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3 years ago

Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)? x = −7 x = −3 x = 3 x = 5

Mathematics

2 answers:

daser333 [38]3 years ago

7 0

Answer: The correct option is

(B) x = - 3.

Step-by-step explanation: We are given to select the correct zero of the following polynomial function :

$f(x)=(x+3)(x-7)(x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The zeroes of the function f(x) are given by

$f(x)=0\\\\\Rightarrow (x+3)(x-7)(x+5)=0\\\\\Rightarrow x+3=0,~~x-7=0,~~x+5=0\\\\\Rightarrow x=-3,7,-5.$

Therefore, the zeroes of the given function are

x = -3, x = 7 and x = -5.

Thus, the correct option is

(B) x = -3.

ANEK [815]3 years ago

4 0

Answer:

x = −3

Step-by-step explanation:

A zero of a function is a value that makes one of the factors be zero.

To make x+3 = 0, x = -3.

To make x-7 = 0, x = 7.

To make x+5 = 0, x = -5.

Of these values that make the factors zero, only x = -3 is on your choices list.

You might be interested in

What is the explicit formula for this sequence

-Dominant- [34]

Answer:

Step-by-step explanation:

Start with the 3.

You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing. The members of the sequence are going up.

n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.

The answer is an = a1 + (n-1)*d

d = 3

a1 = - 7

So let's try the formula out.

a4 = -7 + (4 - 1)*3

a4 = -7 + 3 * 3

a4 = -7 + 9

a4 = 2

Is 2 the 4th term in the series? Yes it is!

8 0

3 years ago

2x - y = 3 show the work and a graph

Galina-37 [17]

First of all, if we want to graph this we will need to make it into slope intercept form

2x - y = 3
add y to both sides
2x = y + 3
subtract 3 from both sides
2x - 3 = y
flip the equation
y = 2x -3

we now know that the y-intercept is at (0, -3)
using that we plot the first point
The slope is 2
(this means up 2 over 1)
using that we make a line

(I'm sure you can graph it ;D)

Hope this helps :)

7 0

3 years ago

The function f(x)= 3(1.4)' gives the length (in inches) of an image after being enlarged by 10% x times.

kondaur [170]

Answer:

3.99 inches

Step-by-step explanation:

The correct question is

The function f(x) = 3(1.1)^x gives the length (in inches) of an image after being enlarged by 10% x times.

What is the length of the image after it has been enlarged 3 times? Round your answer to the nearest hundredth

we have

$f(x)=3(1.1)^x$

This is a exponential growth function

where

f(x) represent the length (in inches) of an image

x is the number of times the image is enlarged

For x=3

substitute in the exponential equation

$f(x)=3(1.1)^3=3.99\ in$

4 0

3 years ago

The length of a rectangular driveway is five feet more than three times the width. The area is 350ft2. Find the width and length

crimeas [40]

Answer:

width -- 10 ft
length -- 35 ft

Step-by-step explanation:

We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.

The area is the product of length and width, so is ...

A = (3x +5)(x) = 3x^2 +5x

To make the area 350, we can find the value of x from ...

3x^2 +5x = 350

This can be solved a number of ways. One of them is "completing the square".

3(x^2 +5/3x) = 350

We choose to divide by 3 and add the square of half the x-coefficient.

x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2

(x +5/6)^2 = 4225/36 . . . . simplify

x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root

x = 10 or -11 2/3 . . . . subtract 5/6

The positive solution is the one of interest: x = 10.

The driveway is 10 ft wide and 35 ft long.

4 0

3 years ago

How to solve question 19 thanks

miskamm [114]

Let $X$ be the random variable for the weight of any given can, and let $\mu$ and $\sigma$ be the mean and standard deviation, respectively, for the distribution of $X$ .

You have

$\begin{cases}\mathbb P(X377)=0.025\end{cases}$

Recall that for any normal distribution, approximately 99.7% of it lies within three standard deviations of the mean, i.e. $\mathbb P(\mu-3\sigma$ . This means 0.3% must lie outside this range, $\mathbb P(X\mu+3\sigma)=0.003$ . Because the distribution is symmetric, it follows that $\mathbb P(X$ .

Also recall that for any normal distribution, about 95% of it falls within two standard deviations of the mean, so $\mathbb P(\mu-2\sigma$ , which means 5% falls outside, and by symmetry, $\mathbb P(X>\mu+2\sigma)=0.025$ .

Together this means

$\begin{cases}\mu-3\sigma=347\\\mu+2\sigma=377\end{cases}$

Solving for the mean and standard deviation gives $\mu=365$ and $\sigma=6$ .

6 0

4 years ago