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My name is Ann [436]

2 years ago

8

Which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x2 – 1) + (2x + 6)

)
(3x + 4) + (5x2 – 1)

(5x2 – 1) + ((3x + 4) + (2x + 6))

((3x + 4) + (5x2 – 1)) + (2x + 6)

(3x + 4) + (5x2 – 1) + (2x + 6)

2 answers:

zlopas [31]2 years ago

9 0

It's C.

Trust me, I had trouble figuring out this answer...

-BARSIC- [3]2 years ago

6 0

Associative Property of Addition
(3x + 4) + [(5x2 - 1) + (2x + 6)]

As given in the definition below, to make it an associative property, we can change the bracket

[(3x + 4) + (5x2 - 1)] + (2x +6)

Your answer will be the third option :)

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Holly had $5,000 in her bank account. She withdrew $800 to buy a new bike. What is the percent decrease in the balance of her ac

sweet [91]

The answer is really 16% becouse if you devide $5,000 by .16 you get $800

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2 years ago

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A composite figure is comprised of a square, trapezoid, and a rectangle. The square has side lengths of 10 centimeters. The trap

Evgesh-ka [11]

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

Step-by-step explanation:

The given is,

Dimensions of square has length of 10 cm

Trapezoid has base lengths of 8 cm and 14 cm

The length of the trapezoid is 4 cm

Rectangle has side length of 20 cm and 6 cm

Step:1

Area of composite figure = Area of square + Area of Trapezoid

+ Area of rectangle.......................(1)

Step:2

Formula for area of square,

$A_{square} = a^{2}$

where, a - side of length = 10 cm

$=10^{2}$

$=100$

Area of square, $A_{square}$ = 100 Square centimeter

Step:3

Formula for area of Trapezoid,

$A_{Trapezoid}$ = $\frac{a+b}{2} h$ .......................................(2)

Where, a - 8 cm

b - 14 cm

h - 4 cm

From equation (2)

= $\frac{8+14}{2} 4$

= $(11)(4)$

= 44

Area of Trapezoid, $A_{Trapezoid}$ = 44 square centimeters

Step:4

Formula for area of rectangle,

$A_{Rectangle} =lb$ ......................................(3)

Where, l = 20 cm

b = 6 cm

Equation (3) becomes,

$= (20)(6)$

= 120

Area of rectangle, $A_{Rectangle}$ = 120 square centimeters

Step:5

From Equation (1),

$A_{Composite}$ = 100 + 44 + 120

= 264 square centimeters

Result:

The area of the composite figure is 264 square centimeters, if a composite figure comprised of a square, trapezoid and a rectangle.

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2 years ago

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Write an equivalent expression for n x a using only addition

bulgar [2K]

Answer:

Equivalent expression for n x a = a+ a+a+a....n times

Step-by-step explanation:

Given: Expression for n x a .

To find : Write an equivalent expression for n x a using only addition.

Solution : We have given that n x a .

Here, we can say Sum of a is n times.

We can rewrite it n x a = a+ a+a+a....n times.

Example : 3 x 2 = 2 +2+ 2.

6 = 6 ( true)

Therefore , equivalent expression for n x a = a+ a+a+a....n times.

7 0

2 years ago

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In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .

⇒ $\cos Z =\frac{3.5}{18}$

⇒ $\cos Z = 0.195$ (approx) or

$Z=\cos^{-1}(0.195)$

Therefore, the angle $\angle Z = 78.7^{\circ}$ .

The sum of the measure of the angle in the triangle is 180 degree.

In triangle XYZ.

$\angle X +\angle Y+\angle Z =180^{\circ}$

Since $\angle X=\angle Z =78.7^{\circ}$

then,

$78.7^{\circ}+\angle Y+78.7^{\circ}=180^{\circ}$

⇒ $157.4^{\circ}+\angle Y=180^{\circ}$

Simplify:

$\angle Y=22.6^{\circ}$ .

Therefore, the measure of each angle are: $\angle X=\angle Z=78.7^{\circ}$ and $\angle Y =22.6^{\circ}$

8 0

2 years ago

Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of so

mojhsa [17]

To determine the cost of each item, we need to set up equations. From the problem statement, we have three unknowns so we need three equations. We set up equations as follows:

let x cost of small pizzas
y cost of soda
z cost of salad

two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14

one small pizza, a liter of soda, and three salads cost $15

x + y + 3z = 15

three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22

Solving for x, y and z, we will have:

x = $ 5
y = $ 1
z = $ 3

6 0

2 years ago