Over what interval is the function decreasing? f(x)=(3−x)^2 + 5
Answers
Answer: It decreases on the interval (-infinity, 3)
This is the same as saying -infinity < x < 3, or simply x < 3
=============================================================
Work Shown:
f(x) = (3−x)^2 + 5
f(x) = (-x+3)^2 + 5
f(x) = (-1(x-3))^2 + 5
f(x) = (-1)^2*(x-3)^2 + 5
f(x) = 1(x-3)^2 + 5
The last equation is in the form y = a(x-h)^2 + k
We have a = 1, h = 3 and k = 5
The vertex is (h,k) = (3,5)
Since 'a' is positive, this means the function decreases on the left and increases on the right (forming a parabola that opens upward). See below.
So the function is decreasing when x < 3, which represents everything to the left of the vertex.
We can expand that out to -infinity < x < 3 which converts to the interval notation (-infinity, 3)
Related Questions
Calculate the total population increase of South Africa from 2001 Difference You may use the following formula: Increase = 2001 Population Calculate the total population of KZN in 2021. Identify the province with the lowest population in 2011. Write down the 2011 total population of South Africa in words.
Answers
the lengths of two sides of a right triangle are 12 inches and 15 inches.What is the difference between the two possible lengths of the third side of the triangle
Answers
Answer:10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
Applying the Pythagoras Theorem
Find the length of the hypotenuse
substitute
Second case
The given lengths are one leg and the hypotenuse
so
Applying the Pythagoras Theorem
Find the length of the other leg
substitute
Find the difference between the two possible lengths of the third side of the triangle
so
Answer:
The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.
Step-by-step explanation:
We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.
And we want to find the difference between the two possible lengths of the third side.
In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+(15)^2=c^2[/tex]
Solve for c:
[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]
In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+b^2=(15)^2[/tex]
Solve for b:
[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]
Therefore, the difference between the two possible lengths for the third side is:
[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]
d) The Princess was allowed to climb trees.
e)
Hector lived a lonely life in the King's castle.
Answer these questions in one or two words only.
a) Who first discovered that the Princess had climbed up a tree?
Answers
Hector is the one who discovered
in the diagram, the measure of angle 3 is 105°
which angle must also measure 105°?
A.1
B.4
C.6
D.8
Answers
Answer:
it's angle 1.
Reason:
vertically opposite angles are equal
A person walks 1/6 mile in 1/18 hour.
The person's speed is _ miles per hour.
Answers
This Is What I Got!
Hope This Helps! :)
Have A Good Day!!
And If You Can I Wouldn't Mind A Brainliest! :))
Answer:
Divide 1/6 miles to 1/12hour since u wanna find our miles per hour
So it’ll be : 1/6 / 1/12
= 1/6 x 12/1
= 2 miles
Find the value of x° in rhombus ABCD.
Answers
How many dimensions does a plane have?
O
A. Three
о
B. Zero
O C. Two
D. One
Answers
A Plane does not have one dimensions.
What is Plane?A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalisation of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.
A plane doesn't only have one dimension, though. The two dimensions of a plane.
A plane is a flat, infinitesimally long two-dimensional surface.
The plane can occasionally be extended into three dimensions.
Consequently, a plane has more than one dimension.
Learn more about Plane here:
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Can you help me with this please (finals)
Answers
Answer:
around 90 cm because that measure is equal to 180 you divide into 2 so the answer is 90
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still water and the rate of the current.
Answers
Step-by-step explanation:
Given that,
A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,
We know that,
Speed = distance/time
The rate while moving downstream[tex]=\dfrac{60}{3}=20\ mph[/tex]
The rate while moving upstream [tex]=\dfrac{60}{5}=12\ mph[/tex]
The rate of the boat in still water is the average of these:
[tex]v_s=\dfrac{20+12}{2}=16\ mph[/tex]
The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph
Hence, this is the required solution.
Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?
Answers
Answer:
[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]
[tex](b)\ t = 6[/tex]
[tex](c)\ t = 1.7[/tex]
Step-by-step explanation:
Given
[tex]G_0 = 100[/tex] --- initial
[tex]G(1) = 120[/tex] --- after 1 year
[tex]r \to rate[/tex]
Solving (a): The expression for g
Since the rate is constant, the distribution of G follows:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(1) = 120[/tex] implies that:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]120 = G_0 * e^{r*1}[/tex]
Substitute [tex]G_0 = 100[/tex]
[tex]120 = 100 * e^{r[/tex]
Divide both sides by 100
[tex]1.2 = e^{r[/tex]
Take natural logarithm of both sides
[tex]\ln(1.2) = \ln(e^r)[/tex]
[tex]0.1823 = r[/tex]
[tex]r = 0.1823[/tex]
So, the expression for G is:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(t) = 100 *e^{0.1823t}[/tex]
Solving (b): t when G(t) = 300
We have:
[tex]G(t) = 100 *e^{0.1823t}[/tex]
[tex]300 = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]3 = e^{0.1823t}[/tex]
Take natural logarithm
[tex]\ln(3) = \ln(e^{0.1823t})[/tex]
[tex]1.099 = 0.1823t[/tex]
Solve for t
[tex]t = \frac{1.099}{0.1823}[/tex]
[tex]t = 6[/tex] --- approximated
Solving (c): When there will be no grass
Reduction at a rate of 80 tons per year implies that:
[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]
To solve for t, we set G(t) = 0
[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]
Rewrite as
[tex]80t = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]0.8t = e^{0.1823t}[/tex]
Take natural logarithm of both sides
[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]
[tex]\ln( 0.8t) = 0.1823t[/tex]
Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]
[tex]t = 1.7[/tex]
A family uses 15 gallons of milk every 3 weeks. At that rate, about how many gallons of milk will they need to purchase in a year’s time?
Give your answer as a whole number.
They will need to purchase
Answers
Answer:
15 gallons of milk at 3 week
15/3= 5
for a month 5 * 4 =20
in a year 12 * 20 = 240
Step-by-step explanation:
What is the slope of the line?
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
m = (7/4)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{The slope formula is rise over run.}}\\\\m=\frac{\text{Rise}}{\text{Run}}\\\\m=\frac{y_2-y_1}{x_2-x_1}\\-------------\\(x_1,y_1) \text{ and } (x_2,y_2) \text{ are two points that are on the line.}[/tex]
⸻⸻⸻⸻
The line passes through the points (3,4) and (-1, -3).
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Slope:}}\\\\\rightarrow m = \frac{-3-4}{-1-3}\\\\\rightarrow m=\frac{-7}{-4}\\\\\rightarrow m=\boxed{\frac{7}{4}}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The height of a square pyramid with a that has 12 cm edges and a lateral area of 240cm sq.
Answers
Answer:
The height of the pyramid = 8 cm
Step-by-step explanation:
Given that,
The edges of a pyramid, a = 12 cm
The lateral area of a pyramid, A = 240 cm²
The formula for the lateral area of a square pyramid is given by :
[tex]A=a\sqrt{a^2+4h^2}[/tex]
Where
h is the height
Squaring both sides,
[tex]A^2=a^2\times (a^2+4h^2)\\\\\dfrac{A^2}{a^2}=a^2+4h^2\\\\\dfrac{A^2}{a^2}-a^2=4h^2\\\\4h^2=\dfrac{(240)^2}{12^2}-12^2\\\\4h^2=256\\\\h^2=64\\\\h = 8\ cm[/tex]
So, the height of the pyramid is equal to 8 cm.
Find the zero of the polynomial 2y – 3
Answers
Answer:
The zero of the polynomial is [tex]y = \frac{3}{2}[/tex]
Step-by-step explanation:
Zero of a polynomial:
The zeros of a polynomial are the values of the independent variable(in this case y) for which the polynomial is 0.
Polynomial 2y - 3
The zero is given by:
[tex]2y - 3 = 0[/tex]
[tex]2y = 3[/tex]
[tex]y = \frac{3}{2}[/tex]
The zero of the polynomial is [tex]y = \frac{3}{2}[/tex]
When an airplane is 35,000 feet from an air traffic control tower, the angle of elevation between the tower and the airplane is.
What is the approximate altitude, a, of the plane at this point?
A. 45,689 feet
B. 26,812 feet
C. 29,369 feet
D. 41,711 feet
Answers
Answer:
26,812 ft
Step-by-step explanation:
The drawing given is very helpful in this case. When solving problems like this, it's important to realize what trigonometric ratio we're going to use. From the given angle (50°), we are given the hypotenuse (35,000 ft) and we're trying to solve for the opposite side ([tex]a[/tex]).
So since we're trying to find the opposite side side and we have the hypotenuse, we should try to find a trigonmetric ratio between the opposite side and the hypotenuse. Using SOH-CAH-TOA, hopefully you can see that we should pick SOH (i.e. [tex]\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]). Therefore, we can set up our equation given the angle [tex]\theta=50^\circ[/tex].
[tex]\sin(50^\circ)=\frac{a}{35000}[/tex]
Since we're solving for [tex]a[/tex], we can just rearrange to get [tex]a=35000\sin(50^\circ)=26812[/tex]
Therefore, the plane's altitude [tex]a[/tex] is 26,812 ft.
The approximation altitude of the plane at 35,000 feet from an air traffic control tower will be 26812 feet hence option (B) will be correct.
What is a trigonometric function?the trigonometric functions are real functions for only an angle of a right-angled triangle to ratios of two side lengths.
The domain input value for the six basic trigonometric operations is the angle of a right triangle, and the result is a range of numbers.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
Given that 35000 feet are the distance between a plane and the air traffic control tower.
Hypotaneous = 35000 feet
The angle of elevation is 50°
By trigonometric function sin
Sinx = perpendicular/hypotaneous
Sin50° = Altitude/35000
Altitute = 35000 × sin50°
Altitude = 26811.55 ≈ 26812 feet will be the correct answer.
For more information about the trigonometric function
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I’m suppose to find the measure of each angle. Thank you
Answers
Answer:
E) π/9
Step-by-step explanation:
The angles are complementary meaning they add up to 90°.
Convert radians to degrees:
7π/18 · 180/π = 70°
Now we know that we need the radian equivalent of 20°.
Convert degrees to radians:
70 · π/180 = π/9
Therefore, the measure of the missing degree is π/9.
29. In the 2010-2011 NBA regular season, the Los Angeles Lakers won 7 more than twice as many games as they lost. The Lakers played 82 games. How many wins and losses did the team have?
Answers
Answer:
Loss 25 Games & Win 57 Games
Step-by-step explanation:
According to question,we have
The Los Angeles Lakers won 7 more than twice as many games as they lost.
Assume Total Loss=L & Thus Total Win = 2L + 7Total Win + Total Loss = Total Games Played
2L + 7 + L = 82
3L = 82-7
3L = 75 ⇔ L = 25
Thus, Total Loss=25 Games & Thus Total Win = 57 Games
a motor pumps out 6704.76 liters of water in 6 hours how many litres of water will it pump in one hour?
Answers
Answer:
Amount of water pumped out by the motor = 1117.46 liters
Step-by-step explanation:
Amount of water pumped out by the motor pump = 6704.76 liters
Time taken by the motor to pump the water = 6 hours
Rate at which the motor pumps out the water = [tex]\frac{\text{Amount of water pumped out}}{\text{Time taken to pump the water}}[/tex]
= [tex]\frac{6704.76}{6}[/tex]
= 1117.46 liters per hour
Therefore, amount of water pumped out by the motor = 1117.46 liters
How much is six dimes, 8 nickels, and three one-dollar bills? *
Answers
Answer:
.60 + .40 + 3.00 = 4.00
Step-by-step explanation:
Answer:
$ 4
Step-by-step explanation:
six dimes (.10 each) = .60
8 nickels (.05 each)= .40
3 dollars (1.00 each) = 3.
Add together
calculate the volume of each cone. Use 3.14 for π. Round answers to the nearest hundredth if necessary.
Answers
Answer:
πr of length
»» 3.14 x (5)²
»» 3.14 x 30 = 94.2cm²
πr of base
»» 3.14 x (4)²
»» 3.14 x 16 = 50.24cm²
Length x base
»» 94.2cm² x 50.25cm²
A= 4733.55cm²
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the area of a tennis court is 2000m2 . a rugby pitch has a legnth of 45m and width of 45m . which has the biggest area?
Answers
Answer:
The area of a rugby pitch is more as compared to the area of the tennis court.
Step-by-step explanation:
Given that,
The area of a tennis court is 2000 m².
The length and width of a rugby pitch are 45 m and 45 m.
The area of a rugby pitch is given by :
A = lb
So,
A = 45×45
A = 2025 m²
So, it is clear that the area of a rugby pitch is more as compared to the area of the tennis court.
HELP HELP HELP
Solve this
Answers
Answer:
What is the cos theta for, i would use sin to solve for theta and then we would get 41.25 degrees.
Step-by-step explanation:
whats the area of a rectangle
:)
Answers
Answer:
Baguette. :)
Step-by-step explanation:
Answer:
I don't know you lollollollll
Please help will mark BRAINLIEST! This is pt.1
Answers
Answer:
See below.
Step-by-step explanation:
Problem 1.
1. QU
2. QW
3. UW
Given
4. QUW
Problem 2.
1. CB
2. <1, <2
Given
3. BD, BE
Given
4. ABD, CBE
SAS
Which expression are greater than 1/2? Choose all the apply
Answers
Answer:
25/30
5/8
Step-by-step explanation:
Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?
to determine which fractions are greater than 1/2, convert the fractions to decimals
to convert to decimals, divide the numerator by the denominator
1/2 = 0.5 less than half
6/14 = 0.43 less than half
5/8 = 0.625 greater than half
25 / 30 = 0.83 greater than half
3 / 6 = 0.5 equal to half
Researchers examine the impact of Omega-3 fatty acids on vasomotor symptoms in menopausal women. Subjects in the study are given either a placebo (0g daily), 1g daily or 1.8g daily and asked to record any vasomotor symptoms they experience. The Omega-3 fatty acid variable is an example of what type of data?
a. interval level
b. nominal
c. ordinal
d. ratio
Answers
Answer:
c. ordinal
Step-by-step explanation:
Possible values of Omega-3 fatty acids:
Placebo(0g daily).
1g daily
1.8g daily
Ordered numbers, each number representing a category, and thus, it is an ordinal variable and the correct answer is given by option c.
The Omega-3 fatty acid variable is an example of Ordinal type of data.
What is an Ordinal data type?An ordinal data type is one that shows order and description. The "Omega-3 fatty acids" term is descriptive in nature. However, its order is also indicated in the rating of the placebo effect as 0, 1, and 1.8 grams.
Thus, the descriptive and order nature of ordinal data is shown.
Learn more about Ordinal Data here:
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Write the following comparison as a ratio reduced to lowest terms. 169 inches to 13 feet
Answers
Answer:
14.0833333333 feet | 13 feet
Step-by-step explanation:
169 Inches is 14.0833333333 feet on calculator compared to 13 feet
and 1.08333333333 is 14.0833333333 divided by 13
if is not it, then 13/14.0833333333 is 0.92307692307
i guess that is the lowest terms in ratio
Create a tree diagram that shows all the possible outcomes for tossing a coin and spinning a spinner with six equal sections numbered 1 through 6.
Answers
Step-by-step explanation:
We can use a tree diagram to help list all the possible outcomes.
probability tree coin dice
From the diagram, n(S) = 12
This may help you....
plzzz mark me as brainlist....
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a 4.
Answers
Answer:
1 : 12
Step-by-step explanation:
P(4) = 4 cards out of 52 = 1/13
P(4') = 48 cards out of 52 = 12/13
Odds in favour of selecting a four
Probability "for" : Probability "against" = P(4) : P(4') = 1/13 : 12/13 = 1 : 12
Simplify ratio to the simplest integers.
the cost price of an articles was 4000 find the marked price of the article so that there will be profit of 20%after allowing a discount of 20%
Answers
Answer:
The marked price of the article was $ 6000.
Step-by-step explanation:
Since the cost price of an article was $ 4000, to find the marked price of the article so that there will be profit of 20% after allowing a discount of 20%, the following calculation must be performed:
4000 x X x 0.8 = 4000 x 1.2
4000 x X x 0.8 = 4800
4000 x X = 4800 / 0.8
4000 x X = 6000
X = 6000/4000
X = 1.5
4000 x 1.5 = 6000
Therefore, the marked price of the article was $ 6000.