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3 years ago

ABCD is a rectangle. Find the length of each diagonal...

Mathematics

1 answer:

Dominik [7]3 years ago

4 0

Setting AC = BD because the diagonals are congruent, then 3y/5 = 3y -4
y=5/3
So then AC = 1 = BD

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Can someone plz help me. How can you find the inequalities of 11/15 and 5/7. Next 5/9 and 7/13. Next 11/15 and 5/7. Lastly 5/9 a

LekaFEV [45]

To make this a little clearer, let's give the pairs of inequalities the same denominator:

Question 1:
 $\frac{11}{15}$ ? $\frac{5}{7}$
First, apply the common denominator to the first fraction:
$(\frac{11}{15})7 \\ \frac{11}{15} * \frac{7}{7} \\ \frac{11*7}{15*7} \\ \frac{77}{105}$
Do the same for the second: $15( \frac{5}{7}) \\ \frac{5}{7}* \frac{15}{15} \\ \frac{5*15}{7*15} \\ \frac{75}{105}$
Nest, compare the two fractions:
$\frac{77}{105} \ \textgreater \ \frac{75}{105}$
Therefore:
$\frac{11}{15}$ > $\frac{5}{7}$

Question Two:
$\frac{5}{9}$ ? $\frac{7}{13}$
Apply the common denominator to fraction one:
$13( \frac{5}{9}) \\ \frac{5}{9} * \frac{13}{13} \\ \frac{5*13}{9*13} \\ \frac{65}{117}$
Fraction two:
$9(\frac{7}{13}) \\ \frac{7}{13} * \frac{9}{9} \\ \frac{7*9}{13*9} \\ \frac{63}{117}$
Evaluate:
$\frac{65}{117}$ > $\frac{63}{117}$
Therefore:
 $\frac{5}{9}$ > $\frac{7}{13}$

Hope this helps!

5 0

3 years ago

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC

Makovka662 [10]

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

3 0

3 years ago

What is the absolute value of -4/5,1/2,0.2,and -0.5

nirvana33 [79]

4/5 1/2 0.2 0.5 and apparently theres a character limit

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0.2436 is the answer

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KATRIN_1 [288]

Answer:

Step-by-step explanation:

The answer is BF because the radius is from the center to the outer edge and that is the only one that does that.

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