All categories

3 years ago

Which of the expressions are equivalent to the one below? Check all that

Mathematics

1 answer:

vivado [14]3 years ago

7 0

Answer:

A. 7·6 + 7·3
B. 7·3 + 7·6
C. 7·9

Step-by-step explanation:

The distributive property and the commutative property of addition both apply here.

Distributive property: a(b+c) = ab +ac

For a=7, b=6, c=3, this becomes ...

7(6+3) = 7·6 +7·3 . . . . . matches A

The commutative property of addition says ...

a + b = b + a

For a=7·6 and b=7·3, this becomes ...

7·6 + 7·3 = 7·3 + 7·6 . . . . . matches B

Of course, the expression can be partially evaluated:

7(6 +3) = 7·9 . . . . . matches C

You might be interested in

Deb has of a brownie. She wants to divide it up into 's of a brownie so she can have it throughout the day. How many 's will she

qaws [65]

The answer would be 3

4 0

3 years ago

Given two parallel lines cut by a transversal same side interior angles are congruent

lozanna [386]

False. The postulate states: If two <span> parallel</span> lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

5 0

3 years ago

In the diagram, point C represents the center of the sphere. Diego says that the part of the sphere labeled D is the radius. Gre

Katen [24]

Answer:

Gregoire is correct; the diameter is a chord that passes through the center of the sphere.

Step-by-step explanation:

A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.

The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.

A diameter is twice of a radius, so that:

Radius = $\frac{Diameter}{2}$

⇒ Diameter = 2 × Radius

Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.

3 0

3 years ago

Read 2 more answers

Solve the given equation by completing the square.

Dmitriy789 [7]

Answer:

a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

Step-by-step explanation:

$x^{2} +8x = 38$

Add 16 to both sides.

$x^{2} +8x+16 = 38 + 16$

$(x+4)^{2} =54$

$x + 4 = \sqrt{54}$ or $x + 4 = -\sqrt{54}$

$x+4=3\sqrt{6}$ or $x+4=-3\sqrt{6}$

$x=-4+3\sqrt{6}$ or $x=-4-3\sqrt{6}$

Therefore, a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

6 0

3 years ago

Read 2 more answers

Enos took out a 25-year loan for $135,000 at an APR of 6.0%, compounded monthly, and he is making monthly payments of $869.81. W

Alborosie

Present value = 135000
Monthly interest, i = 0.06/12 = 0.005
Monthly payment, A= 869.81

Future value of loan after 16 years
$F=P(1+i)^n$ [compound interest formula]
$=135000(1+.005)^{16*12}$
$=351736.652$

Future value of payments after 16 years
$\frac{A((1+i)^n-1)}{i}$
$=\frac{869.81((1+0.005)^{16*12}-1)}{0.005}$
$=279287.456$

Balance = future value of loan - future value of payments
=351736.652-279288.456
= $ 72448.20

Note: the exact monthly payment for a 25-year mortgage is
$A=\frac{P(i*(1+i)^n)}{(1+i)^n-1}$
$=\frac{135000(0.005*(1+0.005)^{25*12}}{(1+0.005)^{25*12}-1}$
$=869.806892$

Repeating the previous calculation with this "exact" monthly payment gives
Balance = 72448.197, very close to one of the choices.

So we conclude that the exact value obtained above differs from the answer choices is due to the precision (or lack of it) of the provided data.

The closest choice is therefore <span>$72,449.19</span>

6 0

2 years ago

Read 2 more answers