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4 years ago

The lines of the equations are parallel, perpendicular, or neither. y = 2x + 3 y = 2x 1)parallel

Mathematics

1 answer:

faltersainse [42]4 years ago

7 0

They are both of the form y = mx + b where m = slope

m = 2 for both so they are parallel

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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:

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

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:

$f(x)=-x+3$

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).

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:

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

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

Read 2 more answers

a solid sphere is cut into 3 equal wedges. the volume of each wedge is V=4/9π^3. solve the formula for r

algol13

$\\ \qquad\quad\sf{:}\dashrightarrow V=\dfrac{4}{9}πr^3$

It is one third of the solid. sphere

$\\ \qquad\quad\sf{:}\dashrightarrow V_{(Sphere)}$

$\\ \qquad\quad\sf{:}\dashrightarrow 3\left(\dfrac{4}{9}πr^3\right)$

$\\ \qquad\quad\sf{:}\dashrightarrow \dfrac{4}{3}\pi r^3$

Now

$\\ \qquad\quad\sf{:}\dashrightarrow \pi r^3=\dfrac{3V}{4}$

$\\ \qquad\quad\sf{:}\dashrightarrow r^3=\dfrac{3V}{4\pi}$

$\\ \qquad\quad\sf{:}\dashrightarrow r=\sqrt[3]{\dfrac{3V}{4\pi}}$

4 0

3 years ago

Read 2 more answers

In how many distinct ways can the letters of the word mathematics be arranged? (first, does the order matter?)

TEA [102]

Our current list has 11!/2!11!/2! arrangements which we must divide into equivalence classes just as before, only this time the classes contain arrangements where only the two As are arranged, following this logic requires us to divide by arrangement of the 2 As giving (11!/2!)/2!=11!/(2!2)(11!/2!)/2!=11!/(2!2).

Repeating the process one last time for equivalence classes for arrangements of only T's leads us to divide the list once again by 2

4 0

3 years ago

How would the following problem be represented using colored tiles? -7 + (-3) seven red tiles plus three blue tiles seven red ti

Lelechka [254]

Answer:

Ok, we have the equation:

-7 + (-3)

Both numbers are negative, so the solution of this will be:

-7 + (-3) = -7 - 3 = -10.

Now, how we can represent it with tiles?

First we need to define, which tiles are the ones representing negative numbers?

We can use:

Red = positive

Blue = negative.

Then:

-7 is represented with seven blue tiles

-3 is represented with tree blue tiles

then:

(-7) + (-3)

will be represented with seven blue tiles, plus tree blue tiles.

When we add them, we have a total of 10 blue tiles, and as blue tiles represent negative numbers, 10 blue tiles is equal to -10.

5 0

3 years ago

Read 2 more answers

No link or bot answer the question

uranmaximum [27]

Answer:top right

Step-by-step explanation:

6^-2÷6^6 = 6^-2-6=6^-8

Whixh will give you 1/6^8

5 0

3 years ago