Given the following information: calculate the perimeter of triangle rst. assume rzx is similar to rst. rz=21, ry= 24, rx= 39, zy=9 and sw=18

Answer:

288π

Step-by-step explanation:

The volume of a sphere can be evaluated by using the following formula:

[tex]A=\frac{4}{3}\pi r^{3}[/tex]

We are given that the radius is 6, so we can plug into the formula to solve:

[tex]A=\frac{4}{3}\pi*6^{3} =\frac{4}{3}*216*\pi =288\pi[/tex] (216/3 is 72, and 72*4 is 288)

Therefore, the volume is exactly 288π. The approximate answer, if you let π be 3.14 and evaluate it out, is around 904.78

9/100

Step-by-step explanation:

[tex]9\% = \frac{9}{100} [/tex]

9% as a Fraction is 9/100

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Answer:

1 19/42

- 1 1/30

3&4 are both 1 1/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Can 10 people be divided into two groups with a ratio of 1 : 2?

Explain.

10 : 3 = 3.33

or 10 : 3 = 9 remaining 1

since it is not possible to divide a person into three parts, your answer is no

The $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

Here,

P = $3000

r = 4% = 0.04

n = 2

t = 3 years

After plugging all the values in the formula:

[tex]\rm A = 3000(1+\dfrac{0.04}{2})^{2\times 3}[/tex]

After solving:

A = $3,378.49

I = A - P = 3,378.49 - 3000 = $378.49

Thus, the $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.

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Answer:

The third one of the first question.

Explanation:

Refer to the graph below. It should be similar to what your teacher gave you, based off the description.

Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.

As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.

In terms of notation, we can write [tex]\displaystyle \lim_{x\to3^{+}}f(x) = 3[/tex]

The portion [tex]x \to 3^{+}[/tex] means we're approaching 3 from the positive side, aka the right hand side on the number line.

Answer:

c) 19

Step-by-step explanation:

To find the length of JH, subtract the length of HM from JM.

Length of JH = JM - HM

                      = 40 - 21

                      = 19

Answer:

JH = 19

Step-by-step explanation:

from the diagram

JH + HM = JM , that is

JH + 21 = 40 ( subtract 21 from both sides )

JH = 19

The number of ways is 497420

The ways can the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled is [tex]22_{C_9}[/tex]

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

22C9 = 22! /(9!*13!) = 497420

Thus, In 497420 ways the team assign field positions to 9 of the 22 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled.

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The total distance the ball has traveled from the moment it is dropped until it hits the floor for the fourth time is: 300 feet.

First  bounce

160 feet

Second bounce

= 1/2×160 = 80 feet

Third bounce

= 1/2×80 = 40 feet

Fourth bounce

= 1/2×40 = 20 feet

Hence:

Total distance= (160 feet+ 80 feet + 40 feet+20 feet

Total distance= 300 feet

Therefore the total distance traveled by the ball is 300 feet.

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The substitution that should be used to rewrite the equation is u = x+5, the correct option is A.

The polynomials of the 2nd degree are called Quadratic Equations.

It has a general form as ax² +bx+c=0

To rewrite the expression as a quadratic equation  

6(x+5)² + 5(x+5)-4 = 0

=6(x+5)(x+5)+5(x+5)-4

=6(x² + 5x + 5x + 25)+5(x+5)-4

=6(x²+10x+25) + 5(x+5) - 4 = 0

=6x² + 60x + 5x + 150 + 25 - 4 = 0

=6x² + 65x + 171 = 0

This is the quadratic equation of the form ax² +bx+c=0

but if directly it has to be written in this ax² +bx+c=0 form , it can be written by substituting u = (x + 5)

6(x+5)² + 5(x+5)-4 = 0

6u²+5u-4 = 0

Therefore, the substitution that should be used to rewrite the equation is u = x+5, the correct option is A.

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The possible values of x be  4.8, 5.6 and 6.4.

The statement of equality between two expressions consisting of variables and/or numbers.

Given:

5x -4y = 24

when y=0

5x = 24

x = 4.8

when y=1,

5x= 28

x= 5.6

when y=2,

5x= 32

x= 6.4

Hence, the possible values of x is 4.8, 5.6 and 6.4.

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The equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is having only one solution.

Given equation 0.75(x+40)=0.35(x+20)+0.35(x-20)

We have to find the number of solutions.

To find the number of solutions we have to solve the equation for the value of variable x. Equation is often solved to find the value of variables.

Equation : 0.75(x+40)=0.35(x+20)+0.35(x-20)

Opening the brackets and multiply the numbers outside by the numbers in the bracket.

0.75x+30=0.35x+7+0.35x-7

Take all the numbers having same variables at one end of equal to.

0.75x-0.35x-0.35x=7-7-30

0.75x-0.7x=-30

0.05x=-30

x=-30/0.05

x=-600

Which is the only value of x.

Hence the number of solutions of the equation 0.75(x+40)=0.35(x+20)+0.35(x-20) is  one.

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The 95% confidence interval for the mean is (1.535, 1.504).

It is given that a machine produces 1.50 pounds of cereal. The sample is 56 cereal boxes. The sample mean filling weight is calculated as 1.52 pounds. The population standard deviation is known to be 0.06 pounds.

Mean = 1.50 pounds

x = 1.52 pounds

Standard deviation = SD = 0.06 pounds

n = 56

We need to find the 95% confidence interval for the mean.

So, z = 1.96

So, the confidence interval would be

[tex]x[/tex]±[tex]z\frac{mean}{\sqrt{n} }[/tex]

[tex]1.52[/tex]±[tex]1.96*\frac{0.06}{\sqrt{56} }[/tex]

= [tex]1.52[/tex]±[tex]1.96*0.00801[/tex]

= [tex](1.52 + 0.0156996),(1.52 - 0.0156996)[/tex]

= [tex](1.535, 1.504)[/tex]

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Answer:

1. Jamaal

2. 42 more dishes

Step-by-step explanation:

1. Jamaal: 25 dishes per hour and works for 3 hours

25(3) = 75 dishes

Daniel: Daniel can wash 22 dishes every two hours.

22 = 2x

11 = x

11(3) = 33 dishes

2. 75 - 33 = 42

Jamaal can wash 42 more dishes than Daniel.

Jamaal washes 25 dishes per hour and works for 3 hours. Daniel can wash 22 dishes every two hours. Jamaal washed 42 more dishes than Daniel in 3 hours.

Let's calculate the number of dishes washed by each person in 3 hours and then compare the results.

Jamaal:

Jamaal washes 25 dishes per hour and works for 3 hours.

Number of dishes washed by Jamaal in 3 hours = 25 dishes/hour * 3 hours = 75 dishes

Daniel:

Daniel washes 22 dishes every two hours.

To find the number of dishes washed by Daniel in 3 hours, we need to find how many times he washes dishes in 3 hours.

Number of times Daniel washes dishes in 3 hours = 3 hours / 2 hours (time for 1 cycle) = 1.5 cycles

Now, multiply the number of cycles by the number of dishes washed per cycle:

Number of dishes washed by Daniel in 3 hours = 1.5 cycles * 22 dishes/cycle = 33 dishes

Comparison:

Jamaal washed 75 dishes in 3 hours.

Daniel washed 33 dishes in 3 hours.

Now, let's find the difference in the number of dishes washed by each person:

Difference = Jamaal's dishes - Daniel's dishes

Difference = 75 dishes - 33 dishes = 42 dishes

Therefore, Jamaal washed 42 more dishes than Daniel in 3 hours.

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The angle for which the sine value is 0.6691 is found to be 42°.

What is the sine value?

A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.

When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.

[tex]sin^{-1}(0.6691)[/tex]=41.99°≈42°

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Answer:

4x + 3y = 12

Step-by-step explanation:

Answer:

4x + 3y = 12

Step-by-step explanation:

At x-intercept, y = 0.

∴ When we substitute y = 0 into the equation, x should equal 3.

• 1st equation:     3x + 4(0) = 12  ⇒  x = 4       ❌

• 2nd equation:  4x + 3(0) = 7    ⇒  x = 7/4    ❌

• 3rd equation:   3x + 4(0) = 7    ⇒  x = 7/3    ❌    

• 4th equation:   4x + 3(0) = 12   ⇒  x = 3       ✅

This means the 4th option is the correct one.

To check, we can replace x = 0 into the 4th equation to see if the y-intercept value comes out to be 4:

4(0) + 3y = 12    ⇒    y = 4     ✅

Answer:

not similar

Step-by-step explanation:

not similar--it doesn't work out for the angles to be similar

if we find the angle x of the right-hand triangle, we can tell it would be 41 degrees

meaning that these triangles are not similar

Answer:

Ends with r and has five or fewer letters

Step-by-step explanation:

Answer:

The answer is : B

Step-by-step explanation:

trust me I did it on edge 2022

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial is x³- 7x² - 6x + 72.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

The polynomial using the given information can be made as shown below.

Given the zeros of the polynomial are -3, 4, and 6.

P(x) = (x+3)(x-4)(x-6) = x³- 7x² - 6x + 72

To check the end behaviour of the function, the graph of the function can be plotted as shown in the below image.

Hence, the polynomial is x³- 7x² - 6x + 72.

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The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

The final value of any quantity growing constantly at a particular rate is given as [tex]V = V_{0}e^{rt}[/tex] ,

where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.

The current population of squirrels (V₀) = 100.

The growth rate (r) = 5% per month.

The time period (t) = 1 year = 12 months.

Hence, the final population of squirrels (V), is given as:

[tex]V = V_{0}e^{rt}[/tex] ,

or, [tex]V = 100e^{(0.05*12)}[/tex] ,

or, [tex]V = 100e^{0.60}[/tex] ,

or, V = 100*1.822119,

or, V = 182.2119 ≈ 182.

Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

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The ship traveled 80 miles in 4 hours while the submarine traveled 75 miles in 5 hours.

Based on the information provided, we can logically deduce that the ship is initially 80 miles away from its destination. Thus, f(x) would be equal to 0, if it traveled 80 miles and 0 miles away from its destination:

f(x) = 80 - 20x

0 = 80 - 20x

20x = 80

x = 80/20

x = 4 hours.

By critically observing the graph (see attachment) for the submarine's voyage, we can logically deduce the following:

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The functions that have complex roots are b and d.

Complex roots are the imaginary root of polynomial functions. The complex roots are represented as α = a + ib, and β = c + id.

When the quadratic equation has a discriminant value less than zero will have imaginary roots.

Out of the given functions, a ,b, c, and d, the function with complex roots are b and d.

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Answer:

b &d is correct. i just took the test. :)

Step-by-step explanation:

Answer:

it is B

Step-by-step explanation:

that is because j3jejejdudduiwjsj

The requried pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1

To determine how many round trips the pilot can make before having to refuel, we need to consider both the fuel capacity and the flight time limit.

Given:

Maximum fuel capacity = 5,300 gallons

Flight time limit before refueling = 400 minutes

Fuel required for one-way flight = 2,000 gallons

Flight time for one-way flight = 190 minutes

First, let's calculate the maximum number of one-way trips the pilot can make based on the fuel capacity:

Max one-way trips based on fuel capacity = Maximum fuel capacity / Fuel required for one-way trip

Max one-way trips = 5,300 gallons / 2,000 gallons = 2.65 trips

Since we cannot have a fraction of a trip, we need to consider the flight time limit.

The total flight time for a round trip is twice the one-way flight time: 2 * 190 minutes = 380 minutes.

The pilot can fly a round trip as long as the flight time for the round trip is within the flight time limit. In this case, the round-trip flight time of 380 minutes is less than the flight time limit of 400 minutes.

Therefore, the pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1

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Answer:

$11.62

Step-by-step explanation:

2.54×3=$7.62

0.76+7.62=8.38

20-8.38=$11.62

Answer:

Step-by-step explanation:

Discussion

3 cappuccinos at 2.54 each     2.54 * 3 = 7.62

1 bottle of water at 0.76              0.76*1  =   .76     Add

Total                                                             8.38

Change = 20 - 8.38 = 11.62

Answer

She should receive 11.62 in change.

Answer:

The slope of the line representing the linear function f(x) is determined as [tex]$-\frac{1}{2}$[/tex]. The function f(x) is decreasing because the slope is less than zero, i.e., m<0.

Step-by-step explanation:

A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).

It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.

Step 1 of 1

Determine the slope of the line.

The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

So, substitute [tex]$4 \& 3$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$0 \& 2$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,[tex]$m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$[/tex]

The slope of the line is obtained as [tex]$-\frac{1}{2}$[/tex]. Now, as [tex]$-\frac{1}{2} < 0$[/tex], so the function f(x) is decreasing.

Answer:

[tex]\textsf{Perimeter}=x^2+10x-1[/tex]

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given sides of a triangle:

Therefore, to find the perimeter of the triangle, sum the given sides:

[tex]\begin{aligned}\sf Perimeter & = (2x+3)+(8x-4)+x^2\\& = 2x+3+8x-4+x^2\\& = x^2 + 2x+8x+3-4\\& = x^2+10x-1\end{aligned}[/tex]

Perimeter=

Answer:

x <= -2 or x >= 3

Step-by-step explanation:

Shaded circles represent <= or >=, and the first arrow points left from -2, and the second arrow points right from 3. Therefore x <= -2 or x >= 3 would represent the graph.