Find the perimeter of the triangle.​

Answer:

bother = 6 years ; sister = 12 years

Step-by-step explanation:

s = sister

b = brother

s - b =  6

s * b = 4(s+b)

s = b + 6

b(b+6) = 4(b+6 + b)

b² + 6b = 4(2b + 6)

b² + 6b = 8b + 24

b² + 6b - 8b - 24 = 0

b² - 2b - 24 = 0

(b-6)(b+4) = 0

b = 6

b = -4 (impossible because an age can’t be negative)

s = 6 + 6

s = 12

The values of x and w on the triangle are given as follows:

w = 14.4, x = 11.2.

The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.

The three trigonometric ratios are given as follows:

For the angle of 48º, we have that:

Hence:

tan(48º) = 16/w

w = 16/tan(48º)

w = 14.4.

For the angle of 32º, we have that:

Hence:

tan(32º) = 16/(14.4 + x)

tan(32º)(14.4 + x) = 16

x = (16 - 14.4tan(32º))/tan(32º)

x = 11.2.

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In the proof of given identity, cos(π - A) = -cos A. Therefore, step 1 is error made.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

The given identity is,

cos(π - A) = -cos A.

Use formula for cos(a − b) = cosa . cosb + sina . sinb

cos(π - A) = cosπcosA + sinAsinπ

                = (−1)(cosA) + (sinA)(0)

                = −1.cosA + (sinA)(0)

                = −cosA + 0

                 = −cosA

Since, in the step 1 the formula is wrongly used,

Therefore, step 1 is error made.

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Answer:  12

Step-by-step explanation:

hope this helps

Answer:

There are 9 small $5 bags and 6 large $8 bags

Step-by-step explanation:

9 x 5 = 45

6 x 8 = 48

45 + 48 = 93

Answer:

I think it’s 4/n and 4 divided by n. Sorry if it’s wrong!

Step-by-step explanation:

Answer:

They would have sold 8.2 eggs

Step-by-step explanation:

^

Answer: 1, 3

Step-by-step explanation:

Two more adults can board the elevator if there are 17 children present inside.

The number of adults who can still enter will be determined by the linear equation solution.

let

20c = 15a ; 5 divided by both sides

4c = 3a

Another 3 kids can enter the elevator if there are already 17 in it.

The fact that;

3c =  9/4 a

3c =  9/4 a

3c = 2.25 a

3c = 2 a (no fraction)

Thus, two more adults can board the elevator if there are 17 children present inside.

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Answer:

Below

Step-by-step explanation:

Slope , m, is calculated  (y1-y2) / ( x1-x2) =

   Using the first two points :   (-5-0) / (-3 -0) = 5/3

slope = 5/3

The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                        = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

             = 58 × 0.94

             = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                   = √ 58 × 0.94 × 0.06

                                   = √3.2712

                                   = 1.808

Variance 'σ²' =  np( 1 - p )

                    = 58 × 0.94 × 0.06

                   = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

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The expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

What is a number line?

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In the given number line, the distance between point A and point B is 5.

Now we have to check each option

| 3 | + | -2 | = 3 + 2  = 5

| -2 + 3 | = | 1 | = 1

| -3 - 2 | = | -5 | =5

3 - ( -2 ) = 3+ 2 = 5

| 3 - ( -2 ) | = |3 + 2| = 5

Hence, the expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

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Answer:

{-1, 0, 1, 3}

Step-by-step explanation:

A relation is a set of ordered pairs of numbers. The domain of a relation is the set of all the first elements (or x-values) in the ordered pairs. In this case, the relation is (-1,5) , (0,4), ( 1,2) , (3,-2), so the domain is the set of all the x-values in these ordered pairs, which is the set {-1, 0, 1, 3}. Therefore, the domain of the relation is {-1, 0, 1, 3}.

Answer:  slope -intercept form = [tex]-\frac{3}{10} x-\frac{7}{10}[/tex] the slope = [tex]-\frac{3}{10}[/tex] and the y-intecept = [tex](0,-\frac{7}{10} )[/tex]

Step-by-step explanation: I used y=mx+b and filled it in with the infomation that I already knew. Hope this helps :)

There are 2 hours of television must you watch in the eighth week to meet your goal.

What is television?

The transmission of audio and video data electronically between a source and a recipient.

The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.

Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.

Suppose x is the hours of watching television in the 8th week.

Let the average of watching television per week is 1.5.

⇒

[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]

Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.

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Answer:

Hi again, use the sine rule for length. answer: 82.42

Step-by-step explanation:

Heather worked 5 hours every evening during each dinner shift.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

Let morning shift = m

evening shift = e

Representing the word problem in an equation;

4(m + e) = 28

Diving both sides by 4

m + e = 7

but she always works 2 hours in th morning shift

2 + e = 7

e = 7 - 2

e = 5

Therefore she worked 5 hours in the evening shift for 4 days.

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Answer:

The volume of the cube is increasing faster.

The volume of the cube with length : [x] is increasing faster.

Given is that the volume of a cube with length [x] is V(x) = x³. The volume of the sphere with radius (1/2)x is shown in the graph.

We have the volume of the cube with length : [x] is -

V{C} = x³

Volume of the sphere with radius : (1/2)x is

V{S} = (4/3)πr³ = (4/3)π(x/2)³ = πx³/6

V{S} = πx³/6

Refer to the graph of the function attached of both the function. It can be seen that the function of the volume of the cube with length [x] is increasing faster.

Therefore, the volume of the cube with length : [x] is increasing faster.

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Answer: The first job seems better.

Step-by-step explanation:

If 1 month = 4 weeks:

40 x 40 = 1600 per week

40 x 160 = 6400 per month

250 per week on gas

250 x 4 = 1000 per month on gas

1600 - 250 = 1350

6400 - 1000 = 5400

You would earn $1350 per week on the first job, and $5400 on this job.

_____________________________________________________

25 x 160 = 4000 per month

25 x 40 = 1000 per week

100 per week on gas

100 x 4 = 400 per month on gas

1000 - 100 = 900

4000 - 400 = 3600

$900 per week on the second job, and $3600 per month on this job.

Hello,

I hope you and your family are doing well!

To compare the two jobs and determine which one is more financially advantageous, you need to calculate the total income and total expenses for each job on a monthly basis.

For the first job, the total income is 40 dollars per hour * 160 hours per month = 6400 dollars per month. The total expenses are 250 dollars per week * 4 weeks per month = 1000 dollars per month. The net income is 6400 dollars per month - 1000 dollars per month = 5400 dollars per month.

For the second job, the total income is 25 dollars per hour * 160 hours per month = 4000 dollars per month. The total expenses are 100 dollars per week * 4 weeks per month = 400 dollars per month. The net income is 4000 dollars per month - 400 dollars per month = 3600 dollars per month.

Based on these calculations, the first job is more financially advantageous because it has a higher net income. You would earn an additional 1800 dollars per month by working the first job instead of the second job.

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Answer:

-----------------------------------

Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):

The matching choice is B.

Answer:

B)  (2x + 3)(4x² - 6x + 9)

Step-by-step explanation:

Given expression:

[tex]8x^3+27[/tex]

Rewrite  8 as 2³  and  27 as 3³:

[tex]\implies 2^3x^3+3^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]

[tex]\implies (2x)^3+3^3[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]

Therefore:

Using the Sum of Cubes formula:

[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]

The coordinates of the midpoint of line segment  A (-4,6) and B (2,-3) is M (-1 , 3/2).

A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.

Given:

Points A (-4,6), and B (2,-3)

Calculate the midpoint of the line segment by the formula given below,

[tex]M [(x_1 + x_2) / 2 \ \ , (y_1 + y_2)/2][/tex]

Substitute the values,

M [(-4 + 2) / 2 , (6 + (-3) / 2)]

M [(-2 / 2) , (3 / 2)]

M (-1 , 3/2)

Therefore, the coordinates of the midpoint of line segment  A (-4,6) and  B (2,-3) is M (-1 , 3/2).

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The amount invested at 8% and 6% is 1000 and 1900 respectively.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, The person invested $2900 in two mutual funds and the total profit is $194.

Let the amount invested at 8% is x, then the amount invested at 6% is:

2900-x

Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194

8x/100 + 6(2900 - x)/100 = 194

8x + 17400 - 6x = 19400

2x = 19400 - 17400

2x = 2000

x = 1000

The amount invested at 6% is:
2900 - 1000

= 1900

Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.

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The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction

Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.

The equation of the reaction is written as

2H₂O + 2K → 2KOH + 2H₂

The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor

The oxidizing agent is water which ended up as Hydrogen molecule

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The probability to get the numbers greater than 2 from the outcomes of  the event of rolling a single fair die is equal to P(A) = 2/3.

As given in the question,

Event is rolling a single fair die.

Number of fair die to be rolled = 1

Possible outcomes =  { 1, 2, 3, 4, 5, 6 }

Total number of possible outcomes = 6

Numbers greater than 2 on rolling a single fair die = { 3, 4. 5,6 }

Number of favourable outcomes = 4

Probability of getting a number greater than 2

= (Number of favourable outcomes) / (Total number of outcomes)

= 4 / 6

= 2 / 3

Therefore, the probability of getting a number greater than 2 while rolling a single fair die is equal to 2 / 3.

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Answer:

P(Success1) =1/6

P(Success2) =1/6

P(2Success) =1/6 × 1/6 = 1/12