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elixir [45]
3 years ago
11

Which is the graph of f(x) = -(x + 3)(x + 1)?

Mathematics
1 answer:
Bas_tet [7]3 years ago
4 0

Answer:

See attachment

Step-by-step explanation:

A function is given to us and we need to tell which graph represents the given function. The function given to us is,

\tt: \implies f(x) = -( x + 3 )( x + 1 )

Let's find out at which points do the graph Intersects x axis / finding the roots. For that substitute f(x) = 0 , we have ,

\tt: \implies  -(x +3)( x + 1 ) = 0

Equate each factor by 0 ,

\tt: \implies \boxed{\blue{ \tt x = -1,-3 }}

Therefore the graph will intersect x axis at x is equal to -1 and x is equal to -3 .

On looking at the given graphs in the options the second graph intersects x axis at -1 and -3 .

<u>Hence</u><u> </u><u>the </u><u>second</u><u> </u><u>option</u><u> </u><u>is </u><u>correct</u><u> </u><u>.</u><u> </u>

{ See attachment }

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Which of the following is not equivalent to the expression below?
il63 [147K]

Answer: I can't see the problem

Step-by-step explanation:

3 0
3 years ago
Why does multiple of 3 add up digits trick work?
kherson [118]
You must be referring to the quick way to determine whether a given integer is divisible by 3; that is, 3 divides an integer x whenever the digits of x sum to a multiple of 3.

Suppose x has n\ge1 digits. We can expand it as a sum of the numbers in any given digits place by the corresponding power of 10. For example, if x=2148, we can write

2148=2\times10^3+1\times10^2+4\times10^1+8\times10^0

More generally, if

x=d_{n-1}d_{n-2}\ldots d_1d_0

(where d_i denotes the numeral in the 10^i-th's place), then we have the expansion

x=d_{n-1}10^{n-1}+d_{n-2}10^{n-2}+\cdots+d_110^1+d_0

Notice that for any integer k, we have

10^k-1=\underbrace{99\ldots99}_{k\text{ 9s}}

which is clearly divisible by 3. So from each power of 10 in the expansion of x, we can add and subtract 1, then rearrange the terms of the sum:

x=d_{n-1}10^{n-1}+\cdots+d_110^1+d_0
x=d_{n-1}(10^{n-1}-1+1)+\cdots+d_1(10^1-1+1)+d_0
x=d_{n-1}(10^{n-1}-1)+\cdots+d_1(10^1-1)+(d_{n-1}+\cdots+d_1+d_0)

We know 10^k-1 is divisible by 3, which means the remainder upon dividing x by 3 is just the sum of the digits of x. If this remainder is divisible by 3, then so must be the original number, x.

Back to our previous example: if x=2148, then we have the expansion

2148=2\times10^3+10^2+4\times10+8
2148=2(999+1)+(99+1)+4(9+1)+8
2148=2\times999+99+4\times9+(2+1+4+8)

Dividing through by 3, we get a remainder of 2+1+4+8=15, which is divisible by 3, and so 2148 must also be a multiple of 3.

In case for some reason you're not convinced 15 is a multiple of 3, you can apply the same trick:

15=10+5
15=9+1+5

Dividing through by 3 leaves a remainder of 1+5=6, which is also a multiple of 3, so that 15 must be, too.
7 0
3 years ago
Will someone plzz help
lbvjy [14]

Answer:

4.4 days

Step-by-step explanation:

375 x 0.14 = 52.5

300 - 52.5 = 247.5

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3 0
3 years ago
HELP ME Write and solve a proportion to find y.
Phoenix [80]

Given:

A figure of dilation and the center of dilation is O.

To find:

The value of y.

Solution:

The distance between center and vertex of image (d') is proportional to the distance between center and the corresponding vertex of original figure (d).

d'\propto d

d'=kd

\dfrac{d'}{d}=k

Where, k is the scale factor or constant of proportionality.

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k=\dfrac{36}{16}

k=\dfrac{9}{4}

We know that,

k=\dfrac{\text{Side length of image}}{\text{Corresponding side length of original figure}}

\dfrac{9}{4}=\dfrac{A'C'}{AC}

\dfrac{9}{4}=\dfrac{27}{y}

9\times y=27\times 4

Divide both sides by 9.

y=\dfrac{27\times 4}{9}

y=3\times 4

y=12

Therefore, the value of y is 12.

6 0
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It is probably 0,2,4,6 because other ones go "out of the sequence".

Hope this helps. :)
8 0
3 years ago
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