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xxMikexx [17]
2 years ago
10

F(x)=2x^3+ax^2-37x-60 The binomial x-4 is a factor of f(x). Find the value of a.

Mathematics
1 answer:
jekas [21]2 years ago
6 0

Given:

The function is

f(x)=2x^3+ax^2-37x-60

The binomial x-4 is a factor of f(x).

To find:

The value of a.

Solution:

If x-c is a factor of f(x), then f(c)=0.

It is given that, x-4 is a factor of f(x), then f(4)=0.

We have,

f(x)=2x^3+ax^2-37x-60

Substituting x=4, we get

f(4)=2(4)^3+a(4)^2-37(4)-60

f(4)=2(64)+a(16)-148-60

f(4)=128+16a-208

f(4)=16a-80

Now,

f(4)=0

16a-80=0

16a=80

a=\dfrac{80}{16}

a=5

Therefore, the value of a is 5.

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A combination lock requires a user to select three numbers to unlock it, where all three numbers are between 1 to 30, inclusive,
Sonbull [250]

Answer:

\frac{1}{270}=0.00370

Step-by-step explanation:

As the numbers are only between 1 and 30

Total number of possible combinations = 30×30×30 = 27000

If there are 100 attempts then

\text{P (someone guesses correct)}=\frac{\text{Number of attempts}}{\text{Total number of possible combinations}}\\\Rightarrow \text{P (someone guesses correct)}=\frac{100}{27000}\\\Rightarrow \text{P (someone guesses correct)}=\frac{1}{270}=0.00370

∴ Probability someone can guess the correct combination given 100 attempts is \mathbf{\frac{1}{270}=0.00370}

5 0
3 years ago
Select the simplification that accurately explains the following statement.
lutik1710 [3]

Answer:

Option (b) is correct.

(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}=2^{1}=2

Step-by-step explanation:

Given: (2^\frac{1}{4} )^4

We have too choose the correct simplification for the given statement.

Consider (2^\frac{1}{4} )^4

Using property of exponents, (a^m)^n=a^m\times a^m\times a^m\times ....\times (n\ times)

We have,

(2^\frac{1}{4} )^4=2^\frac{1}{4} \times 2^\frac{1}{4}\times 2^\frac{1}{4}\times 2^\frac{1}{4}

Again applying property of exponents  a^m\times a^m=a^{n+m}

We have,

(2^\frac{1}{4} )^4=2^{(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{4}+ \frac{1}{4} )}

Simplify, we have,

(2^\frac{1}{4} )^4=2^{\frac{4}{4}}

we get,

(2^\frac{1}{4} )^4=2^{1}=2

Thus, (2^\frac{1}{4} )^4=2

Option (b) is correct.

   

8 0
3 years ago
Read 2 more answers
What is 8 more than twice the sum of a number and 3 is the same as -6?
a_sh-v [17]
This can be solver by creating a small equation with x being the number and solving for x. The equation would be 8 + 2( x + 3 ) = -6
Solve for x:
8 + 2( x + 3 ) = -6
Distribute the 2
8+ (2x+6)=-6
Subtract 8
2x+6= -14
Add 6
2x= 8
Divide by 2
x=4

So the number you are looking for is 4

I hope this helps!
8 0
3 years ago
Jordan saved four fifths of the amount he needs to buy an $80 video game if he earns $7.75 per hour by working at the pizza shop
galina1969 [7]
1/5 of 80 =16
16x4=64
this means he needs 16 more dollars
16/7.75=2.06451612903
this means that he has to work for two more hours.

hope this helps :)
7 0
3 years ago
Explain why a + 2b = 110 in the triangle shown​
Luda [366]

Answer:

Step-by-step explanation:

According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. For us, in our triangle:

a + 2b + 70 = 180 so

a + 2b = 180 -70 and

a + 2b = 110. That's why.

3 0
3 years ago
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