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3 years ago

Please help me with this problem soon

Mathematics

1 answer:

Helga [31]3 years ago

8 0

Answer:

1. a || b ------ Given

2. m<6 = ⅛m<4 ------- Given

3. m<6 + m<4 = 180 ------- Supplementary Angles

4. m<6 + 8<m6 = 180 ---- Substitution

5. m<6 = 20; m<4 = 160 ----- Algebra

Step-by-step explanation:

Required

Fill in the gaps

1. a || b ------ Given

From the question, we understand that m<6 is ⅛ of m<4. This answers (2) as follows:

2. m<6 = ⅛m<4 ------- Given

From the attached figure, m<6 and m<4 are supplementary angles and they add up to 180. So:

3. m<6 + m<4 = 180 ------- Supplementary Angles

In (2): m<6 = ⅛m<4

Multiply both sides by 8

8 * m<6 = 8 * ⅛m<4

8m<6 = m<4

So, substitute 8m<6 for m<4 in (3). This gives (4)

4. m<6 + 8<m6 = 180 ---- Substitution

Solve (4) algebraically,

9m<6 = 180

Multiply both sides by ⅑

⅑ * 9m<6 = ⅑ * 180

m<6 = 20

Recall that m<4 = 8m<6

So:

m<4 = 8 * 20

m<4 = 160

Hence, (5) is

5. m<6 = 20; m<4 = 160 ----- Algebra

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Answer:

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Step-by-step explanation:

Inequalities differs from equalities in that they return a range of values for x and not a single value (case of equalities)

The first one

8 - 2x <4 if you subtract every side 8, you will get -2x<-4

Next divide every side with -2, since its a negative number you have to change the orientation of the inequaiity, thus we have x>4/2, x>2

The second

|x-8| >22, it has to be treated as this. -22>x-2>22 which can be treated as two single inequalities, -22>x-8, and the other, x-8>22. The fist gives you x<-14, and the other x>30, two non intercepting ranges, so your range will be (-inf, -14) and (30, inf)

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4 years ago

A farmer has 220 bushels of beans for sale at a farmer's market. He sells an average of 16 and three fourths bushels each day.

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Answer:

The answer is= 119 Bushels and a half(119.5)

Step-by-step explanation:

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Nonamiya [84]

Hello there!

Given the sequence:

$\displaystyle \large{ 1, - 3,9, - 27,...}$

The question reveals it to be geometric sequence since it has common ratio.

Geometric Sequence / Ratio Formula

$\displaystyle \large{r = \frac{a_{n + 1}}{a_n} }$

Define 'r' as common ratio.

First, let's check the common ratio by using the formula above.

Ratio Check

$\displaystyle \large{r = \frac{ - 3}{1} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ 9}{ - 3} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ - 27}{9} \longrightarrow - 3 }$

Therefore, the common ratio or r-value is -3.

To find the 7th term of sequence, you can by using the General Geometric Terms.

General Term of Geometric

$\displaystyle \large{a_n = a_1 {r}^{n - 1} }$

a1 is defined as the first term of sequence.

r is common ratio.

n is the term.

Since we want to find 7th term:

a1 = 1
r = -3
n = 7

$\displaystyle \large{a_7 =1{( - 3)}^{7 - 1} } \\ \displaystyle \large{a_7 =1{( - 3)}^{6} } \\ \displaystyle \large{a_7 =729 }$

Therefore, the 7th term of this sequence is 729.

Let me know if you have any questions!

Topic: Sequence and Series / Geometric Sequence

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3 years ago