Answers
Answer:
\(\textsf{1.} \quad y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}\:\:\textsf{ where}\:\:x \geq \dfrac{15-\sqrt{769}}{2}\\\\\quad \textsf{or} \quad y=2\sqrt{x+5}\)
\(\textsf{2.} \quad y=-|x+1|+5\)
Step-by-step explanation:
Question 1
Method 1 - modelling as a quadratic with restricted domain
Assuming that the points given on the graph are points that the curve passes through, the curve can be modeled as a quadratic with a limited domain. Please note that as the x-intercept has not been defined on the graph, I am not including this in this first method.
Standard form of a quadratic equation:
\(y=ax^2+bx+c\)
Given points:
(-4, 2)(-1, 4)(4, 6)Substitute the given points into the equation to create 3 equations:
Equation 1 (-4, 2)
\(\implies a(-4)^2+b(-4)+c=2\)
\(\implies 16a-4b+c=2\)
Equation 2 (-1, 4)
\(\implies a(-1)^2+b(-1)+c=4\)
\(\implies a-b+c=4\)
Equation 3 (4, 6)
\(\implies a(4)^2+b(4)+c=6\)
\(\implies 16a+4b+c=6\)
Subtract Equation 1 from Equation 3 to eliminate variables a and c:
\(\implies (16a+4b+c)-(16a-4b+c)=6-2\)
\(\implies 8b=4\)
\(\implies b=\dfrac{4}{8}\)
\(\implies b=\dfrac{1}{2}\)
Subtract Equation 2 from Equation 3 to eliminate variable c:
\(\implies (16a+4b+c)-(a-b+c)=6-4\)
\(\implies 15a+5b=2\)
\(\implies 15a=2-5b\)
\(\implies a=\dfrac{2-5b}{15}\)
Substitute found value of b into the expression for a and solve for a:
\(\implies a=\dfrac{2-5(\frac{1}{2})}{15}\)
\(\implies a=-\dfrac{1}{30}\)
Substitute found values of a and b into Equation 2 and solve for c:
\(\implies a-b+c=4\)
\(\implies -\dfrac{1}{30}-\dfrac{1}{2}+c=4\)
\(\implies c=\dfrac{68}{15}\)
Therefore, the equation of the graph is:
\(y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}\)
\(\textsf{with the restricted domain}: \quad x \geq \dfrac{15-\sqrt{769}}{2}\)
Method 2 - modelling as a square root function
Assuming that the points given on the graph are points that the curve passes through, and the x-intercept should be included, we can model this curve as a square root function.
Given points:
(-4, 2)(-1, 4)(4, 6)(0, -5)The parent function is:
\(y=\sqrt{x}\)
Translated 5 units left so that the x-intercept is (0, -5):
\(\implies y=\sqrt{x+5}\)
The curve is stretched vertically, so:
\(\implies y=a\sqrt{x+5} \quad \textsf{(where a is some constant)}\)
To find a, substitute the coordinates of the given points:
\(\implies a\sqrt{-4+5}=2\)
\(\implies a=2\)
\(\implies a\sqrt{-1+5}=4\)
\(\implies 2a=4\)
\(\implies a=2\)
\(\implies a\sqrt{4+5}=6\)
\(\implies 3a=6\)
\(\implies a=2\)
As the value of a is the same for all points, the equation of the line is:
\(y=2\sqrt{x+5}\)
Vertex form of an absolute value function
\(f(x)=a|x-h|+k\)
where:
(h, k) is the vertexa is some constantFrom inspection of the given graph:
vertex = (-1, 5)point on graph = (0, 4)Substitute the given values into the function and solve for a:
\(\implies a|0-(-1)|+5=4\)
\(\implies a+5=4\)
\(\implies a=-1\)
Substituting the given vertex and the found value of a into the function, the equation of the graph is:
\(y=-|x+1|+5\)
Related Questions
Marcy goal was to collect 10 cans of food for a local food bank. She collected 160 cans use the grid to model to understand how to write this as a ratio, a fraction
Answers
Answer:
We're told that Marcy collected 160 out of 10 cans. That could be expressed as 160/10, but given that the numerator and denominator are both divisible by 10, we can factor that out and express it as 16/1. You can also express it as ratio of 16:1 cans collected to cans intended.
Answer:
As a ratio, this is expressed as
✔ 160 to 100
As a fraction, this is expressed as
✔ 160/100
As a percent, this is expressed as
✔ 160%
Step-by-step explanation:
I just did it!
MAKE SURE YOU ARE RIGHT ANSWER PLEASE I WILL PUT THE BRAINIEST ANSWER
FIND THE VOLUME OF THE SPHERE
Answers
Step-by-step explanation:
Formula:- 4/3*Pi*r^3
= 4/3*22/7*(1/2)^3
Please mark me as brainliest
How do you write 3 7/8 in a decimal form
Answers
Answer:
3.875
Step-by-step explanation:
The way you can do this is if you change 3 7/8 into a improper fraction.
3 7/8
To make improper fraction, you do 8x3+7 and that will be your numertor and 8 will be your denomintator. Then you will get 31/8. Now you do 31 dived by 8. That should igve you 3.875.
Let me know if this helps!! :)
Given the data shown below, which of the following is the best prediction for
the number of years it will take for the population to reach 200,000?
Year
Population
11,920
2
16,800
3
23,300
4
33,000
5
45,750
6
64,000
O A. 9.41
O B. 12.45
O C. 15.82
O D. 18.14
Answers
Answer:
The best prediction for the number of years it will take for the population to reach 200,000 is 9.41
Step-by-step explanation:
Year Population
1 11,920
2 16,800
3 23,300
4 33,000
5 45,750
6 64,000
\(y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)\)
Substitute the values
\(11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2\)
Divide 1 and 2
\(\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238\)
The exponential function that passes through the points (1, 11920) and (2, 16800) is\(y=8457.5238 e^{0.3432t}\)
Now we are supposed to find the best prediction for the number of years it will take for the population to reach 200,000
\(200000=8457.5238 e^{0.3432t}\)
\(\frac{200000}{8457.5238}=e^{0.3432t}\)
\(ln(\frac{200000}{8457.5238})=0.3432t\)
t = 9.41
Hence the best prediction for the number of years it will take for the population to reach 200,000 is 9.41
Ixl b.5 additive property of length
Answers
Answer:
The length of segment SU is 16.8 units
Step-by-step explanation:
From the question
T is a point on the line segment SUThat means T divides SU segment into two parts ST and TUSU = ST + TULet us use this equation to solve the question
∵ The length of ST is 10.6 units
∵ The length of TU is 6.2 units
→ Substitute them in the equation above
∴ SU = 10.6 + 6.2
∵ .6 + .2 = .8
∵ 10 + 6 = 16
∴ 10.6 + 6.2 = 16.8
∴ SU = 16.8 units
The length of segment SU is 16.8 units
Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice’s race?
Answers
I got the answer Antonio had a head start of 3 meters.
Answer: i just did a quiz with this question and the answer is antonio had a head start of 3 meters.
Step-by-step explanation: hope this helped! thx for the points :D
Select all the correct answers.
Which expressions are equal to 105?
(104)1
1
103.102
1
105
(103)2
10.10.10.10.10
Answers
The expressions that equal to 10⁵ are, 10³.10² and 10.10.10.10.10.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents is only possible for same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
The expression that equals to 10⁵ are,
10³.10².
= 10 ³⁺².
= 10⁵.
10.10.10.10.10 ('.' implies multiplication)
= 10¹.10¹.10¹.10¹.10¹.
= 10¹⁺¹⁺¹⁺¹⁺¹.
= 10⁵.
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I’ve been stuck can someone help
Answers
Answer:
(a). \(A_{x}\) = \(\left[\begin{array}{cc}12&-4\\66&6\end{array}\right]\)
Step-by-step explanation:
\(\left \{ {{5x-4y=12} \atop {3x+6y=66}} \right.\)
A = \(\left[\begin{array}{cc}5&-4\\3&6\end{array}\right]\)
\(A_{x}\) = \(\left[\begin{array}{cc}12&-4\\66&6\end{array}\right]\)
\(A_{y}\) = \(\left[\begin{array}{cc}5&12\\3&66\end{array}\right]\)
What’s the inequality?
Answers
Answer:
1/2 (one over two)
Step-by-step explanation:
when you are finding an a slope, or inequality as you wrote here, you are using formula: y/x ( y over x )
the graph dotes show how they are moving 2 to the right(x) and 1 up(y), so it’s 1/2!
How can you write the fraction 4/10 as an equivalent fraction over 100
Answers
Answer:
40/100
Step-by-step explanation:
4/10 can be made into an equivalent fraction by multiplying each number by 10. This is because we need to change the denominator into 100 and 10x10=100.
10(4/10)=40/100
40/100 is the answer
Hope this helps!
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Suppose it takes about 0.5 seconds to hear the echo. How far away is the canyon wall, in feet?
feet
Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?
Answers
Answer:
The sound takes time to go to a point and reflect back to your position.
It means the sound went twice a distance.
=> Suppose it takes about 0.5 seconds to hear the echo, the canyon wall would be [750 x (0.5/3600)]/2 = 0.052 miles
=> Suppose it takes about n seconds to hear the echo, the canyon wall would be [750 x (n/3600)]/2 miles
Hope this helps!
:)
The distance the canyon wall is away is 33000 feet.
The distance the canyon is away in terms of n is 66000n feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Speed = 750 miles per hour
Time = 0.5 seconds
Distance = Speed x Time
Now,
1 mile = 5280 feet
750 miles = 3960000 feet
1 hour = 60 seconds
So,
Speed = (3960000/60) feet per second
Distance = 66000 x 0.5 feet = 33000 feet
This means,
The canyon wall is 33000 feet away.
Now,
For n seconds,
The canyon wall is 66000n feet away.
Thus,
The canyon wall is 33000 feet away.
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if the price of aluminum cans is 32 cents per pound and it takes 32 cans to make 1 pound how many cans do I need to make $100?
Answers
Answer:
1,000 cans
Step-by-step explanation:
Since there are 32 cans per pound and each pound is 32 cents. You divide 32/32 which tells you each can is 1 cent. So 100 dollars divided by 1 cent is 1,000 cents or 1,000 cans since each can is 1 cent.
Answer:
1000 can
u hope it will help you
bbbbbbbbbbbbbbbbbbb
Solve for x. Round to the nearest tenth, if necessary.
Answers
Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:
sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle
We are given the following information from the image above:
Reference angle (∅) = 75 degrees
length of the opposite side = x
length of the hypotenuse = 9
Plug in the values:
sin 75 = x/9
9 * sin 75 = x
x = 8.7 [to the nearest tenth]
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Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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The administration at a high school wants to conduct a survey of student opinion. Administrators want to begin with a simple random sample of 100 students. Which of the following survey methods will produce a simple random sample? (4 points)
A-Survey the first 100 students to arrive at school in the morning
B-Survey every 10th student entering the school gym until 100 students are surveyed
C-Use random numbers to choose 25 each of freshmen, sophomores, juniors, and seniors Number the gym seats. Use a table of random numbers to choose seats and interview the students until 100 have been interviewed.
D- Number the students on the school roster.
E-Use a table of random numbers to choose 100 students from this roster for the survey.
Answers
Answer:
C
Step-by-step explanation:
Each year will have 25 student
help me pls! scammers reported.
Answers
Answer:
10 to the 5 power
Step-by-step explanation:
12 cm
6 cm
What is the area of this
Answers
Answer:
If it's a rectangle, then:
12 x 6 = 72 cm²
Step-by-step explanation:
Answer:
12*6 = 72cm square or you can convert cm into meter
Are these ratio proportional? 16/20 and 4/5
Answers
you multiply the bottom by 4 to get 20 and then you multiply the top by 4 to get 16
Answer:
Yes
Step-by-step explanation:
If you simplify 16/20, you get 4/5. (16 and 20 both go equally in 4. 4x4 = 16; 4x5 = 20)
So, 4/5 = 4/5, thus they're equally proportional.
How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answers
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)
Simplifying the equation:
\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)
\(\qquad\quad\implies 0.1x = 21\)
\(\qquad\qquad\implies \bold{x = 210}\)
\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answers
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
for t>0 the velocity of a particle moving along the x axis is given by v(t)=t^3-6t^2+10t-4 at what time t does the direction of motion of the particle change from right to left?
Answers
The sign of the velocity determines the direction, below you can see a graph of the velocity equation and that:
At t = 0.5 it goes from left to right.At t = 2 it goes from right to left.At t = 3.5 it goes from left to right.At what time t does the direction of motion of the particle change?We know that the velocity equation is:
v(t)=t^3-6t^2+10t-4
When the velocity is positive, the motion is to the right, and when the velocity is negative, the motion is to the left.
So we just need to find the value of t such that the velocity becomes negative.
The graph of the velocity equation is below.
We can see that:
at t = 0.5 it goes from left to right.at t = 2 it goes from right to left.at t = 3.5 it goes from left to right.Learn more about velocity:
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helpppppppppppppppppppppppppppppppppppppp
Answers
Answer:
the last one
Step-by-step explanation:
there is no rhythm
U(x)=x^2+9 and w(x)=sqrt x+8. Find (wu)(8) and (uw)(8)
Answers
Answer:
¿cual es la influencia que tiene la revolución cubana en el surgimiento de grupos armados en Colombia?
Step-by-step explanation:
3
Explain why
64
3,375
15
64
because
64
3,375
15
3,375
(Do not simplify.)
Answers
Answer:
In general, an unresolved nth root, commonly involving a radical symbol ^n√x, is known as a surd. However, the term surd or "surd expression" (e.g., Hardy 1967, p. 25) can also be used to mean a sum of one or more irrational roots. In the mathematical literature, the term arises most commonly in the context of quadratic surds.
Step-by-step explanation:
cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape
Please Give Answer Fast
Answers
The number of millimeters in each glass is 200ml.
How to illustrate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.
It is important to note that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
Since Cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. The amount in each will be:
= (2l - 400ml )/8
= (2000 - 400) / 8
= 1600 / 8
= 200ml
Therefore, based on the calculation, there'll be 200 millimeters on each glass.
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Complete question
cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. How many ml will each contain?
Graph the function shown by the table. Is the function linear or nonlinear?
Answers
Answer:
nonlinear
Step-by-step explanation:
A stem and leaf plot shows data in _____ order.
alphabetical
numerical
reverse
Answers
this is for the extra letters lol
how do i solve for this?
Answers
Step-by-step explanation:
1. KOL = 90
2.KLO = 25
3.NL= 30
4.KL = 17
workings
1.for angle
KOL =90 : the diagonals of rhombus are perpendicular to each other
2. angle LKO + angle KLO + angle KOL =180 : angles of triangle are supplementary(add to 180)
65+ KLO + 90 =180
KLO +155
KLO = 180 - 155
KLO = 25
3. NL = NO + LO: diagonals of the rhombus bisect each other
NL = 15 +15
NL = 30
4. Cos 25 = 15/KL
multiply by KL on both sides
KL × Cos 25 =15
divide by cos 25 on both sides
KL = 17
Suppose Fatima went to buy a $25,000 car and wanted to own it after 5 years. If she got a
4.7% interest rate, what is her monthly payment?
Answers
Therefore, Fatima's monthly payment would be $460.23.
What is interest?Interest is the amount of money that is charged by a lender to a borrower for the use of money or a loan. It is usually calculated as a percentage of the principal amount (the amount of money borrowed) and can be either simple or compound, depending on the type of loan. Interest is typically paid by the borrower to the lender over a set period of time, such as monthly, quarterly, or annually. The interest rate can be fixed or variable, and is determined by a variety of factors including the borrower's creditworthiness, the amount of the loan, and the length of the repayment period.
Here,
To calculate the monthly payment for a car loan, we need to use the formula:
M = P [ i(1 + i)ⁿ] / [ (1 + i)ⁿ – 1]
Where:
M = monthly payment
P = principal (the amount of the loan)
i = monthly interest rate (annual interest rate divided by 12)
n = number of months
First, we need to calculate the monthly interest rate:
i = 4.7% / 12
= 0.003917
Next, we need to calculate the number of months:
n = 5 years x 12 months/year
= 60 months
Now, we can plug in the values and solve for M:
M = 25,000 [ 0.003917(1 + 0.003917)⁶⁰ ] / [ (1 + 0.003917)⁶⁰ – 1]
M = $460.23 (rounded to the nearest cent)
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Complete the table with the number of sit-ups you need to do on Sunday so that the mean number of sit-ups per day is 80.
Monday: 100
Tuesday: 80
Wednesday: 60
Thursday: 70
Friday: 90
Saturday: 100
Sunday: X
If correct you get brainliest!