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Arada [10]
3 years ago
8

Rewrite the quadratic function in intercept or factored form f(n)=-35-2n+n^2

Mathematics
1 answer:
gtnhenbr [62]3 years ago
8 0

Answer: f(n)=(n-7)(n+5)


Step-by-step explanation:

1. You can rewrite the quadratic equation as following:

f(n)=n^{2}-2n-35

2. To factor it, you must find two number that when you add them you obtain -2 and when you multiply them you obtain -35. These would be 5 and -7.

3. Therefore, you can write the function in the following intercept form:

f(n)=(n-7)(n+5)


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5(3a-1)-2(3a-2)=3(a+2)+v
STatiana [176]

Answer:

<u>The answer is option C. 6a-7</u>

Step-by-step explanation:

Given that

5(3a-1)-2(3a-2)=3(a+2)+v

Solve for v

∴ v = 5(3a-1)-2(3a-2) - 3(a+2)

∴ v = 15a - 5 - 6a + 4 - 3a - 6

∴ v = 15a - 6a - 3a - 5 + 4 - 6

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3 years ago
Suppose you always eat a particular brand of cookies out of the standard sized package it comes in from the store. You notice th
Blababa [14]

Answer:

There are 91 cookies in the package of cookies

Step-by-step explanation:

The given parameter for the number of cookies are;

The number of cookies left when eating 3 at a time = 1 cookie

The number of cookies left when eating 5 at a time = 1 cookie

The number of cookies left when eating 7 cookies at a time = No cookie leftover

Let 'n' represent the number of cookies in the pack, let 'a', 'b', and 'c' be the multiples of 3s, 5s, and 7s in 'n', respectively, we have;

The number of cookies in the pack, n < 100

Therefore, we have;

3·a = n - 1

5·b = n - 1

7·c = n

∴ n - 1 is a multiples of 3 and 5 less than 100 which are;

15, 30, 45, 60, 75, and 90

Therefore, the possible values of 'n' are'

n = n - 1 + 1 = 15 + 1 = 16, 30 + 1 = 31, 45 + 1 = 46, 60 + 1 = 61, 75 + 1 = 75, 90 + 1 = 91

Multiples of 7 includes;

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98

Therefore, n = 91 which is the number that appear simultaneously in both search

The number of cookies in a package = 91 cookies

3 0
3 years ago
Find the value of each variable
aniked [119]

Answer:

Answer d)

a= 10*\sqrt{3} b=5*\sqrt{3}, c=15, and d=5

Step-by-step explanation:

Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".

So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

b=10*sin(60^o)= 10*\frac{\sqrt{3} }{2} = 5*\sqrt{3}

where we use the fact that the sine of 60 degrees can be written as: \frac{\sqrt{3} }{2}

We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

d=10*cos(60^o)=10* \frac{1}{2} = 5

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

sin(30^o)= \frac{b}{a} \\a=\frac{b}{sin(30)} \\a=\frac{5*\sqrt{3} }{\frac{1}{2} } \\a= 10*\sqrt{3}

where we used the value of the sine function of 30 degrees as one half: \frac{1}{2}

Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

c=10*\sqrt{3} * cos(30^o)=10*\sqrt{3} *\frac{\sqrt{3} }{2} \\c= 5*3=15

Therefore, our answer agrees with the values shown in option d)

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