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mrs_skeptik [129]

2 years ago

7

Given: P∈ BC , Pabc = 45, Pabp = 30, Papc = 35. Find AP.

1 answer:

Mazyrski [523]2 years ago

8 0

Answer:

10

Step-by-step explanation:

Pabp = AB +BP +AP

Papc = AP +PC +CA

So the sum of perimeters of the two smaller triangles is ...

Pabp +Papc = AB +BP +AP + AP +PC +CA

= (AB +BP +PC +CA) +2AP

= Pabc +2AP

Filling in numbers, we have ...

30 +35 = 45 +2AP

20 = 2AP . . . . subtract 45

10 = AP . . . . . . divide by 2

The length of AP is 10 units.

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Consider the matrix shown below:

velikii [3]

Answer:

$A)\ \ \ \ \left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]$

Step-by-step explanation:

Given the matrix: $\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right]$ , it's inverse is calculated using the formula:

$\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]^{-1}=\frac{1}{det\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] }\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]$

#Therefore, we calculate as;

$\frac{1}{det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] }\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\\#det\left[\begin{array}{ccc}2&5\\3&8\\\end{array}\right] =1\\\\\\\\=\frac{1}{1}\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right] \\\\\\\\=\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]$

Hence, the inverse of the matrix is $\left[\begin{array}{ccc}8&-5\\-3&2\\\end{array}\right]$

8 0

3 years ago

If the perimeter is 74mm and the width 16mm what is the length

weqwewe [10]

P=2w+2l
74=2(16)+2l
74=32+2l
42=2l
21=l

The length is 21 mm.

4 0

3 years ago

Read 2 more answers

M is the midpoint of CD. Given the coordinates of one endpoint C(10,-5) and the midpoint M(4, 0), find the coordinates of the ot

mash [69]

Answer:

D(-2, 5).

Step-by-step explanation:

We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).

And we want to determine the coordinates of D.

Recall that the midpoint is given by:

$\displaystyle M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)$

Let C(10, -5) be (<em>x</em>₁<em>, y</em>₁) and Point D be (<em>x</em>₂<em>, y</em>₂). The midpoint M is (4, 0). Hence:

$\displaystyle (4, 0) = \left(\frac{10+x_2}{2} , \frac{-5+y_2}{2}\right)$

This yields two equations:

$\displaystyle \frac{x_2 + 10}{2} = 4\text{ and } \frac{y_2 - 5}{2} = 0$

Solve for each:

$\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}$

And:

$\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}$

In conclusion, Point<em> </em>D = (-2, 5).

5 0

2 years ago

Graph the system of equations on your graph paper to answer the question. {y=−x+4y=x−2

Rudik [331]

This is the graph that I drew to figure out the answer to this question.

3 0

3 years ago

A 4.3 ounce tomato has about 24 calories. How many calories are in one ounce?

solniwko [45]

there are 7.8 calories in a ounce tomato

3 0

3 years ago

Read 2 more answers