8.ee.5
Andy has 25 apples
Carter has 5 oranges
What is the proportion?
This proportion is 5.
Is the function 𝑔(𝑥)=𝑥2−5g(x)=x2−5 even, odd, or neither?
The function 𝑔(𝑥)=𝑥2−5g(x)=x2−5 is neither even nor odd.
What is the solution to the equation 3(2𝑥−4)=18 3(2x−4)=18?
x=5
There is a right triangle with one vertex at (0,0) and another at (3, 4). What are the coordinates of the third vertex if the hypotenuse is 5 units long?
The third vertex could be at (0, 3) or (3, 0) because the hypotenuse has a length of 5 units.
Which one is a straight line: 𝑓(𝑥)=2𝑥+3f(x)=2x+3 or 𝑔(𝑥)=𝑥2g(x)=x2?
The function 𝑓(𝑥)=2𝑥+3f(x)=2x+3 represents a straight line, while 𝑔(𝑥)=𝑥2g(x)=x2 represents a curve.
Is this proportion equal?
x = 5 y = 15
x = 2 y = 6
Yes
Find the inverse of the function ℎ(𝑥)=2𝑥−7h(x)=2x−7.
The inverse of the function ℎ(𝑥)=2𝑥−7h(x)=2x−7 is ℎ−1(𝑥)=𝑥+72h−1(x)=2x+7
If 4𝑥+3=23 4x+3=23, what is the value of 𝑥x?
x=5
A rectangular garden is 5 units by 6 units. If a dog is tied to one corner with a 7-foot leash, what area can the dog reach?
he dog can reach the entire garden
In 𝑓(𝑥)=3𝑥−1f(x)=3x−1, is the line going up or down? How about in 𝑔(𝑥)=13𝑥+2g(x)=31x+2?
In 𝑓(𝑥)=3𝑥−1f(x)=3x−1, the line goes up because the coefficient of 𝑥x is positive (3). In 𝑔(𝑥)=13𝑥+2g(x)=31x+2, the line also goes up but less steeply because the coefficient of 𝑥x is 1331, which is less than 1.
I have 28 cards
They have 7
Is this proportional?
Yes
What is the domain of the function 𝑓(𝑥)=2𝑥f(x)=x2?
Solve 𝑓(𝑥)=10f(x)=10 and 𝑓(𝑥)=3𝑥−4f(x)=3x−4 simultaneously:
Solve for 𝑥x in the equation 13(9𝑥−6)=53 1(9x−6)=5.
x=3
A ladder is 8 feet long. If it leans against a wall and is 5 feet from the base of the wall, how high does it reach?
The ladder reaches 6 feet up the wall.
For 𝑓(𝑥)=𝑥2f(x)=x2, 𝑓(2)f(2) means you substitute 𝑥=2x=2 into the function, giving 𝑓(2)=22=4f(2)=22=4. For 𝑔(𝑥)=𝑥g(x)=x, 𝑔(2)g(2) means substituting 𝑥=2x=2 into the function, giving 𝑔(2)=2g(2)=2.
For 𝑓(𝑥)=𝑥2f(x)=x2, 𝑓(2)=4f(2)=4. For 𝑔(𝑥)=𝑥g(x)=x, 𝑔(2)g(2) is approximately 1.411.41.
Ray has 42 fishes
Carl has 5
Are they proportional?
No
Find the x-intercept(s) of the function ℎ(𝑥)=−2𝑥2+4𝑥−6h(x)=−2x2+4x−6.
To find the x-intercept(s), set ℎ(𝑥)=0h(x)=0 and solve for 𝑥x: −2𝑥2+4𝑥−6=0−2x2+4x−6=0
If 2(𝑥−3)=10 2(x−3)=10, what is the value of 𝑥x?
x=8
Triangle ABC has vertices at A(1, 2), B(5, 2), and C(5, 6). Is it a right triangle?
Yes, Triangle ABC is a right triangle.
The graph of ∣𝑥∣∣x∣ is a V-shaped graph that opens upwards, while the graph of −∣𝑥∣−∣x∣ is also a V-shaped graph but opens downwards because of the negative sign.
x∣ looks like a V that opens upwards