<span>If Tanya’s three items (x) cost the same as Tony’s four items (y), 3x = 4y. Y is 2.25 less than x, so: 3x = 4x - 4 x 2.25. 3x = 4x - 9. 3x + 9 = 4x. 9 = x. Therefore, y = 9 - 2.25. x = 9 and y = 6.75. Three times 9 and four times 6.75 is 27. Tanya’s items cost $9 each and Tony’s cost $6.75.</span>

3 0

3 years ago

In ∆abc, what is the value of cos b?

Rzqust [24]

$c^2=a^2+b^2-2ab\cos\beta\\\\2ab\cos\beta=a^2+b^2-c^2\\\\\boxed{\cos\beta=\dfrac{a^2+b^2-c^2}{2ab}}$

4 0

3 years ago

Given f ( x ) = 3 x 2 + k x − 13 f(x)=3x 2 +kx−13, and the remainder when f ( x ) f(x) is divided by x + 4 x+4 is 15 15, then wh

Varvara68 [4.7K]

Answer:

k=5

Step-by-step explanation:

We are provided with function, f ( x ) = 3 $x^{2}$ + kx − 13

which is divided by x+4 gives 15.

Here,

since f(x) is divided by x+4 so we can put :

x+4 = 0

x= -4

Putting this in f(x) -----> f(-4)

f(x) = f(-4) = 3 ( $-4^{2}$ ) + k(-4) − 13

f(-4) = 3(16) - 4k - 13

f (-4) = 48 - 4k - 13 ------------------------------------------Equation 1

Since, when f(x) is divided by x+4 , the remainder is 15 so we can say,

f(-4) = 15

putting in equation 1

f (-4) = 15 = 48 - 4k - 13

48 -4k - 13 = 15

35 - 4k = 15

35 - 15 = 4k (Moving - 4k on right hand side and 15 on the left)

or 20 = 4k

or 4k = 20

k = $\frac{20}{4}$

4 0

4 years ago