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10 months ago

Help me wit my math please

Mathematics

1 answer:

White raven [17]10 months ago

7 0

we have the expression

3x+2y

Verify for each ordered pair

a) (0,6)

substitute

3(0)+2(6)=12

b) (3,2)

3(3)+2(2)=13

c) (4,1)

3(4)+2(1)=14

d) (5,-2)

3(5)+2(-2)=11

therefore

maximum value for option C

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A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels 1.86 ti

Veseljchak [2.6K]

Number of miles traveled by light in a light-year is 5.952 × 10^12 miles

Step-by-step explanation:

Step 1: Find the number of miles (distance) in a light year by using the formula for speed = Distance/Time

⇒ Distance = Speed × Time

= 1.86 × 10^5 × 1 yr (convert to seconds)

= 1.86 × 10^5 × 365 days × 24 hrs × 60 mins × 60 sec

= 1.86 × 10^5 × 31,536 × 10³

= 1.86 × 3.2 × 10^5 × 10^7

= 5.952 × 10^12 miles

8 0

3 years ago

Please help asap I need to turn this in on time

Yuliya22 [10]

2. = 16
3. = x + 10y
4. sry, I don't know this one :(
5. = 14
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2 years ago

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80 as the product of its prime factors

hammer [34]

Answer:

2*2*2*2*5

Step-by-step explanation:

80:2=40

40:2=20

20:2=10

10:2=5

5:5=1

3 0

3 years ago

Delia has three pieces of ribbon. Her red ribbon is 2/4 foot long. Her green ribbon is 2/3 foot long. Her yellow ribbon is 2/6 f

Scorpion4ik [409]

The green ribbon is the correct ansser

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2 years ago

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Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

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

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

$\bullet\quad a=\dfrac{1}{4p}$

p is the distance from the vertex to the focus

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

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

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

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

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

2 years ago