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3 years ago

9

Charles has $20 to spend at the bakery he wants to buy six cupcakes and a pie. The pie costs

1 answer:

Oduvanchick [21]3 years ago

8 0

The most he can buy for each cupcake is 1.25

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A sequence is defined recursively by

Andrei [34K]

9514 1404 393

Answer:

an = 4×34^(n-1)

Step-by-step explanation:

If your recursive definition is ...

$\begin{cases}a_1=4\\a_{n}=34a_{n-1}\end{cases}$

this defines a geometric sequence with a first term a1 = 4 and a common ratio of r = 34. The general form of the explicit function is ...

$a_n=a_1\times r^{n-1}$

For the values shown here, the explicit definition of the sequence is ...

$\boxed{a_n=4\times 34^{n-1}}$

8 0

2 years ago

Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

<h3><u>Part (1)</u></h3>

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

<h3><u>Part (2)</u></h3>

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

<h3><u>Part (3)</u></h3>

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

<h3><u>Part 4</u></h3>

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

3 0

2 years ago

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LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

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6 0

4 years ago

Can somebody anybody help me with questions 10-16 PLEASE

gtnhenbr [62]

Answer:

Sure! To help you here is a really good resource that you can use to answer these questions with work being show!

6 0

3 years ago

a diesel train left berlin and traveled north at an average speed of 25 km/h. A cattle train left at the same time and traveled

max2010maxim [7]

Answer:

10 hours

Step-by-step explanation:

Let $N$ represent the distance the train heading north has traveled

Let $S\\$ represent the distance the train heading south has traveled

Let $t$ represent the number of hours that has passed

$N=25t\\S=35t$

$600=N+S$

$600=25t+35t\\600=60t\\t=10$

6 0

3 years ago