please help: perimeter of polygon ABCDEF

Answer:

Step-by-step explanation:

The equation factors into

(x^2 + 14x + 49) =16                      Factor

(x + 7)^2 = 16                                 Take the square root of both sides

√(x + 7)^2 = √16

x + 7 = +/- 4

x + 7 = + 4                                      Subtract 7 from both sides

x  = 4 - 7

x = - 3

x + 7 = - 4                                      Subtract 7 from both sides.

x = - 4 - 7

x = - 11

x1 = -11

x2 = - 3

Answer:

1

Step-by-step explanation:

Choose two points on the line:  (-5, 0) and (0, 5)

Let the first point [tex](x_1,y_1)[/tex] = (-5, 0)

Let the second point [tex](x_2,y_2)[/tex] = (0, 5)

Use the gradient formula:

[tex]\textsf{gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-0}{0-(-5)}=1[/tex]

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If you want to find the equation of the line, use the point-gradient form of a linear equation:  [tex]y-y_1=m(x-x_1)[/tex]

(where [tex]m[/tex] is the gradient and [tex](x_1,y_1)[/tex] is a point on the line)

Substituting the values into the formula:

[tex]\implies y-0=1(x-(-5))[/tex]

[tex]\implies y-0=x+5[/tex]

[tex]\implies y=x+5[/tex]

Therefore, the equation of the line is y = x + 5

Answer:

0.5,0.2,0.3

Step-by-step explanation:

divide 60,23,37 by 120

The function that can be find used to find the number of circles needed to make the nth figure in the sequence is (C + 1) + 4.

The sequence can be illustrated through the function (C + 1) + 4 where C is the previous number. For the third picture, the number of circles will be:

= (C + 1) + 4

= 5 + 4

= 9

The fourth term will be:

= 9 + 4

= 13

Therefore, each figure uses 4 circles more than the previous one.

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Answer:

Step-by-step explanation: This function can be used to find the number of circles needed to make the nth figure in the pattern.

Each figure uses 4 more circle(s) than the previous figure because an additional circle is added to the top, bottom, left, and right sides.

the other half i got incorrect.

The notation just means

(f/g)(-4) = f(-4) / g(-4)

If f(x) = x² + 2 and g(x) = 1 - 3x, then

f(-4) = (-4)² + 2 = 16 + 2 = 18

g(-4) = 1 - 3 (-4) = 1 + 12 = 13

and so

(f/g)(-4) = 18/13

Answer:

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

Answer:

[tex]y = 5[/tex]

Step-by-step explanation:

Given function:

[tex]y=\dfrac{5x}{x+6}[/tex]

[tex]\implies y=5 \left( \dfrac{x}{x+6}\right)[/tex]

[tex]\textsf{As }x \rightarrow +\infty, \ \dfrac{x}{x+6} \rightarrow1[/tex]  

[tex]\implies y\rightarrow5[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \ \dfrac{x}{x+6} \rightarrow1[/tex]  

[tex]\implies y\rightarrow5[/tex]

As [tex]x[/tex] approaches infinity and negative infinity, [tex]y[/tex] approaches 5 (but never gets there).    Therefore, the horizontal asymptote is [tex]y=5[/tex]

The average daily balance of the transactions given for the billing period will be $1798.

From the complete question, the average daily balance is completed below:

Billing date = 2645.92 × 5 = $13229.6

Repayment on June 6 = $1345.92 × 2 = $2691.84

June 8 = $1381.85

June 9: = $1518.53 × 8 = $12148.24

Gas = $1560.90

Groceries = $1687.37 × 10 = $16873.70

Clothing = $1902.49 × 4 = $7609.96

Total = $53935.19

Therefore, the average daily balance will be:

= $53935 / 30

= $1798

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Answer:

4

Step-by-step explanation:

100 divided by 25 equals 4.

Answer:

yes

Step-by-step explanation:

If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.

The conditions for this type of sampling test regarding the wait times at two branches of a bank include:

It should be noted that sampling simply means a statistical process where a predetermined number of observations are taken from a larger population.

In this case, the samples are both randomly selected and the wait times within each group are approximately symmetric without outliers. When there's a symmetric distribution with no outliers, the mean and standard deviation will be used.

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Answer:

1 gallon / 600 sq ft

Step-by-step explanation:

As we can see, we are given that 600 sq ft uses one gallon to cover, therefore one gallon covers 600 sq ft (just vice versa of what's given).

Answer:

Step-by-step explanation:

BF is the angle bisector of ∠B.

Answer:

hope it helps

also do write the givens

Answer:

[tex]x = -5 \pm \sqrt{26}[/tex]

Step-by-step explanation:

[tex]x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}[/tex]

Answer:

(i) 41-45 mins

(ii) 40 mins

(iii) 75 workers

(iv) Rs10500

Step-by-step explanation:

(i)  The modal class is the class with the highest frequency.

Therefore, from inspection of the frequency table, the modal class is 41-45 mins since if has the highest frequency of 14.

(ii) As the data is grouped, to find an estimate of the mean, assume that every worker takes the value of the class mid-point.  As the data is discrete, there are gaps between the classes, and so we also have to use lower and upper class boundaries to calculate the mid-points.

Class 21-25 : lower 20.5 | upper 25.5 | mid-point 23

Class 26-30 : lower 25.5 | upper 30.5 | mid-point 28

Class 31-35 : lower 30.5 | upper 35.5 | mid-point 33

Class 36-40 : lower 35.5 | upper 40.5 | mid-point 38

Class 41-45 : lower 40.5 | upper 45.5 | mid-point 43

Class 46-50 : lower 45.5 | upper 50.5 | mid-point 48

Class 51-55 : lower 50.5 | upper 55.5 | mid-point 53

Class 56-60 : lower 55.5 | upper 60.5 | mid-point 58

Mean = (sum of frequency x class mid-point) ÷ total frequency

⇒ Mean = (2 x 23 + 5 x 28 + 7 x 33 + 10 x 38 + 14 x 43 + 8 x 48 + 3 x 53 + 1 x 58) ÷ 50

⇒ Mean = 40 mins

(iii)  8 hours = 8 x 60 = 480 mins

Total time ÷ average time to make one doll = 480 ÷ 40 = 12

If the mean time to make a doll is 40 minutes, then one person can make 12 dolls in 8 hours.

Therefore, to calculate the number of workers required to make 900 dolls in 8 hours, divide the total number of dolls needed by 12:

900 ÷ 12 = 75

So 75 workers will be needed to make 900 dolls in 8 hours, given the mean time for a worker to make a doll is 40 mins.

(iv) Overtime is paid in excess of 6 hours.  Therefore, each worker will be working 2 hours overtime.

Total amount of overtime pay = hours x rate x workers

                                                  =  2 x Rs70 x 75

                                                  = Rs10500

Answer:

5

Step-by-step explanation:

because 10 divided by 2 is 5

Answer:

45

Step-by-step explanation:

Have a great day!

#EquestrianLion

Answer:

3(C + 5) = 7

Step-by-step explanation:

Let C = unknown number

The sum of a number and 5:

C + 5

Three times the sum of a number and 5:

3(C + 5)

Three times the sum of a number and 5 is 7:

3(C + 5) = 7

To solve

Use the distributive law:  a(b + c) = ab + ac

⇒ 3C + 15 = 7

Subtract 15 from both sides:

⇒ 3C = -8

Divide both sides by 3:

⇒ C = -8/3

So

The expression is

On solving

Answer:

  90°

Step-by-step explanation:

The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.

__

The slope to point 'a' is y/x = 2/1 = 2.

The slope to point 'b' is y/x = (-1/2)/1 = -1/2.

The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.

__

We can also use the trig formula for the tangent of the difference of angles.

  tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangents are the slopes, calculated above, so we have ...

  tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = undefined

The tangent is undefined for angles that are odd multiples of 90°. The angle between the vectors is 90°.

Answer:

(a) yes

(b) 1/36

(c) 1/36

(d) 1/18

Step-by-step explanation:

(a) yes they are independent as the outcome of one does not affect the outcome of the other.

(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(1 on green die) = 1/6

P(2 on red die) = 1/6

Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36

(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.

P(2 on green die) = 1/6

P(1 on red die) = 1/6

Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36

(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)

= 1/36 + 1/36

= 2/36

= 1/18

Answer:

I plotted it out on the graph and here it is:

[tex]\qquad\qquad\huge\underline{{\sf Answer}} \huge♨[/tex]

In the given figure, NQ acts as a diameter and since diameter subtends 90° at the arc of the circle, so we can conclude that ~

[tex]\qquad \sf  \dashrightarrow \:3y = 90 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 90 \degree \div 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 30 \degree [/tex]

Now, Let's use Angle sum property of Triangle to solve for z :

[tex]\qquad \sf  \dashrightarrow \:4z + 3y + 50 \degree = 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \:4z +90 \degree + 50 \degree = 180 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \:4z = 180 \degree - (50 \degree + 90\degree)[/tex]

[tex]\qquad \sf  \dashrightarrow \:4z = 180 \degree - (140\degree)[/tex]

[tex]\qquad \sf  \dashrightarrow \:4z = 40 \degree[/tex]

[tex]\qquad \sf  \dashrightarrow \:z = 40 \degree \div 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:z = 10 \degree [/tex]

I hope you understood the procedure, you can ask me in comments if you have any doubts.

Answer:

D: 699

E: 582.5

F: 116.5

2. 1398

3. 13048

Step-by-step explanation:

Hope this helps!

Answer:

B. 90 in²

Area of white triangle

3×4/2

12/2 = 6 in²

Area of blue triangle

12×16/2

192/2= 96in²

96in² - 6in² = 90 in²