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3 years ago

The image point using the translation (x,) + (x+4,y-1) for the point (3,3) is

Mathematics

1 answer:

jeka57 [31]3 years ago

8 0

Answer: (7, 2)

Step-by-step explanation:

(x, y) → (x + 4, y - 1)

(3, 3) → (3 + 4, 3 - 1)

= (7, 2)

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An insured's roof cost $4,000 when installed 5 years ago. It has been damaged by hail and must be replaced. The new roof will co

hoa [83]

Answer:

ACV=$4,500

Step-by-step explanation:

We have that the actual cash value (ACV) is defined as:

$ACV=\dfrac{R\times(E-C)}{E}$

Where:

$ACV =$ actual cash value

$R =$ replacement cost or purchase price of the item

$E =$ expected life of the item

$C =$ current life of the item

Then we have R=$6,000, C=5years, and to find the expected life of the item we can use the depreciating of the roof, then if the roof is depreciating $200 each year we just need to divide $4,000 by $200 to find the expected life of the roof:

$\dfrac{4,000}{200}=20$

Then the espected life of the roof is 20 years, with this result we have all the data, then:

$ACV=\dfrac{\$6,000\times (20-5)}{20}=\dfrac{\$6,000\times (15)}{20}=\dfrac{\$90,000}{20}=\$4,500$

Then the ACV is $4,500

5 0

4 years ago

Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)

Leona [35]

Given that the hyperbola has a center at (0,0), and its vertices and foci are on y-axis. This, the equation of the hyperbola is of the form
x²/a²-y²/b²=-1 (a>0, b>0)
In the equation, vertices are (0, +/-b) .
Thus,
b=60
Foci (0,+/-√(a²+b²))
thus
√(a²+60²)=65
hence solving for a²
a²=65²-60²
a²=625
a²=25²
hence the equation is:
x²/25²-y²/60²=-1

7 0

3 years ago

Read 2 more answers

Divide. (2x²+17x+28)÷(x+6)

oksian1 [2.3K]

Answer:

2x2+17x+28/x+6

Step-by-step explanation:

6 0

3 years ago

Write a translation rule that maps point D(7,-3) onto point D'(2,5).

Sergio039 [100]

We are given D (7, -3) and D'(2, 5).

SAppy the transformation
D'(x,y) → D(x-5, y+8).
Then
x=7 → x=7-5 = 2
y=-3 → y=-3+8 = 5

Answer: D (x-5, y+8) → D'

6 0

3 years ago

Read 2 more answers

The function f(t) = t2 + 4t − 14 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Sh

Cloud [144]

Answer:

A) The vertex ( h , k) = ( -2 , -18)

B) The minimum value of the given function = - 18

C) The Axis of the symmetry for f(t) is y -axis

Step-by-step explanation:

Given a parabola f(t) = t² + 4 t − 14

f(t) = t² + 2(2) t + (2)²-4− 14

f(t) = (t +2)² - 18

Let comparing y = (x +2)² -18

(x +2)² = y + 18

(x-h))² = 4 a ( y - k))²

The vertex ( h , k) = ( -2 , -18)

Given a parabola f(t) = t² + 4 t − 14

Differentiating with respective to 't'

f¹(t) = 2 t + 4

f¹(t) = 2 t + 4 = 0

now $t = \frac{-4}{2} = -2$

Again Differentiating with respective to 't'

$f^{ll} (t) = 2 (1) >0$

f(x) has a minimum value at t = -2

Given f(t) = t² + 4 t − 14

f( -2) = 4 + 4(-2) -14 = 4 -8 -14 = -18

The minimum value of the given function = - 18

f(t) = (t +2)² - 18

Let comparing y = (x +2)² -18

(x +2)² = y + 18

(x-h))² = 4 a ( y - k))²

The vertex ( h , k) = ( -2 , -18)

The Axis of the symmetry for f(t) is y -axis

8 0

3 years ago