The range of the function is for the population of the deer in the salt lake if found as [P, ∞).
What is defined as the range of the function?A function's range is the set of outputs it produces when applied to its entire set of outputs. The range is the collection of objects that actually come from the machine when individuals feed it all the inputs with in function machine metaphor.The number of deer is proportional to t, the number of years since 1990.
As a result, time t becomes the independent variable as well as the number of deer becomes the dependent variable; the number of deer DEPENDS upon the year.
A function's range is the set of values that the dependent variable can take.
The values in the range in this example represent the number of deer throughout salt lake in specific years.
Let 'P' be the population of the deer in salt lake.
Range: [P, ∞)
Then, the range of the function is for the population of the deer in the salt lake if found as [P, ∞).
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Write the quadratic function [tex]f(x)=\frac{1}{7} (x^{2} +14x+35)[/tex] in standard form and use it to find the axis of symmetry and the vertex.
Answer:
f(x) = 1/7 * (x + 7)^2 - 2
axis of symmetry: x = -7
vertex: (-7 | -2)
Step-by-step explanation:
f(x) = 1/7 * (x^2 + 14x + 35)
f(x) = 1/7 * (x^2 + 14x) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5
f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7
f(x) = 1/7 * (x + 7)^2 + 5 - 7
f(x) = 1/7 * (x + 7)^2 - 2
May you guys/girls please help me I have to submit this before midnight and I do not fail because my parents will get me , so may y'all please help me out!?
Answer:
Slope = 1/2 or 0.5
Step-by-step explanation:
Picking two integer points on the line, (any)
(-3, 2) and (-1, 3)
We can find the slope
(3-2)/(-1-(-3)
=1/2
:]
Can you please help me?
Thank you
Answer:
-2/5
Step-by-step explanation:
m = (10 - 8)/(31 - 36) = 2/(-5) = -2/5
Leo has three times as many colored marbles as he has clear-glass marbles. In total, he has 60 marbles. How many clear-glass marbles does he have?
Answer:
15
Step-by-step explanation:
Supposing:
Coloured marbles = x
Glass marbles = y
According to Question
x = 3y
As,
x + y = 60
3y + y = 60 (putting value of x = 3y)
4y = 60
y = 60/4
y = 15
Hence, Leo has 15 Clear-glass marbles
Nura made a square poster with a side length of 13 inches. Latrice made a square poster with a side length of 15 inches. Whats the difference in square inches between the area of Latrice's poster and the area of Nura's poster?
The difference between the areas of the posters is 56 in².
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.
The area of a square is given by: A= a², where a=the length of the side.
Area of square poster's NuraA=(13 in)²
A= 169 in²
Area of square poster's LatriceA=(15 in)²
A= 225 in²
Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²
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Complete the following statement. Use the integers that are closest to the number in the middle.
? < 90 < ?
The integers that are closest to the number in the middle will be 89 < 90 < 91.
What is an integer?It should be noted that an integer simply means a whole number that can be positive, negative, or zero.
It should be noted that on this case, we have to look for the numbers that are closest to 90 one has to be less than 90 and the other one should be greater than it.
Therefore, the numbers that fits the information will be 89 and 91.
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beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet. how many cans will beth need to buy?
To paint the circular table top Beth need to buy 2 cans of paint .
In the question ,
it is given that ,
the radius of the circular table top is = 3 feet
So , the area of the circular table top is = π*r² = π*(3)²
= 9π
= 28.26
also given that
area covered by 1 small can of paint = 15 sq. feet
So , the number of cans needed to paint the table top is = (area of table top)/(area covered by 1 small can of paint)
On substituting the values , we get
number of cans needed to paint the table top is = 28.26/15
= 1.884
≈ 2
Therefore , To paint the circular table top Beth need to buy 2 cans of paint .
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(1) PQRS is a rhombus. Prove that APQT = APST by using all four conditions of congruency.
Four conditions of congruency are: SSS, ASA, SAS, RHS
Using SSS congruency,
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Side: ST = TQ (by the rule, diagonals bisect each other)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SSS congruency
Using ASA congruency,
Angle: ∠TPS = ∠TPQ (diagonals bisect the angles)
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Angle: ∠PST = ∠PQT (opposite angles are equal, and diagonals bisect the angles)
Therefore, Area(PQT) = Area(PST) by ASA congruency
Using SAS congruency,
Side: ST = TQ (by the rule, diagonals bisect each other)
Angle: ∠PTS = ∠PTQ (by the rule, diagonals bisect each other at 90°)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SAS congruency.
Using RHS congruency,
Right angle: ∠PTS = ∠PTQ (diagonals bisect each other at 90°)
Hypotenuse: PS = PQ (all sides of rhombus are equal)
Corresponding Side: ST = TQ (by the rule, diagonals bisect each other)
Therefore, Area(PQT) = Area(PST) by RHS congruency
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give two examples of each of linear equations
Answer:
(2x + 5)/(x + 4) = 1
and
6x - 19 = 3x - 10
Step-by-step explanation
Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.
Hope this helps you!
Perpendicular to y=-5x+1 passing through (2,-1)
The equation of the line perpendicular to the given line will be equal to 5y = x - 3.
A line may be defined as a straight figure which is drawn and has no end points. The equation of line in slope intercept form may be written as y = mx + c where m is the slope and c is the y intercept. The equation of line passing through a point (x₁, y₂) will be given as (y - y₁) = m(x - x₁). The slope of line perpendicular to a line having slope m is given by -1/m. The equation of line in the question is y = -5x + 1. The slope of the line is -5. The slope of line perpendicular to this line is 1/5. Equation of line passing through (2, -1) and slope 1/5 is given by
(y + 1) = 1/5(x - 2)
5y + 1 = x -2
5y = x - 3 which is the required equation.
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Please help me. I tried every answer possible. Due today. I’ll give brainliest too
Evaluate. Write your answer as a whole number or as a simplified fraction.
(−20/35)÷12/20 What is the quotient
Answer:
-1/420
Step-by-step explanation:
-4/7/12/20
= -1/21/20
= -1/420
He number of nano-related patents that are granted in the us increases by a factor of 1.21.21, point, 2 every year. in 199119911991, there were 606060 nano-related patents. which expression gives the number of patents in 199819981998?
The exponential function y = 60(1.2)7 yields the number of patents in 1998.
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis. Let y be the number of nanotechnology-related patents issued in the US in year x following 1991.
There were 60 patents on nanotechnology in 1991, and since then there has been a factor of 1.2 increase.
y = 60(1.2)ˣ
y = 60 in 1998 (7 years ago) (1.2)⁷
The exponential function is used to calculate the number of patents in 1998.
y=60(1.2)⁷
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x^2 - xy = 14
y^2 +xy = 60
The answer is
x = 7, -7, √2, -√2
Add the two equations to get
x2 + y2 = 74
Eliminate y from the first by solving for y and using that result:
(x2 − 14) = x√74 - x2
square both sides, then condense:
x4 − 51x2 + 98 = 0
These ready factors:
(x−7)(x+7)(x−√2)(x+√2)=0
I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.
Therefore,
x = 7, -7, √2, -√2
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Below are ten scores for two different students. Students have a choice: they can take the median of their scores as their final grade, or they can take the mean of their scores as a final grade. Scores are rounded to the nearest whole number. For each student tell which option would result in the highest grade.
Student A: 25, 78, 80, 82, 85, 86, 88, 89, 96, 99
Student B: 71, 77, 77, 79, 79, 80, 88, 89, 91, 96
Find the median and mean for both students.
Answer:
Step-by-step explanation:
Student A:
Mean 80.8
Median: 85.5
The Median is a higher score.
Student B:
Mean 82.7
Median: 79.5
Mean is a higher score
Answer:
Student A's median and Student B's mean would result in the highest grade.
Step-by-step explanation:
How to find the mean:
The mean is the average.
Therefore, you must add all numbers listed, then divide the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.
- Student A : Mean = 81
Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808
Step 2: 808 ÷ 10 = 80.8
Step 3: 80.8 ---> 81
- Student B: Mean = 83
Step 1: 71+77+77+79+79+80+88+89+91+96 = 827
Step 2: 827 ÷ 10 = 82.7
Step 3: 82.7 ---> 83
How to find the median:
The median is the middle number in a sorted list of numbers.
Therefore, you list all of the numbers from least to greatest. Then, you get rid of a number from each side until you finally get to the center number. If there are two numbers left in the center you then find the mean(average) of those numbers.
- Student A: Median = 86
Step 1: Knock off a number from each side until you reach the center number(s)
25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86
Step 2: Find the mean(average) of the two central numbers
85 + 86 = 171 ---> 171 ÷ 2 = 85.5
Step 3: Round your answer
85.5 ---> 86
- Student B: Median = 80
Step1: Knock off a number from each side until you reach the center number(s)
71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80
Step 2: Find the mean(average) of the two central numbers
79 + 80 ---> 159 ÷ 2 = 79.5
Step 3: Round your answer
79.5 ---> 80
Jim and Maureen are training for a marathon. Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers. At the end of the month, they realize that they have run the same total number of kilometers. What is the smallest number of kilometers that each must run?
The smallest number of kilometers that each must run is 6 kilometers.
What will be the least common multiple?From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.
It should be noted that the question simony had to do with finding the least common multiple. This will be:
Multiple of 3 = 3, 6, 9, 12
Multiple of 6 = 6, 12
The least common multiple is 6.
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Please help me please I’m begging I WILL GIVE YOU BRAINLEST 1-8
Answer: have you tried m a t h w a y
Step-by-step explanation:
Please help!! It’s geometry and I just need the answer quick
Answer:
4.5
Step-by-step explanation:
The gas mileage m(x) (in mpg) for a certain vehicle can be approximated by m(x) = -0. 028x² + 2. 688x – 35. 012, where x is the speed of the vehicle in mph. A. Determine the speed at which the car gets its maximum gas mileage. B. Determine the maximum gas mileage
The speed for maximum car mileage will be 48 mph. The maximum gas mileage will be 29.5 mpg.
We are provided with an equation for mileage of car as
m(x) = -0.028x² + 2.688x -35.012
here , variable 'x' is the speed of the car.
Now
for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by putting the derivative equal to zero.
comparing to the equation ax² + bx + c , if the value of
'a' is positive, then we have minimum value at 1st derivative = 0
'a' is negative we have maximum value .
in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.
so, dm/dx = -0.056x + 2.688
putting the 1st derivative = 0 , we have
x = 48
therefore , car gets maximum gas mileage at speed of 48 mph.
Also , putting this value in equation (1) we will get max. mileage.
so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012
= -64.512 + 129.024 - 35.012
= 29.5
so the maximum gas mileage will be 29.5 mpg .
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please help meee
xddd
Answer:
I'm thinking it's 22, but I could be wrong.
Step-by-step explanation:
What type of pay is modeled below?
A. Hourly pay with a bonus. B. Hourly pay without a bonus. C. Commission pay D. Piece rate
The type of pay which is modeled in the image attached below is: D) piece rate.
What is a pay?Money or something paid for a purpose and especially as a salary or wage
The types of pay.
In Mathematics, there are four 5) different types of pay and these include:
The different types of compensation include:
Salary.
Hourly Wages.
Sales Commission.
Tips.
Stock Options.
Bonuses.
Incentive Pay.
Other Variable Pay.
Salary
Commission
Bonuses
Piece rate
Method of wage payment that remunerates the employees on the basis of quantity they produced is known as piece rate.
Plucking tea
The number of tee-shirts produced.
Pruning fruit trees
Sorting second-hand clothes (garments)
Hence the graph of a piece rate model is characterized by a straight line with the slope upwards as represented in the image attached.
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PLEASE HELP!!!!! It’s algebra
Answer:
k=3/10
Step-by-step explanation:
8y=12x+6 >>>>(÷8) both sides
y= (3/2)x+(3/4)
if x=0, y=3/4
4y=k(3x+10) >>> plug in (0, 3/4)
4(3/4)= k(0+10)
3= 10k >>> (÷10) both sides
k=3/10
simplify 0.027^2/3 PLEASE
Answer:
Hope the picture will help you
Answer:
2.718
Step-by-step explanation:
let x = .027^2/3
x=.027^.67
applying natural log on both sides
lnx = ln.027^.67
lnx = .67ln.027
lnx = 2.42004
applying antilog on both sides
x = e^2.42004
x = 2.718
thus, .027^2/3 = 2.718
Referring to the image how does 2 become 8?
Answer:
see explanation
Step-by-step explanation:
each term inside the parenthesis is raised to the exponent outsie, that is
(2xy)³
= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8
= 8x³y³
Kelly drove 238 miles on 6 1/6 gallons of gasoline. Calculate how many miles per gallon she gets in her vehicle.
Kelly gets 38.59 miles per gallon of gasoline
Miles drove by Kelly = 238 miles
Gasoline used by the car = 6 1/6 gallons
Gasoline used in the car in improper fraction = 37/6 gallons
Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.
To calculate miles per gallon we use the following formula:
Miles per gallon = Miles driven/ Gasoline used in the car
= 238/(37/6)
= 238*6/37
= 38.59
Miles per gallon = 38.59
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A painting in the shape of a rectangle has side lengths of 30 inches and
21 inches. You buy a print of the painting with side lengths of 10 inches and
7 inches. Is the print similar to the original painting? Explain your reasoning
Answer:
Yes! The painting is similar.
Step-by-step explanation:
The sides of the original painting are 30 and 21. If you divide this by 3, it equals 10 and 7 which are the sides of the print. This means that the ratio is right so the paintings are similar.
SAT QUESTION HELLP ME
Answer:
22.5
Step-by-step explanation:
we can use the ratios to turn x+y+z=180 to x+4x+3x= 180
then solve for 180
x = 22.5
Answer: D.) 22.5°
Have a nice day!
Here is a polygon.
Draw a scaled copy of the polygon with scale factor 3.
Scaled copy of the polygon with scale factor 3 is given below.
What is a polygon?A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of planar figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.
A polygonal circuit's segments are referred to as its edges or sides. A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end.
Polygons include shapes like triangles, quadrilaterals, pentagons, and hexagons. The shape's number of sides is indicated by the name. A quadrilateral has four sides, whereas a triangle has three.
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While exercising George walked 1/2 of a mile in 1/3 of an hour. At this rate, how far will he have travelled after an hour?
Answer: 1 1/2 in a hour
Step-by-step explanation:
1/2 every 1/3 so if we add one more half it is 1 and 2/3 the last one is 1 1/2 is 1 full hour.