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elena-s [515]
3 years ago
9

What is the distance between (-6,0) and (5,3)?

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

\sqrt{130} or 11.4

Step-by-step explanation:

Use the distance formula:

d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

Plug in the points:

d = \sqrt{(-6 - 5)^2 + (0 - 3)^2}

Simplify:

d = \sqrt{(-11)^2 + (-3)^2}

d = \sqrt{121 + 9}

d = \sqrt{130}

= approximately 11.4

So, the distance is \sqrt{130} or approx. 11.4

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46°
Lapatulllka [165]

Answer:

m ∠D = 29°

m ∠T  = 105°

Step-by-step explanation:

Given: ΔSTU and ΔDEF

To find: m ∠D and m ∠T

Solution:

According to SSS similarity criteria,

two triangles are said to be similar if their corresponding sides are proportional.

In ΔSTU and ΔDEF,

\frac{ST}{DE}=\frac{15}{6}=\frac{5}{2}   \\\\\frac{TU}{EF}=\frac{10}{4}=\frac{5}{2}\\\\\frac{SU}{DF}=\frac{20}{8}=\frac{5}{2}

So,

\frac{ST}{DE}=\frac{TU}{EF}=\frac{SU}{DF}=\frac{5}{2}

Therefore,

ΔSTU ≈ ΔDEF

If two triangles are similar then measure of their corresponding angles are equal.

m ∠D = m ∠S = 29°

m ∠U = m ∠F = 46°

In ΔSTU,

m ∠S + m ∠T + m ∠U = 180°

29° + m ∠T + 46° = 180°

75° + m ∠T = 180°

m ∠T  = 180° - 75° = 105°

(According to angle sum property of a triangle, sum of measures of angles of a triangle is equal to 180°)

5 0
3 years ago
Simplify the expression and find its value when a = 5 and b = -3 .
kenny6666 [7]

Answer:

\sf\longmapsto \: 38

Step by step explanation:

\sf\longmapsto \:  2a² + 2ab +3-ab

\sf\longmapsto \:  2a² + 3 + ab (2-1)

\sf\longmapsto \: 2a² + 3 + ab (1)

\sf\longmapsto \:  2a² + 3 + ab

\sf\longmapsto \:  2a² + ab + 3

  • Putting a = 5 b = - 3

\sf\longmapsto \: 2(5) {}^{2}  + (5) (-3) +3

\sf\longmapsto \:  2 (25) - 15 + 3

\sf\longmapsto \: 50 - 12

\sf\longmapsto \: 38

7 0
3 years ago
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Answer:

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Step-by-step explanation:

slope (m) = 2

point (-1,2)

so,

b = 2-2×(-1) = 4

y = mx+b

or, y = 2x+4

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Answer:

E

Step-by-step explanation:

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Step-by-step explanation:

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