The give quadratic function is dilated by the given coefficient, and shifted
horizontally to the left.
(a) The transformation of the common function f(x) are;
f(t) is made more wider than f(x) f(t) is shifted more to the left than the common function f(x).Please find attached the required graph created with MS Excel
(b) Where t = 0, represent the year 2,000 we have;
f(t) = 0.0037·(t + 24.979)²(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion
Reasons:
The given function is f(t) = 0.0037·(t + 14.979)²
Year 1990 is t = 0
(a) The given common function is; f(x) = x²
The transformation of the quadratic function are;
The coefficient 0.0037 widens the common function such that f(t) is wider
than f(x).
The constant, 14.979 added to the variable, t, shifts the graph of the
common function horizontally to the left.
Therefore;
f(t) is wider and shifted to the left more than the common function f(x)Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.
(b) The amount of mortgage debt in 2,000 is given as follows;
With t' = 0 represent the year 2,000, we have;
At year 1990, t' = -10
Which gives, t' = t + 10
From which we have;
f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)² = 0.0037·(t' + 24.979)²
Therefore;
The function with t = 0 representing the year 2,000 is presented as follows;
f(t) = 0.0037·(t + 24.979)²
(c) In the year 2014, we have;
t = 2014 - 2000 = 14
Which gives;
f(14) = 0.0037·(14 + 24.979)² ≈ 5.622
The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars
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Divide 3/8 divided by 2/3 and express the answer in the simplest terms.
A projectile is thrown upward so that its distance above the ground after t seconds is h = -156 + 510t. What is its maximum height?
For the parabola:
h(t) = -at2 + bt, the maximum occurs at -b/2a
For h(t) = -16t2 + 576t that is -576/(-2)(-16), or -576/32, or 18.
The projectile is at its highest point at 18 seconds.
Translate this sentence into an equation.
46 is the sum of 20 and Han's savings.
Use the variable h to represent Han's savings. I
Answer:
20+h = 46
Step-by-step explanation:
it doesn't ask to solve it so that's the answer
Answer :-
[tex]20 + h = 46[/tex]• 46 is the sum of 20 and Han's savings. .
So here Question tell that 46 is the sum of Han's Saving .Then it says that to write the equation in this sentence .
• Use the variable h to represent Han's savings.
So 20 and h = 20 + h = 46 .Hope this helps you !!The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?
Answer:
Hayes family: 35 hoursRodrigues family: 40 hoursStep-by-step explanation:
Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.
15x +30y = 1725 . . . . . total liters of use
x + y = 75 . . . . . . . . . total hours of use
The second equation lets us write an expression for y:
y = 75 -x
This can be substituted into the first equation to give ...
15x +30(75 -x) = 1725
-15x + 2250 = 1725 . . . . . . simplify
-15x = -525 . . . . . . . . . . . subtract 2250
x = 35 . . . . . . . . . . . . . . divide by -15
y = 75 -35 = 40
The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.
The population of a slowly growing bacterial colony after t hours is given by
p(t) = 4t² + 27t + 150. Find the growth rate after 2 hours.
bacteria/hour
Submit Question
A function is an expression that defines a relationship between an independent variable and a dependent variable.
The number of bacteria colonies after 2 hours is 220.
What is a function?It is an expression that defines a relationship between an independent variable and a dependent variable.
We have,
P(t) = 4t² + 27t + 150
Where t = time
P(t) = population of a slowly growing bacteria colony after a particular time
The growth rate after 2 hours:
P(2) = 4 x (2)² + 27 x 2 + 150
P (2) = 16 + 54 + 150
P (2) = 220
Thus the number of bacteria colonies after 2 hours is 220.
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A container can hold 2400 litres of water. (a) A large tap alone can fill the container in x hours. Write down an expression, in terms of r, for the amount of water that the large tap can dispense per minute. {b) A small tap alone will take 1 hour longer than the large tap to fill the co tainer. Write down an expression, in terms of x, for the amount of water that the small tap can dispense per minute. (c) When both taps are turned on at the same time, they can fill the container in 3 hours. Form an equation in x and shows that it reduces tox? -5x-3=0. X 20.
Answer:
Determine the required value of the missing probability to make the distribution a discrete probability distribution. x p(x) 3 0.23 4 ? 5 0.51 6 0.08 p(4) = nothing (type an inte...
Carson bought 50 pounds of rice for his restaurant. He cooked the rice and wanted to evenly divide it into 9 containers to be served later. How many pounds of rice should Carson put in each container?
help plss
Answer:
Step-by-step explanation: there you go
Suppose you receive a shipment of 29 engines, two of which are defective. What is the probability of picking a sample of 4 engines with two bad engines in it? (Round approximations to the nearest thousandth.)
Answer:
0.4%
Step-by-step explanation:
2 are defective and 27 are good out of 29. Chance of picking 1 defective is 2/29 or .069. Chance of picking good is 27/29 or .931.
2 good and 2 bad is
.931 * .931 * .069 * .069 = .004
There is a 0.4 % chance of 2 bad.
I thought of a number. This number double is 7 less than 29. What is my number? hurry please
Answer:
11
Step-by-step explanation:
11*2=22
29-7 =22
Answer:
11
Step-by-step explanation:
Let x be your number
Is means equals
2x = 29-7
2x= 22
2x/2 = 22/2
x =11
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Therefore, the solved inequality is z > -4.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
help please
No links
Answer:
62-0.75x8
Step-by-step explanation
$6=discount
8 tickets
Total=62.00
0.75 multiplied by 8= 6
62-6=56
56 is before the discount
Equation would be 62-0.75x8
Solve the inequality 15 ≥ q + 3
Answer:
[tex]q\le \:12[/tex]
Step-by-step explanation:
Solving
[tex]\mathrm{Switch\:sides}[/tex] (Not a required step)
[tex]q+3\le \:15[/tex]
[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]
[tex]q+3-3\le \:15-3\\=q\le \:12[/tex]
[tex]\bold{q\le \:12}[/tex]
Graphing
Jonah and Jesse are taking a trip. Jonah left at 7 a.m. and travel at an average of 40 miles per hour. Jesse left at 10 a.m. and travel at average of 50 mph. At what time are they at the same place at the same time? Write a system of equations to represent this situation. Then use the substitution method with that system to determine at what time they will be in the same location. How many miles away from will they be at that time?
NO LINKS!
Answer:
y=40(t -7); y=50(t-10)t=22; 10 p.m.y=600 miles from homeStep-by-step explanation:
a) Let t represent the clock time (hours after midnight). The distance from home will be ...
distance = speed × time
jonah = 40(t -7)
jesse = 50(t -10)
jonah = jesse . . . . . . . same distance from home at the same time
(Note: you could let y = distance traveled and use y in both equations. That would give 2 equations in 2 unknowns, instead of 3 equations in 3 unknowns.)
__
b) substituting the first two equations into the second, we get ...
40(t -7) = 50(t -10)
4t -28 = 5t -50 . . . . . . . divide by 10, eliminate parentheses
22 = t
Jonah and Jesse will be at the same place at 10 p.m.
__
c) We can find the distance by substituting into either equation.
jonah = 40(22 -7) = 40(15) = 600
They will be 600 miles from home at that time.
Suppose that sin a= 15/17 and 90 degrees
(5x + 3) + (9x + 5)
Help!!!!!!!
pls help me, pls pls plss help
Answer:
1. given
2. inscribed circle theorem
3. substitution
4. definition of congruent angles
The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm
The Formula of the relation is M = 8AT.
The mass of the metal sheet is 960 g.
The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).
Proportionality:
M ∝ ATRemoving the proportionality sign,
M = KATWhere:
K = constant of proportionality.make K the subject of the equation:
K = M/KT.................... Equation 1From the question,
Given:
M = 200 gA = 250 cm²T = 1 mm = 0.1 cmSusbtitute into equation 1
K = 200/(250×0.1)K = 8 g/cm³Formula:
M = 8AT................. equation 2Hence the formula of the relation is M = 8AT
If,
A = 400 cm²T = 3 mm = 0.3Substitute these values into equation 2
M = 8(400)(0.3)M = 960 gHence, the mass of the metal sheet is 960 g
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the product of seven non-zero factors. of which only three are positive. is
a) positive
B) negative
c) null
Answer:
The answer is A
Step-by-step explanation:
This is one of those sneaky questions where you think there is no definite answer, but don't despair. There is an answer.
You have 7 numbers
3 of them are positive which means greater than 0. Let's pick them
3 4 5 = 60
That part's easy. Those 3 numbers give a plus result.
Now try the other 4 numbers
-3 - 2 - 1 - 4
Do you see what's going to happen. You have -3 * - 2 = 6
then you get - 1 * - 4 = 4
All of a sudden you get a positive result 6 * 4 = 24
60 * 24 = 1440
So the answer is any 3 plus numbers multiplied by 4 minus numbers gives a plus result.
Answer:
a) positive
Step-by-step explanation:
If 3 of the 7 numbers are positive, the other 4 are negative. The product of an even number of negative factors is positive. The product of any number of positive factors is positive.
The product is positive.
Find the area of the equilateral triangle.
Answer:
try 6.93 for answer on equilqteral triangle
The sales tax rate is 8% how much money is 8% of $14
Raven can walk 2 2/5 miles in 3/5 hour. At this rate, how far can she walk in 1 hour? You might want to change 2 2/5 to an improper fraction in order to make the math easier for you to do.
The distance traveled by Raven in 1 hour at the given rate is 4.0 miles.
The given parameters:
Distance traveled by Raven = 2 2/5 milesTime of motion, t = 3/5 hourThe speed of Raven motion is calculated as follows;
[tex]V = \frac{Distance}{Time} \\\\V = Distance\ \times \ \frac{1}{Time} \\\\V = 2\frac{2}{5} \ miles \ \ \times \ \ \frac{1}{3/5 \ hr} \\\\V = \frac{12}{5} \ miles \ \ \times \ \ \frac{5}{3 hr} \\\\V = 4 \ mph[/tex]
The distance traveled by Raven in 1 hour at the given rate is calculated as follows;
[tex]D = 4 \times 1\\\\D = 4 \ miles[/tex]
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1. Gavin buys 89 blue pansies and
86 yellow pansies. He will plant the flowers
in 5 rows with an equal number of plants
in each row. Draw a bar model to help you
find how many plants will be in each row,
O
17
Spiral Review
nose nilo que dise perdoooooooon xd
Assume running consumes 95 cal per mile. If you run 9- minute miles, what is your average power output in watts
Find the equation, in standard form, of the line parallel to y=-1/5x+7 and passing through the point (-10,-3).
Show work for brainliest!
ANSWER:
y= -1/5x - 5
Since it is parallel, that means that the slope (-1/5x) is the same.
Since it is passing through the point (-10, 3), substitute the numbers in for x and y which means: -3= -1/5*(-10) + b
b stands for the new y-intercept
do the equation, and you should get the answer above!
The amount of money charged to borrow money, expressed as a percentage,
is called the
A. collateral
B. interest rate
O C. principal
D. loan term
Answer:
Interest rate
Step-by-step explanation:
The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.
Choose a way to solve.
Write or draw to explain.
2. Greg has Il shirts.
3 have long sleeves.
The rest have short sleeves.
How many short-sleeve
shirts does Greg have?
Help please! Thank you in advance!!
Answer:
8 short sleeve shirts
Step-by-step explanation:
Subtract the total amount of of shirts by the number of shirts with long sleeves to find your answer.
Which triangle is a 30°-60°-90° triangle?
Answer:
-90
Step-by-step explanation:
it's right
Answer:
The first one.
Step-by-step explanation:
I took the quiz and got a 100, hope this helps :))
A2 + B2
Best answer gets a brainliest and thank and 5 star
Answer:
a+b)(a-b)
(Step-by-step explanation:
HURRY!! SUPER SUPER QUICK!!
i have 4,757 points!
ILL GIVE CROWN, STARS, and HEARTS if you answer correctly!
Problem:
6.02 Quiz: One-Step Multiplication or Division Inequalities
On k12
PLEASE ANSWER THEM ALL! VERY LEAST IS ALL YOU KNOW BUT PLEASE DO ALL, AMD CORRECTLY FOR CROWN!
Answer: m>-50
x<=3 3/4
at point -2.1 3rd arrow
at 1.33 4th arrow
at 4 2nd arrow
Step-by-step explanation:
The impact on sampling of increasing the sample size is: There is no specific relationship between sample size and sampling error.
Using margin of error, it is found that increasing the sample size results in a smaller sampling error.
The equation for the margin of error is given by:
[tex]M = c\frac{s}{\sqrt{n}}[/tex]
In which:
c is the critical value according to the distribution used.s is the standard deviation, either of the sample or of the population.n is the sample size.From the equation, it can be noted that the margin of error is inversely proportional to the square root of the sample size, hence, increasing the sample size results in a smaller sampling error.
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