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dedylja [7]
3 years ago
8

30 points!!!! Please help!!!!

Mathematics
1 answer:
lara31 [8.8K]3 years ago
5 0

Answer:

T = 2π√[2m/(9.8m/s²)]

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Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Oksi-84 [34.3K]

Answer:

-1/3

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

9x^2-15x

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

9x^2-15x=6

Subtract 6 from both sides:

9x^2-15x-6=0

Divide everything by 3:

3x^2-5x-2=0

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0

Find the x using the Zero Product Property:

3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

x=-1/3

Assume that the correct symbol is >. Thus,

x>-1/3

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

9x^2-15x

0 is indeed less than six, so our first correct solution is:

x>-1/3

For the second one, do the same thing. We have:

x=2

Assume that the correct symbol is <. Thus:

x

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

9x^2-15x

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

x>-1/3 \text{ and } x

Together, we can write them as:

-1/3

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0
3 years ago
Can someone please help me with this? I’m really confused on it.
trasher [3.6K]
For this problem you need to put the x values in for x in the equation. For example, put -10 in for x and calculate y, which is g(x)
8 0
3 years ago
The perimeter of a rectangle is 400 feet and the length of the rectangle is 3 times the width. find the dimensions of the rectan
bazaltina [42]
Width: x
Length: 3x
Perimeter=x+x+3x+3x=8x
8x=400
x=50
Dimension is 150×50 feet (length × width)
8 0
3 years ago
Y=-1\4z+5 please grqph
svet-max [94.6K]

Answer

Attached the graph

Step by step explanation

Y = -1/4z + 5

Let's form the table values

Here z is the independent variable and y is the dependent values.

Let's take z = -1, 0, 1, 2 and find the corresponding y-values

<u>z                           y</u>

-1                         5.25

0                          5

1                           4.75

2                           4.5

Now let's plot the points and draw the graph.

Here is the graph.

5 0
3 years ago
A farmer has both pigs and chickens on his farm there are 78 fee and 27 heads how many pigs and how many chickens are there
Andre45 [30]
Assuming health non-mutated animals:
Feet = 4*Pigs + 2*Chickens
Heads = Pigs + Chickens

By back substitution:
78 = 4*(27-Chickens) + 2*Chickens
78 = 108 -2*Chickens
-30 = -2*Chickens
Chickens= 15

Then:
27 = Pigs + 15
Pigs = 12

To check:
Feet = 4*Pigs + 2*Chickens
78 = 4*12 + 2*15
78 = 48 + 30
78 = 78 CHECKS
6 0
3 years ago
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