In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m

Jenelle will spend a total of $624,644.96 on the home, including the down payment.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο sοlve the prοblem, we'll use the fοllοwing fοrmula:

Lοan amοunt = Purchase price - Dοwn payment

Jenelle paid 18% of $340,000 as a down payment:

Down payment = 0.18 x $340,000 = $61,200

The original amount financed is the purchase price minus the down payment:

Loan amount = $340,000 - $61,200 = $278,800

To calculate the monthly payment, we'll use the formula for the present value of an annuity:

\($ \rm PV = \frac{PMT \times (1 - (1 + r)^{(-n)}}{ r}\)

Where PV is the present value of the loan (which is the amount Jenelle financed), PMT is the monthly payment, r is the monthly interest rate (which is 6.6% / 12 = 0.0055), and n is the total number of payments (which is 30 years x 12 months per year = 360).

Plugging in the values, we get:

\($ \rm \$278800 = \frac{PMT\times (1 - (1 + 0.0055)^{(-360)}} { 0.0055}\)

Solving for PMT, we get:

PMT = $1,724.56

Therefore, Jenelle's monthly payment is $1,724.56.

To calculate the total amount of money Jenelle will spend on the home over 30 years, we need to multiply her monthly payment by the total number of payments:

Total amount spent = (Monthly payment x Number of payments) + Down payment

Total number of payments = 30 years x 12 months per year = 360

Total amount spent = ($1,724.56 × 360) + $61,200 = $624,644.96

Hence, Jenelle will spend a total of $624,644.96 on the home, including the down payment.

To learn more about basic arithmetic operations, Visit

https://brainly.com/question/20628271

#SPJ1

Answer:

These triangles cannot be proven congruent because we do not know if SQ and UT are congruent.

Answer:

4,207 in expanded form is 4,000+200+7.

Step-by-step explanation:

Hope this helps! Have an Amazing day!!

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

For such more question on isometric

https://brainly.com/question/14486229

#SPJ8

Answer: To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on. We can calculate percentages using this knowledge. 50% is the same as a half, so 50% of 10 is 5, because five is half of 10 (10 ÷ 2).

Step-by-step explanation:

the square root of 598 is 24.4540385

Answer:

times 2075 by .30 and that's your answer

The total retail cost of all the jewelry is $2697.5

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Maybell just purchased $2075 worth of jewelry.

Now, marks up her cost by 30% then

= 2075 x 30/100

= 622.5

Thus, the total retail cost of all the jewelry

= 2075+ 622.5

= $2697.5

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ6

The coterminal angle is 190°, the reference angle is 10°, and it lies on the third quadrant.

For any angle A written in degrees, the family of coterminal angles is written as:

B = A + n*360°

Where n can be any integer number different than zero.

Here we want to find a angle coterminal to -890° on the range [0°, 360°]

Then we need to find n such that:

B = -890°+ n*360°

is on the desired range.

If we take n = 3 we will get:

B = -890°+ 3*360°

B = 190°

That is coterminal angle, which is on the third quadrant, and it is 10° more than a 180° angle, so the reference angle (to the nearest axes) is 10°.

Learn more about coterminal angles:

https://brainly.com/question/3286526

#SPJ1

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

Answer:

6.66e+33

Step-by-step explanation:

Is this a real question??

The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7

From the question, we have the following parameters that can be used in our computation:

seven less than four times a number

Represent the number with x

So:

four times a number means 4x

So, we have

seven less than 4x

seven less than means - 7

So, we have

4x - 7

Hence, the english phrase as an algebraic expression is 4x - 7

Read more about expression at

brainly.com/question/4344214

#SPJ1

Complete question

write the english phrase as an algebraic expression. Let x represent the number

Seven less than four times a number

Answer:

49.93

Step-by-step explanation:

it is 0.07 away from 50

The C.50.09 is the number that is within the smallest range of 0.09 from 50.

Among the given options, the number 50.09 is the closest to 50. This is because it is only 0.09 away from 50, whereas the other options are farther away. The numbers 50.1 and 50.101 are slightly farther, being 0.1 and 0.101 away from 50 respectively. Similarly, the numbers 49.93 and 49.01 are also farther away, being 0.07 and 0.99 away from 50 respectively. The number closest to 50 among the options provided is 50.1. It is merely a tenth above 50, while the other numbers—49.93, 49.01, and 50.09—are each farther away from 50 than 0.1. Therefore, based on the given options, 50.09 is the number that is closest to 50.

To know more about range here

https://brainly.com/question/29204101

#SPJ3

Step-by-step explanation:

The rules for significant digits are:

To round each number to one digit, round to the first digit.

a) 300,000

b) £200

c) 20,000 km

The value of x from the equation 3x + 4 = 31 and x + 4 = 13 is 9.

3x + 4 = 31

x + 4 = 13

From equation (2)

x + 4 = 13

subtract 4 from both sides

x = 13 - 4

x = 9

Substitute x = 9 into (1)

3x + 4 = 31

3(9) + 4 = 31

27 + 4 = 31

Learn more about equation:

https://brainly.com/question/2972832

#SPJ1

Answer:

270+150x

Step-by-step explanation:

(-15)(-18)+(-15)(-10x)
270+150x

Answer:

Almost all the letters are missing, 20 letters are missing

Step-by-step explanation:

A B C D F H I J K M N O P Q R S T V X Z

The missing alphabet between Y and W= X

The missing alphabet between W and U= V

The missing alphabet between E and G=F

The missing alphabet between G and I=H

What is alphabet?

An alphabet is a standardized set of basic written symbols or graphemes that represent the phonemes of certain spoken languages.

According to question, we have to find which alphabet is missing Y E W G U I​.

If we  find missing alphabet between bold alphabet  Y E W G U I​,

we get the following

The missing alphabet between Y and W= X

The missing alphabet between W and U= V

If we  find missing alphabet between bold alphabet Y E W G U I​,

we get the following

The missing alphabet between E and G=F

The missing alphabet between G and I=H

Hence , we can conclude that

The missing alphabet between Y and W= X

The missing alphabet between W and U= V

The missing  alphabet between E and G=F

The missing  alphabet between G and I=H

Learn more about  alphabet here:

https://brainly.com/question/14923144?referrer=searchResults

#SPJ2

Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

Learn more about the proportion visit:

https://brainly.com/question/1496357

#SPJ2

Answer:

120 combinations! :)

Step-by-step explanation:

So, there's 4 choices for a sandwich, 3 choices for a side, 2 choices for a dessert and 5 choices for a soda!

The answer is 5 * 4 * 3 * 2 = 120 :)

Answer:

5, 4, 3, 2

Step-by-step explanation:

you would have a total of 120

We have to solve for x: −7< x − 1< 8. The 4th option is correct that is -6<x<9.

Given -7<x-1<8

Here, we have less then symbol.

The symbols greater than and less than signify a difference between two values. ">" and "<" are used to indicate greater than and less than, respectively.

In mathematics, the larger than sign is used between two numbers to indicate that the first number is greater than the second. For instance, 10>5. Therefore, 10 is more than 5 in this case.

In a situation when one number is less than another, a less than symbol is positioned between the two numbers. 5<10 is an illustration of a symbol indicating inequality that is less than. In other words, 5 is less than 10.

Taking the -1 to left and right side we will get +1.

That is,

-7+1<x<8+1

-6<x<9

Therefore, the 2nd option is correct that is -6<x<9.

To learn more about less then visit: https://brainly.com/question/15367899

#SPJ1

Step-by-step explanation:

T = 55 + 6w

after 8 week $103

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

Learn more about limits here:

https://brainly.com/question/12211820

#SPJ1

The speed of the skater will be equal to 12 km/h.

The speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that a cyclist travelled 20 kilometres per hour faster than an in-line skater. In the time it took the cyclist to travel 80 kilometres, the skater had gone 30 kilometres.

The skater speed will be calculated as,

30 / x = 80 / ( x + 20)

30 ( x + 20 ) = 80x

30x  + 600 = 80x

80x - 30x = 600

50x = 600

x = 600 / 50

x = 12 km/hr

Therefore, the speed of the skater will be equal to 12 km/h.

To know more about Speed follow

brainly.com/question/6504879

#SPJ1

Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

Learn more about inequality click

https://brainly.com/question/20383699

#SPJ1

The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Answer:

First triangle x=9

Second triangle x=20

Step-by-step explanation:

Using Pythagorean theorem

40^2+x=41^2

1600+x^2=1681

-1600        -1600

x^2=81

To find x we do the opposite of powers and find the squared

x=9

Second triangle

21^2+x^2=29^2

441+x^2=841

-441        -441

x^2=400

x=20

The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

Learn more about cylinder from the given link

https://brainly.com/question/27440983

#SPJ1

The linear relation is N = 4T - 160 and the rate at 102F is 248 chirps/min

A linear equation can be represented as

N = mT + c

Using the values from the question. we have the following system

120 = 70m + c

160 = 80m + c

Subtract the equations

10m = 40

So, we have

m = 4

This means that

120 = 70 * 4 + c

So, we have

c = -160

So, the fucntion is

N = 4T - 160

When the temperature is 102, we have

N = 4 * 102 - 160

Evaluate

N = 248

Hence, the rate is 248 chirps/min

Read more about linear relation at

https://brainly.com/question/10209928

#SPJ1

Answer:

50/21 or 2 8/21

Step-by-step explanation:

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

For more questions on Polynomial .

https://brainly.com/question/2833285

#SPJ8