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2 years ago

8. What do you know about triangles PDX and triangle CRX? Justify your answer.

Mathematics

2 answers:

Lynna [10]2 years ago

8 0

Answer:

The triangles are Congruent for the same reason as the answer above

Step-by-step explanation:

s2008m [1.1K]2 years ago

5 0

If segment PD is parallel to segment CR then triangle PDX is similar to triangle CRX, due to angle PXD and angle CXR being congruent by the vertical angle theorem, and angle PDX and angle CRX being congruent by the alternate interior angle theorem, these 2 triangles are similar by the A.A similarity postulate.

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Which hyperbola’s asymptote rectangle has the greatest perimeter?

Vitek1552 [10]

Answer:

The greatest perimeter is in (D) ⇒ the perimeter = 60 units

Step-by-step explanation:

* In the hyperbola

- The standard form of the equation of a hyperbola with

center (h , k) and transverse axis parallel to the x-axis is

(x - h)²/a² - (y - k)²/b² = 1

∵ the length of the transverse axis is 2a

∵ the length of the conjugate axis is 2b

∴ The perimeter of asymptote rectangle is 2(2a + 2b)

* Lets check the answers to find the greatest perimeter

A) (x - 4)²/11² - (y + 2)²/3² = 1

* Compare it with the standard form equation

∵ a = 11 ⇒ 2a = 22

∵ b = 3 ⇒ 2b = 6

∴ The perimeter = 2(22 + 6) = 56

B) (x - 2)²/4² - (y + 1)²/10² = 1

* Compare it with the standard form equation

∵ a = 4 ⇒ 2a = 8

∵ b = 10 ⇒ 2b = 20

∴ The perimeter = 2(8 + 20) = 56

C) (x + 5)²/5² - (y - 3)²/9² = 1

* Compare it with the standard form equation

∵ a = 5 ⇒ 2a = 10

∵ b = 9 ⇒ 2b = 18

∴ The perimeter = 2(10 + 18) = 56

D) (x - 7)²/8² - (y - 2)²/7² = 1

* Compare it with the standard form equation

∵ a = 8 ⇒ 2a = 16

∵ b = 7 ⇒ 2b = 14

∴ The perimeter = 2(16 + 14) = 60

* The greatest perimeter is in (D)

4 0

3 years ago

Read 2 more answers

As an estimation we are told 5 miles is 8 km. Convert 76 km to miles.

LUCKY_DIMON [66]

Answer:47.5Miles

Step-by-step explanation:8km÷5=1 .6km.

1mile=1.6km

76km in miles=76km÷1.6km=47.5miles

7 0

3 years ago

20 points pls help quick

masha68 [24]

Answer:

$\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2$

Step-by-step explanation:

We are given the two functions:

$\displaystyle f(x) = 3x^2 + mx +5 \text{ and } g(x) = nx^2 - 4x -2$

And that:

$\displaystyle h(x) = f(x)\cdot g(x)$

With the given conditions that (1, -40) and (-1, 24) satisfy the new function, we want to determine functions f and g.

First, find h:

$\displaystyle \begin{aligned} h(x) & = f(x)\cdot g(x) \\ \\ & = (3x^2 + mx +5)(nx^2 - 4x -2) \end{aligned}$

Because (1, -40) and (-1, 24) are points on the graph of h, we have that h(-1) = 40 and h(-1) = 24. In other words:

$\displaystyle \begin{aligned} h(1) = -40 & = (3(1)^2 + m(1) +5)(n(1)^2 - 4(1) -2) \\ \\ & = (3 + m +5)(n-4 -2) \\ \\ & = (m+8)(n-6) \\ \\ -40 &= mn-6m+8n-48 \end{aligned}$

And:

$\displaystyle \begin{aligned} h(-1) = 24 & = (3(-1)^2 + m(-1) +5)(n(-1)^2 -4(-1) -2) \\ \\ & = (3 - m +5)(n + 4 -2) \\ \\ & = (-m+8)(n+2) \\ \\ 24 & = -mn -2m + 8n +16 \end{aligned}$

Solve the system of equations. Adding the two equations together yield:

$\displaystyle -16 = -8m+16n - 32$

Solve for either m or n:

$\displaystyle \begin{aligned} -16 & = -8m + 16n - 32 \\ \\ 16 & = -8m + 16n \\ \\ 8m & = 16n - 16 \\ \\ m & = 2n -2\end{aligned}$

Substitute this into one of the two equations above and solve:

$\displaystyle \begin{aligned} -40 & = mn - 6m + 8n - 48 \\ \\ 0 & = (2n-2)n -6 (2n-2) + 8n -8 \\ \\ &= (2n^2 - 2n) + (-12n + 12) +8 n - 8 \\ \\ & = 2n^2 -6n + 4 \\ \\ & = n^2 - 3n + 2 \\ \\ &= (n-2)(n-1) \\ \\ & \end{aligned}$

Therefore:

$\displaystyle n = 2 \text{ or } n = 1$

Solve for m:

$\displaystyle \begin{aligned}m &= 2n-2 & \text{ or } m & = 2n-2 \\ \\ & = 2(2) - 1 &\text{ or } & =2(1) -2 \\ \\ &= 2 &\text{ or } & = 0 \end{aligned}$

Hence, the values of n and m are either: 2 and 2, respectively; or 1 and 0, respectively.

In conclusion, functions f and g are:

$\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2$

7 0

2 years ago

PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS THANKS PLS ASAP

tatyana61 [14]

Answer:

-4

Step-by-step explanation:

subtract 4 from each of the x values

y= x-4

6 0

2 years ago

leila and jo are two of the partners in a business.leila makes $3 in profits every $4 that jo makes.if jo makes $60 profit on th

creativ13 [48]

3/4=x/60 so you divide 60 by 4 and get 15x3=45/60

4 0

3 years ago