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3 years ago

6

All vertical lines are perpendicular to what type of line

2 answers:

PSYCHO15rus [73]3 years ago

7 0

I think the answer is horizontal line

Over [174]3 years ago

5 0

All vertical lines are perpendicular to horizontal lines.

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A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.

Verdich [7]

Answer:

$2a - 3b + 4c = 1$

Step-by-step explanation:

Given

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Required

Determine $2a - 3b + 4c$

$a^2 + b^2 + c^2 = 2(a - b - c) - 3$

Open bracket

$a^2 + b^2 + c^2 = 2a - 2b - 2c - 3$

Equate the equation to 0

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0$

Express 3 as 1 + 1 + 1

$a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0$

Collect like terms

$a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0$

Group each terms

$(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

Factorize (starting with the first bracket)

$(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0$

$((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0$

$((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0$

Express 0 as 0 + 0 + 0

$(a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0$

By comparison

$(a - 1)^2 = 0$

$(b + 1)^2 = 0$

$(c + 1)^2 = 0$

Solving for $(a - 1)^2 = 0$

Take square root of both sides

$a - 1 = 0$

Add 1 to both sides

$a - 1 + 1 = 0 + 1$

$a = 1$

Solving for $(b + 1)^2 = 0$

Take square root of both sides

$b + 1 = 0$

Subtract 1 from both sides

$b + 1 - 1 = 0 - 1$

$b = -1$

Solving for $(c + 1)^2 = 0$

Take square root of both sides

$c + 1 = 0$

Subtract 1 from both sides

$c + 1 - 1 = 0 - 1$

$c = -1$

Substitute the values of a, b and c in $2a - 3b + 4c$

$2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)$

$2a - 3b + 4c = 2 +3 -4$

$2a - 3b + 4c = 1$

7 0

3 years ago

When Matthew eats a pizza he always eats a whole slice at a time with no bites left over. Which graph best represents this situa

RoseWind [281]

Answer:

b

Step-by-step explanation:

5 0

3 years ago

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5th grade math. correct answer will be marked brainliest.

nignag [31]

Answer:

15. hhhhhhhhhhhhhhhhhh

6 0

2 years ago

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Jake completed a marathon race in 3 hours and 12 minutes. What would be Jake's running time as a decimal?

VikaD [51]

$\text{Given that Jake completed a marathon race in 3 hours and 12 minutes.}\\
\\
\text{we need to find this time in decimals. so we will convert 12 minutes into hours}\\
\\
\text{We know that there are 60 minutes in 1 hour. }\\
\\
\text{so in 1 minute there will be}=\frac{1}{60 }\text{ hour}$

$\text{hence in 12 minutes we have}=\frac{1}{60}\times 12=\frac{1}{5}=0.2 \text{ hours}\\
\\
\text{hence the Jake's running time is}=3\text{hours + 12 minute}\\
\\
=3\text{ hours}+0.2 \text{ hours}\\
\\
=3.2 \text{ hours}$

Hence, Jake's running time in decimal is: 3.2 hours

4 0

2 years ago

Write 4.5 as a mixed number.

Zolol [24]

Answer:

9/2

Step-by-step explanation:

4.5 = 4 1/2 = 9/2

7 0

2 years ago

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