whats the minimum and maximum value of f(x)=3(x+8)^2−10
Answers
Answer:
(-8,-10)
Step-by-step explanation:
Rewrite (x+8)2(x+8)² as (x+8)(x+8).
f(x)=3((x+8)(x+8))−10
Expand (x+8) (x+8) using the FOIL Method.
Apply the distributive property.
f(x)=3(x(x+8)+8(x+8))−10
Apply the distributive property.
f(x)=3(x⋅x+x⋅8+8(x+8))−10
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
f(x)=3(x2+x⋅8+8x+8⋅8)−10
Move 8 to the left of x.
f(x)=3(x2+8⋅x+8x+8⋅8)−10
Multiply 8 by 8.
f(x)=3(x2+8x+8x+64)−10
Add 8x and 8x.
f(x)=3(x2+16x+64)−10
Apply the distributive property.
f(x)=3x2+3(16x)+3⋅64−10
Simplify.
Multiply 16 by 3.
f(x)=3x2+48x+3⋅64−10
Multiply 3 by 64.
f(x)=3x2+48x+192−10
Subtract 10 from 192.
f(x)=3x2+48x+182
The minimum of a quadratic function occurs at x=\(-\frac{b}{2a}\) If a is positive, the minimum value of the function is f (\(-\frac{b}{2a}\)).
Substitute in the values of aa and b.
x=−\(\frac{48}{2(3)}\)
x=-8
Replace the variable x with −8 in the expression.
f(−8)=3(−8)2+48(−8)+182
Y=-10
Therefore, the minimum value is (-8,-10) but if it is asking for just the y-value it would be -10.
Related Questions
y=-x+6
y = -3x + 1
What is the solution?
Answers
Answer: the solution is (-2.5,8.5)
Step-by-step explanation:
n=c-s solve for c, can anyone solve this?
Answers
Answer: sure ummm...
r
=
1
d
cs
Step-by-step explanation:
Answer: n+s=c
Step-by-step explanation:
n=c-s
+s +s
n+s=c
add s to both sides to get c by itself, and you end up with n+s=c
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 74.5 Mbps. The complete list of 50 data speeds has a mean of x= 17.34 Mbps and a standard deviation of s= 20.79 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]?
Answers
a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:
74.5 - 17.34 = 57.16 Mbps
b. To find the number of standard deviations, divide the difference by the standard deviation:
57.16 / 20.79 = 2.75
So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.
Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.
It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.
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What is the equation for the lines that passes through the coordinates (0,0) and (3.5,3.5)
Answers
The equation of the line which passes through the coordinates (0,0) and (3.5,3.5) is y = x.
The slope intercept form of a line is given by:-
y = mx + c
Where,
m represents the slope of the line
c represents the y -intercept
(x,y) represents the coordinates of each point on the line.
We also know the slope of the line will be:-
(3.5-0)/(3.5-0) = 3.5/3.5 = 1
Hence, m = 1
Putting (0,0) in y = mx + c, we get,
0 = m*0 + c
0 = 0 + c
c = 0
Hence, the equation of the line is given by:-
y = x
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Which equation is represented by the graph below?
Answers
Answer:
y=-1/2x+2
the y-intercept is at 2 and the slope is -1/2
meaning the y coordinates with move down 1 while the x coordinates will move 2 in a positive (right) direction
Select the correct answer.There are 6 adult chaperones, 21 female students, and 23 male students on a bus for a field trip.What is the probability that a randomly chosen person on the bus is an adult chaperone or a male student? A- 1/2 B- 29/50C- 2/3D- 1/29a whole explanation and answer will get marked brainiest
Answers
Let A be the event that we choose an adult chaperone and let B be the event that we pick a male student. Then, we want to calculate the following probability.
\(P(A\cup B)\)where the symbol between A and B means the union of events, which could be understood as "or". Using the properties of probability, we have
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)where the symbol on the right, between A and B, is the intersection, which can be understood as "and". Since we are going to pick only one person, it is impossible that we pick an adult chaperona and a male student. So,
\(P(A\cap B)=0\)So we have
\(P(A\cup B)=P(A)+P(B)\)Now, we want to calculate P(A) and P(B).
To calculate the probability of each event, we first count the number of possibilities that the event is true.
Note that since we have 6 adult chaperones, we have 6 possibilites such that the event A is true. Now, to calculate the probability of A, we simply divide this number by the total number of people on the bus (which is 50). So we get
\(P(A)=\frac{6}{50}\)In the same manner, for event B, we have a total of 23 possibilities such that the event B is true. Then
\(P(B)=\frac{23}{50}\)Finally, by replacing this values in the original expression, we have
\(P(A\cup B)=P(A)+(B)=\frac{6}{50}+\frac{23}{50}=\frac{29}{50}\)Can somebody PLEASE give me the right answer? I have been given 2 different answers 48 and 5.76 ALSO PLEASE SHOW THE WORK
Answers
Step-by-step explanation:
Not much work to show really. It's 36% of 16, which is 5.76
What is the solution to the equation below? Round your answer to two decimal places. log2 X= 1.7 A. x= 8.35 O x B. x= 13.60 O C. x = 10.56 = O D. X = 9.41
Answers
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given logarithmic expression
\(\log_4x=1.7\)STEP 2: Find the value of x
State the rule of logarithm that applies
\(if\text{ }\log_ab=c,b=a^c\)Apply the rule
\(\begin{gathered} \log_4x=1.7 \\ \therefore4^{1.7}=x \\ by\text{ simplification,} \\ 10.55606329=x \\ x\approx10.56 \end{gathered}\)Hence, the value of x is approximately 10.56
I need help with geometry pls
Answers
3) N is vertically opposite to the angle above => N equals the angles above
JK is parallel to ML
JN = NL
4) KJN and MLN have alternate angles => equal
5) JN = NL
angle JNK = angle LNM
angle KJN = angle MLN
A man is 40 years old and his son is 5years old. In how many years will the father be 3 times the age of his son.
Answers
12 1/2 years
Step-by-step explanation:
Let the unknown be n. Then 40+n = 3(5+n).
Performing the multiplication:
40+n = 15+3n
Isolate n and combine the constant terms:
25=2n, so n= 25/2 years
The coordinates of triangle ABC are (1,4), (4, 1) and (1,1). Find the new points of A'B'C' with a dilation centered at the origin and a scale factor of 2.
A' (___)
B' (___)
C' (___)
Draw the image on the Coordinate plane.
Answers
is 5x^7 monomial?
please help :(
Answers
Answer:
No, it is a binomial.
Step-by-step explanation:
Solve the following quadratic equation for all values of x in simplest form.
Answers
Answer:
x=3
Step-by-step explanation:
5(x^2 - 9) - 5 = -5
5x^2 - 45 = 0
5x^2 = 45
x^2 = 9
x = 3
Answer:
3
Step-by-step explanation:
I did the test
Hope this helps :)
A radio is #5400 when a discount of 14%is given for each.What is the cash price?
Answers
The cash price of one radio after a 14% discount is $4644.
The price of a radio is $5400. After giving a 14% discount for each radio, what will be the cash price?
Solution: The given price of the radio is $5400. The discount given on each radio is 14%.
Let's calculate the discount: Discount% = 14% Discount = (Discount%/100%) × Selling Price Discount = (14/100) × $5400 Discount = $756 Therefore, the discount on one radio is $756.
The cash price of one radio after a 14% discount is: Cash Price = Selling Price - Discount Cash Price = $5400 - $756Cash Price = $4644 Therefore, the cash price of one radio after a 14% discount is $4644.
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Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answers
Answer:
Step-by-step explanation:
Which of the following is a true statement?
Answers
Answer: T second one because I divided 108 divided by 9 and it equaled 12.
Step-by-step explanation:
I did not do the other steps but like source: Trust me.
Answer:
The answer is B
Step-by-step explanation:
108/9=12
What is the slope of the line that
passes through these two points?
(-4, 6)
(-4,-2)
Answers
Answer:
slope = undefined
Step-by-step explanation:
To find the slope of a line that passes between two points, use the slope formula, \(m = \frac{y_2-y_1}{x_2-x_1}\). Substitute the x and y values of (-4, 6) and (-4,-2) into the formula and simplify like so:
\(m = \frac{(-2)-(6)}{(-4)-(-4)}\\m= \frac{-2-6}{-4+4} \\m = \frac{-8}{0}\)
However, we can't divide by zero. This must mean that the slope of this line is undefined.
Help aspp please thank you
Answers
The equation of the line would be y = (-3/4)x + 5.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
The given equation is \(y=-\frac{3}{4}x-17\)
The required line is parallel to the given line.
and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4
And the required line passes through (8, -1)
so by using slope - point form of the line,
y - (-1) = (-3/4)(x - 8)
y + 1 = (-3/4)x - (-3/4)8
y + 1 = (-3/4)x + 24/4
y = (-3/4)x + (12/2 - 1)
y = (-3/4)x + 5
Hence, the equation of the line would be y = (-3/4)x + 5.
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In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem. PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34. The standard error for the difference in proportions is 0.011.
Researchers want to decrease the margin of error by adjusting the confidence level. Which confidence interval will have the smallest margin of error (MOE)?
a) 90% confidence interval
b) 95% confidence interval
c) 99% confidence interval
Answers
90% confidence interval will have the smallest margin of error.
What is global warming?
Long-term changes in temperature and weather patterns are referred to as climate change. These changes may be organic, but since the 1800s, human activity has been the primary cause of climate change. This is primarily because burning fossil fuels, such as coal, oil, and gas, releases gases that trap heat.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California.
In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem.
PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34.
The standard error for the difference in proportions is 0.011.
The correct option is (a).
As the confidence level decreases margin of error decreases.
So 90% confidence interval will have the smallest margin of error.
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Do the side lengths 4 5 and 10 form a triangle select the correct answer and reasoning?
Answers
The one of the inequalities is false, then the sides do not form a triangle.
Now, According to the question:
Side 1 of the triangle is = 4
Side 2 of the triangle is = 5
Side 3 of the triangle is = 10
Form a triangle :
To check if they form a triangle or not, we make use of triangle inequality theorem which states that; for sides a, b and c
a + b > c
a + c > b
b + c > a
So for sides 4, 5 and 10, we have:
4 + 5 > 10
4 + 10 > 5
5 + 10 > 4
Since the one of the inequalities is false, then the sides do not form a triangle.
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Express the internal shown on the number line in interval notation
Answers
The interval is from -10 to 8 on the number line.
What is a number line?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided. How a number is used, such as when graphing a point, depends on the question that goes with it.
What are negative numbers?
A negative number in mathematics represents the reverse. A negative number is any number that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.
in the given number line, we can observe that all the numbers from -10 to 8 are -8,-6,-2,0,2,4, and 6 (including -10 and 8).
thus the interval is from -10 to 8,
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PLEASE HURRRY I NEED HELP!
Answers
From the given angles of the triangle, it was possible to find the angle x=29°.
TrianglesTriangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.
Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.
For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three equal sides.
Regardless of its classification, the sum of the a triangle's angles will always be 180°.
The question gives two angles: 50° and 101°. And, it asks the value of angle x.
Therefore,
50+101+x=180
x+151=180
x=180-151
x=29°
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consider the function f(x) =xlnx.
let Tn be the nth degree Taylor approximation of f(2) about x=1. Find T1= T2= T3=
use 3 decimal places in your answer but make sure you carry all decimals when performing calculations
T3 is an over/under estimate of f(2)
If R3 is the remainder given by the Lagrange Remainder formula
R3<=
Answers
The first degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T1(x) = f(1) + f'(1)(x-1) = 0 + 1(x-1) = x-1. Therefore, T1(2) = 2-1 = 1.
The second degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T2(x) = T1(x) + f''(1)/2(x-1)^2. We have f''(x) = -1/x^2, so f''(1) = -1. Thus, T2(x) = x-1 - (1/2)(x-1)^2. Therefore, T2(2) = 2-1 - (1/2)(2-1)^2 = 1/2.
The third degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T3(x) = T2(x) + f'''(c)/3!(x-1)^3, where c is some number between 1 and x. We have f'''(x) = 2/x^3, so f'''(c) = 2/c^3.
Thus, T3(x) = x-1 - (1/2)(x-1)^2 + (2/3!c^3)(x-1)^3. To find an upper bound for the error R3 = f(2) - T3(2), we need to find the maximum value of |f'''(x)| on the interval [1,2].
We have |f'''(x)| = 2/x^3, which is decreasing on the interval. Therefore, the maximum value occurs at x = 1, and we have R3 <= (2/3!)(2-1)^3/1^3 = 2/3.
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A certain number is increased by 30 and the result is divided by two. The number obtained is three times the original number. Find the number.
Plss show working
Answers
Answer:
x = 6, PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
Let this number be x:
1) Increase x by 30 = x + 30
2) Divide the result by 2 = \(\frac{x+30}{2}\)
3) The number obtained is 3 times the original number =
\(\frac{x + 30}{2} = 3x\)
\({x + 30} = 6x\)
\(30 = 5x\)
\(x = \frac{30}{5}\)
\(x = 6\)
if x+1 is a factor of the polynomial 2x²-x+k, then find the value of k
Answers
Answer:
k = -3
Step-by-step explanation:
In this question, you would have to work backward. You know that the whole polynomial is 2x^2 - x + k and a factor of it is (x + 1). That will lead to you getting (2x + ?). It takes a little bit of guessing and checking to get the ? value, but in the end, you should find it. and figure out the other factor is (2x - 3). Multiplying (x + 1) and (2x - 3), you should get that the equation is 2x^2 - x - 3, so the value of k is -3.
how many legs do a spider have
Answers
Answer: 8
Step-by-step explanation:
Answer:
8 legs
This is no joke; spiders have 8 legs that they walk with, however, they also have a pair that they use sort of like hands. These front pair of legs are referred to pedipalps or just palps for short.
a poster of area 15360 cm215360 cm2 has blank margins of 10 cm10 cm wide on the top and bottom and 6 cm6 cm wide on the sides. find the dimensions that maximize the printed area. (use decimal notation. give your answers as whole or exact numbers.)
Answers
The dimensions that maximize the area are, 96cm and 84cm.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let the height of poster be h and breadth be b,
bh = 15630cm square........(1)
Height of the printed area=h-10-10 = h - 20
(decrement of 10 from top and bottom)
the breadth of the printed area b-6-6 = b-12
(decrement of 9 from both sides)
for maximum printed area:
A=(h-20)(b-12) should be maximum
\(A = (h - 20)(\frac{15360 }{h}-12)\)
From equation (1)
\(A = 15360-12h-\frac{307200}{h} +240\)
A = 15600 - 12h - (307200/h)
differentiate with respect to h (it should be=0)
\(\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}\)
\(12 = \frac{307200}{h} \\h = 160 cm\)
from equation (1),
\(bh = 15630cm^2\\b = 96cm\)
dimension of printed area,
= h - 20
= 160 - 20
= 140 cm
= b - 12
= 96 - 12
= 84 cm
Therefore, the dimensions that maximize the area are, 96cm and 84cm.
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Semielliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 8 meters above the center of the river (see the figure). Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch. Type the left side of the equation below.
Answers
The equation of the ellipse is (x2/100) + (y2/50) = 1. The left side of the equation is:x2/100 + y2/50 = 1The equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch is x2/100 + y2/50 = 1.
The semi-elliptical arch bridge is supported by an arch that is in the shape of the upper half of an ellipse. To find an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch, we have to use the given dimensions and the equation of the ellipse, which is (x2/a2) + (y2/b2) = 1. Here a is the length of the semi-major axis and b is the length of the semi-minor axis.Given,
The width of the river is 20 meters.The center of the arch is 8 meters above the center of the river. The semi-elliptical arch is symmetric. Hence, the center of the arch is (0, 8).Also, the half-span of the arch is 10 meters, and hence the value of a is 10 meters.
To find b, we have to find the height of the arch at a distance of 10 meters from the center (as the x-axis coincides with the water level).Using the equation of the ellipse, we get:(102/102) + (y2/b2) = 1b2 = (100 - y2)(x2/a2) + (y2/b2) = 1(20/2)2 = x2 + (y2/b2)(10)2 = y2 + (y2/b2)(100/b2) = y2 + y2b2b2 + y2 = 100b2 = 100/2b2 = 50
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20) How can professional development impact human capital and income potential?
Question 20 options:
Professional development provides training that can increase employee value (capital) and impact earnings.
Professional development costs the company money and may fail to increase an employee's abilities.
Professional development helps employees learn new skills but is unlikely to affect salaries.
Professional development is ineffective at increasing employee value but may help employees get a promotion.
Answers
Professional development provides training that can increase employee value (capital) and impact earnings. So, correct option is A.
Professional development refers to the process of acquiring new knowledge, skills, and competencies that enhance an employee's ability to perform their job duties more effectively.
This process can take various forms, such as attending conferences, workshops, or training sessions, taking online courses, or pursuing a degree. Professional development can impact human capital and income potential by providing employees with new skills and knowledge that make them more valuable to their employer.
This increased value can lead to higher salaries, bonuses, and better job opportunities. Employers often seek individuals who have relevant and updated skills, and employees who continually invest in their professional development can stand out from the competition.
Additionally, professional development can enhance an employee's overall job satisfaction, leading to increased productivity and retention rates. In conclusion, professional development is an important investment for both employees and employers, as it can lead to increased human capital and income potential.
So, correct option is A.
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Use the formula to find the surface area of the figure.
Answers
Answer:
1260 is the answer
Step-by-step explanation:
you solve for the area of the rectangle and multiply it by 3 because there are three sides so 17x20=340x3=1020 then, you solve for the area of a triangle which is 1/2 x base x height so, 1/2 x 16 x 15 = 120 then you multiply that by 2 since there are 2 triangles so 120 x 120=240 finally, you add 1020+240 = 1260