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9514 1404 393

Answer:

  x = (8/9)(4 +√7) ≈ 5.9073

Step-by-step explanation:

Maybe you want to know the value of x.

The Pythagorean theorem can be used to find the length of the bottom side of the right triangle. It is ...

  bottom = √((5x)² -(3x)²) = √(16x²) = 4x

Then the cosine of the angle at lower left is ...

  cos(α) = Adjacent/Hypotenuse

  cos(α) = 4x/5x = 4/5

Now, the law of cosines can be used to find x. Using the angle whose cosine we just found, we have ...

  (4x)² = (5x)² +8² -2(5x)(8)cos(α)

  16x² = 25x² +64 -80x(4/5)

  9x² -64x +64 = 0 . . . . . put in standard form

The quadratic formula can be used to find the solutions.

  x = (-(-64) ±√((-64)² -4(9)(64)))/(2(9))

  x = (64 ±√1792)/18 = (32 ±8√7)/9 ≈ {1.204, 5.907}

In this context, only the larger solution makes sense.

  x = (8/9)(4 +√7) ≈ 5.9073

_____

Formulas used

Law of Cosines

For sides a, b, c and angle C opposite side c, ...

  [tex]c^2=a^2+b^2-2ab\cdot\cos(C)[/tex]

Quadratic formula

For quadratic ax²+bx+c=0, the solutions are ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Pythagorean theorem

For legs a, b, and hypotenuse c of a right triangle, ...

  c² = a² + b²

_____

Alternate solution

As an alternative to using the Law of Cosines, you can define "y" to be the length of the dashed bottom leg of the triangle whose hypotenuse is 4x. Two equations can be written using y and the Pythagorean theorem for the right triangles in which y is all or part of a leg. This set of equations can be solved for x to get the same result as the one shown above.

Area of triangle: 3m

Area of rectangle: 24m

Area of semi-circle: 6.28m

Answer:

33.28 m²

Step-by-step explanation:

The figure consists of three shapes:

1) A semicircle of radius 2 m.

2) A rectangle 4 m by 6 m.

3) A triangle with base 3 m and height 2 m.

area = ½πr² + LW + ½bh

area = 3.14 * (2 m)^2/2 + (6 m)(4 m) + (3 m)(2 m)/2

area = 6.28 m² + 24 m² + 3 m²

area = 33.28 m²

b

x is 10 times greater then y 3+n 5

Answer:

A down payment of $5,388.50  to get the principle to $19611.50  for a monthly payment of $400 for 60 months at 8.25%

Step-by-step explanation:

I used a payment calculator

I don't know how else to solve the problem.  I thought I could find the equation, but I don't think this is it, since P didn't equal 19611.50

A = P[r(1+r)n] / [(1+r)n - 1]    

if you have the correct formula follow this process

A = 400        P principle ???    r = i%/12 = 0.0825/12 =  0.006875    n= 5×12 = 60

     solve for P      then    down payment = 25000 - P

 P = A / [r(1+r)n] / [(1+r)n - 1]    

    = A [(1+r)n - 1]  /  [r(1+r)n]

    =  400 [(1 +.006875)60 -1]  /  [0.006875( 1 +0.006875)60]

Answer:

angle=63°

I hope it's helps you

1. Jim is tracking the progress of his plant’s growth. Today the plant is 8cm high. The plant grows 3.5cm per day. What will the height of the plant be on day 28? (Hint: “today” is day 0).

"The plant grows 3.5 cm per day" means that the function grows by 3.5 cm each day. We can make a function like this:

y = 8 + 3.5x

Day 0 -> Day 28 is +28 days, so plug-in x with 28 to find out how much it would have grown in 28 days PLUS the original height of the plant, 8 cm.

y = 8 + 3.5(28) <-- see how I replaced x with 28

Simplify

y = 8 + 98 = 106 cm at day 28

2. The average inflation rate of the U.S. dollar over the last six years is 2.8% per year. If a new car cost $29,000 six years ago, how much would it cost today?

2015, 2016, 2017, 2018, 2019, 2020, 2021

Just to help you imagine the years, we need to find the car's value from $29,000 in 2015 to 2021 using the idea that the car's value increases by 2.8 percent. What does 2.8 percent mean and how do we use this information to find out how much it increases? We need to convert this to a decimal so we can multiply it by 29,000 easily. First, convert 2.8% to a decimal = 0.028. Then we have to add 1 to 0.028. Why? Because we need to make sure that we still have the original 100% of the 29,000. If we forget the 1 then we're just finding 2.8% of 29,000! So, now we know that our multiplier by each year is 1.028. Now we have to multiply.

29,000 x (1.028)^6 (we have a power of 6 because remember, we are multiplying the 1.028 every year, and there are 6 years!)

Simplify: 34,226.0425 that rounds to 34,226.0425 dollars

3. The population of Mickey Village is 48,000 today. Every other year the population increases by 1,550 people. In approximately how many years will the population exceed 70,000 people?

The details of this question are confusing, so I won't answer this. Sorry, I'm really short on time. I hope I could help the best I could.

Answer:

32600

Step-by-step explanation:

Answer:

58m^2

Step-by-step explanation:

2x9 = 18

8x5 = 40

18+40 = 58

Answer:

answer:

answe:

answ:

ans:

an:

as:

a:

:

Answer:

20[tex]\pi[/tex]

Step-by-step explanation:

Circumference formula: [tex]2\pi r[/tex]

Since the diameter is 20, the radius will be half of the diameter

r=d/2, where d=20

r=20/2=10

C=[tex]2\pi r[/tex]

C=2(10)[tex]\pi[/tex]

C=20[tex]\pi[/tex]

Answer:

ok

Step-by-step explanation:

Answer:

post the whole problem it's cut off

Answer:

(x,y)=(4,-9)

Step-by-step explanation:

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The solution of the equation means the value of the unknown or variable.

The system of the equation is given below.

7x + 4y = – 8      …1

8x + 5y = –13     …2

Multiply equation 1 by 5 and equation 2 by 4. Then subtract the equation 1 from 2, then we have

32x – 35x = –52 – (–40)

          –3x = –12

              x = 4

Substitute the value of x in equation 1, then the value of y will be

7(4) + 4y = – 8

 28 + 4y = –8

          4y = –36

            y = –9

The solution of the equation 7x + 4y = – 8 and 8x + 5y = –13 will be (4, –9).

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ5

Answer:

x = 140   y = 105                x · y = 14700 m²

Step-by-step explanation:

good question

it looks like 3 sides of length x

and 4 sides of length y

area 1 = area 2

and the length of all the sides sum to 840

  3x + 4y = 840      find the maximum area = 2· x · y

This is a calculus problem that I can't remember how solve

 if x = 0   y = 210

           if   y = 0   x = 280       280 / 2 = 140   the mid-point  the logical answer

if x = 140   y = 105                x · y = 14700 m²         this appears to be the max

if x = 135   y = 108.75            x · y = 14681.25 m²      smaller area

if x = 145   y = 101.25             x · y = 14681.25 m²      smaller area

I need an eqaution with a quadratic and take the first derivative

 y = (840 - 3x) / 4      xy = max area     y = max area/x

(max area) / x = (840 - 3x) / 4      solve for x

    max area  = x(840 - 3x) / 4

    max area  = [840x/4 - 3x²/4] '        

    max area  = 210x  -  3x²/4            take the first derivative  

    max area  = 210  -  6x/4               maximum occurs when slope = 0

           0   =  210 - 3x/2    

        3x/2 = 210

           x  = 210·2/3

           x  = 420 / 3

          x  = 140   y = 105

3(140) + 4(105) =   420 + 420  = 840    checks

Answer:

3 weeks 5 days

Step-by-step explanation:

A week is 7 days

26/7 = 3 remainder 5

3 weeks 5 days

Answer:

c. [tex] \frac{3x + 4}{x^2} [/tex]

Step-by-step explanation:

Given:

[tex] \frac{3}{x} + \frac{4}{x^2} [/tex]

Required:

The sum

Solution:

[tex] \frac{3}{x} + \frac{4}{x^2} [/tex]

Common denominator is x².

Therefore, divide x² by the denominator of each fraction and multiply by each of its denominator.

Thus, we would have:

[tex] \frac{3x + 4}{x^2} [/tex]

Answer:

All I know is that the total of the provided numbers make 58 feet and that you should probably break down the shapes into 2 different shapes. Then try to find the perimeters of each shape. I'm not sure what to do afterwards. Maybe I helped jogged your memory on what to do? I hope I helped some.

Answer:

a) 375 = 3 × 3 × 3× 3 × 5

in index form it is 3 × 5³.

prime factor of,

150 = 2 × 3 × 5 × 5.

To find the HCF, multiply all the prime factors common to both numbers: Therefore, HCF = 3 × 5 × 5.

ANS : 75

hope this helps you☺️☺️

Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Write down the percent divided by 100 like this:

25% = 25/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As 25 is an integer, we don't have numbers after the decimal point. So, we just go to step 3

(or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(25,100) = 25. So,

(25÷25)/(100÷25) = 1/4 when reduced to the simplest

Answer:

3600ft.

Step-by-step explanation:

12blocks x 50ft/block = 600 feet/5min.

30min/5min = 6

600 x 6 = 3600 ft.

Answer:

D. 32.3

Step-by-step explanation:

Length-a  

Width-b

A=ab=6.8×4.75=32.3

Answer:92.7

Step-by-step explanation:

Use the compound interst formula: A= P(1+r)^n

750(1+.06)^2=842.7

Now substract the principal to find the compound interest : 842.7-750= 92.7

Hope it helps

Complete question is;

The attached chart shows the (approximate) total number of subprime home mortgages in a state in November 2008, broken down into four categories.

What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)

Answer:

Probability that the one randomly selected was not current = 0.36

Step-by-step explanation:

From the attached image, we can see that the four mortgage categories are mutually exclusive. This means that none of the 4 status depends on any other.

From the image attached;

Total number of subprime mortgages = 196,280

Number of current mortgages = 126,330

Thus;

Probability of a randomly selected subprime mortgage being current = 126330/196280 = 0.64

Then;

Probability that the one randomly selected was not current = 1 - 0.64

Probability that the one randomly selected was not current = 0.36

Answer:

1hr: $9

2hr: $18

3hr: $27

4hr: $36

5hr: $45

6hr: $54

Step-by-step explanation:

You can use Desmos, the graphing calculator (online tool)  

Answer:

512

16 · 4 = 64

64 · 8 = 512

Answer:

X=35 Y=73

Step-by-step explanation:

use the opposite angle theorem for x. X would equal 35.

we know that x is 35. So 2y+35=180

180-35=2y

y=72.5 or 73

srry I can’t help with question 2. I don’t know how

Answer:

that's confusing.. is there a picture?

Answer:

Step-by-step explanation:

The answer is TRUE

True