Which statement must be true?

6 to the 2nd power ÷ 2 ( 3 ) + 4 =

Slav-nsk [51]

Use the order of operation, PEMDAS.

6²÷2(3) +4

36/2(3)+4

=(18)(3)+4

=54+4

=58

5 0

3 years ago

What is the value of the expression 2^2 + 4^2 ÷ 2^2? 3 6 8 16

slamgirl [31]

The answer is 8 because you use the order of operations. So it would be 16 divided by 4, then you would do 4+4 which is 8

4 0

3 years ago

What is the volume of this square pyramid?

tatuchka [14]

Answer: 1296 cm³

Step-by-step explanation:

Since, the volume of a square pyramid is,

$V = \frac{a^2h}{3}$

Where a = side of the square base,

h = height of the pyramid,

By the given diagram,

a = 18 cm,

h = 12 cm,

Hence, the volume of the given pyramid,

$V = \frac{18^2\times 12}{3}$

$= \frac{324\times 12}{3}$

$=\frac{3888}{3}$

$=1296$ cube cm.

⇒ First option is correct.

5 0

3 years ago

1) What is the surface area? 1 ft 8 ft 4 ft

WITCHER [35]

Answer:

88 ft^2

Step-by-step explanation:

For a rectangular prism with dimensions 1 ft by 8 ft by 4 ft, there are two opposite faces with dimensions

1 ft by 8 ft,

two opposite faces with dimensions

1 ft by 4 ft,

and two opposite faces with dimensions

4 ft by 8 ft.

We find their area and add them.

SA = 2 * 1 ft * 8 ft + 2 * 1 ft * 4 ft + 2 * 4 ft * 8 ft

SA = 16 ft^2 + 8 ft^2 + 64 ft^2

SA = 88 ft^2

5 0

3 years ago

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

7 0

3 years ago

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