How to find the intersection of a linear and exponential function?
Answers
The graph attached shows the point of intersection of a linear and exponential function.
What is a function? What is a linear function? What is an exponential function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.A linear function is given by the function → y = ax + b.An exponential function is given by the function → y = eˣGiven is a linear function and a exponential function.
We can write the equations as -
y = ax + b
y = eˣ
For the points of intersection -
ax + b = eˣ
Refer to the graph attached. It shows the point of intersection of a linear and exponential function.
Therefore, the graph attached shows the point of intersection of a linear and exponential function.
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Related Questions
You have decided to buy a new car, but you are concerned about the value of the car depreciating over time. You do some research on the model you are looking at and obtain the following information:
Suggested retail price - $18,790
Depreciation per year - $1385 (It is assumed that this value is constant.)
The following table represents the value of the car after n years of ownership.
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3125 = 3200*(d)^3
3125/3200 = d^3
3-root (3125/3200) = d
d = 0.992125657...
1 - d = 0.007874...
Therefore it depreciates at about 0.8% monthly
To find the depreciation 6 months from now, or 9 months from the beginning:
v = 3200 (d)^9
= 2980.232239...
So after 9 months the car would be about $2980.23
Answer: D on edge
Step-by-step explanation:
Six times a number decreased by 10 is eight
Answers
6n - 10 = 8
Six times a number decreased by 10 is 8
Your equation is
6x - 10 = 8
Now solve for x
6x - 10 = 8
Add 10 to each side
6x - 10 + 10 = 8 + 10
6x = 18
Divide each side by 6
6x ÷ 6 = 18 ÷ 6
x = 3
Jenny has saved $3,800 over the last 12 months. She saved either $250 or $350 a month. During the 12 month period, how many times did Jenny save $250 for the month? A) 3 B) 4 C) 5
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Here is your answer:
The proper answer to the question is option A "3".
Here is how:
There is only two options 250 and 350 and there is 12 months which means there can only be three for both.
Your answer is A.
If you need anymore help feel free to ask me!
Hope this helps!
Answer:
the answer is actually 4
Step-by-step explanation:
if point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1 then p must have coordinates of?
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[tex]P=\left(\frac{x_1+x_2}{2}\;,\; \frac{y_1+y_2}{2} \right) \\ \\ P=\left(\frac{-5+1}{2}\;,\; \frac{11+5}{2} \right)=\left(\frac{-4}{2}\;,\; \frac{16}{2} \right) \\ \\ P=(-2\;,\;8)[/tex]
If the ratio is 1:1 then the point must be a mid-point. Then the coordinate of the mid-point P is (–2, 8).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.
If point P lies on segment AB with endpoints at A(-5,11) and B(1,5) such that AP:PB = 1:1.
We know that if the ratio is 1:1 then the point must be a mid-point.
Let the coordinate of point P be (x, y)
Then we have
[tex]\rm (x,y) = ( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})\\\\(x,y) = (\dfrac{-5+1}{2}, \dfrac{11+5}{2})\\\\(x,y) = (\dfrac{-4}{2} , \dfrac{16}{2})\\\\(x,y) =(-2, 8)[/tex]
The coordinate of the mid-point P is (–2, 8).
More about the coordinate geometry link is given below.
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f(5)= 3.14r^{2}
pls help
Answers
.. F(r) = πr^2
and you want to evaluate it for r=5, you put 5 in place of every instance of r, then do the arithmetic.
.. F(5) = π*5^2
.. F(5) = 3.14*25 = 78.5
the equation Y= -16t2 + 120 can be used to represent the fruit's height above the ground, where t represents time, in seconds, after she threw the apple. How long did it take the apple to hit the ground? Round your answer to the neares hundreth.
Answers
Let y = 0
Solve for t.
0 = -16t^2 + 120
-120 = -16t^2
-120/-16 = t^2
7.5 = t^2
sqrt{7.5} = sqrt{t^2}
2.7386127875 = t
We now round to the nearest hundredths, which means to 2 decimal places.
Answer: t = 2.74 seconds
Elliot got some new trading cards.He has 4 packs with 20 cards each. Another pack has only 8 cards which equation show a way to find how much cards Elliot has in all?
A.c=(4×8)+20
B.c=4+20+8
C.c=(4×20)+8
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Find the GCF of the monomials 118a^2 and 121b^2.
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118a^2 = 2 * 59 * a * a
121b^2 = 11 * 11 * b * b
The greatest common factor is 1. Nothing else is common
2.
How can you tell when a quadratic equation has two identical, rational solutions? (1 point)
when the radicand is negative
when b in the quadratic formula is greater than the radicand
when the radicand equals zero
when the radicand is not a perfect square,
Answers
ax² + bx + c = 0
are given by:
x₁₂ = [- b +- √(b²-4ac) ] / 2a
You have three cases:
1) the radicand is positive: you then have two dinstinct soutions, one with the root added to (-b) and then divided by 2a, and the other one with the root subtracted to (-b) and then divided by 2a.
2) the radicand is negative: you then have no solutions, because the root can't be performed. This case means that the given polynomial is never equal to zero.
3) the radicand is equal to zero: you then have the same value for both the solutions, which is -b/(2a).
Therefore your answer should be: C) when the radicand is equals to zero.
Which of the following polynomials corresponds to the product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3?
Answers
The product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3 is 4x^2 + 5x + 5xy - 16y^2 + 19y - 27.
Explanation:The product of two multivariate polynomials can be found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. In this case, we have:
(4x - 3y + 5)(x + 2y - -3) = 4x(x + 2y - -3) - 3y(x + 2y - -3) + 5(x + 2y - -3)
Using the distributive property, we can simplify this to:
4x^2 + 8xy - 12x - 3xy - 6y^2 + 9y + 5x + 10y - -15
Combining like terms:
4x^2 + 5x + 5xy - 16y^2 + 19y - 27
Is (a-3) a factor of (a^3-6a^2+29)?
Answers
f(3) = 8 - 6*9 + 29
f(3) = 8 - 54 + 29
f(3) = - 17
As further "proof", here is the graph. Notice that the graph cuts the x axis around -2 , 2.5 and 4.2 (These are rough guesses). The factors are
(a+2)(a - 2.5)(a - 4.2)
Which of the following sets of whole numbers represents all the even three-digit numbers with a 6 in the hundreds place and 3 in the tens place? 361; 363; 365; 367; 369 630; 632; 634; 636; 638 360; 633; 635; 637; 639
Answers
630, 632, 634, 636, and 638 :)
@ganeshie8
Which of the following would appear in the Credits column of a bank statement for a checking account?
A. An online bill payment
B. Interest earned
C. Bank fees
D. An ATM withdrawal
Answers
Answer:
Interest earned
Step-by-step explanation:
(APEX)
Patrick compared the slope of the function g(x) = -2x - 8 to the slope of the linear function shown in the table below. Let m = the slope of g(x) and n = the slope of h(x).
Which statement is true? Choose all that apply.
A. m < n
B. m > n
C. m = n
D. both slopes have the same sign.
E. both slopes have different signs.
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A segment can have more than one bisector.
True
False
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The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0
4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___
Answers
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]
Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]
We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].
To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
Explanation:To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).
If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.Therefore, f(-3) = -8 and f(2) = 4.
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Can someone please explain how to find this answer? thanks
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.. 5x -2y = 5(-2) -2(3) = -16
Then solve for y.
.. 2y = 5x +16 . . . add 2y+16; then divide by 2 for the next equation
.. y = (5/2)x +8 . . . . . . . corresponds to selection (B)
[tex]\bf 5x-2y=-12\implies 5x+12=2y\implies \cfrac{5x+12}{2}=y \\\\\\ \cfrac{5x}{2}+\cfrac{12}{2}=y\implies \stackrel{slope}{\cfrac{5}{2}}x+6=y[/tex]
so, notice, from the slope-intercept form, it happens that the slope is 5/2, well, the line will have the same slope.
so we're looking for the equation of a line whose slope is 5/2 and runs through -2,3
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~ -2 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{5}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=\cfrac{5}{2}[x-(-2)] \\\\\\ y-3=\cfrac{5}{2}(x+2)\implies y-3=\cfrac{5}{2}x+5\implies y=\cfrac{5}{2}x+8[/tex]
The highest point in Africa is Mount Kilimanjaro in Tanzania, with an altitude of 5895 meters above sea level. The lowest point on the continent is Lake Assal in Djibouti. It is 155 meters below sea level. FInd the difference between the altitudes.
Answers
To find the difference between the two values, you just have to subtract them.
Our problem is: 5895 - (-155)
To do this, we change it to 5895 + 155 = 6050
We change it because we are subtract a negative number and subtracting a negative number is the same thing as adding it.
Answer:
6050 meters
Step-by-step explanation:
The difference between the altitudes will be the distance from the highest point of kilimanjaroto the lowest point on lake assai.
This distance will be the distance from the highest point of kilimanjaro to the sea level (5895m) plus the distance from the sea level to the lowest point on lake assai (155m, this distances wont be negative because it is taken as a distance from a point of reference not as a value below 0). Like this:
[tex]5895m+155m=6050m[/tex]
At a store, customers are randomly selected to participate in a survey. On Friday, there were 500 customers at the store. Out of all those people, 90 were selected to participate in the survey. On Saturday, the store manager expects 700 customers in the store. If the probability of being selected to participate in the survey on Saturday is the same as it was on Friday, how many customers will be selected to participate in the survey on on Saturday?
Answers
90/500 = .18
This means that 18% of the customers were selected for the survey.
If the probability is the same on Saturday, then we can multiply the expected customers by our .18
700 x .18 = 126
126 should be selected for the survey on Saturday.
Alisha has a $15,000 car loan with a 6 percent interest rate that is compounded annually. How much will she have paid at the end of the five-year loan term?
total amount = P (1 + i)t
$19,500.25
$15,900.50
$20,073.50
Answers
r = 6 / 1,200 = .005
Principal = 15,000
n = number of payments = 5 yrs * 12 months = 60
TOTAL Loan Cost = (.005 * 15,000 * 60) / 1 -(1.005^-60)
TOTAL Loan Cost = 4,500 / (1 - 0.7413721962)
TOTAL Loan Cost = 4,500 / 0.2586278038
TOTAL Loan Cost = 17,399.52
Although it is NOT one of the choices, I think my answer of 17,399.52 is correct. Using a monthly loan payment calculator, I get 289.99 for the monthly payment. 290*60 months = 17,400 so that seems correct.
I do not think that formula you posted is correct. (Compare it to the one I posted.)
Answer:
20,073.50
Step-by-step explanation:
i used the formula
Which best describes the relationship between the successive terms in the sequence shown?
9, –1, –11, –21, …
a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.
I believe i understand it but have to ask it would be the common difference is -10 bevause you would take -1-9 and get -10?,
Answers
Jovan bought a bond with a face value of 15,000 and a coupon rate of 8.5%. The bond will mature in 15 years. How much interest will he receive semiannually
Answers
19,125
Explanation
The value of bond has an interest of 8.5% annually. Monthly it will be 8.5/2%=4.25%
The initial value of bond is 15,000.
The formula for calculating the interest is;
Interest=PRT
Where p is the money deposited, R is the interest rate and T is the period.
Since the interest semiannually for 15 years, the interest period is (15×2) = 30.
Interest=15,000×0.045×30
=19,125.
Sophie did an anyonymous survey and collected her friends' credit scores. the scores she found are listed in the table below. what is the mean credit score in this group? (round to the nearest whole point, if applicable.) 682 601 744 674 701 790 676 638 773
a. 698
b. 695
c. 676
d. 701
Answers
To find the mean of the data, you will combine all values together and then spread them all out evenly to create one value that represents the data.
In math this involves adding the data together and then dividing the sum by how many pieces of data there are.
682 + 601 + 744 + 674 + 701 + 790 + 676 + 638 + 773 = 6279
6279/9 = 697.66...
The rounded credit score is 698 (Choice A).
Using the mean concept, it is found that the mean credit score in this group is given by:
a. 698
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, there are 9 observations, which are:
682 601 744 674 701 790 676 638 773
Hence, the mean is given by:
[tex]M = \frac{682 + 601 + 744 + 674 + 701 + 790 + 676 + 638 + 773}{9} = 698[/tex]
Hence option a is correct.
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helppppppppppppppppppppppp
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someone help a sister out
Answers
x= -2 for the bottom
∠ RQS and ∠ TQS are a linear pair where m∠ RQS = 2x + 4 and m∠ TQS = 6x + 20
1. Solve for x.
2. Find m∠ RQS and m∠ TQS
3. Show how you can check your answer
I want help to understand how to solve the problem because I have others to solve also.,
Answers
m∠ RQS + m∠ TQS = 180
Now let's answer the questions.
1. Solve for x
m∠ RQS + m∠ TQS = 180
2x + 4 + 6x + 20 = 180
2x + 6x + 4 + 20 = 180
(2 + 6)x + 24 = 180
8x + 24 = 180
8x = 156
x = 19.5
2. Find m∠ RQS and m∠ TQS
m∠ RQS = 2x + 4
m∠ RQS = 2*19.5 + 4
m∠ RQS = 39 + 4
m∠ RQS = 43
m∠ TQS = 6x + 20
m∠ TQS = 6*19.5 + 20
m∠ TQS = 117 + 20
m∠ TQS = 137
3. Show how you can check your answer.Verify that they do add up to 180.
So 43 + 137 = 180
This demonstrates that they do make up a linear pair.
Answer:
∠RQSangle r q s and ∠TQSangle t q s are supplementary angles, so the sum of the angles should equal 180.
Step-by-step explanation:
Estimate 92.49 - 63.854 by first rounding each number to the nearest whole number.
Answers
____
Actual difference is 28.636.
PLEASE HELP!!!!!! MEDAL TO RIGHT ANSWER! Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.
A.) Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0
B.) Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
1.)0= -16t^2 + 135t + 76; 0.5 s
2.)0= -16t^2 + 135t + 76; 9 s,
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Determine whether the statement is always, sometimes, or never true. Complete the explanation. In parallelogram MNPQ, the diagonals MP and NQ meet at R with MR = 7 cm and RP = 5 cm. ; diagonals of a parallelogram each other.
Answers
In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, the statement is always true.
Explanation:The statement is always true. In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, if MR = 7 cm and RP = 5 cm, then NR = 7 cm and RQ = 5 cm. The diagonals MP and NQ meet at point R, so we have MR = NR and RP = RQ, confirming that the statement is always true.
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What’s is the value of the digit 5 in the number 57,634?
5,000
1,000
50,000
10,000
Answers
(5)7,,634= The 5 would equal the ten thousands because first, once the number would have it's (first) comma, this would be in the thousands. And also, this number has (2) numbers in it's thousands, and not just 1. But if it were to have 3, this would be another story, and from this, it would clearly explain to be your (option (b)).