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2 years ago

Write an equation in point-slope form of the line having the given slope that contains the given point. then graph the line

Mathematics

1 answer:

Natali5045456 [20]2 years ago

6 0

Answer:

$y=-\frac{5}{3}x-3$

Step-by-step explanation:

Equation of straight line in point slope form is given a s

$(y-y_1)=m(x=x_1)$

Here

$m=-\frac{5}{2} \ and\ (x_1, y_1)=(0, -3)$

$(y+3)=-\frac{5}{3}(x-0)$

$y=-\frac{5}{3}x-3$

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If j and k are parallel lines, A and B are points on j, and C and D are points on k, how many planes contain points A, B, C, and

natita [175]

A and B are points on j.

C and D are points on k.

Join AD and BC.

ABCD is a quadrilateral.

Clearly, the quadrilateral ABCD is the only plane that contains the points A, B, C and D.

Hence, correct answer is option A. Exactly one.

8 0

2 years ago

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

Step-by-step explanation:

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Proof LHS → RHS

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

2 years ago

Mrs. Santiago is buying bagels for her office.Each box contains 6 plain, 4 blueberry, and2 onion bagels. Write and interpret a r

yawa3891 [41]

Explanation:

Each box contains

$\begin{gathered} 6plain \\ 4blueberry \\ 2onionbagels \end{gathered}$

The ratio that compares the number of blueberry bagels in one box to the number of onion bagels in one box will be calculated below as

$\begin{gathered} 4:2 \\ in\text{ the simplest form } \\ 2:1 \end{gathered}$

This means that for every one onionbagels in the box, there are 2 blueberry bagels

Part B:

Given that there are 20 blueberry bagels, the number if onion bagels will be calculated below as

$\begin{gathered} \frac{2}{1}=\frac{20}{x} \\ cross\text{ multiply, we will have} \\ 2x=20 \\ \frac{2x}{2}=\frac{20}{2} \\ x=10 \end{gathered}$

Hence,

The final answer is

$10\text{ }onion\text{ }bagels$

7 0

9 months ago

2d(3*6)=48y when y=1/4

vaieri [72.5K]

Answer: d = 1/3

Step-by-step explanation: 48y = 48/4 = 12. So, 2d(18) is equal to 12. 12/18 is 2/3 so 2d has to equal 2/3. That means d = 1/3.

8 0

1 year ago

18- 8x = 8 + 3(1 - 3x) Work shown please!

AleksAgata [21]

Answer

7 = -x

Step-by-step explanation:

18- 8x = 8 + 3(1 - 3x)

18- 8x = 8 +3-9x

18- 8x = 11 - 9x

7- 8x = -9x

7 = -x

5 0

2 years ago

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