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3 years ago

What is the value of x? Enter your answer in the box.

Mathematics

2 answers:

hichkok12 [17]3 years ago

8 0

Answer:

x = 25

Step-by-step explanation:

Step 1: Identify the similar triangles

Triangle DQC and triangle DBR are similar

Step 2: Identify the parallel lines

QC is parallel to BR

Step 3: Find x

DQ/QB = DC/CR

40/24 = x/15

x = 25

Sever21 [200]3 years ago

8 0

Answer: $x=25$

Step-by-step explanation:

In order to calculate the value of "x", you can set up de following proportion:

$\frac{BQ+QD}{QD}=\frac{RC+CD}{CD}\\\\\frac{24+40}{40}=\frac{15+x}{x}$

Now, the final step is to solve for "x" to find its value.

Therefore, its value is the following:

$1.6=\frac{15+x}{x}\\\\1.6x=x+15\\\\1.6x-x=15\\\\0.6x=15\\\\x=\frac{15}{0.6}\\\\x=25$

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Two planes leave an airport at the same time. Thier speeds are mph 130 and 150 mph, and the angle between thier courses is 36 de

Reil [10]

Answer:

132.89 miles

Step-by-step explanation:

Let plane A travel at 130 mph and plane B travel at 150 mph.

After 1.5 hours, the total distance traveled by each plane is:

$A = 1.5 *130\\A = 195\ miles\\B = 1.5 *150\\B = 225\ miles$

The law of cosines can be used to find the distance (D) between both planes as follows:

$D^2 = A^2+B^2-2AB*cos(36)\\D=\sqrt{195^2+225^2-(2*195*225*cos(36))}\\D=132.89\ miles$

They are 132.89 miles apart after 1.5 hours.

5 0

3 years ago

Ralph Chase plans to sell a piece of property for $170000. He wants the money to be paid off in two ways monica short-term not

natima [27]

Answer:

The amount of 12% note is $90,000

The amount of 9% note is $80,000

Step-by-step explanation:

Missing word "The amount of the 12% note is $ and the amount of the 9% note is $"

Selling price = $170,000

Let x be the amount of money paid short term, therefore the amount of money paid long term is (170000 - x)

Given total annual interest = $18,000

Total annual interest = Interest due to short term (x) + interest due to long term (170000 - x)

18,000 = 0.12x + 0.09*(170000 - x)

18,000 = 0.12x + 15,300 - 0.09x

18,000 = 0.03x + 15,300

0.03x = 18,000 - 15,300

0.03x = 2,700

x = 2,700/0.03

x = 90,000

So, the amount of 12% note is $90,000

So long term paid money = $170,000 - $90,000 = $80,000

So, the amount of 9% note is $80,000

6 0

3 years ago

Which of the following is not a polynomial? a 11p-7q b 8xy^4-5x^3y c 2-x d-4/y

Len [333]

A polynomial is an expression of more than two algebraic terms. Among the given expressions above, the answer that is not a polynomial would be option D. -4/y. This does not follow the rules of being a polynomial because y is a denominator; therefore, this is not a polynomial.

3 0

3 years ago

Sample annual salaries (in thousands of dollars) for employees at a company are listed. (a) Find the sample mean and sample s

Helen [10]

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

The value is attached in the image file please find it.

In point a:

First, we calculate the find the mean,

Formula:

$\to Mean (\bar{x}) = \frac{( \sum x)}{n}$

$=\frac{540}{13}\\\\ = 41.54$

To calculate the standard deviation, subtract the mean value from all observations then square its value:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{339.2308}{13-1}}$

$= \sqrt{ \frac{339.2308}{12}}\\\\= \sqrt{28.269}\\\\=5.31$

please find attached file

In point b:

New $x_i = 1 x_i + 0.05 x_i = 1.05 x_i$

Calculate new mean:

$\to \bar{x} = \frac{\sum x}{n} \\$

$=\frac{567}{13} \\\\= 43.62$

calculating the standard deviation:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{374.0022}{13-1}}$

$= \sqrt{ \frac{374.0022}{12}}\\\\= \sqrt{31.16}\\\\=5.58$

please find attached file

In point C:

Calculate new mean:

$\to \bar{x} = \frac{\sum x}{n} \\$

$=\frac{47.25}{13} \\\\= 3.46$

calculating the standard deviation:

$SD = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} \\$ $= \sqrt{ \frac{2.5975}{13-1}}$

$= \sqrt{ \frac{2.5975}{12}}\\\\= \sqrt{0.216}\\\\=0.46$

please find attached file

In point d:

for b,

New $\bar{x}= 1.05 \bar{x}= 1.05(41.54) =43.62$

New $s= 1.05s= 1.05(5.31)=5.57$

for c,

New $\bar{x}= \frac{ \bar{x}}{12}= \frac{41.54}{12} = 3.46$

New $s = \frac{s}{ 12} = \frac{5.31}{12}= 0.44$

4 0

3 years ago

Jeff is designing the seating arrangement for a concert in his high school theater. To give everyone a good view, each row must

denis-greek [22]

Answer:

12+5x X being the row number, may need to minus 1. 12+5(25)=135 or 12+5(24)=132 if you need to minus one

Step-by-step explanation:

The reason why I said you might need to minus 1 from the row number because if you plug in 2 for x, 2 being row 2, you would get 22 when you truly would only need 17. If you do need to minus 1 the sample equation would be 12+5(x-1)

Hope that helps and is right! sorry if it isn't

4 0

3 years ago

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