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3 years ago

15x ( 7 - 5y ) + 3 ( 5y - x ) - ( 4x + 3 ) ( 5y - 2 )

Mathematics

2 answers:

olga2289 [7]3 years ago

5 0

Answer:

$110x-95xy+6$

Explanation:

$15x ( 7 - 5y ) + 3 ( 5y - x ) - ( 4x + 3 ) ( 5y - 2 )$

expand:

$105x-75xy+15y-3x-\left(4x+3\right)\left(5y-2\right)$

simplify:

$105x-75xy+15y-3x-(20xy-8x+15y-6)$

open the brackets:

$-20xy+8x-15y+6+102x-75xy+15y$

$110x-75xy-20xy+15y-15y+6$

final answer:

$110x-95xy+6$

Sedbober [7]3 years ago

4 0

15x ( 7 - 5y) + 3 ( 5y - x) - ( 4x + 3) (5y - 2) = -95xy + 110x + 6 is your solution hope it helps :)!

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Unit 8 right triangles and trigonometry homework 3 similar right triangles and geometric mean

Ugo [173]

The right triangles that have an altitude which forms two right triangles

are similar to the two right triangles formed.

Responses:

1. ΔLJK ~ ΔKJM

ΔLJK ~ ΔLKM

ΔKJM ~ ΔLKM

2. ΔYWZ ~ ΔZWX

ΔYWZ ~ ΔYZW

ΔZWX ~ ΔYZW

3. x = 4.8

4. x ≈ 14.48

5. x ≈ 11.37

6. G.M. = 12·√3

7. G.M. = 6·√5

<h3>What condition guarantees the similarity of the right triangles?</h3>

1. ∠LMK = 90° given

∠JMK + ∠LMK = 180° linear pair angles

∠JMK = 180° - 90° = 90°

∠JKL ≅ ∠JMK All 90° angles are congruent

∠LJK ≅ ∠LJK reflexive property

ΔLJK is similar to ΔKJM by Angle–Angle, AA, similarity postulate

∠JLK ≅ ∠JLK by reflexive property

ΔLJK is similar to ΔLKM by AA similarity

By the property of equality for triangles that have equal interior angles, we have;

ΔKJM ~ ΔLKM

2. ∠YWZ ≅ ∠YWZ by reflexive property

∠WXZ ≅ ∠YZW all 90° angle are congruent

ΔYWZ is similar to ΔZWX, by AA similarity postulate

∠XYZ ≅ ∠WYZ by reflexive property

∠YXZ ≅ ∠YZW all 90° are congruent

ΔYWZ is similar to ΔYZW by AA similarity postulate

Therefore;

ΔZWX ~ ΔYZW

3. The ratio of corresponding sides in similar triangles are equal

From the similar triangles, we have;

$\dfrac{8}{10} = \mathbf{ \dfrac{x}{6}}$

8 × 6 = 10 × x

48 = 10·x

$x = \dfrac{48}{10} = \underline{4.8}$

3. From the similar triangles, we have;

$\mathbf{\dfrac{20}{29}} = \dfrac{x}{21}$

20 × 21 = x × 29

420 = 29·x

$x = \dfrac{420}{29 } \approx \underline{14.48}$

4. From the similar triangles, we have;

$\mathbf{\dfrac{20}{52}} = \dfrac{x}{48}$

20 × 48 = 52 × x

$x = \dfrac{20 \times 48}{52} = \dfrac{240}{13} \approx \underline{18.46}$

5. From the similar triangles, we have;

$\mathbf{\dfrac{13.2}{26}} = \dfrac{x}{22.4}$

13.2 × 22.4 = 26 × x

$x = \dfrac{13.2 \times 22.4}{26} \approx \underline{ 11.37}$

6. The geometric mean, G.M. is given by the formula;

$G.M. = \mathbf{\sqrt[n]{x_1 \times x_2 \times x_3 ... x_n}}$

The geometric mean of 16 and 27 is therefore;

$G.M. = \sqrt[2]{16 \times 27} = \sqrt[2]{432} = \sqrt[2]{144 \times 3} = \mathbf{12 \cdot \sqrt{3}}$

The geometric mean of 16 and 27 is 12·√3

7. The geometric mean of 5 and 36 is found as follows;

$G.M. = \sqrt[2]{5 \times 36} = \sqrt[2]{180} = \sqrt[2]{36 \times 5} = \mathbf{ 6 \cdot \sqrt{5}}$

The geometric mean of 5 and 36 is 6·√5

Learn more about the AA similarity postulate and geometric mean here:

brainly.com/question/12002948

brainly.com/question/12457640

7 0

3 years ago

Can you help me pls. Thanks.

UNO [17]

Answer:

The answer is d, 2.011*10^-5. This is because 2 is in the ones place, and when moved 5 units back, it gets the result shown above.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

2>8−4/3h Solve the inequality

Goryan [66]

It'd be best if you were to enclose that fraction 4/3 inside parentheses:

2>8−(4/3)h

Mult. all 3 terms by 3: 6>24 -4h
Add 4h to both sides: +4h +4h
------------------
7+4h > 24
Subtract 7 from both sides: -7 -7
------------------
4h > 17

Then h>17/4 (answer) Note: We want h to be positive. That's why I moved (-4/3)h to the other side of the = sign.

8 0

3 years ago

using the given information above, which of the following statements can be proved by CPCTC and is needed to work toward the pro

Roman55 [17]

Answer:

∠DCE≅∠BAE

Step-by-step explanation:

CPCTC is basically used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. Corresponding means they're in the same position in the 2 triangles

two side CE and AE are equivillant in the expression

hence

∠DCE≅∠BAE is right option.

8 0

4 years ago

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Karla makes paper airplanes. Today, it takes her 32 min to make 16 paper airplanes.

Pavel [41]

Answer:

48/b

Step-by-step explanation:

32÷16=2 so it takes two minutes per airplane. if she makes airplanes for 96 minutes at the same pace (2 min per airplane) then you need to divide 96 by 2 which gives you 48!

7 0

3 years ago

15x ( 7 - 5y ) + 3 ( 5y - x ) - ( 4x + 3 ) ( 5y - 2 )​

15x ( 7 - 5y ) + 3 ( 5y - x ) - ( 4x + 3 ) ( 5y - 2 )