Which of the following sets represents the range of the function shown?

Answer:

D. -1,1,-2i, 2i

Step-by-step explanation:

We should have 4 roots since this is a 4th degree polynomial.  We just have to watch since some of them may be multiple roots.

x^4+3x^2-4 = 0

Factoring this equation

(x^2 - 1) (x^2+4) = 0

We can factor the first term

(x-1) (x+1) (x^2+4) =0

Using the zero product property

x-1 =0  x+1 = 0  x^2+4 =0

x=1        x=-1        x^2 = -4

                            Taking the square root of each side

                           sqrt(x^2) =± sqrt(-4)

                                     x =± sqrt(-1) sqrt(4)

                                       x =±i *2

                                       x = ±2i

So firstly, I will be factoring by grouping. Firstly, what two terms have a product of -4x⁴ and a sum of 3x²? That would be -x² and 4x². Replace 3x² with -x² + 4x²:

[tex]0=x^4-x^2+4x^2-4[/tex]

Next, factor x⁴ - x² and 4x² - 4 separately. Make sure that they have the same quantity on the inside:

[tex]0=x^2(x^2-1)+4(x^2-1)[/tex]

Now you can rewrite it as:

[tex]0=(x^2+4)(x^2-1)[/tex]

However, we can simplify it even further. With the second factor, apply the difference of squares rule (x² - y² = (x + y)(x - y)):

[tex]x^2-1=(x+1)(x-1)\\\\0=(x^2+4)(x+1)(x-1)[/tex]

Now it's fully factored. With this, apply the zero product property and solve:

[tex]x^2+4=0\\x^2=-4\\x=\pm \sqrt{-4}=\pm \sqrt{4}i\\x=\pm\ 2i\\x=2i,-2i\\\\x+1=0\\x=-1\\\\x-1=0\\x=1[/tex]

In short, your answer is D. -1, 1, -2i, 2i

Answer:

Hey!

Your answer is £2121.80 in the account!

Step-by-step explanation:

So to do this, you have to first find out how much would be left after 1 year...

=     3 / 100 x 2000 = £60 *we now add this on to the £2000*

=     2000 + 60 = £2060 *this is what is in the account after 1 YEAR*

Then, find out the amount for the second year!

=     3 / 100 x 2060 = £61.80 *we now add this on to the £2060*

=     2060 + 61.80 = £2121.80 *this is what is in the account after 2 YEARS*

SO AFTER 2 YEARS, THERE IS AN AMOUNT OF £2121.80 IN THE BANK ACCOUNT!

HOPE THIS HELPS!!

Answer:

5feet per year

Step-by-step explanation:

We need to find the distance it grew in that 7 1/2 years:

63 - 25 1/2 = 37 1/2

Now to find the average yearly growth we can divide this by 7 1/2:

37.5 ÷ 7.5 = 5

So the yearly rate of growth of the tree is 5f/y

Answer:

1 / 4 US cups = 4 US tablespoons

Step-by-step explanation:

trust me its right

Answer: 2/3

Step-by-step explanation:

Slope Intercept Form: y = mx + b

m = slope

So, since 2/3 fits the form above, 2/3 is the slope in this equation.

The slope of the given line equation is [tex]m=\frac{2}{3}[/tex]. Since the given equation is in the form of slope-intercept form of a line y=mx+c.

The slope-intercept form of a line is expressed by the equation y=mx +c. where m is the slope and c is the y-intercept of the line.

Give that the equation of the line is y=2/3x+1

Comparing this equation with the standard form, we get

m = 2/3 and c=1

So, the slope of the given equation of the line is 2/3.

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Answer:

See below.

Step-by-step explanation:

There is no statement given so we can only guess. There is a way of finding out.

Slope ZY = - 1/2

Slope XY = 2

Those two slopes (when multiplied) will equal - 1 (2 * -(1/2) = - 1). That is the definition of two lines meeting at right angles or one line being perpendicular to another.

Answer:

The slopes of XY and ZY are opposite reciprocals.

Step-by-step explanation: Hope this helps

Final answer:

We find that there are 6 rows in the array.

Explanation:

To solve the student's question, we need to find the number of rows in an array made with 24 tiles, where the number of rows is 2 more than the number of tiles in each row.

Let's denote the number of tiles in each row as x, and the number of rows as y.

According to the problem statement, y = x + 2.

Also, the total number of tiles in the array is the product of the number of rows and the number of tiles per row, hence 24 = x * y.

Substituting the expression for y from the first equation into the second equation, we have

24 = x * (x + 2).

To find the value of x, we need to solve this quadratic equation. Starting with simplification, we get

x^2 + 2x - 24 = 0.

This factors to (x + 6)(x - 4) = 0, so x could be -6 or 4.

Since the number of tiles in a row can't be negative, we disregard -6, leaving us with x = 4.

Hence, y = 4 + 2 = 6 rows.

To find the formula for the nth term of a quadratic or cubic sequence, we can analyze the differences between consecutive terms and use a corresponding formula. For quadratic sequences, the second differences should be the same, while for cubic sequences, the second differences will differ.

To find the formula for the nth term of a quadratic sequence, we need to examine the differences between consecutive terms. Let's analyze each given sequence:

a) 15, 19, 25, 33

The first differences are 4, 6, and 8. Notice that the second differences are the same, which means the formula is quadratic. To find the formula, we can use the quadratic formula:

an = dn2 + cn + b

By substituting the values, we can solve for d, c, and b:

Solving this system of equations will give us the formula for the nth term.

b) 19, 15, 9, 1

The first differences are -4, -6, and -8. Again, the second differences are the same, indicating a quadratic sequence. Following the same process as above, we can solve the equation to find the formula for the nth term.

c) -2, -1, 1, 4

In this case, the first differences are 1, 2, and 3, while the second differences differ. This tells us that the sequence is not quadratic, but rather cubic. To find the formula for the nth term, we need to use a cubic formula instead.

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To find the formula for the nth term of a quadratic sequence, look for a pattern in the differences between consecutive terms. Sequence a) 15, 19, 25, 33 has the formula n^2 + 2n - 2. Sequence b) 19, 15, 9, 1 has the formula -n^2 + 4n + 15. Sequence c) -2, -1, 1, 4 has the formula n^2 - 3n - 2.

To find the formula for the nth term of a quadratic sequence, we need to look for a pattern in the differences between consecutive terms. Let's analyze each given sequence:

Sequence a) 15, 19, 25, 33:

The differences between consecutive terms are 4, 6, and 8. Notice that these differences are increasing by 2 each time. This indicates a quadratic sequence with a common second difference of 2. The formula for this sequence is n^2 + 2n - 2.

Sequence b) 19, 15, 9, 1:

The differences between consecutive terms are -4, -6, and -8. Again, these differences are decreasing by 2 each time. This indicates a quadratic sequence with a common second difference of -2. The formula for this sequence is -n^2 + 4n + 15.

Sequence c) -2, -1, 1, 4:

The differences between consecutive terms are 1, 2, and 3. Just like sequence a), these differences are increasing by 1 each time, indicating a quadratic sequence with a common second difference of 1. The formula for this sequence is n^2 - 3n - 2.

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Answer:

Step-by-step explanation:

Answer with explanation:

x        -7        -1     3     4       7    

f(x)     -11       1     9    11      17

Slope between two points

     [tex]m=\frac{1-(-11)}{-1+7}\\\\=\frac{9-1}{3-(-1)}\\\\=\frac{11-9}{4-3}\\\\=\frac{17-11}{7-4}\\\\=2[/tex]

Equation of line will be

  ⇒y-(-11)=2×[x-(-7)]

  →y+11=2×(x+7)

 →y+11=2x+14

 →2x-y+14-11=0

→2x-y+3=0

 →y=2x+3

Option B

[tex]\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=-5\\ n=10\\ a_{10}=13 \end{cases} \\\\\\ a_{10}=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies 2=d[/tex]

Answer:

Common difference = 2

Step-by-step explanation:

[tex]n^{th}[/tex] term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference.

Here first term is given as -5

           a = -5

Tenth term is 13

           n = 10

          [tex]n^{th}[/tex] term = 13

We have

       -5 + (10-1)d = 13

         9 d = 13 + 5

            9 d = 18

               d = 2

Common difference = 2

Answer:

Step-by-step explanation:

Diagonal =9cm

Diagonal of a square is  √2 x length of the side

 √2 x side =9

side =9/ √2

√2 =1.414

side =9 / 1.414 =6.364 cm

The side length of a square with a 9cm long diagonal can be estimated to be approximately 6.36cm using the Pythagorean theorem.

To answer your question about estimating the side length of a square with a 9cm long diagonal, we will make use of the Pythagorean theorem. The Pythagorean theorem is applied in a right-angled triangle and states that the square of the hypotenuse side (the side opposite the right angle, or in this case, our square's diagonal) is equal to the sum of the squares of the other two sides. In case of a square, these two sides are equal in length. So, if we call one of these sides 'a', we can write the theorem as a² + a² = 9². Solving this equation leads us to approximately 6.36cm as the side length of the square.

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Answer:

4(x +3)(x +4)

Step-by-step explanation:

First of all, recognize that each coefficient is a multiple of 4.

Factoring that out makes it easier to see that you need factors of 12 that add to give 7. Those are not hard to find as being 3 and 4. These numbers go into the binomial factors to give ...

... 4x^2 +28x +48 = 4(x^2 +7x +12) = 4(x +3)(x +4)

Answer:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

Step-by-step explanation:

We are given the following information in the equation:

[tex]4x^2 + 28x +48[/tex]

We have to factorize the given expression.

We will use the technique of splitting the middle term to factorize.

Factorization can be done in the following manner:

[tex]4x^2 + 28x +48\\\Rightarrow 4(x^2 + 7x + 12)\\\Rightarrow 4(x^2 + 4x + 3x + 12)\\\Rightarrow 4[x(x+4)+3(x+4)]\\\Rightarrow 4(x+3)(x+4)[/tex]

Hence, the given expression can be factorized as:

[tex]4x^2 + 28x +48 = 4(x+4)(x+3)[/tex]

(5q2 − r2s)(25q^4+5q^2r^2s+1r^4s^2)

To factor the expression, identify the difference of squares in the first part and the sum of cubes in the second part. Apply the relevant factoring formulas to obtain the fully factored form.

To factor the expression[tex](q^2 - r^2s) (q^4 + q^2r^2s + r^4s^2),[/tex] we must first recognize that the second part is a sum of cubes. The formula for factoring a sum of cubes is [tex]a^3 + b^3 = (a + b)(a^2 - ab +b^2)[/tex]. The first part, [tex]q^2 - r^2s,[/tex] can be recognized as the difference of squares, which factors as (q - rs)(q + rs). Therefore, after applying these patterns the factored form of the expression is:

[tex](q - rs)(q + rs)(q^2 + qrs + r^2s^2)[/tex]

Answer:

the answer is y=8

Step-by-step explanation:

i hope this help u

Answer:

40.5 g

Step-by-step explanation:

Find how much salt is in 450 g of a 9% salt solution.

Note that

450 g - 100%,

x g - 9%,

then

[tex]\dfrac{450}{x}=\dfrac{100}{9},\\ \\x=\dfrac{450\cdot 9}{100}=40.5\ g.[/tex]

If you evaporated all water from this solution, then you would get 40.5 g of salt.

Answer:

40.5g

Step-by-step explanation:

RSM anyone?

Answer: 24480

Step-by-step explanation:

just multiply the two numbers since 24 is distributing to 1020...24 times 1020

Answer:

the answer is 24480

Step-by-step explanation:

A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given fractions 7/8 and 13/15

Multiply 15 numerators and denominators to 7/8

(7/8) × 15/15 = (7 × 15/8)/15

⇒ 13.125/15

Since 13.125 > 13

Since A fraction will be bigger than another if for the same denominator the numerator is bigger.

So 7/8 > 13/15.

Hence " A fraction will be bigger than another if for the same denominator the numerator is bigger therefore fraction 7/8 will be bigger than 13/15".

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Answer:

The first one

Step-by-step explanation:

Hello.

X= −5/14 y

Step 1: Add -15x to both sides.

x−5y+ −15x= 15x+ −15x

−14x−5y=0

Step 2: Add 5y to both sides.

−14x −5y+5y= 0+5y

−14x=5y

Step 3: Divide both sides by -14.

−14x/−14= 5y/−14

x= −5/14 y

Have a nice day

Answer:

Step-by-step explanation:

7-9x=56

Answer:

C. 4x + y = 21

Step-by-step explanation:

(4 x 3) + 9

12 + 9 = 21

Answer:

It's C.

Step-by-step explanation:

It's right on edmentum. Also, just use substitution. Not that hard.

Answer:

Out of every 5 rectangles 2 shall be purple.

3 scarves have 3 times 5 rectangles.

Thus they shall be 3 times 2 that are purple.

Answer:

.23  ,1/5  , 1/8 ,.01

Step-by-step explanation:

.I will put them all in decimal form

.01 = .01

1/8 = .125

.23  = .23

1/5 = .2

largest to smallest

.23 >..2  < .125  < .01

Put them back in their original form

.23  >1/5  > 1/8  >.01

.23  ,1/5  , 1/8 ,.01

It is given that, Altitude above sea level =Positive Values

                                          =Positive Integer{1,2,3,4,5,6,7,8,.......}

Altitude below sea Level=Negative values

                                     =Negative Integer{-1,-2,-3,-4,-5,-6,.......}

Now, The situation given is

 A hiker in Death Valley stopping at an altitude of 0 feet

Zero(0)= The Point 0, means neither Positive nor Negative, that is additive Identity with respect to Addition of Integers.That is when two integers having Opposite sign, means additive Inverse of each other, are added together it yields Zero.

For example

-2 + 2=0

2 and -2 are Additive Inverse of each other.

The given expression is simplified as x² + 3x - 4.

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

((4x²+ 12x - 16) / (2x + 10)) / ((6x + 24) / (x ²+ 9x + 20))

It can be simplified as,

((4x²+ 12x - 16) (x ²+ 9x + 20)) / (2x + 10) (6x + 24)

Now, (4x²+ 12x - 16)  and  (x ²+ 9x + 20) can be factorised as,

4x²+ 12x - 16 = 4x²+ 16x - 4x - 16

                   = 4x(x + 4) - 4(x + 4)

                   = (4x - 4) (x + 4)

And, x ²+ 9x + 20 = x ²+ 5x + 4x + 20

                           = x(x + 5) +4(x + 5)                            = (x + 4) (x + 5)

Substitute the factors to get the expression as,

(4x - 4) (x + 4) (x + 4) (x + 5) /  (2x + 10) (6x + 24)

= (4x - 4) (x + 4) (x + 4) (x + 5) /  2 × 2(x + 5) (x + 4)

=  (4x - 4) (x + 4) / 4

= 4(x - 1) (x + 4) / 4

= (x - 1) (x + 4)

= x² + 3x - 4

Hence, the given expression can be simplified as  x² + 3x - 4.

Answer:

x = 27976.22021

Step-by-step explanation:

10x + .0085x = 280000

Combine like terms

10.0085x = 280000

Divide by 10.0085 on each side

10.0085x /10.0085= 280000/10.0085

x = 27976.22021

Answer:

trrtrtrtrtrtrtrtrt

Step-by-step explanation:

Answer:

3/2 or 1.5

Step-by-step explanation:To find the perimeter you need to multiply the four sides why the same number like: 3/8in(4)wich equal 3/2in or in decimal point 1.5 hope it helps. :)