A plane can fly 520 miles in the same time as it takes a car to go 200 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.

Step-by-step explanation:

[tex]y = - 2x + 3[/tex]

The slope of the above line = -2

slope of the line perpendicular to the above line = 1/2

If it passes through point (4,-3) , it's equation

[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]

[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]

[tex]2(y + 3) = x - 4[/tex]

[tex]2y + 6 = x - 4[/tex]

[tex]x - 4 - 2y - 6 = 0[/tex]

[tex]x - 2y - 10 = 0[/tex]

A = 1, B = -2 and C = -10

A+B+C= 1+(-2)+(-10)

= 1-2-10

= 1-12

= -11

Answer:

A = 1, B = -2 and C = -10

Step-by-step explanation:

The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.

The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.

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Answer:

10.7°

Step-by-step explanation:

1 mile = 5280 feet

Tan(X) = 1000/5280 = 25/132

X = (tan^-1)(25/132)

X = 10.72444854

Answer:

Step-by-step explanation:

The movement of the forms a right angle triangle with the ground. The vertical distance which the plane moves represents the opposite side of the right angle triangle. The horizontal distance covered by the plane represents the adjacent side of the right angle triangle.

1 mile = 5280 feet

To determine the angle of elevation, θ, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan θ = 1000/5280 = 0.189

θ = Tan^-1(0.189)

θ = 10.7°

Answer:

c

Step-by-step explanation:

I think you missed attaching the photo, please see my attachment.

And the correct answer is C,

When you look at where the arc meets the parallel lines, if you create a seam between two points, you get a straight line parallel to the horizontal lines  so it makes the corresponding angles are congruent.

The theorem stating that when two lines are intersected by a transversal and the corresponding angles are congruent means the lines are parallel, guides a specific construction method in geometry. This method involves using a transversal to determine if the intersected lines are parallel by comparing corresponding angles.

The theorem 'when two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel' justifies a particular construction of parallel lines in geometry.

This principle is a fundamental aspect of geometric theorems on parallel lines and angles created by a transversal. To construct parallel lines using this theorem, one might follow these steps:

Identify or draw a transversal that intersects two lines.

Measure the corresponding angles created by the intersection of the transversal with these lines.

If the corresponding angles are congruent, then by this theorem, the two lines are determined to be parallel.

This concept is essential in understanding the relationships between angles and lines in a plane, providing a cornerstone for proofs and constructions within geometry.

Answer:

Therefore the shortest man of 65.6 cm was more extreme.

Step-by-step explanation:

A z-test is a statistic test. It is used to determine whether two population mean are different when the variances of the population are known and the sample size large.

[tex]z=\frac{x- \mu}{\sigma}[/tex]

z= the standarized z score

x = the height of sample

μ = mean  = 172.27 cm

σ = standard deviation = 8.82 cm

For tallest

x = 259

[tex]z= \frac{259-172.27}{8.82}[/tex]

  ≈9.83

For shortest

x= 65.6

[tex]z= \frac{65.6-172.27}{8.82}[/tex]

  ≈ - 12.09

The most extreme value has a z score that the furthest from 0.

Since -12.09 is further from 0 than 9.83.

Therefore the shortest man of 65.6 cm was more extreme.

Answer:

Each boy will get 25 marbles.

Step-by-step explanation:

Given:

William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.

Now, to write an expression using parentheses to find number of marbles each boy get.

Let the number of marbles each boy get be [tex]x.[/tex]

Total number of boys = 2.

Number of marbles first jar holds = 12.

                          Second jar holds = 21.

                        And third jar holds = 17.

As given, William shares marbles equally with his brother.

Now, we write the expression to find the number of marbles each boy get:

[tex]x=\frac{(12+21+17)}{2}[/tex]

[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]

[tex]x=6+10.5+8.5[/tex]

[tex]x=25.[/tex]

Therefore, each boy will get 25 marbles.

Answer: z = 280

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.

The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be

z = kx

When x is 10, z has the value 140. It means that

140 = 10k

k = 140/10

k = 14

The equation becomes

z = 14x

the value of z when x = 20 is

z = 14 × 20

z = 280

Answer:  a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.

Step-by-step explanation:

Since we have given that

264.34928 rounded to the nearest tenth.

So, it becomes [tex]264.3[/tex]

264.34928 rounded to the nearest thousandths.

So, it becomes [tex]264.349[/tex]

264.34928 rounded to the nearest one.

So, it becomes [tex]265[/tex]

264.34928 rounded to the nearest hundreds.

So, it becomes [tex]300[/tex]

264.34928 rounded to the nearest tens.

So,it becomes [tex]260[/tex]

264.34928 rounded to the nearest hundredths.

So, it becomes [tex]264.35[/tex]

Hence, a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.

a. 264.34928 rounded to the nearest tenth = 264.3

b. 264.34928 rounded to the nearest thousandth = 264.349

c. 265.34928 rounded to the nearest one = 265

d. 264.34928 rounded to the nearest hundred = 264.35

e. 265.34928 rounded to the nearest ten = 265.3

f. 264.34928 rounded to the nearest hundredth = 264.35

Here are the answers matched with their properly rounded values along with explanations:

a. 264.34928 rounded to the nearest tenth: 264.3

Explanation: The tenths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.3.

b. 264.34928 rounded to the nearest thousandth: 264.349

Explanation: The thousandths digit is 9, which is greater than or equal to 5. So, you round up to 264.349.

c. 265.34928 rounded to the nearest one: 265

Explanation: The nearest one for 265.34928 is simply 265 because it is already a whole number.

d. 264.34928 rounded to the nearest hundred: 264.35

Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.

e. 265.34928 rounded to the nearest tens: 270

Explanation: The tens digit is 6, and the digit immediately to the right of it is 5 or greater. So, you round up to 270.

f. 264.34928 rounded to the nearest hundredth: 264.35

Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.

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Answer: last option.

Step-by-step explanation:

There are several transformations for a function f(x). Some of them are shown below:

1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.

2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.

3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.

4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.

In this case you have the following function:

[tex]h(x)=log_6x[/tex]

And the function m(x) is obtained by transformating the function h(x). This function is:

[tex]m(x)=log_6(x+3)[/tex]

Then, based on the transformatios shown before, you can identify that:

[tex]m(x)=h(x+3)[/tex]

Therefore, you can determine that you could graph the function  [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.

Answer:

36 π square feet

Step-by-step explanation:

so the formula for area of a circle is  πr^2

so the radius is 6, which we can just plug in

π(6)^2

36π

so option 3

The required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression.
= x ² + 8x + 12 / x² - 2x -8
= (x + 6)(x + 2) / (x + 2)(x  - 4)

Since, if we put x = -2 and x = 4, the expression will we undefined.

And,
= x + 6 / x -4

Thus, the required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.

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A. 95     95x50=4750    then you divide 4750 by 50 and you get your answer

To find how long George will take to mop the floor, calculate the area of the court (95 ft x 50 ft = 4,750 ft²) and divide it by his mopping rate (50 ft²/min). The calculation shows it will take George 95 minutes to mop the floor.

To determine how long it will take George to mop the gym floor, we first calculate the area of the rectangular court.

Multiplying the length by the width gives us the total area that needs to be mopped:

Now, since George can mop 50 ft² in 1 minute, we divide the total area by the rate at which George can mop:

Therefore, it will take George 95 minutes to mop the gym floor, which corresponds to option (a).

Answer:

Step-by-step explanation:

Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14

They bought a movie for $12. The amount that they have left is

14 - 12 = $2

They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is

2/1 = 2

If they split the containers evenly between themselves, then each person would get

2/2 = 1 container of fruit salad

The mat adds 3 inches to each side, so the length would be 3+20 = 23 inches. The width would become 3 + 9 = 12 inches.Area = Length x width:

23 x 12 = 276 square inches

Answer:

b. AA postulate

Step-by-step explanation:

Answer:

The bottom answer

Step-by-step explanation:

Answer:

24p8 - 36p6 + 36p2 = 48p

Step-by-step explanation:

I hope this helps!

Answer:

PR² = PQ² + QR²

Step-by-step explanation:

Since the triangle PQR is a right triangle, according Pythagorean theorem:

So:

as

Answer:

PR² = PQ² + QR²

Step-by-step explanation:

Answer:

I have a feeling its B

Step-by-step explanation:

Vicky's Gross Monthly Income for the job at Southside High School is $3708.33.

Gross income of an individual is the income he/she receives before deduction and taxes.

Given that,

Base salary per year = $43,600

Income for coaching JC softball = $900

Free life insurance coverage = $15,000

Health & dental or medical premiums = $78/month

Gross income is the income an employee receives before all the deductions.

Insurance premiums are deducted from the base salary. So it is not included in gross income.

Annual Gross income = $43,600 + $900 = $44,500

Monthly Gross Income = $44,500 / 12 = $3708.33

Hence the monthly gross income is $3708.33.

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Answer:

The answer to your question is Ariel is correct, x = 27 ft

Step-by-step explanation:

Data

angle = Ф = 47°

Adjacent side = 25

Opposite side = x

Process

1.- To solve this problem, we must use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.

            tan Ф = Opposite side / Adjacent side

- Solve for Opposite side

            Opposite side (x) = Adjacent side x tan Ф

-Substitution

                                      x = 25 tan 47

                                     x = 25 (1.0724)

-Result

                                    x = 26.8 ≈ 27 ft

Ariel is correct

Answer:

Incorrect angle; 23 feet

Step-by-step explanation:

She has marked the angle incorrectly

Angle of depression is marked between the line of sight and the hypotenuse

The angle she should use is:

90 - 47 = 43

tan(43) = x/25

x = 25tan(43)

x = 23.31287715

Answer:

he ded

Step-by-step explanation:

\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \tohe no alive  because ⇆ω⇆π⊂∴∨α∈\neq  \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right.  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[tex]\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[/tex]

Answer:

Option B is correct.

Stephanie should add Jim to her health care plan.

Step-by-step explanation:

Let's take the options one by one.

Option 1

If Jim's employers insure him and his wife.

Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.

It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.

Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09

Option 2

If Stephanie's employers insure both of them.

Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.

It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.

Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2

Option 3

If each of them does an insurance plan with their respective employers

Jim’s employer pays 42% of his $378 monthly premium.

Stephanie’s employer pays 35% of her $298 monthly premium

Jim would pay (0.58 × $378) for himself = $219.24

Stephanie would pay (0.65 × $298) for herself = $193.7

Total they would pay in this option = $219.24 + $193.7 = $412.94

Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.

Hope this Helps!!!

Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.

An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.

The correct answer is option B.  Stephanie should add Jim to her health care plan.

The evaluation of each and every option is as follows:

Option 1

If Jim and his wife are covered by Jim's employer's insurance.

Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.

Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.

Jim's payment = = $471.09

Option 2

If both of them are protected by Stephanie's company's insurance.

Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.

Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.

Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).

Option 3

If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.

Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.

For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24

Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.

Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.

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Answer:

About 8 cans.

Step-by-step explanation:

Given:

She starts with nine cans of tomato sauce.

Then use is 9/10 of the cans for her first batch of calzones

To find:

How many cans of tomato sauce does Hannah use for the first batch of calzones ?

Solution:

She starts with number of cans = 9

Then use is [tex]\frac{9}{10}[/tex] of the cans.

Now, we will find number of cans used for the first batch of calzones by multiplying number of cans she starts with by fraction of  cans she used  for the first batch of calzones .

[tex]\frac{9}{10} of 9 cans = \frac{9}{10} \times9\\\frac{81}{10} = 8.1[/tex]

Therefore,  number of cans used for the first batch of calzones is about 8 cans.

Answer:

Therefore the length of aluminum surrounding the pool is 88 feet.

Step-by-step explanation:

Circle:

Given that the circular swimming pool has walls made of aluminum.

To find out the length of the of aluminum, we need to find out the circumference of the pool.

The radius of the circular pool is = 14 feet.

Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]

                                                                       [tex]=2\times \frac{22}{7} \times 14[/tex]  feet

                                                                     =88 feet

Therefore the length of aluminum surrounding the pool is 88 feet.

Answer:

This is the volume of cube V = 729 [tex]in^{3}[/tex]

Step-by-step explanation:

Surface area of cube = 486 [tex]in^{2}[/tex]

Surface area of the cube is given by A = 6 × [tex]a^{2}[/tex]

⇒ 6 × [tex]a^{2}[/tex] = 486

⇒ [tex]a^{2}[/tex] = 81

⇒ a = 9 in

This is the value of side of the cube. so volume of the cube is given by

⇒ V = [tex]a^{3}[/tex]

Put the value of a in above formula w get,

⇒ V = [tex]9^{3}[/tex]

⇒ V = 729 [tex]in^{3}[/tex]

This is the volume of cube

To find the volume of a cube with a surface area of 486 in², calculate the side length using the formula A=6s², leading to a side length of 9 inches, and then calculate the volume as V=s³, resulting in 729 cubic inches.

The volume of a cube with a given surface area using the formula A=6s², where A is the surface area and s is the side length of the cube. First, find the side length by dividing the given surface area by 6, then take the square root. After finding the side length, calculate the volume using the formula V=s³.

Given the surface area A=486 in², the side length s can be found as follows:

1) EF = 2 and DF = 4

2) KL = 4√3 and JL = 8

3) ST = 6 and RS = 6√3

4) PQ = 4.5√3 and RQ = 4.5

Step-by-step explanation:

Rules for special triangles 30°,60°,90° :

1) DE = 2√3 is opposite to 60°

⇒ 2√3 = a√3

⇒ a = 2

EF = a which is opposite to 30°.

⇒ EF = 2

DF = 2a which is opposite to 90°.

⇒ DF = 4

2) KJ = 4 is opposite to 30°

⇒ a = 4

KL = a√3 which is opposite to 60°.

⇒ KL = 4√3

JL = 2a which is opposite to 90°.

⇒ JL = 8

3) RT = 12 is opposite to 90°

⇒ 2a = 12

⇒ a = 6

ST = a which is opposite to 30°.

⇒ ST = 6

RS = a√3 which is opposite to 60°.

⇒ RS = 6√3

4) PR = 9 is opposite to 90°

⇒ 2a = 9

⇒ a = 4.5

PQ = a√3 which is opposite to 60°.

⇒ PQ = 4.5√3

RQ = a which is opposite to 30°.

⇒ RQ = 4.5

Sure, what do you need help finding?

Answer:

to find a percentage of a number u multiply/divide 100

Answer:

The plant makes 34,802,178 ball bearings in a single day

Step-by-step explanation:

The total output of a plant in a 5-day week is 4335 pounds

Each ball bearing weighs 0.0113g

We are to calculate the number of ball bearings made per day

First, we ensure both mass are in the same unit

Now 1 pound =453.5924 grams

4335 pounds=453.5924 X 4335 =1966323.054 grams

Number of bearings made in a week therefore

= 1966323.054 /0.0113=174010889.7

≈174010890 (to the nearest whole number)

Since there are 5 days in a week of production,

Daily Production=174010890/5

=34802178

The plant makes 34,802,178 ball bearings in a single da

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Vertex = (-5, -2)

Point = (-4, 2)

This is a vertical parabola the opens upwards.

The equation is

                             (x - h)² = 4p(y - k)

Substitution

                             (-4 + 5)² = 4p (2 + 2)

Simplification

                                      1² = 4p(4)

                                      1 = 16p

                                      p = 1/16

Equation of the parabola

                          (x + 5)² = 4/16(y + 2)

                          x² + 10x + 25 = 1/4y + 1/2

Conclusion

The coefficient of the squared expression is 1