In a right triangle the two legs are measures of 4x and 3x with a hypotenuse measurement of 5x. If the area of the triangle is 24 square units, find the cosine of each acute angle.

Answers

Answer 1

The cosine of the acute angles are 0.80 and 0.60 respectively

The given parameters are:

[tex]Leg\ 1 = 4x[/tex]

[tex]Leg\ 2 = 3x[/tex]

[tex]Hypotenuse = 5x[/tex]

Let the acute angles be [tex]\alpha[/tex] and [tex]\beta[/tex]

The cosine of the acute angles is calculated using:

[tex]\cos(\alpha) = \frac{Leg\ 1}{Hypotenuse}[/tex]

[tex]\cos(\beta) = \frac{Leg\ 2}{Hypotenuse}[/tex]

So, the formula becomes

[tex]\cos(\alpha) = \frac{4x}{5x}[/tex]

[tex]\cos(\alpha) = \frac{4}{5}[/tex]

[tex]\cos(\alpha) = 0.80[/tex]

and

[tex]\cos(\beta) = \frac{3x}{5x}[/tex]

[tex]\cos(\beta) = \frac{3}{5}[/tex]

[tex]\cos(\beta) = 0.60[/tex]

Hence, the cosine of the acute angles are 0.80 and 0.60 respectively

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Related Questions

Whats different for the functions

Answers

This would cause the function to shift 4 units to the left, because it affects the x value/ the input of the function.

10^x

And with the g(x), you’ll get 10^(x+4). But if it were out of the parentheses, 10^x + 4 then it would shift upward 4 units.

solve the system of inequalities x>17, x>12

Answers

Answer:

x is greater than 17

Step-by-step explanation:

x > 12

x > 17

x can be greater than 17

Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1

Answers

The only 2-digit number that is lesser than 50 and the sum of its digits remain unaffected despite being multiplied by a number < 1 would be '18.'

To prove, we will look at some situations:

If we add up the two digits of 18. We get,

[tex]1 + 8 = 9[/tex]

And we multiply 18 by 2 which is greater than 1. We get,

[tex]18[/tex] × [tex]2 = 36[/tex]

The sum remains the same i.e. [tex]3 + 6 = 9[/tex]

Similarly,

If 18 is multiplied to 3(greater than 1), the sum of the two digits comprising the number still remains the same;

[tex]18[/tex] × [tex]3 = 54[/tex]

where (5 + 4 = 9)

Once more,

Even if 18 is multiplied to 4 or 5(greater than 1), the sum of its digits will still be 9.

 [tex]18[/tex] × [tex]4 = 72[/tex]

[tex](7 + 2 = 9)[/tex]

[tex]18[/tex] × [tex]5 = 90[/tex]

[tex](9 + 0 = 9)[/tex]

Thus, 18 is the answer.

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5+a2+ab-9c if a=5 b=4c=0

Answers

5+a2+ab-9c

let's just substitute a with 5, b with 4 and c with 0

5+5*2+5*4-9*0

= 5+10+20+0

= 35

please answer this!!​

Answers

triangle is always 180

both sides are equal so both sides are 51
51+51=102

180-102=78

equivalent expression: 3 + 4(2z - 1)

Answers

Answer:

8z - 1

Step-by-step explanation:

Given

3 + 4(2z - 1) ← multiply each term in the parenthesis by 4

= 3 + 8z - 4 ← collect like terms

= 8z - 1

Answer:

-1 + 8z

Step-by-step explanation:

First use the distributive property of multiplication (Just multiply 4 with all numbers in the parenthesis):

3 + 4(2z - 1)

3 + 8z - 4

Group like terms:

3 + 8z - 4

-1 + 8z

The answer is -1 + 8z

Hope this helped.

cho hình thang vuông abcd vuông tại A và D có AD= a căn 3, DC=3,AB= 2a. chứng minh AC vuông góc với BD

Answers

I am not understanding the language

Answer:

its Vietnamese

Step-by-step explanation:

I just dont understand what that type of math is? sorry ):

Elliot is 2 times as old as Tanya. 10 years ago, Elliot was 4 times as old as Tanya​. How old is Elliot now?

Answers

Answer:

Step-by-step explanation:

To solve this, we are going to make an age table:

                       Age Now                 Age 10 years ago

Tanya

Elliot

Filling the in the Age Now column comes from the first sentence. If Elliot is 2 times Tanya's age and we don't know Tanya's age, then Tanya's age is x and Elliot's age is 2x:

            Age Now                Age 10 years ago

Tanya         x

Elliot         2x

Filling in the Age 10 years ago column simply requires that we take their ages in the Age Now column and subtract 10 from each age:

         Age Now                Age 10 years ago

Tanya     x                              x - 10

Elliot      2x                           2x - 10

Since the question is How old is Elliot now based on the fact that 10 years ago....blah, blah, blah, we are using the ages in the 10 years ago column to write our equation. It says:

10 years ago, Elliot was 4 times as old as Tanya. Translated into mathspeak:

2x - 10 = 4(x - 10) and

2x - 10 = 4x - 40 and

-2x = -30 so

x = 15. That means that Elliot is 30 and Tanya is 15

As gamers progress through a video game, they earn a higher rank. In an online gaming network, gamers can see what fraction of the way they
are to the next rank. The line plot displays the fraction of the way to the next rank for all the gamers in the network. What fraction of gamers
have bof the way to go to the next rank?
Gamers Progress to Next Rank
Number
of
Gamers
Fraction of Progress to Next Level
A
A.
c.)

Answers

Question isn't well formatted, a picture if the question is attached below.

Answer:

1 / 4

Step-by-step explanation:

From the plot, each dot represent a gamer ; therefore, the total number of gamers will be counting all the dots ;

Total number of gamers = 24

Fraction of gamers that have 7 / 8 of the way to go ;

This means that they have 7/8 of the way left to proceed to next level ;

The fraction is : 1 - 7/8 = 1 /8

This means the number of of people whose progress are on 1/8 ; this is 6

Hence, fraction of gamers that have 7/8 of the way to go :

6 / 24 = 1 / 4

The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.

Answers

Answer:

The sample size needed is of 10,484.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars.

This means that [tex]\sigma = 88[/tex]

Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.

This is n for which M = 2. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 2.327\frac{88}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 2.327*88[/tex]

[tex]\sqrt{n} = \frac{2.327*88}{2}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*88}{2})^2[/tex]

[tex]n = 10483.3[/tex]

Rounding up:

The sample size needed is of 10,484.

Which is the graph of y = log4(x+3)?

Answers

Answer:

Step-by-step explanation:

Answer:

Option c points at (-2,0) (-1, 0.5) and (1,1)

Step-by-step explanation:

32 x square Y - 2 y cube

Answers

Answer:

207y

Step-by-step explanation:

Select the correct answer.


Look at ΔABC. Which triangle is congruent to ΔABC by the ASA criterion?

Answers

Your answer to this equation is A

Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants his
hourly salary to be at least $35.

Answers

The inequality that relates the number of hours to the weekly sales is:

[tex]450 + 0.20x \ge 35y[/tex]

The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales

We make use of the following representation:

[tex]x \to[/tex] weekly sales from cars.

[tex]y \to[/tex] hours worked in a week

His weekly salary is then calculated as:

Salary (S) = Earnings per week + Commission * Sales from car

So, we have:

[tex]S = 450 + 20\% * x[/tex]

Express percentage as decimal

[tex]S = 450 + 0.20* x[/tex]

[tex]S = 450 + 0.20x[/tex]

Assume he works for y hours in a week.

His hourly rate is:

[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours

[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]

For this rate to be at least [tex]\$35[/tex], the following condition must be true

[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35

So, we have:

[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]

Multiply both sides by y

[tex]450 + 0.20x \ge 35y[/tex]

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A line of best fit predicts that when x equals 28, y will equal 27.255, but y actually equals 26. What is the residual in this case?
A. 0.745
B. -0.745
C. -1.255
D. 1.255​

Answers

Answer:

C) -1.255

Step-by-step explanation:

We are tasked to solve for the residual value given that when x equals 29, y will be equals to 27.255. But, when it is tested, y actual value is 26. The formula in solving residual is shown below:

Residual value = Observed value - predicted value

Residual value =  26 - 27.255

Residual values = -1.255

The answer is -1.255 for residual value.

Who is the first prime miniter of india ​

Answers

Answer:

Jawaharlal Nehru was the first

Answer:

Jawaharlal Nehru is the first prime minister of India

The number of mice living in a field triples each year. What type of function
represents this pattern?

Answers

Answer:

C - exponential growth

Step-by-step explanation:

Answer:

The answer should be C

Step-by-step explanation:

right triangle hypotenuse is 16 angle is 22° and adjacent angle is x

Answers

Answer:

68 degrees 90+22=112 180 subtract 112 = 68

given a geomatric progression 2,6,18,54... find the smallest value of n such that the nth term is greater than 100000​

Answers

Answer:

hello,

Step-by-step explanation:

[tex]u_1=2=2*3^0\\u_2=6=2*3^1\\u_3=18=2*3^2\\u_4=54=2*3^3\\\\....\\u_n=2*3^{n-1}\geq 100000\\\\3^{n-1}\geq 50000\\\\(n-1)*ln(3)\geq ln(50000)\\\\n-1\geq 9,848586...\\\\n\geq 10.848586....\\\\\boxed{n=11}\\[/tex]

i am having troubles solving this 4(x+3)=x+42 can i get some help please.

Answers

Answer:

x=10

Step-by-step explanation:

Step 1: Multiply 4 with X and 3. You'll get 4x+12=x+42

Step 2: Keep the variable on one side and the number on the other side. you would subtract X and subtract 12. You'll get 3x=30

Step 3: Divide by the 3 on both sides and you'll get x=10

Given:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ [/tex]

Solution:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ \\ \\ \tt⇢ 4x + 12 = x + 42 \: \: \\ \\ \\ \tt \: ⇢4x - x = 42 - 12 \: \\ \\ \\ \tt \: ⇢3x = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢x = \frac{30}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: \pink{ \pmb{ \mathfrak{⇢x = 10}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ [/tex]

Verification:

[tex] \\ ⇢ \tt \: 4(10+ 3) = 10+ 42 \\ \\ \\ \tt⇢ 40 + 12 = 10 + 42 \: \: \\ \\ \\ \tt \: ⇢52 = 52 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: ⇢ \purple{ \pmb{ \bold{L.H.S = R.H.S}}}\\ \\ \\ [/tex]

Hence Verified!

What is the area of this figure?

Answers

Answer:

answer of this qn is 15in^2

[tex]5x- \dfrac{ \sqrt{ 9 { x }^{ 2 } -6x+1 \phantom{\tiny{!}}} }{ 1-3x }[/tex]

Answers

Answer:

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

The problem asks one to simplify the expression, the first step in solving this equation is to factor the equation.  Rewrite the numerator and denominator of the fraction as the product of two expressions. Remember the factoring patterns:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]=5x-\frac{\sqrt{9x^2-6x+1}}{1-3x}[/tex]

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{-(3x-1)}[/tex]

Now simplify the numerator. Remember, taking the square root of a squared value is the same as taking the absolute value of the expression,

[tex]=5x-\frac{\sqrt{(3x-1)^2}}{1-3x}[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

Rewrite the expression without the absolute value sign in the numerator. Remember the general rule for removing the absolute value sign:

[tex]|a-b|\\=a -b[/tex]           or           [tex](-a-b) = b-a[/tex]

[tex]=5x-\frac{|3x-1|}{-(3x-1)}[/tex]

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

Simplify both expressions, reduce by canceling out common terms in both the numerator and the denominator,

[tex]=5x-\frac{3x-1}{-(3x-1)}[/tex]          or          [tex]=5x-\frac{-(3x-1)}{-(3x-1)}[/tex]

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

Simplify further by rewriting the expression without the parenthesis, remember to distribute the sign outside the parenthesis by the terms inside of the parenthesis; note that negative times negative equals positive.

[tex]=5x-(-1)[/tex]          or          [tex]=5x-(1)[/tex]

[tex]=5x+1[/tex]          or          [tex]=5x-1[/tex]

(PICTURE) Im really struggling with questions like these at the moment, if you could please help me out thank you

Answers

Answer:

Arthur should select the Mount Joy Pool when there are less than 10 people at the party

Step-by-step explanation:

The initial fee to rent the Woodbridge Pool = $50

The additional fee per person after renting = $5

The initial fee to rent at Mount Joy Pool = 0 (no initial fee)

The fee per person at Mount Joy Pool = $10

The equation of a straight line is y = m·x + c

Ley y  represent the total cost of renting the pool, x, represent the number of persons in the pool, m represent the fee per person and c represent the initial charges, we get;

The total cost of renting Woodbridge Pool, y = 5·x + 50

The total cost of renting the Joy Pool, y = 10·x

Equating both values of y gives;

5·x + 50 = 10·x

∴ 5·x = 50

x = 50/5 = 10

x = 10

From the above equations, the cost of renting the pool is lower for the Joy Pool when there are less than 10 persons at the pool

It will cost the same amount to rent the pool when the number of persons in the pool are 10 persons and the cost of renting the Mount Joy Pool  will be more than the cost of renting the Woodbridge Pool, when there are more than 10 persons

Therefore, Arthur should select the Mount Joy Pool when there are less than 10 people at the party.

Click the photo to solve the photo

Answers

Answer:

A=2

B=4

C=6

D=5

E=7

F=8

G=3

H=1

Step-by-step explanation:

explanation is in the picture!

the LCM of 30 , 45,90​

Answers

Answer:

540 is the answer

Step-by-step explanation:

hope u liked!

which is the graph of g(x) = sqrt x-16

Answers

Answer:

Step-by-step explanation:

I am not sure if you are asking for the graph of

√(x-16) that has a x intercept at (16,0)

or

√ x -16 that has a y intercept at (0, -16)

If f(x) = 3x + 10x and g(x) = 2x - 4, find (f- g)(x).
O A. 15x-4
B. 3X + 8x+4
O c. 3* – 8x+4
D. 3% + 12x-4

Answers

Answer:

B. 3ˣ + 8x + 4

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3ˣ + 10x

g(x) = 2x - 4

Step 2: Find

Substitute in function values:                                                                          (f - g)(x) = 3ˣ + 10x - (2x - 4)[Distributive Property] Distribute negative:                                                    (f - g)(x) = 3ˣ + 10x - 2x + 4Combine like terms:                                                                                         (f - g)(x) = 3ˣ + 8x + 4

Answer:

3^x+8x+4

Step-by-step explanation:

f(x) = 3^x + 10x

g(x) = 2x - 4

(f- g)(x)=3^x + 10x  - (2x - 4)

Distribute the minus sign

(f- g)(x)=3^x + 10x  - 2x + 4

Combine like terms

         3^x+8x+4

What describes the correct way to convert minutes to an hour

Answers

Answer:

Yo mean correct way??

yo can divide minute by 60 to convert minute into hour

For example

To convert 10 minute into hour. then we should divide 10 by 60. 10/60

Answer:

In any conversion you have to establish  ratios (or rates) for the different units being converted.

The process will be performed by a series of multiplications that will cancel out the "unwanted" units.

multiplication by one (1) does not change the value in an equation.

you have to multiply by a "series of ones" that take into account the units being converted..

for example  

1 minute/60 seconds   or  1 inch = 2.54 cm   or  1 day = 24 hours

in your problem you have minutes... lets say you have 100 minutes

100 minutes * 1 hour             minutes cancel and you have  100/60 = 1 [tex]\frac{2}{3}[/tex] hrs

                       60 minutes

Step-by-step explanation:


If you roll a number cube 96 times, how many times would you expect to roll a prime number?

Answers

We can expect to roll a prime number 48 times.

Theoretically, when you roll a number cube all the possible numbers have the same probability, 1/6.

We know that the numbers in a number cube are {1, 2, 3, 4, 5, 6}

Of these, the primes are: 2, 3, and 5.

So half of the outcomes of a number cube are primes.

This means that, in every single roll, the probability of getting a prime number is 1/2.   (1/6 + 1/6 + 1/6 = 3/6 = 1/2)

Then for 96 rolls, we should expect to see in half of these a prime number as an outcome.

This means that we should expect to roll a prime number 96/2 = 48 times.

If you want to learn more about probability, you can read:

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You should expect to roll a prime number 64 times.

To determine, if you roll a number cube 96 times, how many times would you expect to roll a prime number, the following calculation must be performed, knowing that the prime numbers are those that can only be divided by 1 or by themselves:  

A cube has 6 sides. Therefore, the numbers in the cube will be 1, 2, 3, 4, 5 and 6. Of these numbers, only 4 and 6 are not prime, since 4 is divisible by 2 and 6 is divisible by 2 and 3.

Therefore, 4/6 numbers are prime, that is, 66.66% of the numbers in the cube.

Therefore, if you roll a number cube 96 times, since 96 x 4/6 equals 64, you should expect to roll a prime number 64 times.

Learn more in https://brainly.com/question/23715861.

Which best describes the relationship between the line that
passes through the points (1, -6) and (3,-2) and the line that
passes through the points (4,8) and (6, 12)?
A. parallel
B. same line
C. neither perpendicular nor parallel
D. perpendicular

Answers

Same line so the correct answer is b
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