What is the mass of the decoration and of each passenger car?

Jace invested $380 in an account paying an interest rate of 6.2% compounded continuously. Assuming no deposits or withdrawals ar

SOVA2 [1]

Answer: 960

Step-by-step explanation:

5 0

2 years ago

what is the perimeter of triangle PQR vertices P(-2, 9), Q(7,-3), and R(-2, -3) in the coordinate plane?

kipiarov [429]

This is a diffficult question was there a chart

6 0

3 years ago

Give the property that justifies each step.

frosja888 [35]

Answer:

Please check the explanation below.

Step-by-step explanation:

Some of the properties are defined as:

Distributive property

$a(b+c) = ab+ac$

For example,

suppose a=3, b=4, c=5

3(4+5) = 3(4) + 3(5)

3(9) = 12+15

27 = 27

Subtraction property of Equality

if (a=b), then a-c = b-c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a-c = b-c ⇒ 2-5 = 2- 5 ⇒ -3 = -3

Addition property of Equality

if (a=b), then a+c = b+c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a+c = b+c ⇒ 2+3 = 2+3 ⇒ 5 = 5

Multiplicative property of Equality

if (a=b), then a×c = b×c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a×c = b×c ⇒ 2×5 = 2 × 5 ⇒ 10 = 10

Division property of Equality

if (a=b), then a÷c = b÷c

For example,

suppose a=2, b=2, c=5

if a = b ⇒ 2 = 2

then a÷c = b÷c ⇒ 2÷5 = 2 ÷ 3 ⇒ 2/5 = 2/5

Let us solve the given equation using the above properties.

7n-16=47 Given

7n-16+16=47+16 1) Addtion property of Equality ∵ if (a=b), then a+c = b+c

7n=63 2) simplify

n = 9 3) Division property of Equality ∵ if (a=b), then a÷c = b÷c

3 0

3 years ago

A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular

Tcecarenko [31]

If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.

Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.

The top angle of each triangle is obtained by dividing the full angle by 8.

So, each top angle = $\frac{360}{8}$

= 45°

Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.

This altitude OC bisects the top angle 45°.

Therefore, ∠ AOC = 22.5°.

Now, in Δ AOC,

$sin 22.5=\frac{AC}{OA}$

$=\frac{AC}{x}$

So, AC = x sin 22.5°

Note that, AB = 2 AC.

Therefore, AB = 2x sin 22.5°.

Also, $cos 22.5=\frac{OC}{OA}$

$=\frac{OC}{x}$

So, OC = x cos 22.5°.

Area of Δ AOB = $\frac{1}{2}(AB)(OC)$

= $\frac{1}{2}$ × (2x sin 22.5°) × (x cos 22.5°)

= $\frac{1}{2} x^{2}$ (2 sin 22.5° cos 22.5°)

= $\frac{1}{2} x^{2}$ sin 45°

= $x^{2}$ / $2\sqrt{2}$

Area of the octagonal gazebo = 8 × one triangular area

= 8 × ( $x^{2}$ / $2\sqrt{2}$ )

$=2\sqrt{2} x^{2}$

$=2.828x^{2}$

Area required for mulch = circular area - area of the gazebo

$=3.14x^{2} -2.828x^{2}$

$=0.312x^{2}$

Now, cost per unit area = $1.50.

Hence, total cost g(m) = area × cost per unit area

Total cost g(m) = $0.312x^{2}$ × 1.5

$=0.468x^{2}$

Hence, total cost g(m) = $0.468x^{2}$ .

4 0

3 years ago

What is the density ?

zhannawk [14.2K]

Density is the degree of compactness of a substance. It is the degree of consistency measured by the quantity of mass per unit volume. It is the relationship between the mass of the substance and the amount of space it takes up. I hope it helps.

7 0

3 years ago

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