All categories

3 years ago

Is quadrilateral DEFG a parallelogram? Why or why not?

Mathematics

1 answer:

svet-max [94.6K]3 years ago

4 0

Answer:

D ig?

Step-by-step explanation:

Because opposite angles are equal in parallelogram

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The answer is 8.9 ft

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At a sale this week, a desk is being sold for $561. This is 68% of the original price. What is the original price?

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Answer:

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Step-by-step explanation:

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2 years ago

A car is traveling at a constant velocity. After two hours the car has traveled 110 miles. After four hours the car has traveled

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4 years ago

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

x = 0 or 1 or -1

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

x= 5 or x = -7

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

The above function has no x intercept.

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

3 years ago

ΔPQR has angle measurements of 80°, 50°, and 50°. What kind of triangle is ΔPQR?

trasher [3.6K]

Answer:

Isosceles Triangle; Acute Triangle

Step-by-step explanation:

Review your definitions of the different types of triangles:

acute triangle- a triangle that has three acute (less than 90 degrees) angles

obtuse triangle- a triangle that has an obtuse (greater than 90 degrees) angle.

right triangle- a triangle that had one right (90 degrees) angles

isosceles triangle- a triangle with two congruent sides and one unique side and angle.

equilateral triangle- a triangle with three congruent sides and three congruent angles.

scalene triangle- a triangle with no congruent sides and no congruent angles.

With these definitions, we can classify ΔPQR as an isosceles acute triangle.

8 0

3 years ago