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posledela
3 years ago
7

Rectangle ABCD was dilated to create rectangle A'B'C'D.

Mathematics
2 answers:
Mademuasel [1]3 years ago
5 0

Answer:

6

Step-by-step explanation:

Let's setup a proportion to find AB.

AB corresponds to A'B'.

BC corresponds to B'C'.

So setting up proportion this would look like:

[\tex]\frac{AB}{A'B'}=\frac{BC}{B'C'}[/tex]

[\tex]\frac{AB}{15}=\frac{3.8}{9.5}[/tex]

Cross multiply:

AB(9.5)=15(3.8)

Divide both sides by 9.5:

AB=\frac{15(3.8)}{9.5)}

Put into calculator:

AB=6

Dmitry_Shevchenko [17]3 years ago
3 0

Answer: AB=6 so A is correct, hope this help! Branliest would be awesome :)

Step-by-step explanation:

Since the larger rectangle and the smaller rectangle are essentially the same just bigger, they will be proportionate.

Therefore..

9.5/3.8=15/AB

You can cross multiply to find AB...

9.5AB=57

Divide 57 by 9.5 to separate AB, which you can think of like x...

AB=57/9.5

AB=6

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How many distinct positive integer-valued solutions exist to the equation (x2 - 7x + 11)(x2 - 13x + 42) = 1
Anna35 [415]

Answer:

The given equation has TWO positive integer valued solutions, {6, 7}

Step-by-step explanation:

Here we are given two trinomial factors, each of which needs to be set equal to zero and in each case the resulting quadratic equation solved.

(x^2 - 7x + 11) has the coefficients {1, -7, 11}, and so the discriminant of this quadratic is b^2 - 4(a)(c), or 49 - 4(11), or 5.

Because this discriminant is positive, we know immediately that this quadratic has two real, unequal roots involving √5 (NO integer roots).

Next we focus on (x^2 - 13x + 42).  The discriminant is b^2 - 4(a)(c), or

169 - 168, or 1.  Again we see that there are two real, unequal roots:

      +13 ± √1                  +13 ± 1

x = ---------------  or  x = -------------

             2                            2

OR x = 14/2 = 7 (integer) or x = 12/2 = 6 (integer).

The given equation has TWO positive integer valued solutions, {6, 7}

5 0
3 years ago
PLEASE HELP VERY URGENT WILL GIVE BRAINILY PLEASE I BEG YOU PLEASE
yuradex [85]

Answer: 20.5 units

Step-by-step explanation:

P=Perimeter

JI=3-(-3)

JI=3+3

JI=6

IK=7-1

IK=6

JK=(6^2+6^2)^1/2   ==> Distance Formula

JK=(36+36)^1/2

JK=(2*36)^1/2

JK=6(2)^1/2

P=JI+IK+JK

P=6+6+6(2)^1/2

P=12+6(2)^1/2

P=20.485 units

P=20.5 units

5 0
1 year ago
Perform the indicated operation to write given polynomial in standard form: (2x^3 − 6x^2 − 7x − 2) +(x^3 +x^2 +6x − 12)
Kipish [7]

Answer:

\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=3x^3-5x^2-x-14

Step-by-step explanation:

To add the polynomials

Remove parentheses:

\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=2x^3-6x^2-7x-2+x^3+x^2+6x-12

Group like terms:

=2x^3+x^3-6x^2+x^2-7x+6x-2-12

Add similar elements:

=3x^3-6x^2+x^2-7x+6x-2-12\\=3x^3-5x^2-7x+6x-2-12\\=3x^3-5x^2-x-2-12\\=3x^3-5x^2-x-14

The Standard Form for writing down a polynomial is to put the terms with the highest degree first,its term of 2nd highest is 2nd etc..

In our case the standard form is  

\left(2x^3-6x^2-7x-2\right)+\left(x^3+x^2+6x-12\right)=3x^3-5x^2-x-14

3 0
3 years ago
Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
vfiekz [6]
Let the two required numbers be x and 100 - x, then
Sum of its squares is given by S = x^2 + (100 - x)^2
For the sum of the squares to be minimum, dS/dx = 0

dS/dx = 2x - 2(100 - x) = 0
2x - 200 + 2x = 0
4x = 200
x = 50.

The two numbers is 50 and 50.
4 0
3 years ago
Please help! The question is in the picture!
Kamila [148]

Answer:

A.

Step-by-step explanation:

Distributive property means (in this case) to multiply what's inside the () by what's outside the (). Therefore, I believe A is the only one that makes sense.

Hope this helps!

5 0
3 years ago
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