Given: AD = BC and AD || BC Prove: ABCD is a parallelogram.

Mathematics

2 answers:

maksim [4K]2 years ago

5 0

Answer:

ABCD is a parallelogram

Step-by-step explanation:

Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a

parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC

1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.

definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.

alternate interior angles are congruent 4. AC ≅ AC 4.

reflexive property 5. △CAD ≅ △ACB 5. SAS congruency

theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.

Katen [24]2 years ago

4 0

Answer:

Step-by-step explanation:

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The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to t

Serggg [28]

ANSWER

The correct option is,
$k(x - 2)(x - 7) = 0$

EXPLANATION

We were given that the solutions of the quadratic equation are
$x = 2$
and
$x = 7.$

This tells us that,

$x - 2$

and
$x - 7$

are factors of the quadratic equation.

This implies that the quadratic equation is of the form,

$(x - 2)(x - 7) = 0$

We were also told that

$k$

is a non zero constant.

This means that we can use k to multiply the whole equation and the solution will not be affected.

Our equation now becomes,

$k(x - 2)(x - 7) = 0$

Hence the correct answer is A.

5 0

2 years ago

Read 2 more answers

Write the polynomial of least degree with roots -2, 5, and 7.

fomenos

For roots of -2, 5, and 7.

x = -2, x = 5, and x = 7

x = -2 x = 5    x = 7

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

The polynomial of least degree would be:
(x -2)(x - 5)(x - 7) = 0

(x -2)(x -5) = x(x - 5) - 2(x -5)

   = x² - 5x - 2x + 10

   = x² - 7x + 10

(x² - 7x + 10)(x -7)

x(x² - 7x + 10) - 7(x² - 7x + 10)

x³ - 7x² + 10x - 7x² + 49x - 70

x³ - 7x² - 7x² + 10x + 49x - 70

x³ - 14x² + 59x - 70

The least is   x³ - 14x² + 59x - 70

3 0

2 years ago

A maple syrup company is making a new label for its barrels of syrup. If the barrels are 5 feet tall and have a radius of 2 feet

Elanso [62]

Answer:

(A)62.8 square feet

Step-by-step explanation:

Height of the barrels = 5 feet

Radius of the barrels= 2 feet

$\pi$ =3.14