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SIZIF [17.4K]
3 years ago
9

Hi can you guys help me. The topic is similiar shapes in this case triangles do you guys know how to find a length. I got some p

ictures. I really appreciate.

Mathematics
1 answer:
Airida [17]3 years ago
4 0

PR=18mm
AB=7mm

All lengths of triangle PRQ are twice the lengths of ACB





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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.
Nezavi [6.7K]

Answer: 1) Vertex: (6, -2)    Focus: (6, -7/4)     Directrix: y = -9/4

              2) Vertex: (-2, -1)   Focus: (-7/4, -1)     Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k   or   x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = x² - 12x + 34

y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}

*******************************************************************************************

2) x = y² + 2y - 1

x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}

4 0
3 years ago
a rectangle has a width of 4 cm and a length of 8cm is scaled by a factor of 6.what are the side lengths of the scaled copy
vichka [17]

Answer:

\huge\boxed{\text{Width: } 24 \ \ \ \text{Length: } 32}

Step-by-step explanation:

When we scale an object by a scale factor, the side lengths become the scale factor times bigger than the previous sides. Therefore, with a scale factor of 6, the side lengths would be multiplied by 6.

4 \cdot 6 = 24\\\\4 \cdot 8 = 32

Hope this helped!

6 0
3 years ago
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-n+(-3)+3n+5<br><br> Combing like terms :
Karolina [17]

Answer: 2n + 2 should be your answer

3 0
2 years ago
-1/2 (−4n+6)+3n=47 solve n=?
Sidana [21]

Answer:

N:10

Step-by-step explanation:

8 0
3 years ago
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Find the volume of the cylinder. Use pi = 3.14* the height of 6 inches and a radius 4.5in​
ArbitrLikvidat [17]

Answer: 381.51 cubic inches

Step-by-step explanation:

1. Use the formula: V = πr^{2}h, or in this case, 3.14(4.5^{2})(6)

2. Simplify to 3.14(20.25)(6)

3. Simply multiply all three numbers using a calculator, or one by one if that's the preferred option.

4. You get: 381.51 cubic inches.

8 0
3 years ago
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