Which of the following is the length of the unknown leg of a right triangle that has one leg length of 8 feet and a hypotenuse of 12 feet? (Round tethe nearest tenth.)14.4 feet4 feet40 feet8.9 feet

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

Read more about division at:

brainly.com/question/11421834

#SPJ1

A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

Learn more about line equation here:

https://brainly.com/question/29813143

#SPJ4

The volumes of the prisms are :- 1) 11760 units³, 2) 7938 units³, 3) 9261 units³, 4) 22800 unit³, 5) 11781 units³, 6) 38936 units³, 7) 23125 units³, 8) 26208 units³ and 9) 14688 units³

A prism is a solid shape that is bound on all its sides by plane faces.

Given are prisms, we need to find their volumes :-

Volume = area of base × height

1) Base is a rectangle, area = length × width, height = 24

Volume = 24·14·35 = 11760 units³

2) Base is a rectangle, area = length × width, height = 21

Volume = 21·14·27 = 7938 units³

3) This is a cube, with side 21 units

Volume of cube = side³ = 9261 units³

4) This is a trapezoidal prism,

Volume = 1/2(b1+b2) × height × length = 1/2(36+24) × 38 × 20

= 22800 unit³

5) This is a triangular prism,

Volume = 1/2 × height × length × base

= 1/2 × 33 × 34 × 21 = 11781 units³

6) This is a cylinder,

Base is circular, volume = π·radius²·height

= 3.14·20·20·31 = 38936 units³

7) Base is a rectangle, area = length × width, height = 37

Volume = 25·37·25 = 23125 units³

8) Base is a rectangle, area = length × width, height = 28

Volume = 39·24·28 = 26208 units³

9) Base is a rectangle, area = length × width, height = 36

Volume = 36·24·17 = 14688 units³

Hence, the volumes of the prisms are :- 1) 11760 units³, 2) 7938 units³, 3) 9261 units³, 4) 22800 unit³, 5) 11781 units³, 6) 38936 units³, 7) 23125 units³, 8) 26208 units³ and 9) 14688 units³

Learn more about prisms, click;

https://brainly.com/question/29722724

#SPJ9

Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

The solution of the equation using the substitution method is given as x = -1 and x = 2.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into one linear equation with just one variable, making it much simpler to solve.

The two equations are y+3x=0 and y-6=-3x².

The first expression can be written as:

y + 3x = 0

y = -3x

Substitute the value of y in the second equation:

y-6=-3x²

-3x - 6 = - 3x²

Rearrange the equation:

3x² - 3x - 6 = 0

Take 3 as the common term from the equation:

x² - x - 2 = 0

x² - 2x + x - 2 = 0

x(x - 2) + 1(x - 2) = 0

(x + 1) (x - 2) = 0

x = -1 and

x = 2

Hence, the solution of the equation using the substitution method is given as x = -1 and x = 2.

Learn more about substitution method here:

https://brainly.com/question/22340165

#SPJ1

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

The following triangle is a right-angle triangle. Option B is correct.

If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.

From the given triangle, it is observed that one of the angles is 90°, showing the given triangle is a right-angle triangle.

Hence, option B is correct.

To learn more about the right-angle triangle, refer;

https://brainly.com/question/3770177

#SPJ2

The number of months to reach 51 can be illustrated as 3060 - 100x = 51.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both.

The farmer planted 3,060 tomato plants in his garden.

Let's assume there's a decrease of 100 monthly.

The number of months, x, it will take for the number of tomato plants in his crop to reach 51 = c

This will be:

3060 - 100x = 51.

This illustrates the equation for the number of months.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

Answer:

41.6 or 42

Step-by-step explanation:

AP = EP / YP 50 x 8 = 400 / .60 = 666.66 / 16 = 41.6 or 42

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Answer:

Slope

Step-by-step explanation:

Answer: 25cm

Step-by-step explanation:

Since the field is square we can understand each side is an equal length

This means we just have to use the formula...  

\(A^2 = 625\)

\(\sqrt{a^2} = \sqrt{625}\)

a = ±25

Since it is a real thing, we are only looking at positive values, therefore your answer is

25cm

If the two stations have the same bit rate, they will both have to be on air for the same amount of time to broadcast 4 minutes of news, regardless of the specific bit rate

What is time in maths ?

In mathematics, time is often thought of as a dimension, similar to length, width, and height. However, time is unique in that it only moves in one direction, from the past to the future. Time can be measured in various units such as seconds, minutes, hours, days, weeks, months, and years.

The length of time a station will have to be on air to broadcast 4 minutes of news depends on the bit rate of the broadcast.

The bit rate is the amount of data transmitted per second in a digital signal. The higher the bit rate, the more data can be transmitted per second, resulting in higher audio or video quality but also a larger file size.

Assuming the two stations have different bit rates, the station with the lower bit rate will have to be on air longer to broadcast the same 4 minutes of news than the station with the higher bit rate. This is because the station with the lower bit rate can transmit less data per second, so it will take longer to transmit the same amount of information.

For example, if Station A has a bit rate of 128 kbps (kilobits per second) and Station B has a bit rate of 256 kbps, Station A will have to be on air for twice as long as Station B to transmit the same 4 minutes of news, as it can transmit only half as much data per second as Station B.

Hence, If the two stations have the same bit rate, they will both have to be on air for the same amount of time to broadcast 4 minutes of news, regardless of the specific bit rate

To learn more about Time from given link.

https://brainly.com/question/27792043

#SPJ1

Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.

To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.

Number of jars sold in the second month: 203

Number of jars sold in the first month: 145

Percentage of second month's sales = (203 / 145) * 100 ≈ 140%

For such more question on multiply

https://brainly.com/question/29793687

#SPJ8

Answer:

the answer I got is 91

hope that help

Answer:

(B) 98

Step-by-step explanation:

12x-10=10x+8

=)12x-10x=8+10

=)2x=18

=)x=9

AFC=12x-10

=){12(9)}-10

=)108-10

=)AFC= (B) 98

Hope this helps

LMK if its wrong and sorry!! if it is

Answer:

For an overall profit, we need at least 97 people to go mushroom hunting.

Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.

Step-by-step explanation:

The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.

If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x

The amount of mushroom obtained is given as

M = (100x - x²) in pounds

The selling price of 1 pound = $60

The cost of M pounds = 60M = 60(100x - x²)

= (6000x - 60x²)

At socially optimal number,

200x = 6000x - 60x²

60x² - 6000x + 200x = 0

60x² - 5800x = 0

x(60x - 5800)

x = 0 or (60x - 5800) = 0

x = 0 or x = (5800/60) = 96.67

Socially optimal number of people = 0 or 96.67

For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67

Any number above this number will result in an overall profit, and any number below it results in an overall loss.

So, for an overall profit, we need at least 97 people to go mushroom hunting.

Hope this Helps!!

Answer:

48 people

Step-by-step explanation:

When allocating resources to a particular task it is important to assign optimal units of resources.

In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.

Optimal = (M÷x)Px - 200= 0

Optimal= {(100x -x^2) ÷ x} * 60 = 200

Optimal = 6000 - 60x = 200

x= 96.666~ 97 people

However to maximise profit MTB = MTC

Socially Optimal quantity = 60(100x - x^2) -200

∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200

x = 48.33~ 48 people

So 48 more people go mushroom hunting than is socially optimal

Answer:

2.5 mg

Step-by-step explanation:

Given the data:

23 24 23 29 28 26 27 28 26

The sample standard deviation, s

s = sqrt[Σ(x - mean)²] ÷ (n - 1)

Mean, m = ΣX / n

n = 9

Mean = 234 /9 = 26

Using a calculator :

s = 2.236

The margin of error, MOE

MOE = Tcritical * s/sqrt(n)

Tcritical at df = (n-1) = 9-1 = 8 , α = 0.01 = 3.35536

MOE = 3.35536 * 2.236/sqrt(9)

MOE = 3.35536 * 2.236/3

MOE = 3.35536 * 0.7453333

MOE = 2.50086

MOE = 2.5

The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).

Here,

To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.

For the first equation, we can simplify it as follows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simplify it as follows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angles in each triangle.

In triangle ARST, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle R = 2x

= 2(14)

= 28 degrees

angle S = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

angle T = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

In triangle ANSP, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle N = 3x + 9

= 3(14) + 9

= 51 degrees

angle S = 180 - (angle A + angle N)

= 180 - (28 + 51)

= 101 degrees

angle P = 180 - (angle N)

= 180 - 51 = 129 degrees

To know more about angle,

brainly.com/question/14569348

#SPJ1

Answer:

$25705.38

Step-by-step explanation:

$46,900/ ?= 46,900/1*1.62^4 *10   =  46,900/68.8747536 *100 = 68094.6175 = $68094.62     we can deduct to see how much he saves instead say compared to approx monthly rental $800 -$1000 = $68094.62 -$46,900 =$21,194.62 over 10 years because investment is cheaper than rental as $21,194.62 /10 =$2119.462 yearly =2119.462/12 monthly =£176.621833 and even if rental if say was as low as $600 it is still more than 200% cheaper to invest. however this question suggests compound of savings before purchase. It is same indifference of interest so we deduct again....$46,900 -$21,194.62 =$25705.38= 68094.6175-46,900 =21194.6175 and 46,900-21194.6175 =25705.3825

Given data:

The first condition is AB=XY.

The second condition is BC=YZ.

The third condition is ∠B=∠Y.

Follow the above condition then, triangle ABC is congruent to the triangle XYZ by SAS.

Thus, the first statement is true.

Answer:

let Elijah age be a

Then

2*a + 17 =47

2a=47-17

2a=30

a=15

Step-by-step explanation:

The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

To learn more about the algebraic identities visit:

https://brainly.com/question/16857438

#SPJ1

Given:

x=1 y=-3 m=1/2

We need to find the intercept by substituting the above values into y=mx + b and then solve for intercept(b).

That is

-3 = (1/2)(1) + b

-3 = 1/2 + b

subtract 1/2 from both-side of the equation.

-3 - 1/2 = b

The y-intercept is (0, -7/2)

The equation of the line can be formed by substituting the value of m and b.

That is;

For the graph, we can just plot this two points;

(1, -3) and (0, -3.5)

Below is the sketch of the graph;

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

For more such questions on numbers visit:

https://brainly.com/question/24644930

#SPJ8

Answer:

Kathleen ran  2 3/16miles

Answer:

The correct answer is option B

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer: 20,085

Step-by-step explanation: 2,000x10=20,000. 8.5x10=85. 20,000+85=20,085.

                               I hope I got this right and if I did it right.

The sinusoidal function graph has a period of 2·π and a minimum point

with coordinates (-0.5·n·π, -6) where n = -5, -1, 3, ...

Response:

The minimum value of a function is the lowest vertex value of the

function.

The given graph description, is the graph of the following function;

f(t) = 0.5·sin(t) - 5.5

The minimum value is given at the location where, sin(t) = -1, which gives;

f(t) = 0.5 × (-1) - 5.5 = -6

The minimum value of the function is therefore;

Learn more about the graphs of functions here:

https://brainly.com/question/26254100

Given: A function-

Required: To determine the domain of the function.

Explanation: The domain of a function is the set of all the input values or x-values at which the function f(x) exists.

The square root of a negative number does not give any real value. Hence, the function will exist for-

Hence, the domain is-

Final Answer: Option D is correct.