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3 years ago

1. Which of the following is a true statement?

Mathematics

1 answer:

kykrilka [37]3 years ago

6 0

Answer:

Step-by-step explanation:

Example: 4^3 = 64

A means 4*3, which is 12.

B means 2/(4^3), which wouldn't cancel out anything.

C is 4^3 = 64.

D means 4^4 would make a perfect square just because 4 is to the power of an even number. 4^4 = 256, which can't be divided by x to get x.

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Amir throws a stone off of a bridge into a river. The stone's height (in meters above the water) ttt seconds after Amir throws i

Harrizon [31]

Answer:

1) The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ , 2) The stone reaches its maximum height 2 seconds after being thrown.

Step-by-step explanation:

1) Given that height of the stone is represented by a second-order polynomial, which depicts a parabola as graph. The best approach to determine the instant when stone reaches its highest is by vertex form, whose form is:

$h-k = C\cdot (t-r)^{2}$

Where:

$r$ , $k$ - Instant and maximum height of the stone, measured in seconds and meters.

$C$ - Vertex constant, which must be negative as there is an absolute maximum, measured in meters per square second.

Let be $h(t) = -5\cdot t^{2}+20\cdot t +160$ , which is transformed into vertex form:

i) $h = -5\cdot t^{2}+20\cdot t +160$ Given

ii) $h = -5\cdot (t^{2}-4\cdot t -32)$ Distributive property/ $(-a)\cdot b = -a\cdot b$

iii) $h = -5\cdot [(t^{2}-4\cdot t +4)+(-36)]$ Existence of additive inverse/Definitions of addition and subtraction

iv) $h = (-5)\cdot (t-2)^{2}+180$ Distributive property/ $(-a)\cdot (-b) = a\cdot b$ /Perfect square binomial

v) $h -180 = -5\cdot (t-2)^{2}$ Compatibility with addition/Existence of additive inverse/Modulative property/Definition of subtraction/Result

The vertex form of $h(t) = -5\cdot t^{2}+20\cdot t +160$ is $h -180 = -5\cdot (t-2)^{2}$ .

2) The time can be extracted from previous results, which indicates that stone reaches its maximum height 2 seconds after being thrown.

4 0

3 years ago

PLEASE HELP! Thank you so much, I’m just a little confused.

Whitepunk [10]

The domain is the values of x from the x-axis that 'cover' the given function.

Look at the end points of the graph and the corresponding values of x on the x-axis. These go from - 5 to 4

Thus the domain is x ∈ [- 5, 4 ] ← domain

The square bracket indicates that the values of - 5 and 4 are included in the domain

Whereas (- 5, 4 ) indicates that - 5 and 4 are not included but all values in between are

The range is the values of y from the y-axis that cover the given function

Look at the minimum value and maximum value of the function along the y-axis

The minimum is 0 and the maximum is 5

range is y ∈ [0, 5 ]

To determine the value of y when x = -3

Locate x = - 3 on the x-axis, move up vertically until the line representing the function is met, and read off the corresponding y value to the right on the y-axis

The value of f(x) when x = - 3 is 2

6 0

3 years ago

Read 2 more answers

write a equation in a point-slope form fir the line through the given point with the given slope (9,-1);m=4/3

gavmur [86]

Answer:

y +1 = 4/3( x-9)

Step-by-step explanation:

Point slope form of an equation is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on a line

y - -1 = 4/3( x-9)

y +1 = 4/3( x-9)

6 0

3 years ago

a store advertises that customers can take 25%off the original price and then take an extra 10%off is this 35% of? explain

GrogVix [38]

No its not 35%. Its 32.5 %
If it costs 100$
25% × 100$ = 25$
So price after 25% off is 100$ - 25$ = 75
10% × 75$ = 7.5 $
75$ - 7.5$ = 67.5$
100 - 67.5 = 32.5

8 0

3 years ago

How do I find the absolute value of |2y-9|=1<br>

Ray Of Light [21]

Answer:

y=4,5

Step-by-step explanation:

Anything inside an absolute value will become postive.

So, 2y-9 can be -1 because the absolute value of -1 is 1.

Knowing this,

2y-9 = 1

2y-9 = -1

2y-9=1

2y=10

y=5

and

2y-9=-1

2y=8

y=4

y=4,5

6 0

3 years ago

Read 2 more answers