Given the equation f(x) = (x + 3)2 – 8, fill in the blanks:
Axis of symmetry: x =
Vertex:( , )
Number of real solutions:
Answers
In your equation, h = -3 and k = -8.
Axis of symmetry: x = -3
Vertex: (-3, -8)
Number of real solutions: 2
Final answer:
This detailed answer explains the axis of symmetry, vertex, and number of real solutions for the given quadratic equation.
Explanation:
Given the equation f(x) = (x + 3)² – 8
Axis of symmetry: x = -3
Vertex: (-3, -8)
Number of real solutions: 1
Related Questions
Professor smith conducted a class exercise in which students ran a computer program to generate random samples from a population that had a mean of 50 and a standard deviation of 9 mm. each of smith's students took a random sample of size n and calculated the sample mean. smith found that about 68% of the students had sample means between 48.5 and 51.5 mm. what was n? (assume that n is large enough that the central limit theorem is applicable.)
Answers
-1 is (48.5 - 50)/(9/sqrt n)
-9/sqrt n is -1.5
n is (9/1.5²) is 36
when xbar is 51.5
+1 is (51.5 - 50)/(9/sqrt n)
9/sqrt n is1.5
n is (9/1.5)² is 36
Using the Normal distribution, the Empirical rule and the Central limit theorem, it is found that n is 36.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The empirical rule states that 68% of the measures are within 1 standard deviation of the mean.The central limit theorem states that for sampling distribution of sample means of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem, since 68% of the students had sample means between 48.5 and 51.5 mm, we have that:
When X = 51.5, Z = 1.When X = 48.5, Z = -1.Using one of them, we can find the standard error. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1 = \frac{51.5 - 50}{s}[/tex]
[tex]s = 1.5[/tex]
Then, since [tex]\sigma = 9[/tex], the sample size is found solving the following equation:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.5 = \frac{9}{\sqrt{n}}[/tex]
[tex]1.5\sqrt{n} = 9[/tex]
[tex]\sqrt{n} = \frac{9}{1.5}[/tex]
[tex](\sqrt{n})^2 = (\frac{9}{1.5})^2[/tex]
[tex]n = 36[/tex]
n is 36.
A similar problem is given at https://brainly.com/question/13002303
Is -6.175 is an irrational number?
Answers
Any number you can write completely is a rational number.
Any number with a repeating decimal fraction is also a rational number.
___
Any number that goes on forever without repeating is an irrational number. These are usually represented symbolically (because they cannot be written "exactly" any other way). These include such numbers as √2, π, e, ∛(-4), and an infinite number of others.
What is the value of the function f(x)= -x+4 when x= -2?
A) 6
B) -6
C) -2
D) 2
Answers
Substitute x = -2 to the equation:
f(-2) = -(-2) + 4 = 2 + 4 = 6
Answer: A) 6
Hope this helps!
Please rate brainliest!
PLZ HELP ASAP LAST CIRCLES
Answers
70 + 90 + 90 + O = 360
O = 110 degrees.
When you agree to pay a car dealer for the use of a new car during a set period of time for a set amount of money and you have to return it at the end of that period of time, you are _____
Answers
Vehicle leasing is the leasing (or the use) of a motor vehicle for a fixed period of time at an agreed amount of money for the lease. It is commonly offered by dealers as an alternative to vehicle purchase but is widely used by businesses as a method of acquiring (or having the use of) vehicles for business, without the usually needed cash outlay. The key difference in a lease is that after the primary term (usually 2, 3 or 4 years) the vehicle has to either be returned to the leasing company or purchased for the residual value.
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%. If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answers
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
y = A * (B) ^ t
Where:
A: initial population.
B: annual exchange rate.
T: Time in years.
Then the equations of the system that must be used to find the time in which both are equal are:
1, 3,00,000 * (1-0,038) ^ t for the type of insect A
2, 1 00 000 * (1-0,046) ^ t for the type of insect B.
A factory's worker productivity is normally distributed. one worker produces an average of 77 units per day with a standard deviation of 22. another worker produces at an average rate of 66 units per day with a standard deviation of 19.
a. what is the probability that in a single day worker 1 will outproduce worker 2?
Answers
The probability that worker 1 will outproduce worker 2 in a single day is approximately 0.352 or 35.2%.
To find the probability that worker 1 will outproduce worker 2 in a single day, we need to compare their production rates using their respective means and standard deviations.
Let X be the production of worker 1 and Y be the production of worker 2. We are interested in finding P(X > Y).
Given:
Worker 1: X ~ N(77, 22^2)
Worker 2: Y ~ N(66, 19^2)
First, we standardize the variables:
Z1 = (X - 77) / 22
Z2 = (Y - 66) / 19
Now, we find P(X > Y) = P(X - Y > 0):
= P((X - 77) - (Y - 66) > 0)
= P((X - Y) > (77 - 66))
Now, we find the mean and standard deviation of the difference:
Mean of (X - Y) = 77 - 66 = 11
Standard deviation of (X - Y) = sqrt(22^2 + 19^2) = sqrt(484 + 361) = sqrt(845) ≈ 29.07
Now we standardize the difference:
Z = (11 - 0) / 29.07 ≈ 0.378
Finally, we find the probability using the standardized normal distribution table:
P(Z > 0.378) ≈ 0.352
So, the probability that worker 1 will outproduce worker 2 in a single day is approximately 0.352 or 35.2%.
the probability that Worker 1 will outproduce Worker 2 in a single day is approximately 0.7202 or 72.02%.
To find the probability that Worker 1 will outproduce Worker 2 in a single day, we can use the z-score formula for normal distributions.
The z-score formula is given by:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
- ( X ) is the value we want to find the z-score for (in this case, Worker 1's productivity).
- [tex]\( \mu \)[/tex]is the mean (average) productivity.
- [tex]\( \sigma \)[/tex] is the standard deviation.
For Worker 1:
- [tex]\( X_1 = 77 \)[/tex] units per day (average productivity)
- [tex]\( \mu_1 = 77 \)[/tex]units per day (average productivity)
- [tex]\( \sigma_1 = 22 \)[/tex] units per day (standard deviation)
For Worker 2:
-[tex]\( X_2 = 66 \)[/tex]units per day (average productivity)
- [tex]\( \mu_2 = 66 \)[/tex]units per day (average productivity)
- [tex]\( \sigma_2 = 19 \)[/tex] units per day (standard deviation)
First, we find the z-score for Worker 1's productivity relative to Worker 2's productivity:
[tex]\[ z = \frac{{X_1 - \mu_2}}{{\sigma_2}} = \frac{{77 - 66}}{{19}} = \frac{{11}}{{19}} \approx 0.579 \][/tex]
Next, we look up the z-score in the standard normal distribution table or use a calculator/tool that can calculate probabilities from the standard normal distribution. The z-score of 0.579 corresponds to a probability of approximately 0.7202.
Therefore, the probability that Worker 1 will outproduce Worker 2 in a single day is approximately 0.7202 or 72.02%.
Solve the inequality, then identify the graph of the solution. 2x – 1 > x + 2
Answers
2x - 1> x + 2
To solve it, we must clear the value of x.
Clearing x we have:
2x - x> 1 + 2
x> 3
Therefore, the solution is given by:
(3, inf)
Answer:
(3, inf)
See attached image.
The answer would be
B)
PLZ HELP ASAP TANGENTS OF A CIRCLES PROBLEMS
Answers
AO = AB + OB
AB = 8
OB = Radius of circle = 5
So,
AO = 8 +5 = 13
The tangent of the circle is at 90 degrees to its radius. So we can say that triangle ACO is a right angled triangle, with side AO the hypotenuse.
Using the Pythagorean theorem we can find the length of tangent AC.
13² = AC² + 5²
AC² = 169 - 25 = 144
AC = 12
So, the length of side AC is 12
Tumblr's stock price is $38 per share. Anjie purchased 600 shares. Assuming a broker's commission of $0.10 per share to purchase the 600 shares, what was Anjie's total cost? A. $22,860 B. $22,740 C. $23,400 D. $22,800
Answers
Anjie's total cost for purchasing 600 shares of Tumblr stock at $38 per share plus a broker’s commission of $0.10 per share is $22,860. Hence, correct option is A $22,860.
To determine the total cost of Anjie’s purchase, follow these steps:
First, calculate the purchase cost of the shares:600 shares* $38 per share = $22,800.
2. Next, calculate the broker’s commission:
600 shares* $0.10 per share = $60.
3. Add the purchase cost and the broker’s commission to get the total cost:
$22,800 + $60 = $22,860.
Thus, Anjie's total cost is $22,860 which corresponds to option A.
Suppose a ⊆ c, and b and c are disjoint. prove that if x ∈ a then x ∈/
b.
Answers
A country's population in 1990 was 59 million. In 2002 it was 63 million. Estimate the population in 2018 using exponential growth formula. Round your answer to the nearest million
Answers
P = new population
A = starting population
k is a constant
and t is number of years.
e is a logarithm function
using the 2 known years
we know 2002-1990 = 12 years
the population in 2002 was 63 million, population in 1990 was 59 million
so using the above equation we can solve for k:
63 = 59e^k12
divide both sides by 59:
63/59 = e^k12
1.06779 = e^k12
find logorithm of left side to get rid of the e on the right side:
ln 1.06779 = k12
0.06559 = k12
divide both sides by 12 for k:
k = 0.06559 / 12 = 0.00546644
now we want to find population in 2018
2018 - 1990 = 28 years
so now t = 28 using the same formula we have:
P = 59e^(0.00546644*28)
P = 68.758 million
rounded to nearest million = 69 million people
Jenna bought n notebooks which cost 5 dollars each, and 3 pens which cost r dollars each. How much money did she spend?
Answers
5n (this is the amount she spent on notebooks) + (and) 3r (this is the amount she spent on pens)
5n + 3r would show how much money she spent. If you know how many notebooks she bought and how much each pen costs, you would multiply these numbers by the 5 and the 3 and add them.
*Please help, will thank and award brainliest*
Which costs are paid by the origination fee?
A. Title search
B. Attorney and notary fees
C. Credit check and administrative costs associated with loan processing
D. Property appraisal
Answers
for apex!!
Answer:
The answer "attorney and notary fees" made me get the question wrong on brainly. The correct answer it showed me after I got it wrong was C. Credit check and administrative costs associated with loan processing
Step-by-step explanation:
Stefano calculated the mean absolute deviation for the data set 32, 4, 12, 40, 20, and 24. His work is shown below. Step 1: Find the mean. mc006-1.jpg Step 2: Find each absolute deviation. 10, 18, 10, 18, 2, 2 Step 3: Find the mean absolute deviation. mc006-2.jpg What is Stefano’s error? Stefano should have divided by 5 when finding the mean. Stefano found the absolute deviation of 20 incorrectly. Stefano should have divided by 6 when finding the mean absolute deviation. Stefano did not find the correct value for the mean.
Answers
To find the mean, you will find the sum of all the numbers and divide by how many numbers there are.
Mean: 4 + 12 + 20 + 24 + 32 + 40 = 132
132/6 = 22
Mean: 22
To find the mean absolute deviation, you find how far away each of the numbers are from the mean. Find the sum of these and divide by the same number of numbers.
(22 - 4) + (22-12) + (22-20) +(24 - 22) + (32-22) + (40-22)
18 + 10 + 2 + 2 + 10 + 18 = 60
60/6 = 10
The MAD is 10.
I think the correct answer is that Stefano should have divided by 6 when finding the mean absolute deviation.
Answer:
Stefano should have divided by 6 when finding the mean absolute deviation. ed quiz correct
Step-by-step explanation:
Two numbers rolled can be added to get a sum. Find P(sum is even.)
Answers
You get an even sum only if you sum two numbers that are both even or both odd, therefore the outcomes wanted are two: EE and OO.
Therefore:
P(sum is even) = 2 / 4 = 0.5
Hence, there is a 50% probability that, when you roll two numbers, their sum will be even.
how do you know if two lines are parallel?
Answers
Hope this helps/works.
Amber believes triangle ABC and triangle GFE are congruent. She has recorded the measures of some of the angles and the lengths of some of the sides in the triangles below.
What additional measurement would support Amber’s hypothesis?
a.The measure of c is 32
b.The measure of c is 40
c.The measure of c is 50
d.The measure of c is 90
Answers
b. The measure of c is 40.
_____
In actual fact, the triangles not only are not congruent, they cannot exist. The total of sides FG and FE (82 cm) is less than the length of side GE (38 in). 82 cm is about 32.3 inches, about 5.7 inches too short.
Even if you overlook the units problem, the sum of squares of the sides of the triangle is 32² +38² = 2468, somewhat short of 50² = 2500. That is, the largest angle is slightly more than 90°. It is closer to 90.754° ≈ 91°.
You can label a diagram any way you want, but that doesn't mean the numbers are consistent or sensible.
Answer:
B
Step-by-step explanation:
Tom shoveled 12.5 yards of sand in 2.5 hours. At that rate how many yards did he shovel in one hour?
Answers
HELP ME PLEASE!! ASAP!!
Estimate the size of a crowd at an outdoor concert venue that occupies a rectangular space with dimensions of 300 feet by 500 feet (to the nearest whole number). Assume that 5 people occupy a square measuring 5 feet by 5 feet.
A. 15,000 people
B. 20,000 people
C. 25,000 people
D. 30,000 people
Answers
A1 = (300) * (500)
A1 = 150000 feet ^ 2
The area occupied by 5 people is:
A2 = (5) * (5)
A2 = 25 feet ^ 2
Then, we can make the following rule of three:
5 --------> 25
x --------> 150000
Clearing x we have:
x = (150000/25) * (5)
x = 30000
Answer:
D. 30,000 people
from the sum of 5 – 9i and -4 + 7i, subtract 14 – 3i. brainly
Answers
Combine like terms; two negatives make a positive when you remove parentheses
= (5 + -4 + -14) + (-9i + 7i + 3i)
= -13 + 1i or -13 + i
ANSWER: -13 + i (first choice)
Hope this helps! :)
9/4x-1/2y =-3 x and y intercept form
Answers
Solve for y.
-1/2y = -3 - 9/4x
y = 6 + 4.5x
y intercept = 6
Solve for x.
9/4x = -3 + 1/2y
x = -1 1/3 + 0.2y
x intercept = -1 1/3
The x and y intercepts of the equation 9/4x - 1/2y = -3 are -4/3 and 6 respectively. These were calculated by separately setting the x and y to zero and solving for the other variable.
Explanation:To find the x and y intercepts of the equation 9/4x - 1/2y = -3, we need to set each of the variables x and y to zero separately and solve for the other variable.
Set y = 0 in the equation for the x-intercept. This gives us 9/4x = -3, and solving for x, we get x = -4*3/9 = -4/3.
For the b, set x = 0 in the equation. This gives us -1/2y = -3, and solving for y, we get y = 2*3 =6.
So the x-intercept and y-intercept of the equation are -4/3 and 6 respectively.
Find out more about X and Y Intercepts here:https://brainly.com/question/32051056
#SPJ2
Which solution to the equation (1/x-1)=(x-2/2x^2 -2) is extraneous?
a. x=1 and x=-4
b. nether x=1 or x=-4
c. x=1
d. x=-4
Answers
The appropriate choice is ...
c. x=1
_____
This can be solved without extraneous solutions by subtracting the right side.
(2(x +1) -(x -2))/(2(x -1)(x +1)) = 0
(x +4) = 0 . . . . . . . . . . . . . . . . . . . . . multiply by the denominator
x = -4 . . . . . . . . . . . . . . . . . . . . . . . . subtract 4
express 15 x^1/3y^1/5 using a radical
Answers
[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------[/tex]
[tex]\bf \cfrac{15x^{\frac{1}{3}}}{y^{\frac{1}{5}}}\qquad \begin{cases} \frac{1}{3}=\frac{1\cdot 5}{3\cdot 5}\\ \qquad \frac{5}{15}\\\\ \frac{1}{5}=\frac{1\cdot 3}{5\cdot 3}\\ \qquad \frac{3}{15} \end{cases}\implies \cfrac{15x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{\sqrt[15]{x^5}}{\sqrt[15]{y^3}} \\\\\\ 15\sqrt[15]{\frac{x^5}{y^3}}[/tex]
Answer:
[tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex]
Step-by-step explanation:
We have been given an expression [tex]15x^{\frac{1}{3}}y^{\frac{1}{5}[/tex]. We are asked to express our given expression using a radical.
Using fractional exponent rule [tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex], we can write terms of our given expression as:
[tex]15\cdot\sqrt[3]{x^1}\cdot \sqrt[5]{y^1}[/tex]
[tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex]
Therefore, our required expression would be [tex]15\cdot\sqrt[3]{x}\cdot \sqrt[5]{y}[/tex].
10 POINTS
The graph below shows the price, y, in dollars, of different amounts of pounds of cheese, x: A graph titled Cheese Prices shows Number of Pounds on x axis and Price in dollars on y axis. The scale on the x axis shows numbers from 0 to 12 at increments of 2, and the scale on the y axis shows numbers from 0 to 72 at increments of 12. A straight line joins the ordered pairs 0, 0 and 12, 72 Which equation best represents the relationship between x and y? y = x + 6 y = 12x y = x + 12 y = 6x
Answers
y = kx
You are given the point (12, 72), so you know
72 = 12k
6 = k . . . . . . . divide by 12
Then the equation of the line is ...
y = 6x
The answer to the question is y=6x
Find the value of x when 5-x=1/2x+4
Answers
Answer:
2/3
Step-by-step explanation:
which of the following is the maximum value of the function y=-2x^2+5
Answers
Now multiplying -x² by 2 stretch it vertically, however 2 times 0 is still 0 so maximum value is still 0.
Now we add it by 5 which makes it shifts 5 units up, so this affects maximum value.
So everything will be shifted 5 units up, so new maximum would be 5.
Final answer: 5
Hope this helps.
Find the value of -7 + (-9) + 11 + 8
Answers
-7-9+11+8
Simplify:
-16 + 19 = 3
The value is 3
Given z, find |z| -4+5i
Answers
|z| = √41
Multiply 3i(−1 + 2i). What is the simplified version written in standard form, a + bi, where a and b are real numbers?
Answers
3i (-1) + (2i)(3i) Look at the first set of brackets around the -1
-3i + 6i^2 But i^2 = - 1[ I hope that's the way you are using it]
-3i - 6 or -6 - 3i or -3(2 - i) <<<<< answer