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sleet_krkn [62]
3 years ago
13

25 POINTS

Mathematics
2 answers:
lys-0071 [83]3 years ago
8 0

Answer:

4

Step-by-step explanation:

The original has a side length of AB =2

The new has a side length A'B' of 8

2 * what = 8

Divide each side by 2

2 * what /2 = 8/2

what =4

The scale factor is 4

raketka [301]3 years ago
6 0

Answer:

4!!!!

Step-by-step explanation:

The small box has a top length of 2 while the dilated box has a top length of 8

8/2= scale factor

8/2= 4!!!!

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
zlopas [31]
<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

5 0
3 years ago
Julien threw x number of pitches at baseball practice. Jacob threw 1/5 fewer than that
Naily [24]

Answer:

ok so jacob threw 1/5 of x

Step-by-step explanation:

if you say julien threw x and jacob threw 1/5 of that than jacob threw 1/5 of x

5 0
3 years ago
A college is currently accepting students that are both in-state and out-of-state. They plan to accept three times as many in-st
densk [106]

Answer:

\[y < = 300\]

Step-by-step explanation:

Let x = number of out-of-state students at the college

Let y = number of in-state students at the college

As per the given problem, the constraints are as follows:

\[x < = 100\]    --------- (1)

\[y = 3 * x\]      --------- (2)

From the given equations (2), \[ x = y/3 \]

Substituting in (1):

\[y/3 < = 100\]

Or, \[y < = 300\] which is the constraint representing the incoming students.

7 0
3 years ago
Read 2 more answers
Find the midpoint of points A(-6, -5) and B(4,3) graphically.
Zigmanuir [339]

Answer:

(-1,-1)

Step-by-step explanation:

4-6         3-5

-------   ,   ---------

 2               2

(-2/2,-2/2)=(-1,-1)

7 0
3 years ago
The second step in solving problems using order of operations is solving the
inna [77]
PEMDAS.....parenthesis, exponents, multiplication/division, addition/subtraction

so step 2 is solving the exponents <==
6 0
3 years ago
Read 2 more answers
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