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Serjik [45]
2 years ago
5

A shelter has 5 dogs for every 4.cats. How many cats will the shelter have if they have 25 dogs?

Mathematics
2 answers:
Ipatiy [6.2K]2 years ago
8 0
The shelter will have 20 cats. If the shelter has five dogs for every four cats,then every five dogs that are added into the shelter four cats will be added.
olga_2 [115]2 years ago
5 0

Answer:

20 cats

Step-by-step explanation:

A proportion has to be setup to answer this

5/4 = 25/x

x represents the missing number of cats

This fraction represents the relationship amongst dogs and cats

----

To solve cross multiply

5x = 100

(let me down below if you need an explanation on how to cross multiply)

Divide both sides by 5 in order to get the variable by itself

100/5 = 20

x = 20

The shelter has 20 cats

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11000 is compounded semiannually at a rate of 12% for 21 years. Find the total amount in the compound interest account
marishachu [46]

\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\dotfill &\$11000\\
r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semiannually, thus twice}
\end{array}\dotfill &2\\
t=years\dotfill &21
\end{cases}


\bf A=11000\left(1+\frac{0.12}{2}\right)^{2\cdot 21}\implies A=11000(1.06)^{42}\implies A\approx 127127.359416

5 0
3 years ago
9.<br> What is the range of the function<br> f(x) = 3.3?
klemol [59]

Answer:

69

Step-by-step explanation:

6 0
3 years ago
Point A is located at (3,4) and is rotated 90 degrees counterclockwise about the origin. What is the new point of A?
sineoko [7]

A'(- 4, 3 )

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

A(3, 4 ) → A'(- 4, 3 )


5 0
3 years ago
Write 3x^2-18x-6 in vertex form
Vedmedyk [2.9K]
The standard form of a quadratic equation is \displaystyle{ y=ax^2+bx+c, while the vertex form is:

                      y=a(x-h)^2+k, where (h, k) is the vertex of the parabola.

What we want is to write \displaystyle{ y=3x^2-18x-6 as y=a(x-h)^2+k

First, we note that all the three terms have a factor of 3, so we factorize it and write:

\displaystyle{ y=3(x^2-6x-2).


Second, we notice that x^2-6x are the terms produced by (x-3)^2=x^2-6x+9, without the 9. So we can write:

x^2-6x=(x-3)^2-9, and substituting in \displaystyle{ y=3(x^2-6x-2) we have:

\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11].

Finally, distributing 3 over the two terms in the brackets we have:

y=3[x-3]^2-33.


Answer: y=3(x-3)^2-33
6 0
3 years ago
Which system of equations does this graph represent?
jeyben [28]

Answer:

1

Step-by-step explanation:

First, we can find the equation of the parabola. The standard form of a parabola is ax^2 + bx + c,

where c is the y-intercept. The y-intercept on the graph is -5, and every option starts with x^2, so the equation must be x^2 - 5. This rules out options 3 and 4.

Next, we can find the equation of the line. The options are all given in slope-intercept form: y = mx + b, where b is the y-intercept. The y-intercept on the graph is 1, and option 1 has 1 in the place of b. Therefore, option 1 is the answer.

7 0
2 years ago
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