Solve the equation by factoring. z2 − 6z − 27 = 0
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.
The interior angles formed by the sides of a hexagon have measures that sum to 720 degrees. What is the measure of angle F?
ln(2m 8th power) exapnad in logarithmic expression
The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie? Explain.
Final answer:
Ordered pairs with opposite signs for their coordinates are located in the second or fourth quadrants of a Cartesian plane, depending on the signs of the x and y-coordinates.
Explanation:
The coordinates of an ordered pair with opposite signs indicate its position in the coordinate plane. When the x-coordinate and y-coordinate have opposite signs, the ordered pair lies either in the second or fourth quadrant. This is because the sign of the x-coordinate is positive on the right side of the y-axis (first and fourth quadrants) and negative on the left side (second and third quadrants), and similarly, the sign of the y-coordinate is positive above the x-axis (first and second quadrants) and negative below it (third and fourth quadrants). Thus, if an ordered pair has coordinates with opposite signs, it lies in the quadrant where one axis is positive and the other is negative. For example, if the x-coordinate is positive and the y-coordinate is negative, the ordered pair will be in the fourth quadrant. Conversely, if the x-coordinate is negative and the y-coordinate is positive, it will lie in the second quadrant.
Landry is opening two savings accounts. He is opening the first account with an initial deposit of $500. The account will compound continuously each year at a rate of 3%.
He is opening the second account with an initial deposit of $300. The account will compound continuously each year at a rate of 5%.
Landry would like to know how long it will take for the balance of the two accounts to be equal.
Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.
There are two solutions and both are viable.
There is only one solution and it is viable.
There is only one solution and it is not viable.
There are no solutions.
Answer:
B. there is only one solution, and it is viable
Step-by-step explanation:
Use the euclidean algorithm to find
a.gcd(12, 18).
b.gcd(111, 201).
c.gcd(1001, 1331).
d.gcd(12345, 54321).
e.gcd(1000, 5040). f ) gcd(9888, 6060).
The Euclidean Algorithm is used to find the greatest common divisor (GCD) of two numbers, this method has been applied to find the GCDs of multiple pairs of numbers.
Explanation:The Euclidean Algorithm is basically a method to find the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers is the same as the GCD of the remainder when the larger number is divided by the smaller one.
gcd(12, 18): Using the Euclidean algorithm, 18 = 12*1 + 6. Now replace 18 with 12 and 12 with the remainder 6. So, 12 = 6*2 + 0. As we reached 0, our GCD is 6. gcd(111, 201): Apply the Euclidean algorithm, the GCD is 3. gcd(1001, 1331): The GCD is 11. gcd(12345, 54321): The GCD is 3. gcd(1000, 5040): The GCD is 40. gcd(9888, 6060): The GCD is 68. Learn more about Euclidean Algorithm here:
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Based in the graph, what is the initial value of the linear relationship
A)-4
B)-3
C)5/3
D)5
Answer:
D)5
Step-by-step explanation:
The initial value of the linear relationship is the value that exists in the "Y" axis when the "x" value is 0, as you can see in the graph, when the X value is 0, the Y value is 5, so the inital value of the linear relationship is 5.
If you wish to calculate this on an inequality, you just have to insert in the inequality 0 as the value for x, and you will get as a result the initial value.
When scholastic achievement test scores (sats) are sent to test-takers, the percentiles associated with scores are also given. suppose a test-taker scored at the 59th percentile on the verbal part of the test and at the 36th percentile on the quantitative part. interpret these results?
is 4,286 divisqble by 6
Helpp me graph thesse on a scatter plot sooo confused eee!! @musiclover helpp plzz lol
Answer:
1. The scatter plot does not show a linear model.2. Since the plotted data are all around the temperature of 10, the slope would be a horizontal line at 10. A horizontal line does not have any slope, this tell me that the average temperature stays an average of 10 no matter what the humidity level is.3. There is no vertical intercept shown.2nd page:1. yes, because there were 2 small clusters separated by a little bit of space.2. I think the location of the area the data came from may change the relationship between the variables.3. I think by switching the axis's the data may be grouped closer together since most of the data points are along a vertical line.
Step-by-step explanation:
Cameron used 1 3/4 ounces of hydrochloric acid in one experiment. She used 2 1/8 ounces of the acid in a second experiment. How much more acid did Cameron use in the second experiment?
Answer:
Amount required is [tex]x=\frac{3}{8}[/tex]
Step-by-step explanation:
Given : Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid in one experiment. She used [tex]2\frac{1}{8}[/tex] ounces of the acid in a second experiment.
To find : How much more acid did Cameron use in the second experiment?
Solution :
In one experiment,
Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid
i.e [tex]1\frac{3}{4}=\frac{7}{4}[/tex]
In second experiment,
She used [tex]2\frac{1}{8}[/tex] ounces of the acid.
i.e. [tex]2\frac{1}{8}=\frac{17}{8}[/tex]
Let x amount more she used then experiment 1 in experiment 2.
So, the equation became
[tex]\frac{7}{4}+x=\frac{17}{8}[/tex]
[tex]x=\frac{17}{8}-\frac{7}{4}[/tex]
[tex]x=\frac{17-14}{8}[/tex]
[tex]x=\frac{3}{8}[/tex]
Therefore, Amount required is [tex]x=\frac{3}{8}[/tex]
what is 231 scaled down by a factor of 1/10
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely.
An accountant was struck by lightening three times in his lifetime.
Possible and likely
Possible, but very unlikely
Impossible
Option B is the right answer.
Step-by-step explanation:
An accountant was struck by lightening three times in his lifetime. This event is Possible, but very unlikely.
We know that a probability near 0 means an unlikely event. Probability around 1/2 indicates an event that is neither unlikely nor likely. Similarly, probability near 1 indicates a likely event.
Here, in a lifetime the accountant was struck 3 times. If the average lifetime is 70 years, so probability becomes [tex]\frac{3}{70}= 0.04[/tex]. This is close to zero, indicating that the event is very unlikely.
And people are struck by lightening so it is a possible event.
Combining both, we get option B as the final answer.
Use the normal distribution of fish lengths for which the mean is 1111 inches and the standard deviation is 44 inches. assume the variable x is normally distributed. left parenthesis a right parenthesis(a) what percent of the fish are longer than 1212 inches? left parenthesis b right parenthesis(b) if 300300 fish are randomly selected, about how many would you expect to be shorter than 77 inches?
Tyler bought a large bag of peanuts at a baseball game. Is it more reasonable to say that the mass of the peanuts is 1 gram or 1 kilogram?
10,456 to the nearest tenth
The results of a survey are shown below.in the survey,12 students said that they would like to learn French.
8% of what is 2.8??
From a basket of mangoes, the king took 1/6, the queen took 1/5 of the remainder, the three chief princes to ¼, 1/3, and ½ of the successive remainders, respectively. the youngest child took the remaining 3 mangoes. how many mangoes were in the basket originally
Final answer:
The original basket contained 72 mangoes, determined by working backward from the known remainder of 3 after the sequential distribution between the king, queen, and princes.
Explanation:
From a basket of mangoes, the distribution among the royal family leads to a classic fractional subtraction problem. The solution involves working backward from the known remainder. The youngest child took the remaining 3 mangoes, which indicates that this was what was left after the king, the queen, and the three chief princes took their respective shares.
Let's denote the original number of mangoes as x. The king took 1/6 of x, leaving 5/6x. The queen then took 1/5 of the remainder (5/6x), leaving 4/5 * 5/6x = 4/6x or 2/3x. Successively, the three chief princes took 1/4, 1/3, and 1/2 of their respective remainders, each action further reducing the quantity of mangoes. The problem states that after these distributions, 3 mangoes were left, which were taken by the youngest child.
To find the original number of mangoes, we begin by denoting the final 3 mangoes as the remaining half after the last prince's share, work through the inverse operations for each prior transaction, and solve for x. Through this back calculation, we find that the original number of mangoes was 72.
The Science Club went on a two-day field trip. The first day the members paid $30 for transportation plus $18 per ticket to the planetarium. The second day they paid $85 for transportation plus $15 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer:
n(30 +18 +85 +15) , and if you slove the expression it'll be $148 dollars .
Step-by-step explanation:
What is the value of 1*2+ 3 / 6*5 - 4? Express as a fraction.
you roll a standard number cube. Find P(number greater than 5)
On a standard number cube there are 6 numbers and only one of them is greater than 5.
The probability of getting the one number out of 6 total numbers is 1/6
P( number greater than 5) = 1/6
Graph The Parabola. y=3x^2+18x+20
If 555 is divided by 2, what is the remainder? A) 1 B) 2 C) 3 D) 5
Step-by-step explanation:
If 555 is divided by 2 then the quotient is 277 and remainder is 1.
The lateral area of a cone is 555 pi cm^2. The radius is 15.1 cm. What is the slang height to the nearest tenth of a centimeter?
A- 36.8 cm
B- 11.7 cm
C- 83.8 cm
mike purchased two blankets at $44.99 each, one mattress for $59.00 and a sheet for $19.99. The sales tax rate is 5.75%. what is the total purchase price, including sales tax?
The total purchase price, including sales tax, for the two blankets, one mattress, and one sheet that Mike purchased is $178.69.
Explanation:To work out the total purchase price, including sales tax, for the items Mike purchased, first, we need to calculate the total cost of the blankets, mattress, and sheet before tax:
Two blankets: 2 × $44.99 each = $89.98One mattress: $59.00One sheet: $19.99Add these amounts together to find the subtotal:
$89.98 + $59.00 + $19.99 = $168.97
Next, we compute the sales tax. Convert the percent to a decimal by moving the decimal point two places to the left (5.75% becomes 0.0575), and then multiply by the subtotal:
0.0575 × $168.97 = $9.7161
Round the sales tax to the nearest cent: $9.72
Finally, add the sales tax to the subtotal to get the total purchase price:
$168.97 + $9.72 = $178.69
Therefore, the total purchase price, including sales tax, is $178.69.
Four sizes of scaled text are shown. What is the unknown scale size?
Answer:
font size of top line will be 1.067
Step-by-step explanation:
Scale factor between 4th line text size to the 3rd line text will be
= [tex]\frac{0.937}{0.878}=1.067[/tex]
Scale factor between 3rd line and second line will be = [tex]\frac{1}{0.937}=1.067[/tex]
Therefore, scale factor between 2nd and 1st text size will be = [tex]\frac{x}{1}=1.067[/tex]
x = 1.067
It reveals that the font size of top line will be 1.067
Find the directional derivative of f(x, y, z) = xy + yz + zx at p(1, −1, 7) in the direction from p to q(2, 4, 5). duf(1, −1, 7)
The directional derivative of f(x, y, z) = xy + yz + zx at p(1, -1, 7) towards q(2, 4, 5) is found by first calculating the unit vector in the direction from p to q, then the gradient of f at p, and calculating the dot product of the two vectors. The directional derivative comes out to be 16/ √30.
Explanation:The directional derivative of the function f(x, y, z) = xy + yz + zx at a point p(1, -1, 7) towards the point q(2, 4, 5) can be found by first getting the unit vector in the direction from p to q, then calculating the gradient of the function at p, and finally calculating the dot product of these two vectors (the unit vector and the gradient of the function).
First, calculate the unit vector u = (q - p) / |q - p|. That gives u = (1, 5, -2), and normalize it to get u = 1/ √30 (1, 5, -2).
Next, get the gradient of the function at p(1, -1, 7), which is the vector of first order derivatives. The partial derivatives of f(x, y, z) with respect to x, y, z are y+z, x+z, and x+y respectively. This gives the gradient vector at p as (-8, 8, 0).
Finally, the directional derivative is the dot product of the unit vector and the gradient, which comes out to be 1/ √30 * ((1*-8) + (5*8) + ((-2)*0)) = 16/ √30.
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A bearing, measured at 1.234 inches with a caliper, must be replaced. Since the bearings are sized in 64ths of an inch, find the closest fractional size.
Rewrite the equation below in standard form 2/3x=-5/2y+2
Answer:
4x + 15y = 12
Step-by-step explanation:
The standard form of a linear equation is Ax + By = C where A and B cannot be fractions and A is not negative. To write in standard form, move -5/2y to the other side of the equal sign. Then clear the denominators by multiplying the equation by 6.
2/3x=-5/2y+2
2/3x + 5/2y = 2
6(2/3x + 5/2y = 2)
4x + 15y = 12