There are two possible answers:
t = 2/3 or t = -1/3
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Explanation:
The expression x+3 is the same as x-(-3). It is of the form x-k
Recall that by the remainder theorem, we know that p(x) is divisible by (x-k) if and only if p(k) = 0.
In this case, k = -3. Plug this into the p(x) function and we get
p(x) = t^2*x^3 - 3t*x + 6
p(-3) = t^2*(-3)^3 - 3t*(-3) + 6
p(-3) = -27t^2 + 9t + 6
Set that equal to 0
p(-3) = 0
-27t^2 + 9t + 6 = 0
-3(9t^2 - 3t - 2) = 0
9t^2 - 3t - 2 = 0
Now apply the quadratic formula to solve for t

We get two possible solutions for t.
Answer:
I think it’s B
Step-by-step explanation:
I did the math and I’m pretty sure that it’s B
Answer:
5
Step-by-step explanation:
Refer to attachment for marking of sides.
In the given figure , ∆ABC , ∆ABD and ∆ADC are right angled triangles . Therefore here we can use the Pythagoras theorem , as ,
base² + perpendicular² = hypotenuse ² .
<u>•</u><u> </u><u>In </u><u>∆</u><u>A</u><u>B</u><u>D</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>
AB² + BD² = AD²
AB² + x² = 10²
AB² = 10² - x²
AB² = 100 - x²
<u>•</u><u> </u><u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>D</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>
AC² + AD² = CD²
AC² = 20² - 10²
AC² = 400 - 100
AC² = 300
<u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>B</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>,</u>
AC² = AB² + BC²
Substituting the values from above ,
300 = 100-x² + (20-x)²
300 = 100 - x² + 400 + x² - 40x
40x = 500 - 300
40x = 200
x = 200/40
x = 5
<h3>
Hence the required answer is 5 .</h3>
Answer:
the solution is (3,4) (the second one)
Step-by-step explanation:
Answer:
The cost is the same after 15 video rentals
Step-by-step explanation:
Let the total cost be y
Let the number of video rentals made be x
Discount card for Big video = $9.99
Discount card for Main Street video = $20.49
Cost of 1 big video rental = $2.49
Cost of 1 Main Street video rental = $1.79
Cost of video rentals with big video:
Y = 9.99 + 2.49x………….(1)
Cost of video rentals with main street video
:
Y = 20.49 +1.79x…………(2)
For the two costs to be equal, the two equations have to be equal to each other
Equating equations (1) and (2)
9.99 + 2.49x = 20.49 +1.79x
0.7x = 10.5
X = 10.5/0.7
X = 15 video rentals