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3 years ago

5/10 plus 2/9 simplified

Mathematics

2 answers:

Genrish500 [490]3 years ago

7 0

5/10+2/9=13/18

=1/2+2/9

=9/18+4/18

=9+4/18

answer: 13/18

Elena-2011 [213]3 years ago

5 0

Question:

5/10 + 2/9

Steps:

1. Find the least common denominator (LCD): 90

5 * 9/90 + 2 * 10/90

2. Simplify

45/90 + 20/90

= 65/90

3. Simplify

= 13/18 <======= <em>Answer</em>

Hope this helped!!

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Given: KLMN is a trapezoid m∠N = m∠KML

horrorfan [7]

Answer:

The length of sides KM, LM and KN are $\sqrt{109}, \frac{48}{5}$ and 16 respectively. The area of KLMN is $\frac{192\sqrt{5}}{5}$ square unit.

Step-by-step explanation:

According to given information: KLMN is a trapezoid, ∠N= ∠KML, $\frac{LM}{KN}=\frac{3}{5}$ , ME ⊥ KN, KE=8 $ME=3\sqrt{5}$ .

Use pythagoras theorem is triangle EKM

$Hypotenuse^2=base^2+perpendicular^2$

$(KM)^2=(KE)^2+(ME)^2$

$(KM)^2=(8)^2+(3\sqrt{5})^2$

$KM^2=64+9(5)$

$KM=\sqrt{109}$

Let angle N and angle KML be θ.

Since angle KML and angle MKE are alternate interior angles, therefore angle MKE is θ.

In triangle KME,

$\tan\theta=\frac{3\sqrt{5} }{8}$ .... (1)

In triangle KNE,

$\tan\theta=\frac{3\sqrt{5} }{EN}$ .... (2)

Equate (1) and (2),

$\frac{3\sqrt{5} }{8}=\frac{3\sqrt{5} }{EN}$

$EN=8$

The length of side KN is

$KN=KE+EN=8+8=16$

Sides LM:KN are in the ratio 3:5. Let the side lengths are 3x and 5x respectively.

$5x=16$

$x=\frac{16}{5}$

$3x=3\times \frac{16}{5}=\frac{48}{5}$

The area of KLMN is

$Area=\frac{1}{2}(b_1+b_2)h$

$A=\frac{1}{2}\times (LM+KN)\times ME$

$A=\frac{1}{2}\times (\frac{48}{5}+16)\times 3\sqrt{5}$

$A=\frac{192\sqrt{5}}{5}$

Therefore length of sides KM, LM and KN are $\sqrt{109}, \frac{48}{5}$ and 16 respectively. The area of KLMN is $\frac{192\sqrt{5}}{5}$ square unit.

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4 years ago

−3(6x+ 7) + 4(7x + 2) equivalent expression

Lera25 [3.4K]

Answer:

10x - 13.

Step-by-step explanation:

−3(6x+ 7) + 4(7x + 2)

= -18x - 21 + 28x + 8

= 10x - 13.

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3 years ago

If tan θ=3\4 , find csc

Rom4ik [11]

In a rectangular triangle $\tan\theta\dfrac{opposite}{adjacent}$ .

We have $\tan\theta=\dfrac{3}{4}$

Therefore opposite = 3uints and adjacent = 4units.

$\csc\theta=\dfrac{hypotenuse}{opposite}$

We need the length of hypotenuse.

Use the Pythagorean theorem:

$h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\to h=5units$

Substitute:

$\csc\theta=\dfrac{5}{3}$

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bija089 [108]

Answer:

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Step-by-step explanation:

$135-$12=

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shusha [124]

The answer is C because in y=mx+b form, the “m” stands for the slope.

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