Answer:
A first-order polynomial best fits the given situation.
Step-by-step explanation:
The statement indicates a constant rate of change in a given time interval, so the model that best fits the given situation is a first-order polynomial model, which is a generalized form of a model with direct proportionality. That is:
[tex]T = T_{o} + r \cdot t[/tex]
Where:
[tex]T[/tex] - Current temperature, measured in Fahrenheit degrees.
[tex]T_{o}[/tex] - Initial temperature, measured in Fahrenheit degrees.
[tex]r[/tex] - Temperature rate of change, measured in Fahrenheit degrees per minute.
[tex]t[/tex] - Time, measured in minutes.
The statement describes the temperature rate of change, which is equal to:
[tex]r = \frac{5\,^{\circ}F}{20\,min}[/tex]
[tex]r = \frac{1}{4}\,\frac{^{\circ}F}{min}[/tex]
Show all work to factor x^4-10x^2+9 completely
Answer:
[tex](x^{2}-9)(x^{2} -1)[/tex]
Step-by-step explanation:
Step 1: Find what adds to _ and multiples to_
It needs to multiple to the 'c' term or 9
It needs to add to the 'b' term or -10
Step 2: Find the numbers
We know -9 and -1 make 10 and multiple to 9
-9 x -1 = 9
-9 + (-1) + -10
Step 3: Write equation in form a(x-r)(x-s)
a = 1
r = -9
s = -1
Plug in the equation to get the factored form of the equation:
[tex](x^{2}-9)(x^{2} -1)[/tex]
Therefore the factored form of the equation is [tex](x^{2}-9)(x^{2} -1)[/tex]
Quadratic equations are also a type of algebraic fractions that have factors.
The factor of [tex]x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)[/tex]
In order to completely factor [tex]x^{4} - 10x^{2} + 9[/tex] we would apply the formula:
a(x-r)(x-s)
To find the variables a, x, r and s, we have to love at the coefficients of [tex]x^{2}[/tex] which is -10 and the term 9 and find out what can we multiply together to give us 9 and add together to give us -10
That would be , -9 and - 1 because:
-9 x -1 = 9
-9 + (-1) = -10
Hence: the value for a = 1
, r = -9 and s = -1
Putting this into the equation:
1(x -(-9)(x - (-1))
Hence, we have:
[tex](x^2-9)( x^{2} - 1)[/tex]
Factorizing the above expression further, we have
[tex](x - 3)(x + 3)(x - 1)(x + 1)[/tex]
Therefore, the factor of [tex]x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)[/tex]
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what's the square root of 57?
Answer:
the square root of 57 is 7.549834435
=7.5
Step-by-step explanation:
press square root followed by 57 on your calculatorFind the value of an exterior angle of a polygon with 12 sides
Answer:
[tex]\huge \boxed{30\°}[/tex]
Step-by-step explanation:
To find the value of an exterior angle of a regular polygon, we can apply a formula.
[tex]\displaystyle \frac{360}{n}[/tex]
[tex]n = \sf number \ of \ sides[/tex]
[tex]\displaystyle \frac{360}{12}=30[/tex]
Answer:
30°
Step-by-step explanation:
For a regular n -gon, the measure of an exterior angle is 360 ˚ / n
Since the sides give has 12 sides, (dodecagon)
the exterior angles is 360° / 12 = 30°
Find the midpoint of the line segment joining the points R(3,2) and S(-5,5).
The x coordinates are 3 and -5. They add to 3+(-5) = -2
Cut this in half to get -2/2 = -1
The x coordinate of the midpoint is x = -1
-------------------
The y coordinates are 2 and 5. They add to 2+5 = 7.
Then we cut this in half to get 7/2 = 3.5
The y coordinate of the midpoint is y = 3.5
-------------------
Overall, the midpoint is (-1, 3.5)
Answer: (-1, 3.5) which is the same as (-1, 7/2)Thirty years ago, police would check a highway for speeders by sending a helicopter up in the air and observing the time it would take for a car to travel between two wide lines placed 1/10th of a mile apart. On one occasion, a car was observed to take 7.2 seconds to travel this distance.
What is the speed of this car in miles per hour?
==============================================
Work Shown:
1/10 = 0.1
0.1 mile = 7.2 seconds
1 mile = 72 seconds (multiply both sides by 10)
1/72 mile = 1 second (divide both sides by 72)
3600/72 = 3600 seconds (multiply both sides by 3600)
50 miles = 3600 seconds
50 miles = 1 hour
The car's speed is 50 mph
Note: 1 hour = 60 min = 60*60 = 3600 seconds
Aaron and Betty went bowling. Betty scores twice the difference of Aaron's score and 5 . The sum of their scores is 320. Find each students bowling score.
Answer:
Aaron=110
Betty=210
Step-by-step explanation:
the photo contains the needed working out
SOMEONE PLZ HELP ME ASAP!!!!
Answer:
hyp=12.76
Step-by-step explanation:
sin36=opp/hyp
hyp=opp/sin36
hyp=7.5/sin36
hyp=12.76 rounded to the nearest hundredth
Given the function f(x)=-x^2+3x, express the value of {f(x+h)-f(x)}{h} in simplest form.
Answer:
[tex]f'(x) = 3-2\cdot x[/tex]
Step-by-step explanation:
Let be [tex]f(x) = -x^{2}+3\cdot x[/tex], such that:
[tex]f'(x) = \frac{f(x+h)-f(x)}{h}[/tex]
Hence,
[tex]f(x+h) = -(x+h)^{2}+3\cdot (x+h)[/tex]
[tex]f(x+h) = -(x^{2}+2\cdot x\cdot h + h^{2})+3\cdot x + 3\cdot h[/tex]
[tex]f(x+h) = -x^{2}+(3-2\cdot x) \cdot h - h^{2}+3\cdot x[/tex]
[tex]f(x) = -x^{2}+3\cdot x[/tex]
Then,
[tex]f'(x) = \frac{-x^{2}+(3-2\cdot x)\cdot h-h^{2}+3\cdot x+x^{2}-3\cdot x}{h}[/tex]
[tex]f'(x) = \frac{(3-2\cdot x)\cdot h-h^{2}}{h}[/tex]
[tex]f'(x) = 3-2\cdot x -h[/tex]
If [tex]h \longrightarrow 0[/tex], then:
[tex]f'(x) = 3-2\cdot x[/tex]
i think this is rlly easy but here ya go :/
Create a table of points from the equation f (x) = 3x2 – 8x + 2. (1 point)
Answer/Step-by-step explanation:
Using [tex] f(x) = 3x^2 - 8x + 2 [/tex], simply plug each value of x into the function to get f(x) values.
Thus, when x = -1
[tex] f(-1) = 3(-1)^2 - 8(-1) + 2 [/tex]
[tex] f(-1) = 3*1 + 8 + 2 = 3 + 8 + 2 [/tex]
[tex] f(-1) = 13 [/tex]
[tex] f(0) = 3(0)^2 - 8(0) + 2 [/tex]
[tex] f(0) = 0 - 0 + 2 = [/tex]
[tex] f(0) = 2 [/tex]
[tex] f(1) = 3(1)^2 - 8(1) + 2 [/tex]
[tex] f(1) = 3*1 - 8 + 2 = 3 - 8 + 2 [/tex]
[tex] f(1) = -3 [/tex]
[tex] f(2) = 3(2)^2 - 8(2) + 2 [/tex]
[tex] f(2) = 3*4 - 16 + 2 = 12 - 16 + 2 [/tex]
[tex] f(2) = -2 [/tex]
[tex] f(3) = 3(3)^2 - 8(3) + 2 [/tex]
[tex] f(3) = 3*9 - 24 + 2 = 27 - 24 + 2 [/tex]
[tex] f(3) = 5 [/tex]
The correct table for the function is the last option.
e Ann, Claire, and Josh collect stickers. One week, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire. If they collect a total of 157 stickers, how many stickers did each collect?
Answer: Ann = 67 Josh = 60 Claire = 30
Step-by-step explanation: You get the equation 5x+7 = 157. You get the equation because for example, Claire = x then josh = 2x and Ann = 2x + 7. You do all the math and boom! You get the answer :)
The number of stickers collected are:
Ann = 67
Claire = 30
Josh = 60
Given,
Ann, Claire, and Josh collect stickers.
One week, Ann collects 7 more stickers than Josh.
Josh collects twice as many stickers as Claire.
Total tickets collected = 157 stickers.
We need to find out how many stickers each collected.
Let the tickets collected by Ann, Claire, and Josh be A, C, and J.
We can write the following equation:
Ann collects 7 more stickers than Josh.
A = 7 + J _______(1)
Josh collects twice as many stickers as Claire.
J = 2C_______(2)
Total tickets collected = 157 stickers.
A + C + J = 157 ______(3)
Solve the equation (1), (2), and (3).
A = 7 + J _____(1)
J = 2C _______(2)
A + C + J = 157 ______(3)
Put J = 2C in A = 7 + J
A = 7 + 2C ______(4)
Put (2), (4) in (3)
7 + 2C + C + 2C = 157
7 + 5C = 157
Subtracting 7 on both sides.
7 + 5C - 7 = 157 - 7
5C = 150
Dividing both sides by 5.
C = 30
Putting C = 30 in J = 2C
J = 2x30 = 60
J = 60
Putting J = 60 in A = 7 + J
A = 7 + 60
A = 67
Thus the number of stickers collected are:
Ann = 67
Claire = 30
Josh = 60
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Solve each absolute value inequality. Graph the solutions on a number line. |x-7|>1
Answer:
x>8 and x<6
Step-by-step explanation:
well first the values of x-7 have to be greater than 1 or, less than -1
because if x-7=-2 then |-2|=2>1 satisfying the equation
so we have
[tex]x-7>1\\\\x-7+7>1+7\\\\x>8[/tex]
and we have
[tex]x-7<-1\\\\x-7+7<-1+7\\\\x<6[/tex]
to graph it it goes from (-∞,6)∪(8,∞)
escribe la ecuación canónica de la elipse con centro en el origen que pasa por el punto (2,1) y cuyo eje menor mide 4 y se encuentra sobre el eje Y
Answer:
Ur mummm u cheater
Step-by-step explanation:
An object in geometry with no width, length or height is an:
A. Point
B. Line
C. Ray
D. Angle
Answer:
A. Point
Step-by-step explanation:
It has no size. It tells about the location only.
Answer:
A. Point
Step-by-step explanation:
A point is a zero- dimensional object as it has no length, width, or height. It also has no size and tells about location only.
Terry is filling spherical water balloons with a faucet that puts out 100 cm^3 of water per second. At least rate, it takes Terry 6 seconds to fill a balloon. What is the radius of a filled balloon?
Answer:
its 5 cm
Step-by-step explanation:
its what I got off of Khan
The radius of a filled balloon is approximately 5.22 cm.
What is the volume of a sphere?The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
Let's first find the volume of a filled balloon.
Since Terry can fill a balloon in 6 seconds and the faucet puts out 100 cm³ of water per second, the volume of a filled balloon is:
V = 6 × 100 = 600 cm³
Now we can use the formula for the volume of a sphere to find the radius.
Rearranging the formula, we get:
[tex]r = [\dfrac{3V}{4\pi}]^{(1/3)}[/tex]
Substituting V = 600 cm³, we get:
[tex]r = [\dfrac{3\times600}{4\pi}]^{(1/3)}[/tex]
r ≈ 5.22 cm
Therefore, the radius of a filled balloon is approximately 5.22 cm.
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One card is to be drawn from a deck of 52 cards.The deck includes four types of cards.Red heart, red stars , black triangles , black circles .Each type has 13 cards numbered 1-13.What is the probability of drawing a red one a, black three , or a six of hearts.Give your answer in the simplify form .
Answer:
red one = 1/26
black three = 1/26
six of hearts = 1/52
The ratio of the profit, material cost and production labour is 5:7:13. If the material cost is 840 more than that of labour, find the total cost of producing the article. Plss
Answer:
Total cost of producing is 2800.
Step-by-step explanation:
Given
Ratio of profit, material cost and production labour is 5:7:13.
Material cost is 840 more than that of labour cost.
To find:
Total cost of producing the article.
Solution:
Cost of producing the article includes material cost and the labour cost.
Profit will not be included in the production cost because profit comes in the picture after the article is sold.
We are given that, the ratio is:
Profit: Material Cost: Production Labour = 5:7:13
So, we can let Material Cost = 7[tex]x[/tex] and
Production Labour = 13[tex]x[/tex]
As per the question statement:
[tex]13x-7x=840\\\Rightarrow 6x=840\\\Rightarrow \bold{x=140}[/tex]
Total cost of producing = Material Cost + Production Labour
Total cost of producing = 7[tex]x[/tex] + 13[tex]x[/tex] = 20[tex]x[/tex] = 20 [tex]\times[/tex] 140 = 2800
So, Total cost of producing is 2800.
How are you? Question of the day is ..... 270 + 19 x 673 =
Answer:
13,057
Step-by-step explanation:
mona started making oatmeal cookies at 11:40 A.M. It took her 1 hour and 10 minutes to make the dough and 1 hour and 50 minutes to bake all of the cookies. What time was it when mona finished making cookies.
Answer:
14:40 P.M or 2:40 P.M
Step-by-step explanation:
Mona started making oatmeal cookies at 11:40 A.M. What time did she finish:
Making the dough = 1 hour and 10 minutes (1:10)
Baking all the cookies = 1 hour and 50 minutes (1:50
11:40 + 1:10 = 12:50 P.M
12:50 + 1:50 = 14:40 P.M
She finished making cookies at 14:40 P.M or 2:40 P.M
there are 8 knives and 12 forks in a package of plastic utensils. Which ratio is equivelent to 8/12?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If you divide [tex]\frac{8}{12}[/tex] by 4 (both numerator and denominator)
You get [tex]\frac{2}{3}[/tex] which is equivalent to the given ration
What is the circumference of a tire in inches given the following data: P255/95R20 (25.4mm/ inch)? (MAAD_A2014-1a & MAMDMN1a) Question 2 options: a) none of the other choices b) 92.68 inches c) 1,584.93 inches d) 122.77 inches
Answer:
Step-by-step explanation:
None of the other choices
Astrid is in charge of building a new fleet of ships. Each ship requires 404040 tons of wood, and accommodates 300300300 sailors. She receives a delivery of 444 tons of wood each day. The deliveries can continue for 100100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 210021002100 sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?
Answer:
10 Ships
Step-by-step explanation:
Khan Academy
The number of ships Astrid can build is 10, assuming she receives the maximum possible amount of wood.
What is multiplication is mathematics?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.
Given that:
Astrid receives a delivery of 4 tons of wood each day.
The deliveries can continue for 100 days at most.
At most, she received amount of wood = 4 × 100 tons = 400 tons.
Each ship requires 40 tons of wood.
Number of ships required = (400÷40) = 10.
Each ship accommodates 300 sailors.
She have to build enough ships to accommodate = (300 × 10) = 3000 sailors.
Again, she wants to build enough ships to accommodate at least 2100 sailors.
As 3000>2100; the number of ships Astrid can build is 10.
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Evaluate 5/8-(1/4)2=
Answer:
0.125
Step-by-step explanation:
(5 divided by 8) - ((1 divided by 4) x 2) = 0.125
Answer:
1/8
Step-by-step explanation:
Because of BEDMAS, we first multiply, then subtract.
We multiply 1/4 and 2, getting 2/4, or 1/2.
Then, our expression becomes 5/8 - 1/2.
We can evaluate:
5/8 - 1/2 = 5/8 - 4/8 and simplify, getting 1/8.
PLS HELP!!
24a-3+4a-3y+7
Answer:
28 a − 3 y + 4
The house Trevor's family lives in has 666 people (including Trevor) and 333 bathrooms. In the past month, each person showered for an average of 480480480 minutes and used an average 727272 liters of shower water (over the entire month). Water costs 0.200.200, point, 20 dollars per liter. How much did Trevor's family pay per minute on shower water?
Using proportions, we find that: Trevor's family paid $0.03 per minute on shower water.
---------------------------------
This question is solved using proportions.
There are 6 people in the house.There are 3 bathrooms in the house.Each person used an average of 72 liters of shower.Thus, the total amount of liters used is:
[tex]L = 72 \times 6 = 432[/tex]
---------------------------------
432 liters used.Each liter costs $0.2.Thus, the total amount paid was of:
[tex]A = 432 \times 0.2 = 86.4[/tex]
---------------------------------
Total of 86.4 dollars.Total of 6x480 = 2880 minutes.The amount of dollars per minute is:
[tex]D = \frac{86.4}{2880} = 0.03[/tex]
Trevor's family paid $0.03 per minute on shower water.
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Trevor's family paid $ 1.33 per minute on shower water.
Since the house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms, and in the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month), and water costs 0.20 dollars per liter, to determine how much did Trevor's family pay per minute on shower water, the following calculation must be performed:
You must multiply the number of liters by its value, and divide that result by the number of minutes that each person consumed, in order to obtain the value per minute on shower water.
((480 x 6) x 0.2) / (6 x 72) = X(2880 x 0.2) / 432 = X576/432 = X1.333 = XTherefore, Trevor's family paid $ 1.33 per minute on shower water.
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A: 15
B: 21
C: 26
D: 105
Answer:B=21
Step-by-step explanation:
it is because combined J an N are 105 across from that is the same so x is 21 because 5(x) = 21 u do 105 divided by 5 to get the answer
THE SEVEN APPLEWOMEN
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?
Answer:
zero
Step-by-step explanation:
If the same sum is received for the sale of 20 apples at price p as is received for the sale of 140 apples at price p, then we must have ...
20p = 140p
120p = 0 . . . . . . subtract 20p
p = 0 . . . . . . . . . divide by 120
The price was zero.
Answer:
Price was 1 unit of money per each 7 apples and 3 units of money per each extra appleEach woman received 20 unit of moneyStep-by-step explanation:
This is the tricky one
I think 'The Seven Apple' is the hint. Let's see what the numbers have to do with 7:
20 = 7*2 + 640 = 7*5 + 560 = 7*8 + 480 = 7*11 + 3100 = 7*14 + 2120 = 7*17 + 1140 = 7*20 + 0Assume each '7 apples' sold for a fixed price x and each 'extra' apple sold for a different price y. Since all add up to make same amount, we get:
2x + 6y = 5x + 5y = ... = 20xLet x = 1, then we get y = 3
So we get the sold price:
20 apples cost: 2*1 + 6*3 = 2040 apples cost: 5*1 + 5*3 = 20...140 apples cost: 20*1 = 20So each apple woman got 20 units of money for their apples.
Price was 1 unit of money per each 7 and 3 units of money per each extra apple
Calculate the slope of a line that passes through the points (2, 6) and (4, 2) *
Answer:
-2
Step-by-step explanation:
Given:
Points (2, 6) and (4, 2)Slope formula:
m = (y2-y1)/(x2-x1)Using the given points:
m = (2- 6)/(4 - 2) = -4/2 = -2how do you do this?
What word also means to put or replace a variable with a number?
Answer:
Hey there!
Substitute would be your answer.
Let me know if this helps :)