35,750</em>

<em>Year 3 Population: 35,750 + 750 = 36,500 </em>

And so on and so forth.<em> </em>

So we want to express the above as a Linear Model of the form:

<em> y = ax + b   </em>Eqn(1).

Thus from Eqn (1) and all information given (i.e. pluging in values) we finally obtain:

y(x)=35,000+750x

Which for every different value of  x (i.e. every year) we can obtain the new and increased population  y(x).

7 0
3 years ago
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