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3 years ago

5

. George inherited 125 football cards from his cousin. Each month, he is going to add 3 to his collection. Which inequality can

be used to find m, the number of months it will take George to accumulate at least 200 football cards?

1 answer:

Andru [333]3 years ago

4 0

Answer:

y=3m+125

Step-by-step explanation:

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I can't seem to figure it out

tekilochka [14]

The slope is 2 because remember, y= mx+b
m= slope
the slope is always multiplied by x

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3 years ago

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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

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2 years ago

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A coin is tossed 7 times . Which of the following represents the probability of the coin landing on tails all 7 times

Studentka2010 [4]

Answer:

○ C. $\frac{1}{64}$

Step-by-step explanation:

Using the formula $\frac{1}{2^{n}}$ , where <em>n</em> represents the number of tosses, substitute 7 in for <em>n</em> to get this:

$\frac{1}{64} = \frac{1}{2^{7}}$

I am joyous to assist you anytime.

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3 years ago

Which two values of x are roots of 4x^2-6x+1

aleksandr82 [10.1K]

x= 3+√5/4,3-√5/4

Step-by-step explanation:

1.In general, given ax^2+bx+c=0, there exists two solutions where:

x= -b+√b^2 - 4ac/2a, -b-√b^2-4ac/2a

2.In this case, a=4, b=-6 and c=1.

x=6+√(-6)^2-4×4/2×4, 6-√(-6)^2-4×4/2×4

3.Simplify.

x=6+2√5/8, 6-√5/8

4.Simplify solutions.

x=3+√5/4, 3-√5/4

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2 years ago

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Simplify 4^2 ⋅ 4^8.

Savatey [412]

In terms of exponents:

1.) 4,294,967,296
2.) 1,048,576
3.) 1.84467441 x 10^19
4.) 1,099,511,627

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