LESSON 8.2
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.

[tex] \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4[/tex]

Answer:

3+3+3+3=12

48-12-12-12=12

Step-by-step explanation:

common sense :)

If y and x vary directly, the value of y=2.6 then value of x is 1.14.

The tenths place is represented by the initial digit following the decimal. The hundredths place is denoted by the digit that followed the decimal. Up until there are no additional digits, the remaining ones keep the place values filled in the quantity.

For example, 2.84620364 can be round to two decimal places as 2.85, and 0.8035 can be round to two decimal places as 0.80.

Here x and y vary directly,

So , x/y = k

Therefore K is constant

For x = 3.2 and y = 1.4

Then x/y = k

3.2/1.4 = k

K = 1.6/0.7

If y = 2.6 what is x

y = 2.6 and k = 1.6/0.7

2.6/x = 1.6/0.7

1.6x = 18.2

X = 1.1375.

Hence, the Round to two decimal places of x is 1.14

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The length of the rectangular garden given the area and width is 8/7 miles

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.

Area of a rectangular garden = length × width

16 = x × 14

16 = 14x

x = 16 / 14

x = 8/7 miles

Therefore, the length of the rectangular garden given the area and width is 8/7 miles.

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Answer:

The expanded form of 300684 can be written with only 4. Add ends, explain how this is possible for a number with 6 digits. When we look at this number, we want to write that in expanded form, which means we want to write the value of each digit. So i look at the value the 4 in the one's place, so its value is 4 actually 4. The 8 is in the tense place, so its value is 810 point. The 6 is in the hundreds place, so its value is 600 point. The 0 is, in the thousands place, that's 0. Thousands. This 0 is in the 10000 point, so we have 010000 and i'm running out of room. So this 3 is in the 100000. Place of its value is 3 times 100000. It just think of it like money, you have 810 dollar bills, 600 dollar bills, etcetera. So if you have 41 dollar bills, you have 4 dollars. If you have 810 dollar bills, you have 80 dollars: 600 dollar bills. You have 600 dollars now. If you have 0 thousands and 010000, you don't have any money in this, so you don't need to write that down. So now i have 300 dollar bills. Some got a value of 300000 point, so they could leave me only 4 digits that i'm adding together reason being this was 0, so there was no value there.

Answer:

Hope the picture will help you

Answer:

  x = 155°

Step-by-step explanation:

Given hexagon ABCDEF, you want to find the measure of interior angle E. Angles at vertices A, B, C, D, and F are specified.

The sum of the interior angles of an n-sided polygon is ...

  angle sum = (n -2)180°

For the 6-sided polygon given, the sum of interior angles is ...

  (6-2)180° = 720°

The interior angle at vertex B is 360° -80° = 280°.

The interior angle at vertex D is 180° -115° = 65°.

Then the sum of interior angles is ...

  A +B +C +D +E +F = 720°

  85° +280° +30° +65° +x +105° = 720° . . . . . substitute known values

  565° +x = 720° . . . . . . . collect terms

  x = 155° . . . . . . . . . . subtract 565°

__

Additional comment

The angles in the attached figure are drawn to scale.

An alternate solution might draw segment CX through vertex B so that the figure containing angle x has no reflex interior angles. Then the interior angles of pentagon ABXEF will total 540°. Known angles in that figure are A=85°, B=100°, X=95°, F=105°. Then E=x=540° -385° = 155°.

We took this approach initially, to verify that the angle sum of the given hexagon remained 720° even with the reflex interior angle at B.

The graph that shows the correct synthetic division process is given at the end of the answer.

For this problem, we have that:

Then, from the graph, we have that:

Hence, the result of the division of 3x² - x - 2 by (x + 4) is 3x - 13 with a remainder of 50.

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After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.:

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

What is coordinates of the vertices?

The triangle's vertices' coordinates are [tex](x_{1} ,y_{1} )[/tex], [tex](x_{2},y_{2})[/tex], and [tex](x_{3},y_{3} )[/tex]. The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

Given:

Triangle PQR and vertices of triangle are

[tex]P=(3,8)\\Q=(-5,7)\\R=(0,2)[/tex]

The following rule results in a reflection about the y-axis:

                      [tex](x, y) ---- > (-x, y)[/tex]

Using the rule on each of our vertices, we have:

[tex](3, 8) ---- > (-3, 8)\\(-5, 7) ---- > (5, 7)\\(0, 2) ---- > (0, 2)[/tex]

Therefore,

After the picture is reflected along the y-axis, its vertices will have the coordinates P'Q'R.

[tex]P' = (-3,8)\\Q' = (5,7)\\R'=(0,2)[/tex]

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Answer:

f(1) = 9

Step-by-step explanation:

where x is 1, y is 9

Answer:

She had $160 at first

Step-by-step explanation:

Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?

In order to find how much she had at first

we have to add how much she spent plus how much she has left with her

➟ $121 + $39

➟ $160

∴ She had $160 at first

The dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long, which gives an area of 275 ft².

The dimensions of the rug include the width and the length.

Cynthia is budget-constrained to buy 275 ft² only.

When we factorize 275, we have 1, 5, 11, 25, 55, and 275.

The possible combinations of width and length to get 275 ft² and also ensure that a uniform strip of the floor is left around the rug are 11 ft and 25 ft.  This width and length are less than the room's width and length and satisfy the requirement for a uniform strip.

The strip from the room's width and length must be 8 ft each (from all sides).

Width of room = 19 ft

Length of room = 33 ft

Area of room = 627 ft²

Width of rug = 11 ft(19 - 8)

Length of rug = 25 ft (33 - 8)

Area = 275 ft² (11 x 25)

Thus, the dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long.

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Answer:

72

Step-by-step explanation:

$48 + $20 = $68

$68 - $32 = $36

$36 × 2 = $72

Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Question 2

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

here u go I hope this is the answer ur looking for!

The probability of rolling a number less than 5 is 0.667.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event asked. The value is expressed from zero to one. An outcome is a value we can obtain.

As we are given a 6-sided dice therefore,

Total possible outcomes = 6

Favorable outcomes (that is less than 5) = 4                 [that are; 1, 2, 3, 4]

probability = number of favorable outcomes/number of possible outcomes

probability = 4/6

4/6 = 2/3

= 0.6666666666666

To round the value to three decimal places, we need to see if the fourth value after decimal is more than 5 or not. If it is more than 5, preceding digit is increased by 1. therefore, by applying the rule to the value we get

= 0.667                         [rounded to three decimal places as needed]

therefore, the probability of the event given, that is rolling a number less than 5 is 0.667.

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The height of the ball is given as 7.74 ft.

We have the value of h(X) to be

-[tex]-\frac{44x^{2} }{v^{2} } +x+6[/tex]

The initial velocity is given as v which is = 26

v = 26² = 676

the value of x is given as 2

We have to put these values in the formula

[tex]-\frac{44(2)^{2} }{676 } +2+6[/tex]

= 44 * 4/676 + 2 + 6

= -0.26 + 2 + 6

= 7.74

Hence we can say that the height of the ball is given as 7.74 ft.

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After calculation the percentage, we have come to find that 66.5 20% percent of 332.5 .

A percentage is a number or ratio in mathematics that could be expressed as a fraction of 100. If we need to calculate a percentage of a number, divide it by 100. As a result, the percentage denotes a part out of a hundred. The word % means "per 100." The symbol for it is "%."

Percentages can also be expressed as decimals or fractions, for example, 0.6%, 0.25%, and so on. Academic grades are calculated in terms of percentages. Ram, for example, received a 78% on his final exam. As a result, this percentage is calculated based on Ram's total marks across all subjects.

To find out percentage, We multiply the fraction of given numbers with 100

= 66.5/332.5 × 100

= 1/5 × 100

= 20%

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Answer:mkpewmg pmblembmfe

Step-by-step explanation:

7 t8gt385uhg

Based on the commutative property of addition, 2x + 21 = 21 + 2x.

The commutative property of addition states that when we change the order of arrangement of the addends, the value of the sum remains the same.

For example, 3 + 4 = 4 + 3.

Also, given the statement 2x + 21, we can state that:

2x + 21 = 21 + 2x

Therefore, based on the commutative property of addition, 2x + 21 = 21 + 2x.

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The number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A piece of wood was 12 feet long. Kendra cut the wood into pieces __

2/3 foot.

Let x be the number of pieces:

12/x = 2/3

x = 36/2

x = 18

Thus, the number of pieces are 18 if the piece of wood was 12 feet long. Kendra cut the wood into pieces 2/3 foot.

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Answer:

11

Step-by-step explanation:

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Answer:

4.69 x 10⁵

Step-by-step explanation:

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 469,000

New Number: 4.69000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 4 . 6 9 0 0 0

Decimal Count: 1 2 3 4 5

There are 5 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 4.69 (Please notice any zeroes on the end have been removed)

b = 5

Now the whole thing:

4.69 x 10⁵

Step 4

Check your work:

105 = 100,000 x 4.69 = 469,000

Answer:   [tex]4.61 \times 10^5[/tex]

Reason:

The original number is 461,000 or 461000

Place a decimal point between the first two nonzero values. Erase the zeros and we get 4.61

To get back to 461000, we need to move the decimal point 5 spaces to the right. This is the exponent for the [tex]10^5[/tex] portion.

So [tex]461,000 = 4.61 \times 10^5[/tex]

The number line which shows the solution to the inequality is option C

3x + 2 ≤ -11

or

4x - 3 > 9

3x + 2 ≤ -11

3x ≤ -11 - 2

3x ≤ -13

x ≤ -13/3

x ≤ -4.33

or

4x - 3 > 9

4x > 9 + 3

4x > 12

x > 12 / 4

x > 3

Ultimately, the answer to the inequalities is x ≤ -4.33 and x > 3

Therefore, the number line which shows the solution to the inequality is option C

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(a) X is distributed normally.

(b) The median recovery time is 3 days.

(c) The z score of the patient who takes 4.2 days to recover is 0.75.

(d) The probability of spending more than 2.3 days in recovery is 66.64 %.

(e) The probability of spending between 3.7 and 4.2 days in recovery is 10.7 %.

(f) The 85th percentile for recovery times is 5.24 days.

(a) We are informed that a certain surgical procedure's recuperation time for patients is typically distributed. As a result, X is distributed normally.

(b) The median will be equal to the mean because the patient recovery time has a normally distributed distribution. The median is therefore 3 days.

(c) The formula for z score is given as:

z = X - μ / σ

Now, we have the mean μ = 3 days.

Standard deviation, σ = 1.6 days

The observed value, X = 4.2 days

Therefore,

z = ( 4.2 - 3) / 1.6

z = 1.2 / 1.6

z = 0.75

(d) When X = 2.3 days

Then the z score will be:

z = X - μ / σ

z = 2.3 - 3 / 1.6

z = - 0.7 / 1.6

z = - 0.4375

The corresponding area for z = 0.4375 is 0.3336.

In order to determine the likelihood for a period longer than 2.3 days, we must look at the region to the right, which we can locate by deducting 0.3336 from 1.

Therefore, the probability will be:

p = 1 - 0.3336

p = 0.6664

p = 66.64 %

(e) Now, for the probability between X = 3.7 days and 4.2 days.

z₁ = (3.7 - 3) / 1.6 = 0.7/1.6 = 0.4375

z₂ = (4.2 - 3) / 1.6 = 1.2 / 1.6 = 0.75

The area for a z score of 0.4375 is 0.1664 and the area to left for a z score 0.75 is 0.2734.

Then the probability between 3.7 days and 4.2 days will be:

p = 0.2734 - 0.1664

p = 0.107

p = 10.7 %

(f) For the 85th percentile:

For 0.85 the z score from the table is 1.4.

So, z = 1.4

z = X - μ / σ

1.4 = ( X - 3) / 1.6

(1.4)(1.6) = X - 3

2.24 = X -3

X = 2.24 + 3

X = 5.24 days

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The complete question is mentioned below:

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X?

b. What is the median recovery time? __________days

c. What is the Z-score for a patient that took 4.2 days to recover?

d. What is the probability of spending more than 2.3 days in recovery?

e. What is the probability of spending between 3.7 and 4.2 days in recovery?

f. The 85th percentile for recovery times is _________days.

Answer:

-39

Step-by-step explanation:

Hello, to do this problem, we need to use substitution.

c=-4 and x=7

-5x+c

-5(7)+-4

-35-4

=-39

Hope that helps

:D

Answer:

c = -4

x = 7

- 5 (7) + (- 4)

- 35 + (- 4)

= - 39

Hope this helps :)