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eimsori [14]
3 years ago
12

Ainsley made a $75 deposit to her savings account.what integer represents the deposit?

Mathematics
2 answers:
OLga [1]3 years ago
8 0

The integer that represents her deposit would be positive 75 (aka just 75)

The integer that describes the opposite of her transaction (a withdraw) would be -75

The opposite of her transaction would also be -75

Hope this helps

Dima020 [189]3 years ago
5 0

In this case, Ainsley is <em>adding </em>money to her savings, so the $75 deposit could be represented as the <em>positive </em>integer 75.

The opposite, of course, would be if Ainsley <em>withdrew </em>that money from her savings. In that case, we'd be subtracting money from the account, so we could use the <em>negative </em>integer -75 to represent that scenario.

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Solve for X.<br> - 4x + 10 = 50
erastovalidia [21]

Answer: -10

Step-by-step explanation:

10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50

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2 years ago
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F(x) = 3x-1 , (f of g)(x) = x^2 , Find g(x)
fomenos

Answer:

g(x)=\dfrac{x^2+1}{3}

Step-by-step explanation:

<u>Given functions</u>:

\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}

Composite functions are when the <u>output</u> of one function is used as the <u>input</u> of another.

Therefore, the given <u>composite function</u> (f o g)(x) means to <u>substitute</u> function g(x) in place of the x in function f(x).

\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}

Therefore:

\boxed{g(x)=\dfrac{x^2+1}{3}}

6 0
1 year ago
The coordinates of quadrilateral PQRS are P(–3, 0), Q(0, 4), R(4, 1), and S(1, –3). What best describes the quadrilateral?
denis-greek [22]

Answer:

Square

Step-by-step explanation:

Plot the vertices of the quadrilateral PQRS on the coordinate plane (see attached diagram). The diagram shows that this is a square. Let's prove it.

1. Find all sides lengths:

PQ=\sqrt{(-3-0)^2+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\QR=\sqrt{(0-4)^2+(4-1)^2}=\sqrt{(-4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5\\ \\RS=\sqrt{(4-1)^2+(1-(-3))^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5\\ \\SP=\sqrt{(1-(-3))^2+(-3-0)^2}=\sqrt{(4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5

All sides have the same lengths.

2. Find the slopes of all lines:

PQ:\ \dfrac{4-0}{0-(-3)}=\dfrac{4}{3}\\ \\QR:\ \dfrac{1-4}{4-0}=-\dfrac{3}{4}\\ \\RS:\ \dfrac{-3-1}{1-4}=\dfrac{4}{3}\\ \\SP:\ \dfrac{0-(-3)}{-3-1}=-\dfrac{3}{4}

Since the slopes of PQ and RS are the same, lines PQ and RS are parallel. Since the slopes of QR and SP are the same, lines QR and SP are parallel.

The slopes \frac{4}{3} and -\frac{3}{4} have the product of

-\dfrac{3}{4}\cdot \dfrac{4}{3}=-1,

then lines are pairwise perpendicular.

This means PQRS is a square.

4 0
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Andreyy89

Answer:

Step-by-step explanation:

can you translate that into English please?

6 0
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