Brianna wants to save the $250 she earned by babysitting over the summer. She's trying to decide which

Mathematics

1 answer:

Nookie1986 [14]3 years ago

8 0

Answer:

Total cost = Cost per month × 12 months per year × Number of years

= $21 × 12 × 8

= $2,016

Step-by-step explanation:

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How many ounces of pure gold and a 16 carry the old change and it weighs 2.5 ounces

sladkih [1.3K]

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3 years ago

A rectangle has an area of x^2 -6x -7 and a width of x-7 what’s the length

iogann1982 [59]

Answer:

x+1

Step-by-step explanation:

We know that x^2 -6x-7 is the product of two binomials.

We can solve this two ways, but the easier way is to simply factor rather than divide the area by width.

Two numbers, one of which being -7 allows for the sum of -6 and the product of -7.

Using this information, we can identify the other number is 1, so the length is x+1.

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3 years ago

If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

alexgriva [62]

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

$\left[\begin{array}{ccc}7&6\\4&5\end{array}\right]$

The inverse of the matrix is

$\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]$

So, the Inverse Transformation is given by

$T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})$