Question 9 Multiple Choice Worth 1 points)

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

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Eduardo mixed 5 pounds o cashews and almonds. Cashews cost $8 per pound and almonds cost $6 per pound. The total cost of the mix

NemiM [27]

Answer:

3.5 pounds of the mixture was almonds

Step-by-step explanation:

Assume that the mixture contains x pounds of cashews and y pounds of almonds

∵ x represents the amount of cashew

∵ y represents the amount of almond

∵ Eduardo mixed 5 pounds of cashews and almonds

∴ x + y = 5 ⇒ (1)

∵ Cashews cost $8 per pound

∵ Almonds cost $6 per pound

∵ The total cost of the mixture was $33

→ Multiply x by 8 and y by 6 and equate their sum by 33

∴ 8x + 6y = 33 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by -8 to eliminate x

∵ -8(x) + -8(y) = -8(5)

∴ -8x - 8y = -40 ⇒ (3)

→ Add equations(2) and (3)

∵ (8x + -8x) + (6y + -8y) = (33 + -40)

∴ -2y = -7

→ Divide both sides by -2

∴ y = 3.5

∵ y represents the amount of almond

∴ 3.5 pounds of the mixture was almonds

7 0

3 years ago

What kind of triangle would the measurements 7ft 15ft 17ft

devlian [24]

Answer:

This is an Obtuse triangle.

Step-by-step explanation:

A Equilateral Triangle is a triangle where all sides are equal. Here all sides are different so it is not an Equilateral Triangle.

Isosceles triangle is a triangle that has 2 sides that are equal. Here all sides are different therefore this is not an Isosceles triangle.

A right angled triangle is a triangle whose sides satisfy the following equality.

Lets say A triangle has sides a, b and c. Where c is the highest value.

Then, $a^{2} +b^{2} =c^{2}$

Lets substitute the values to the above equation to see whether it the triangle we are given satisfies the above equality,

$7^{2} +15^{2}$ = $49+225$ = $274$

$17^{2} =289$

Therefore, $7^{2} +15^{2}$ ≠ $17^{2}So it is not a Right Angled Triangle.If the sum of squares of the shorter sides is greater than the square of the longer side then it is an Acute angle if not it is an obtuse angle.[tex]7^{2} +15^{2}$ = $274$ ≤ $17^{2} =289$

Therefore, This is an Obtuse triangle.

8 0

3 years ago

The cone has a base diameter of 17 inches and a height of 6 inches. Find the volume of the cone using 3.14/pi. Round your answer

a_sh-v [17]

Answer:

453.73cm³

Step-by-step explanation:

V

=

π

r

2

h

3

3.14× 8.5²× 6/3

6 0

3 years ago

Anyone know how to work this out?

andrey2020 [161]

72.6

total all of them

but if you want a quicker way then 16multiplys2 and 13 multiplys 2 then add 7.3 times 2

6 0

4 years ago

Read 2 more answers