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3 years ago

Help I over slept and only have one period to finish this test!!

Mathematics

2 answers:

Blababa [14]3 years ago

6 0

Answer:

68°

Step-by-step explanation:

Okay, so m<8 is on the same plane as m<7 because line <em>q </em>is intersecting line <em>t </em>and that's supposed to add up to 180° so:

180° - 112° = 68°

So, m<7 = 68°

hope this helps:)

Nitella [24]3 years ago

4 0

68* explanation: to find that you need to subtract 180 minus 112

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Please answer this its for 50 whole points

svlad2 [7]

Answer:

its c

Step-by-step explanation:

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3 years ago

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Solve (2x-1/4)+(x/3)=2<br> Please provide a step by step with explanation

andrew11 [14]

Answer:

x = 27/10 or x = 2.7

Step-by-step explanation:

Step 1: Get rid of the denominator.

LCD of 4 & 3: 12

Multiply both sides by 12.

12 ( 2x - 1 / 4 ) + 12 ( x / 3 ) = 12 (2)

Reduce the numbers.

3 ( 2x - 1) + 4x = 24

Step 2: Distribute.

6x - 3 + 4x = 24

Step 3: Collect like terms.

6x + 4x = 24 + 3 ( - 3, the sign change when moved to the other side)

10x = 27

Step 4: Solve for x.

Multiply both sides by 10.

10x / 10 = 27 / 10 (the 10 cancels out)

x = 27 / 10 or x = 2.7

Answer: x = 27 / 10 or x = 2.7

7 0

2 years ago

Four families went out for lunch. The total food

dybincka [34]

Answer:

Each family spent about 34.25 on dinner

Step-by-step explanation:

$167 - $30 (tip) = 137

137 ÷ 4 (for each family) = 34.25

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if each family is seperate than they each spent about 11.75 on dinner

167 - (30 x 4) = 47

47 ÷ 4 = 11.75

I'm pretty sure the first one is the answer though

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3 years ago

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Polynomial expressions with matching

yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

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3 years ago

Please help me with this math question

scZoUnD [109]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=\dfrac{8}{6}e\to d=\dfrac{4}{3}e\\\\\text{Substitute it and}\ f=2e\ \text{to the ratio}\ d:e:f:\\\\\dfrac{4}{3}e:e:2e\qquad\text{cancel}\ e\\\\\dfrac{4}{3}:1:2\qquad\text{multiply by 3}\\\\\huge\boxed{4:3:6}$

$\bold{METHOD\ 2}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=\dfrac{8}{6}e\qquad\text{divide both sides by}\ e\neq0\\\\\dfrac{d}{e}=\dfrac{4}{3}\to d:e=4:3\\\\2e=f\qquad\text{divide both sides by 2}\\\\e=\dfrac{f}{2}\to e=\dfrac{1}{2}f\qquad\text{divide both sides by}\ f\neq0\\\\\dfrac{e}{f}=\dfrac{1}{2}\to e:f=1:2\\\\\text{We have}\ d:e=4:3\ \text{and}\ e:f=1:2.$

$\text{We know}\ \dfrac{1}{2}=\dfrac{1\cdot3}{2\cdot3}=\dfrac{3}{6}\\\\\text{threfore}\ e:f=3:6\\\\\text{Now we have}\\\\\left\begin{array}{ccc}d:e=4:3\\e:f=3:6\end{array}\right\}\large{\boxed{d:e:f=4:3:6}}$

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3 years ago