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2 years ago

How many terms are in the binomial expansion of (3x + 5)9? 8 9 10 11

Mathematics

2 answers:

Stells [14]2 years ago

6 0

The number of terms in the binomial expansion of (3x-5)^9 is 10

Mkey [24]2 years ago

6 0

Answer: 10

Step-by-step explanation:

We know that in the binomial expansion of $(a+b)^n$ , the total number of terms = n+1

For the binomial expansion of $(3x + 5)^9$ , n= 9

Then, the total number of terms in binomial expansion of $(3x + 5)^9$ will be :-

$n+1=9+1=10$

Hence, there are 10 terms are in the binomial expansion of $(3x +5)^9$ .

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B/5 -34<-41 what is B

snow_tiger [21]

Answer:

b<-35

Step-by-step explanation:

b/5-34<-41

b/5<-41+34

b/5<-7

b<-7*5

b<-35

4 0

3 years ago

Question Help Factor the expression. 7y squared+10y+ 3

kirill [66]

7y^2 + 10y + 3

7y^2 + 7y + 3y + 3

(7y^2+7y) + (3y+3)

7y(y+1) + 3(y+1)

(7y+3)(y+1)

So the final answer is (7y+3)(y+1)

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3 years ago

Solve the following exponential equations. 2(4^x )+ 4^(x+1 )= 342

Cloud [144]

Answer:

x ≈ 2.91644500708

Step-by-step explanation:

The equation can be simplified to ...

2(4^x) +4(4^x) = 342

6(4^x) = 342

4^x = 57

Taking logarithms, we get ...

x = log₄(57) = log(57)/log(4)

x ≈ 2.91644500708

5 0

3 years ago

Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

Step-by-step explanation:

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

$\bullet\quad a=\dfrac{1}{4p}$

p is the distance from the vertex to the focus

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

***************************************************************************************

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

3 years ago

Less than 75% of workers got their job through internet resume sites. A researcher thinks it has increased.

Vera_Pavlovna [14]

Answer:

H0 : p = 0.75 against H1: p > 0.75 One tailed test.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0 : p = 0.75 against H1: p > 0.75 One tailed test.

In this case H0 is not defined as p≤ 0.75 because the acceptance and rejection regions cannot be set up. Therefore we take the exact value of H0 : p= 0.75.

The claim is that the probability of the workers getting their job through the internet is greater than 75% or 0.75.

As H0 is supposed to be less than we choose H1 to be greater than equality.

5 0

3 years ago