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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please help ASAP! i have been struggling on this question and need help!
Answer:
841.53
Step-by-step explanation:
equation for annual intrest is
[tex]I*y^x=f[/tex]
where I is your initial amount, y is equal to [tex]1+(interest /100)[/tex]
and x is equal to the amount of years you're looking for, with f being the final balance
so for this questions, the equation is as follows
[tex]600*(1+7/100)^5=f\\600*1.07^5=f\\600*1.40255=f\\841.53=f\\[/tex]
Find the probability of selecting a 3 or 4 when a single die is rolled once
Answer:
1/3
Step-by-step explanation:
there are 6 sides to a die : 1, 2, 3, 4, 5, 6.
as one can interpret, 3 & 4 take up 2 parts of the 6 possible options
each result has equal oppurtunity to occur
so for 3 or 4 to be rolled, there is a 2/6 chance, or 1/3 when simplified
Triangle JKL is dilated by a scale factor of 5 to form triangle J'K'L'. Side K'L'
measures 65. What is the measure of side KL?
Question 17 of 20
How did women's roles change as a result of the Industrial Revolution in
Europe?
O A. Women earned the right to vote in most democracies by
organizing protests.
OB. Women earned salaries equal to men's for the first time in history,
O C. Women gained increased economic independence by working in
factories
O D. Women largely controlled agriculture by replacing male farmers
who moved to cities.
As a result of the Industrial Revolution, things changed for women in that C. Women gained increased economic independence by working in factories
The Industrial Revolution:
Allowed for women to be employed in certain factories Allowed for women to get paid salaries as a resultWhen women started earning salaries, they did not have to rely on men as much as they could not provide for themselves which led to increased economic independence.
In conclusion, the industrial revolution allowed for the economic independence of women to increase.
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Question 1: Four expressions are shown below:
A. 2(4x + 2)
B. 2(3x + 3)
C. 6x + 6
D. 8x + 4
Which two expressions are equivalent to 2(3x + 2 + x)? (5 points)
A and D
B and D
A and C
C and B
Question 2:
Which of the values in the set {3, 4, 5, 6} is a solution to the equation 4x + 2 = 22?
3
4
5
6
Answers;
Question 1 answer: The first and last option.
Question 1 explanation: 2(4x + 2) is 4x = 12 = 2 = 14 x 2 = 28 and 8x + 4 is 8 x 4 = 32 + 4 = 36 which is 8 more than 28 then, 3x = 9 + 2 + 3 x 2 = 28.
2(4x + 2) = 28 and 8x + 4 equals 36 which is 8 more and they're both equivalent to 2(3x + 2 + x) because 2(3x = 2 = x) equals 28.
2 lines are not parallel, how many solutions are there
Answer:
Either one: the two line have a point in common, or infinite: they are the same line.
I want a way to solve such a problem
Answer:
none of these is the answer
hope it helps you
Step-by-step explanation:
Hope it will help you...
Read Fred's conclusion. If the sum of the digits of a number is a multiple of 3. then the number is a multiple of 6. Which statement best summarizes Fred's conclusion? The conclusion is true.
A .The number 42 is an example The conclusion is true.
B There are no counterexamples The is false.
C There are no counterexamples. The conclusion is false.
D The number 45 is a counterexample
Answer:
the answer would be a because 42÷6=7 and 42÷3=14.
The correct answer is option A) The number 42 is an example The conclusion is true.
42 is a multiple of both 3 and 6.
How many does multiple mean?
Containing more than once, or more than one; consisting of more than one; manifold; repeated many times; having several, or many, parts.
What is a multiple in math?A multiple in math is the number you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.
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What is the answer to the question. Solve for x
Answer:
[tex]x=\frac{75}2[/tex]
Step-by-step explanation:
Give letters, as in the attached image.
The triangles ABE and CDE are similars (AAA). In particular [tex]AE:CE=BE:DE \rightarrow 46:30=(x+20):x \rightarrow 46x=30(x+20) \rightarrow 23x=15x+300 \rightarrow 8x=300\rightarrow x=\frac{75}2[/tex]
8. The circle centered at Q is a scaled copy of the circle center
at R. (Lesson 3-1)
גן תט
a. Find the scale factor
х
3
R
5
LO512 D
Subo
Orion V Com odnos
shs on
was born and stoclips na
b. Find the value of x.
Q
diale 2020 Dins besipnon ripA
Answer:
scale factor is: 1:4
the value of x is: x=4
Step-by-step explanation:
to find the answer, you do
x= √5² - 3² = √25 - 9 = √16 = 4
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone.
Answer:
5 weeks
Step-by-step explanation:
75 w + 55 ≥ 400
75 w ≥ 345
15 w ≥ 69
w ≥ [tex]\frac{23}{5}[/tex] = 4.6 weeks ⇒ the minimum number of weeks Jordan must work is 5 weeks
Given the function f (x) = 3x — 2, what is the value of f (3)?
Answer:
7
Step-by-step explanation:
Simply plug in 3 for x. 3 times 3 is 9 and 9 minus 2 is 7.
if the length of a cuboid is 60cm and width 40cm and its surface area is 14800cm² find its height
Please Guyz I Want Full Solved Not Just Answer Please
Answer:
The height of cuboid is 50 cm.
Step-by-step explanation:
Given :
➺ Length of cuboid = 60cm➺ Width of cuboid = 40cm.➺ Surface area of cuboid = 14800cm²To Find :
➺ Height of cuboidUsing Formulas :
[tex]\star\small{\underline{\boxed{\sf \pink{SA_{(Cuboid)} = 2(lb + bh + lh)}}}}[/tex]
»» SA = surface area »» l = length »» b = breadth »» h = heightSolution :
Substituting all the given values in the formula to find height of cuboid :
[tex]{\longrightarrow{\sf{SA_{(Cuboid)} = 2(lb + bh + lh)}}}[/tex]
[tex]{\longrightarrow{\sf{14800= 2(60 \times 40 + 40 \times h + 60 \times h)}}}[/tex]
[tex]{\longrightarrow{\sf{14800= 2(2400 + 40h + 60h)}}}[/tex]
[tex]{\longrightarrow{\sf{14800= 2(2400 + 100h)}}}[/tex]
[tex]{\longrightarrow{\sf{14800= 4800 + 200h}}}[/tex]
[tex]{\longrightarrow{\sf{200h = 14800 - 4800}}}[/tex]
[tex]{\longrightarrow{\sf{200h = 10000}}}[/tex]
[tex]{\longrightarrow{\sf{h = \dfrac{10000}{200}}}}[/tex]
[tex]{\longrightarrow{\sf{h = \cancel{\dfrac{10000}{200}}}}}[/tex]
[tex]{\longrightarrow{\sf{\underline{\underline{\red{h = 50 \: cm}}}}}}[/tex]
Hence, the height of cuboid is 50 cm.
[tex]\underline{\rule{220pt}{3.5pt}}[/tex]
2+2+4+6+9+2+4+5+7+0+10+3
Answer:
The answer is 54.
Step-by-step explanation:
You add all these numbers up.
Pls answer this question
Yesterday, 5/6 of the 120 students in a contest gave their speeches. How many students gave their speeches.
Answer:100 Estudiantes dieron su discurso
Step-by-step explanation:
120÷6=20
20x5=100
100 Students
How?
120÷6=20
You can do this,
or you can do
120×1/6=20
_____________________________________________
20×5=100
Therefore,
100 students gave their speeches.
One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?
2.5 inches
5.0 inches
7.1 inches
9.8 inches
PLZ ANSWER ASAP
Answer:
C
Step-by-step explanation:
This means that there is another leg of an isosceles triangle that is also 5 inches.
a^2 + b^2 = c^2
a = 5
b = 5
c = ?
c^2 = 5^2 + 5^2 Combine
c^2 = 25 + 25
c^2 = 50 Take the square root of both sides.
sqrt(c^2) = sqrt(50^2)
c = sqrt(5 * 5 * 2) Take out 1 of two factors under the root sign.
c = 5 * sqrt(2) The 2 is left over because there is only 1 of them
sqrt(2) = 1.4142
c = 5 * 1.4142
c = 7.07 = 7.1
What is the probability of rolling a 4 on a number cube and pulling a red marble out of a bag that contain 3 red, 2 black, and yellow marbles?
Answer:
1/12
Step-by-step explanation:
rolling 4 on a cube= 1outcome/6 total=1/6
pulling red marble= 3 possible red marble/6 total marbles=1/2
1/6*1/2=1/12
Everything in the store was at 30% discount . A dress was originally for 65$ . What was the discount price ?
Answer: $45.50
Step-by-step explanation:
30% discount means 30% off the original price
1. find 30% of 65$
=.3*65
=19.5
2. subtract that from 65$
=65-19.5
=45.5
the discount price was $45.50
It takes 4 3/8 cups of cheese,7/8 cups of olives,and 2 5/8 cups of sausage to make a signature pizza. How much of each ingredient is used for 10 pizzas
The amount of milk in a carton is modeled by the equation y = 64 - 4x. The number of ounces of milk left
is represented by y. The number of servings of milk poured from the carton is represented by x.
4.) How many ounces of milk are in an unopened carton?
5.) How many ounces of milk are in each serving?
Answer:
-Below.
Step-by-step explanation:
4) When the carton is unopened the number of servings x = 0.
So there are 64-4(0) = 64 ounces in an unopened carton.
5) When all the milk has been poured out no. ounces left (y) = 0 so
64 - 4x = 0
4x = 64
x = 16
So each serving contains 16 ounces of milk.
what is the slope of
12(x−6)=4(y+3)
Step-by-step explanation:
the slope is always the factor a of x in the form
y = ax + b
so let's transform the original equation into this form :
12(x - 6) = 4(y + 3)
12x - 72 = 4y + 12
12x - 84 = 4y
3x - 21 = y or y = 3x - 21
therefore, the slope is 3.
A self-storage center has many storage rooms that are 6 feet wide, 10 feet deep, and 12 feet high. What is the volume of the room?
Answer:
720 ft^3
Step-by-step explanation:
6 * 10 *12
v = l * w * h
6 * 10 * 12 = 720
Volume is a three-dimensional scalar quantity. The volume of the self-storage centre room is 720 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a room or box that is the shape of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
Volume = Length × Width × Height
Given that the self-storage centre room's are 6 feet wide, 10 feet deep, and 12 feet high. Therefore, the dimension of the room can be written as,
Length = 10 ft
Width = 6 ft
Height = 12 ft
Now, the volume of the room can be written as,
Volume of the room = 10ft × 6ft × 12ft
= 720 ft³
Hence, the volume of the self-storage centre room is 720 ft³.
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A store pays $270 for a bike and there is a 45% markup. What is the selling price (total price) of the bike?
Work Shown:
1.45*270 = 391.50
The multiplier 1.45 represents a 45% increase
Think of it as 1.45 = 1+0.45 = 100% + 45%
Answer:
391.5
Step-by-step explanation:
the 45% of $270 is $121.5
Find the area in square feet of a rectangle with a base of 3 feet and a height of 4 1/3 feet.
Answer:
13 ft^2
Step-by-step explanation:
Area = Base * Height
= 3 * (4+1/3)
=3*(13/3)
=13
a length of top is stretched between the top edge of a building and a stake in the ground the head of the stake is at ground level. the rope also touches a tree that is growing half way between the stake and the building. if the tree is 38 ft tall how tall is the building?
The relationship between the rope, the building, the tree and the ground is an illustration of similar triangles and equivalent ratios.
The building is 76ft tall
The height of the tree is given as:
[tex]Height = 38ft[/tex]
The position of the tree is halfway between the building and the stake.
From the figure, the rope touches the top of the building, and the top of the tree.
This means that: the height of the building is twice the height of the tree.
So, we have:
[tex]Building=2\times 38ft[/tex]
[tex]Building=76ft\\[/tex]
Hence, the building is 76ft tall
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solve and check the equation
2(4-5x) = 2(3x+2)
What is thirty three and a third percent of 237?
Answer:
79
Step-by-step explanation:
(237)(1/3) = 79
The table below shows the deposits (+) and withdrawals ( - ) each week for a newly opened bank account with a starting balance of $100.
DEPOSITS AND
WITHDRAWALS
Week 1+120
Week 2 -100
Week 3 +50
Week 4 P
Week 5 +200
Week 6 -100
Week 7 -25
Week 8 +50
Part A: What is the value of p if the account shows a zero balance after 4 weeks?
From the given table, the positive sign connote deposit while the negative sign connotes withdrawal.
If the account shows a zero balance after 4 weeks, we will take the sum of all deposits and withdrawals for the first four weeks and equate to zero as shown:
[tex]+120+(-100)+50+p=0[/tex]
Open the parenthesis:
[tex]+120-100+50+p=0\\20+50+p=0\\70+p=0[/tex]
Subtract 70 from both sides
[tex]70+p-70=0-70\\p=-70[/tex]
Hence the value of p if the account shows a zero balance after 4 weeks is -70
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1. Find the area of the sector by multiplying the area of the circle by the ratio of the _________________________ to 360.
2. Subtract the area of the triangle from the area of the sector.
length of the radius
length of the diameter
measure of the central angle
circumference of the circle
Answer: measure of the central angle
Step-by-step explanation: trust
Answer:
measure of the central angle
Step-by-step explanation:
The heights of adult men in America are normally distributed, with a mean of 69.1 inches and standard deviation of 2.65 inches. It is sometimes said that women don't like to dance with shorter men. To get a dancing partner, a 6-foot two-inch tall woman draws from a hat the name of an adult American male. What is the probability that he will be as tall as she?