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Kitty [74]
3 years ago
9

Select the number property that will justify the step in the following expression.

Mathematics
2 answers:
Lostsunrise [7]3 years ago
5 0
Associative property of multiplication which states :
(a * b) * c = a * (b * c)
IRISSAK [1]3 years ago
3 0
2(5 • 17) = <span>(2 • 5) 17

It is Associative Multiplication</span>
You might be interested in
Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives
lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                     

                    t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t =  \frac{27 + 37}{16} \\\\t = 4

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0
3 years ago
Write in simplest form:<br> <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24a%5E%7B10%7Db%5E%7B6%7D%7D" id="TexFormula1" ti
Charra [1.4K]

Answer:

2a^3b^2\sqrt[3]{3a}

Step-by-step explanation:

Use the following rules for exponents:

a^m*a^n=a^{m+n}\\\\\sqrt[3]{x^3}=x

Simplify 24. Find two factors of 24, one of which should be a perfect cube:

8*3=24\\\\2^3=8

Insert:

\sqrt[3]{2^3*3a^{10}b^6}

Now split the exponents. Split 10 into as many 3's as possible:

10=3+3+3+1

Insert as exponents:

\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^6}

Split 6 into as many 3's as possible:

6=3+3

Insert as exponents:

\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^3*b^3}

Now simplify. Any terms with an exponent of 3 will be moved out of the radical (rule #2):

2\sqrt[3]{3*a^3*a^3*a^3*a^1*b^3*b^3}\\\\\\2*a*a*a\sqrt[3]{3*a^1*b^3*b^3}\\\\\\2*a*a*a*b*b\sqrt[3]{3*a^1}

Simplify:

2a^3b^2\sqrt[3]{3a}

:Done

6 0
3 years ago
The ratio of two numbers is 2/3. The sum of the numbers is 105. What are the two numbers?
Pepsi [2]
A) x/y = 2/3
B) x + y = 105
Solving Equation A for y
A) y = 1.5x
Substituting A into B
B) x + 1.5x = 105
2.5x = 105
x = 42
y = 63


8 0
3 years ago
2Y=5XSquared<br> I don’t have the power symbols on my phone.<br> How do I solve for Y?
gizmo_the_mogwai [7]
Divide both sides by two.
6 0
3 years ago
Of the 125 guests invited to a wedding, 100 attended the wedding. What percent of the invited guests attended the wedding?
RSB [31]
100/125 * 100 = 80 % (80 percent)
6 0
3 years ago
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