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elena-14-01-66 [18.8K]

3 years ago

9

Tell wheather the system has one solution, infinitely many solutions, or no solution.

1 answer:

ipn [44]3 years ago

5 0

<h3>Answer:</h3>

One solution: (x, y) = (2, 0)
Infinitely many solutions: 2x -5y = 17

<h3>Step-by-step explanation:</h3>

1. When you put the second equation in standard form, it is ...

... 5x +3y = 10

This is a different equation than the first one, so there will be one solution where the lines interect. (Adding the two equations gives 10x=20 ⇒ x=2. Since adding or subtracting y gives the same result, y must be zero.)

2. When you put the second equation in standard form, it is the same as the first:

... 2x -5y = 17 . . . . . divide the equation by 3

That is, any (x, y) values that satisfy the first equation will also satisfy the second equation (since they are the same). There are an infinite number of (x, y) values that do so.

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Answer:

B. 12.5

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3 years ago

Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC

e-lub [12.9K]

Answer:

$DC=\frac{8}{3}\ units$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

$BM^2=AB^2-AM^2$

we have

$AB=5\ units\\AM=x\ units$

substitute

$BM^2=5^2-x^2$

$BM^2=25-x^2$ -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

$BM^2=BC^2-MC^2$

we have

$BC=7\ units\\MC=AC-AM=(9-x)\ units$

substitute

$BM^2=7^2-(9-x)^2$

$BM^2=49-(81-18x+x^2)$

$BM^2=49-81+18x-x^2$

$BM^2=-x^2+18x-32$ ----> equation B

equate equation A and equation B

$-x^2+18x-32=25-x^2$

solve for x

$18x=25+32\\18x=57\\\\x=\frac{57}{18}$

Simplify

$x=\frac{19}{6}$

<em>Find the length of DC</em>

$DC=AC-2x$

substitute the given values

$DC=9-2(\frac{19}{6})$

$DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units$

8 0

3 years ago

In engineering, equilateral triangles can support the most weight and so are commonly found in the design of bridges and buildin

Dafna1 [17]

Answer:

60°

Step-by-step explanation:

Am equilateral triangle is a triangle that has all its sides and angles equal. Note that an equilateral triangle has 3 sides and angles.

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Since a = b = c

The equation becomes;

a+a+a = 180°

3a = 180

a = 180/3

a = 60°

Hence the measure of the angles of an equilateral triangle is 60° for the three angles.

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