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Triss [41]
3 years ago
13

Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

Mathematics
1 answer:
Leni [432]3 years ago
4 0

Answer:

(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

m_1=\frac{7-0}{3-0}=\frac{7}{3}

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)

The slope of the line joining E(7,0), and F(3,7). is:

m_1=\frac{7-0}{3-7}=-\frac{7}{4}

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)

The point of intersection of equation 1 and equation 2 is the orthocenter. Solving equation 1 and 2 simultaneously gives:

x = 3, y = 1.7

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-2(2x+3)=-4(x+1) - 2
mario62 [17]

Answer:

All real numbers are solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

−2(2x+3)=−4(x+1)−2

Step 1: Simplify both sides of the equation.

−2(2x+3)=−4(x+1)−2

(−2)(2x)+(−2)(3)=(−4)(x)+(−4)(1)+−2(Distribute)

−4x+−6=−4x+−4+−2

−4x−6=(−4x)+(−4+−2)(Combine Like Terms)

−4x−6=−4x+−6

−4x−6=−4x−6

Step 2: Add 4x to both sides.

−4x−6+4x=−4x−6+4x

−6=−6

Step 3: Add 6 to both sides.

−6+6=−6+6

0=0

Answer:

All real numbers are solutions.

8 0
3 years ago
Solve: 1/7x + 3/4=9/8
kherson [118]
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</span>Hope that helped!!</span>
8 0
3 years ago
All statements of equality below are correct.<br> A.True<br> B.False
igor_vitrenko [27]

Answer:

A

Step-by-step explanation:

5 0
3 years ago
PLZ HELP ASAP!!! What is the area of sector DEF in terms of pi ?<br> 120°<br> 3 cm<br> E
Serjik [45]

Answer:

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6 0
2 years ago
Which graphs have rotational symmetry? Check all that apply
Triss [41]

Answer:

Option A and C have rotational symmetry.

Step-by-step explanation:

The graph of odd functions have rotational symmetry about its origin.

Here the first graph is a graph of f(x)=f(x)=x^3 which is an odd function bearing an exponent of 3.

A function is "odd"  when we plug in any negative value in f(x) then it gives negative of f(x).

And we also know that when a graph is mirroring about the y-axis then it is an even functions.

For even functions we have reflection symmetry rather than rotational symmetry.

The second graph is a graph of f(x)=-modulus (x) which is an even function as we can see that its graph is mirroring about the y-axis.

The third graph is a graph of an ellipse which is possessing  rotational symmetry.

The order of symmetry of an ellipse is generally 2.

Order of symmetry:

The order of rotational symmetry of an object is how many times that object is rotated and fits on to itself during a full rotation of 360 degrees.

So graph A and C have rotational symmetry.

4 0
3 years ago
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