Solve the equation by factoring. z2 − 6z − 27 = 0

Answers

Answer 1

The answer is x= 9 and -3

You must fine 2 number that multiply to equal -27 and add to equal -6

(x-9) (x+3)
Then equal the parts of the binomial to zero

x - 9 = 0
x + 3 = 0

You must get x by its self.
When you do so, you'll have the answer as -3 and 9

Answer 2

To solve the quadratic equation z² -6z - 27 = 0, factor it to get (z - 9)(z + 3) = 0. Using the Zero Product Property, we find that the solutions are z = 9 and z = -3.

Solving Quadratic Equations by Factoring

To solve the quadratic equation z ²
- 6z - 27 = 0 by factoring, we must find two numbers that add up to -6 and
multiply to -27. After identifying these numbers, we can factor the quadratic expression
into a product of two binomials and then apply the Zero Product Property to find the
values of z.

The two numbers that meet these criteria are -9 and 3, as (-9)*(3) = -27 and (-9)+(3) =
-6. Therefore, we can express the quadratic equation as:

(z - 9)(z + 3) = 0

By the Zero Product Property, we find the solutions to the equation by setting each
binomial equal to zero:

z - 9 = 0
z = 9

z + 3 = 0
z = -3

Thus, the solutions to the quadratic equation are z = 9 and z = -3. These are the z-values that satisfy the original equation.

Related Questions

Find the sum: (x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.

Answers

For this case we have the following polynomials:
(x5 - 3x4 + x2 - 4)
(5x4 + 3x2 + 2x + 1)
Adding we have:
(x5 - 3x4 + x2 - 4) + (5x4 + 3x2 + 2x + 1)
= x ^ 5 + x ^ 4 (-3 + 5) + x ^ 2 (1 + 3) + 2x + (-4 + 1)
Rewriting we have:
= x ^ 5 + 2x ^ 4 + 4x ^ 2 + 2x - 3
Answer:
The sum of the polynomials is:
x ^ 5 + 2x ^ 4 + 4x ^ 2 + 2x - 3

Use technology to determine an appropriate model of the data. (0,0), (1,3), (2,4), (3,3), (4,0)

f(x) = – x2 + 4x
f(x) = x2 - 4x
f(x) = - x2 + 4x - 1
f(x) = x2 - 4x + 1

Answers

A.

Each of the ordered pairs satisfies the expression.

Answer:

Option A.

Step-by-step explanation:

To determine an appropriate model of the data each data should satisfy the expression.

For function 1. f(x) = -x² + 4x

Now for each point

f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0

therefore the given points lie on the function.

For option 2

f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0

Therefore points do not lie on the function.

For Option 3.

f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1

Therefore the points do not satisfy the expression.

For option 4.

f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1

Therefore, the points do not satisfy the expression.

Option A. is the correct option.

Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.

Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?

Answers

The information you would need to create a two-variable equation is how much was her allowance and how much money did she have. Also you would need to know how many arcade games she played and how much each one cost and how many times she rode the Ferris wheel and how much each ride cost.

Hope this Helps!!

Answer:

To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

Step-by-step explanation:

Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain.

Answers

Gabriel and his sister are in apparent agreement. There is insufficient information to tell whether they are correct or not.

Gabriel's representation is a more compact form of his sister's representation, but they mean the same thing.*

_____
* In some computer applications, one gets a different result from computing 2.5x than from computing x + x + 0.5x. This has to do with the way numbers are represented in the computer and the way they are rounded during multiplication and/or addition. For the purposes of algebra, the expressions mean the same thing.

Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.

According to the question;

Gabriel representation is; 2.5x + 2y – 2.His sister's expression is; x + x + 0.5x + y + y – 2.

Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.

However, we must note that the information available is not sufficient to determine if both parties are correct or not.

Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.

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Peter makes $7,000 a month plus some extra commission he makes 6% of everything he sells if Peter sold $55,000 of jewelry this month what his salary this month

Answers

Comment
I'm taking this to mean that he does not have to sell above 7000 to start getting a commission. Furthermore, he makes 6% on the full 55000.

Formula
T = Base Salary + 6% Total Sales
T = Take home salary
Base Salary = 7000
Total Sales = 55000

Substitute and Solve
T = 7000 + 6% * 55000 Change the % to a decimal
T = 7000 + 6/100 * 55000
T = 7000 + 0.06 * 55000
T = 7000 + 3300
T = 10300 dollars.

Conclusion
His take home salary = 10300 dollars <<<< answer.

I need help on this please

Answers

Answer: the points that show the maximum and you have to draw are:

(0, 1.5); (2, 1.5); (4, 1.5);(6,1.5),...

Explanation:

1) formula given:

h(t) = 0.5 sin (πt + π/2) + 1

2) You want the points (t, h) where h is maximum.

3) The mamimum of 0.5 sin (πt + π/2) + 1 is when 0.5 sin (πt + π/2) is maximum, and the maximum of 0.5 sin (πt + π/2) is when sin (πt + π/2) is maximum.

4) Now, the maximum of the sine function is 1, so you must solve this equation:

sin (πt + π/2) = 1.

5) As you know, sine function is equal to 1 when the argument is π/2 + 2nπ

So, find the first positive value of t doing

πt + π/2 = π/2

⇒ πt = 0 ⇒ t = 0

So, the first solution is t = 0.

Since the periodicity is 2π, the same value is obtained for t = 0, 2, 4, 6, ... 2n

6) The corresponding height is the same for all those t:

h(0) = 0.5 sin ( 0×t + π/2) + 1 = 0.5×1 + 1 = 1.5.

7) Therefore the points that you have to draw are: (0, 1.5); (2, 1.5); (4, 1.5);(6,1.5)...

I attach a figure just in case you need more help to visualize the answer.

Graph the quadratic function
F(x)=3x^2+6x-24

Answers

For this case we have the following function:
F (x) = 3x ^ 2 + 6x-24
We observe that it is a quadratic equation.
The graph is therefore a parabola.
Its cut points are:
(-4, 0)
(2, 0)
Answer:
See attached image to see graph of the function

1¼ gallons equals how many pints?

Answers

Answer:

10 pints

Step-by-step explanation:

There are 8 pints in a gallon, so ...

(1.25 gal) × (8 pt/gal) = 10 pt

Mr zucco baked a total of 270 cupcakes and muffins. After ue sold 1/3 of the cupcakes and baked 18 more miffins, he had twice as many cupcakes as muffins. How many cupcakes and muffins did mr. Zucco bake to begin with?

Answers

Let:

c = cupcakes
m = muffins

total = 270

c/3 = 2m
c + m = 270

solving for the variables with 2 eqs 2 unknowns

m = 38.57 = 39
c = 231.43 = 231

less 18 muffins initially

21 muffins
231 cupcakes

When a number is decreased by 24% of itself the result is 171. What is the number?

Answers

let
x----------> original number

we know that
if a number is decreased by 24% of itself the result is
x*(100%-24%)/100%------> x*0.76
171=0.76*x
x=171/0.76---------> 225

the answer is
the number is 225

write (-5,2) and (-5,6) in standard form [if you can describe how to do this for the future]

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& 2~) % (c,d) &&(~ -5 &,& 6~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-2}{-5-(-5)}\implies \cfrac{6-2}{-5+5}\implies \stackrel{und efined}{\cfrac{4}{0}}[/tex]

now, an undefined slope, simply means a vertical line, check the picture below.

The music teacher has a list if 128 students who have signed up for music classes. The music teacher can register 6 students in each class. What is the LEAST number of classes needed for all the students to be registered in a class?

Answers

The least number of classes needed for all the students to be registered in a class is 21 classes.

128 divided by 6 is 21.3 so you will need at least 22 classes.

A 12 pack of soda is roughly $3.75. What is the cost per can of soda?

Answers

So you just need to divide the cost of 12 pack of soda by 12 pack of soda.

That would be $3.75 / 12 = $0.3125

So answer is $0.3125 per can of soda or you can round it to approximately $0.31 per can of soda.

Hope this helps.

QM Q6.) Write the slope-intercept equation of the function f whose graph satisifies the given conditions.

Answers

Greetings!

The equation of a line in slope-intercept form is:

y = mx + b

m is the slope
b is the y- intercept

What we need to do is to re-arrange 2x - 9y - 18 = 0. We wanna make it looks like y = mx + b

So, the equation is:

2x - 9y - 18 = 0

Subtract 2x - 18 from both sides

→ -9y = -2x + 18

Since we want y, we need to divide both sides by -9

[tex] \frac{-9y}{-9} = \frac{-2x + 18}{-9} [/tex]

Thus,

y = 2/9 x - 2 which is in the slope intercept form

Slope m = 2/9 and the y-intercept is = - 2

Given a line with slope m then the slope of a line perpendicular is:

[tex] m_{perpendicular} = - \frac{1}{m} [/tex]

[tex] m_{perpendicular} = - \frac{1}{2/9 } [/tex] = - 9/2

Thus,

The equation of the function is:

[tex]y = - \frac{9}{2} x - 2 [/tex]

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you!

Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.

5.2 × 1010

620,004

206,661

2730

Answers

The sum of n terms of a geometric sequence with first term "a" and common ratio "r" is given by
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
You have a=21, r=3, so the sum of 10 terms is
[tex]S_{10}=21\cdot \dfrac{3^{10}-1}{3-1}=620004[/tex]

The appropriate choice is the 2nd one:
620,004

The sum of the first 10 terms for the sequence given is 620,004.

What is Geometric sequence?

A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,

Sum of n terms of GP = aₙ = arⁿ-1 / r-1,

a₁ = 21

r = 3

So,

a₁₀ = 21 × 3¹⁰-1 / 3-1

a₁₀ = 21 × 29,524

a₁₀ = 620,004

Hence the sum is 620,004.

Learn more about geometric sequence, click;

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Hey can you please help me posted picture of question

Answers

A compound event is an event that consists of more than one simple event. The answer is option C. because option C. consists of two events, the rolling of one die followed by the rolling of another die. All other options are a single event.

i need help with this

Answers

8. The mean of the grades (74) is substantially below the median (88), so the distribution is not symmetrical. Of course, half the grades are below the median, just as half are above the median. However, the mean being 88-74 = 14 points below the median means that the lower half of the grades will have an average at least twice that much, or 28 points, below the median. The distribution of grades must extend quite a bit further to the left of the median than it does to the right. Hence ...
B. The distribution is skewed left.

9. It seems likely the distribution has a number of low grades pulling the average down. There certainly exists the possibility that at least one of them qualifies as an outlier by being more than 1.5 times the IQR below the first quartile. That rule, however, only applies when the distribution is relatively symmetrical, which this one is not. There does not appear to be any recommended way to describe an outlier when the distribution is skewed and has a long tail.*
TRUE: The distribution likely has an outlier.

_____
* Math instruction these days rarely recognizes such subtleties. Since it is probable that at least one value is well below the bottom quartile, I've shown my guess at the expected answer as TRUE. In a real set of grades, I expect the tail of the distribution to have enough low grades that they cannot be considered to be outliers.

The base of a triangular prism is an equilateral triangle with a perimeter of 15in. If the height of the prism is 4in, find the surface area.

Answers

we know that
surface area=2*[area of the base]+perimeter of the base*height
find the area of the base

is an equilateral triangle
b=15/3----> 5 in
applying the law of sines to find the area
Area=(1/2)*b²*sin 60°------> area=(1/2)*5²*sin 60°----> 10.8253 in²

alternative method to find the area of the equilateral triangle
find the h value
applying the Pythagoras theorem
h²=5²-2.5²-----> h=√18.75-----> h=4.33 in
area=b*h/2----> area=5*4.33/2----> 10.8253 in²

surface area=2*[10.8253]+15*4-----> 81.65 in²

the answer is
81.65 in²

a disk jockey wants to select five songs from a new CD that contains 12 songs. How many ways can a disc jockey choose 5 songs

Answers

Well this is a permutation/combination problem. If the order that the four songs is in does not matter then it will be a combination, if the order does matter it will be a permutation.

The formula for combinations is: n!/r!(n-r)! where n is the total number possible options and r is the number taken at a time. For this problem n = 12 and r = 5

12!/5!7! = 792 different possible combinations.

The formula for a permutation is n!/(n-r)! where n and r represent the same things as above.

12!/7! = 95,040 different possible permutations

The reason for more permutation than combinations is because if you have 12 songs think of them as 1,2,3,4,5,6,7,8,9,10,11,12. Under a combination songs 1,3,6,9 and 3,6,1,9 are the same, but in a permutation the order matters so these are both different possible outcomes.

[tex]\text {Number of ways} = C(12, 5) = \dfrac{12 \times 11 \times 10 \times 9 \times 8}{1 \times 2 \times 3 \times 4 \times 5} = 792[/tex]

Answer: There are 792 ways to pick 5 songs from 12 songs.

Identify the problem with the following poll.

A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.

correlation and causality

loaded questions

nonresponse

self interest

Answers

It is Nonresponse. We can infer that the entire population cannot be made.

Find the area of a rectangle with a length of (4x^2) and a width of (x+6)

Answers

Substitute the given values into the formula for area of a rectangle.
area = length*width
area = (4x^2)*(x +6)
Use the distributive property to eliminate parentheses.
area = 4x^3 +24x^2

An open box with a square base should be constructed. the bottom, should be constructed from a heavy duty cardboard that cost $3 per square inches and the sides from a medium duty cardboard that cost $2 per square inches. if the volume of the box must be 120 cubic inches, what should be the dimensions of the box in order to minimize the cost for the material?

Answers

I made several boxes with different sized square bases, such as 1x1, 2x2, 3x3, 4x4, 5x5, and 6x6. I calculated the heights of all of them, being 120, 30, 13.333, 7.5, 4.8, and 3.333 respectively. By using the $2/sq. in. for the sides and $3/sq. in. for the square base, I found that the box with the dimensions: 5x5x4.8 produced the most minimal cost at $267:

(5x4.8)x4 = 96 sq. in. x 2 = $192
5x5 = 25 sq. in. x 3 =$75

$192 + $75 = $267

Mary has been $50 to spend on T-shirts from an online store. there is $10 shipping and handling fee and each t-shirt cost $5 which inequality represents the number of t-shirts s Mary can buy the answer choices are 5S + 10 greater than equal to 50, 5S + 10 less than equal to 50, 10s + 5 greater than equal to 50, 10s - 5 greater than equal to 50, 5S - 10 greater than equal to 50

Answers

Hello there!
The inequality that represents this situation is 5S + 10 is less than or equal to 50.
The $10 is just a fee, and you don't have to multiply it by anything. However, when the problem says each it means that you have to multiply the given number.
Hope this helped!

In a right triangle, if the measures of the other two angles are 2x – 5 and 3x + 10, what are the measures of these two angles?

A. 30° & 60°

B. 29° & 61°

C. 50° & 40°

D. 51° & 39°

Answers

Sum of angles in a triangle = 180

2x – 5 + 3x + 10 + 90 = 180
5x + 95 = 180
5x = 85
x = 17

2x – 5 = 2(17) - 5 = 29
3x + 10 = 3(17) + 10 = 61

Answer: 29° and 61° (Answer B)

Answer: B. 29° & 61°

Step-by-step explanation:

Solve for e.

9e^2f=49

e=±√7f/3

e=±7√f/3

e=±7√f/3f

e=±√7f/3f

Answers

[tex]9e^{2}f=49[/tex]
Divide by the coefficient of e², multiply by f/f, then take the square root.
[tex]e^{2}=\dfrac{49}{9f}=\dfrac{49}{9f}\cdot \dfrac{f}{f}=\dfrac{49f}{9f^{2}}\\\\e=\pm \dfrac{\sqrt{7^{2}f}}{\sqrt{(3f)^{2}}}\\\\e=\pm \dfrac{7\sqrt{f}}{3f}[/tex]

The appropriate selection is ...
e = ±7√f/(3f)

The height of a free falling object at time t can be found using the function, h(t) = - 12t2 + 36t. Where h(t) is the height in feet and t is the in seconds. Find the time when the object hits the ground

Answers

Given that height of the object can be found using the function h(t)=-12t²+36t, the time taken for the object to hit the ground is calculated as follows:
At the time the object hits the ground, height h(t)=0. Substituting this value in the equation we get:
0=-12t²+36t
solving for t we obtain.
12t²=36t
12t=36
hence
t=4
thus the time taken for the object to hit the ground is 4 seconds

How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12

Answers

This is a problem regarding permutation.

[tex]P\left(3,3\right)=3!=3\times 2\times 1=6[/tex]

There are 6 different ways.

Answer:

Answer is 6 ways

Step-by-step explanation:

Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.

We have to find the number of ways these three can be visited.

Here this is a question of permutation since order matters.

There are 3 cities and these can be visited in 3P3 ways =3!

=3x2x1 =6 ways

There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.

When ordering a student desk priced at $69.00, the shipping charges are 6%. What is the total cost of the desk?

Answers

Since the desk is $69.00 and the shipping charges are 6%

69*.06= 4.14

Your tax would be $4.14 so,

$4.14+$69.00= A total of $73.14

Shipping charges = 6% x $69 = 0.06 x 69 = $4.14

Total cost = $69 + $4.14 = $73.14

Answer: $73.14

Hey can you please help me posted picture of question

Answers

The code contains 4 letters and 3 numbers

Number of ways to select a letter = 26
So, number of ways to select 4 letters = 26 x 26 x 26 x 26 = 26⁴

Number of ways to select a number = 6
So, number of ways to select 3 numbers = 6³

Number of key code combinations = 26⁴ x 6³ = 98706816

So, option C is the correct answer

Using the graph below, what are the common ratio and the general term equation, an, of the geometric sequence?

Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.

Answers

Given that the geometric series is given by:
an=a1(r)^(n-1)
where:
a1= first term
r=common ratio
n=number of terms:
from the graph, our sequence is:
-32,-24,-18,...
where:
a1=-32
a2=-24
a3=-18
thus
common ratio, r=-24/-32=3/4

thus the general form will be:
an=-32(3/4)^(n-1)

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