A scale drawing for an apartment is shown below. In the drawing, 2cm represents 3m. Assuming the bedroom is rectangular, find the area of the real bedroom. ​

Answer:

(-1.875, -1.625)

Step-by-step explanation:

We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)

Remember that the distance between two points (a, b) and (c, d) is:

D = √( (a - c)^2 + (b - d)^2)

First we can write our equation as a line in the slope intercept form:

y = -(2/6)*x - 1

Now we could minimize the equation:

D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)

D = √(  ( x + 5)^2 + (  -(2/6)*x - 1 + 3) ^2)

Then we can minimize:

D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2

       = x^2 + 10*x + 25  + (4/36)*x^2  - (8/6)*x + 4

       =  (1 + 4/36)*x^2 + (10 - 8/6)*x + 29

        = (40/36)*x^2 + (52/6)*x + 29

This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.

The vertex is at the x-value such that (D^2)' = 0

Then:

(D^2)' = 2*(40/36)*x + (52/6)

This needs to be zero then:

0 = 2*(40/36)*x + (52/6)

-52/6 = (80/36)*x

(-52/6)*(36/80) = x

-1.875 = x

And the y-value when x = -1.875 is:

y = -(2/6)*-1.875 - 1

y = -1.625

Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)

Let p = number of people that cast their vote.

p = 0.35(15, 000)

p = 5,250

Uhm... I’m sorry I don’t really know the answer to your question I’m just answering it for points....

Answer:

11. 78

12. 4x² - 3x - 1

Step-by-step explanation:

11. Sum of n whole numbers = ½(n² + n)

Multiply

½*n² + ½*n

= n²/2 + n/2

To find the sum of the first 12 whole number, substitute 12 for n into the equation.

= 12²/2 + 12/2

= 144/2 + 12/2

= 72 + 6

= 78

12. Area of trapezoid = ½(a + b)*h

Where,

a = 5x - 4

b = 3x + 2

h = x + 1

Area = ½(5x - 4 + 3x + 2)*(x + 1)

Area = ½(8x - 2)*(x + 1)

Area = ½[8x(x + 1) -2(x + 1)]

= ½[8x² + 8x - 2x - 2]

Add like terms

= ½(8x² - 6x - 2)

= ½(8x²) - ½(6x) - ½(2)

= 4x² - 3x - 1

Answer:

cbzxnphfgzhohdxhlkvcdtbcdil to m kl nhi aaugi

Answer:

-5.5

Step-by-step explanation:

Answer:

02920

Step-by-step explanation:

92823

Answer: 9 hours

Step-by-step explanation:

13.5 hours / 1.5 hours = 9 hours

9514 1404 393

Answer:

  Chun is correct

Step-by-step explanation:

The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.

Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:

  top short : bottom short = top long : bottom long

  5 / 8 = 15 / x

__

Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...

  top short : bottom long = bottom short : top long

She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.

__

Chun's proportion correctly gives x=24.

Answer:

Step-by-step explanation:

Chun; by the Triangle Angle Bisector Theorem, the correct proportion is  58=15x.

Answer:

1.4

Step-by-step explanation:

7 ÷ 5 = 1.4 or 7/5 as a fraction

Answer:

[tex]T_7 = 11[/tex]

[tex]T_n = 2n- 3[/tex]

Step-by-step explanation:

Given

[tex]S_n = n^2 -2n[/tex]

[tex]T_n = S_n - S_{n-1}[/tex]

Solving (a): T7

Substitute 7 for n in [tex]T_n = S_n - S_{n-1}[/tex]

[tex]T_7 = S_7 - S_{7-1}[/tex]

[tex]T_7 = S_7 - S_6[/tex]

Calculate S7 and S6

[tex]S_n = n^2 -2n[/tex]

[tex]S_7 = 7^2 - 2 * 7 = 35[/tex]

[tex]S_6 = 6^2 - 2 * 6 = 24[/tex]

So:

[tex]T_7 = 35 -24[/tex]

[tex]T_7 = 11[/tex]

Solving (b): Tn

[tex]T_n = S_n - S_{n-1}[/tex]

Where [tex]S_n = n^2 -2n[/tex]

Calculate[tex]S_{n-1}[/tex]

We have:

[tex]S_{n-1} =(n-1)^2 - 2(n-1)[/tex]

Open brackets

[tex]S_{n-1} = n^2 -2n + 1 -2n +2[/tex]

[tex]S_{n-1} = n^2 -2n-2n + 1 +2[/tex]

[tex]S_{n-1} = n^2 -4n + 3[/tex]

So:

[tex]T_n = S_n - S_{n-1}[/tex]

[tex]T_n = n^2 - 2n - (n^2 -4n + 3)[/tex]

[tex]T_n = n^2 - 2n - n^2 +4n - 3[/tex]

Collect Like Terms

[tex]T_n = n^2 - n^2- 2n +4n - 3[/tex]

[tex]T_n = 2n- 3[/tex]

Answer:

27

Step-by-step explanation:

Carlotta can feed 3 times her dog with leftover in this bag of dog food

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that Carlotta has 2/3 of a bag of dog food  and She gives her dog 2/9 of the bag at each feeding.

The bag of dog food = 2/3

Let she feed her dog with leftover in this bag of dog food = X

Therefore, X = 2/3 × 9/2

X = 18 / 6

X = 3

Hence, Carlotta can feed 3 times her dog with leftover in this bag of dog food

Learn more about the unitary method, please visit the link given below;

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Answer:

D. 18

Step-by-step explanation:

The polygon given is a 5-sided polygon (pentagon). Sum of all interior angles of a 5-sided polygon = (n - 2) * 180°

= (5 - 2) * 180 = 540°

Therefore:

95° + (7x - 4)° + (3x + 23)° + (9x - 6)° + 90° = 540°

Solve for x

95 + 7x - 4 + 3x + 23 + 9x - 6 + 90 = 540

Add like terms

198 + 19x = 540

19x = 540 - 198

19x = 342

x = 342/19

x = 18

Answer:

Step-by-step explanation:

the answer is in the pic open it

hope it help mark me as a brill please

Answer:

your answer will be option B

Step-by-step explanation:

[tex]\frac{10}{12} =\frac{a}{38} \\\\a=\frac{(10) (38)}{12} \\\\=31.6[/tex]

Answer:

6.633249581 and I would say it's irrational

Step-by-step explanation:

:)

Answer:

12 square units

Step-by-step explanation:

The area of a given figure is the measure of space occupied by the figure on a 2 dimensional plane.

Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height

From the given grid, the following can be observed for triangle STU.

base SU = 6 units

height = 4 units

Thus,

area of triangle STU =  [tex]\frac{1}{2}[/tex] x base x height

                                  =  [tex]\frac{1}{2}[/tex] x 6 x 4

                                  = 3 x 4

area of triangle STU = 12 square units

The required area of triangle STU is 12 square units.

Answer:

Top is A bottom is B. ........

Answer:

3:5

Step-by-step explanation:

To find the simplest ratio, divide each number by 2:

6/2

= 3

10/2

= 5

So, the simplest ratio of triangles to squares is 3:5

Answer:

b is the correct answer

Step-by-step explanation:

btw can i have brainliest please

Answer:

Speed = distance / time

= 6/3 =2 ft/sec

Time = distance / speed

= 60/2

= 30 seconds

Answer:

pretty sure youre right kiddo

Answer:

Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages

Step-by-step explanation:

Let x represent the number of messages that Keiko sent.

Since Dale sent 7 less than Keiko, his number can be represented by x - 7

Since Tony sent 4 times as many as Keiko, his number can be represented by 4x

Using these variables, create an equation:

(x) + (x - 7) + (4x) = 95

Add like terms and solve for x:

6x - 7 = 95

6x = 102

x = 17

So, Keiko sent 17 messages.

Subtract 7 from this to find how many Dale sent:

17 - 7

= 10

Multiply it by 4 to find how many Tony sent:

17(4)

= 68

So, Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages

Answer:

B: x = -5

Step-by-step explanation:

Answer:

x≥1

Step-by-step explanation:

Answer:19

Step-by-step explanation:perimeter is everything added since it’s a rectangle 10 on both length sides will be 20 so 58-20 is 38 divide that by 2 and that’s your answer.

Answer:

[tex]x\\[/tex] ± [tex]\frac{s}{\sqrt{n}}[/tex] = [tex]9.78[/tex] ± [tex]\frac{10.45}{\sqrt{60}}[/tex]

Step-by-step explanation:

x is the value of our population/sample mean. Given that it's 98.75, we substitute x for 98.75.

We follow this pattern for s and n, which are the standard deviation and sample size respectively, to fill out the rest of our equation. This means that s is 10.45 and n is 60

Since we know the formula is [tex]x\\[/tex] ± [tex]\frac{s}{\sqrt{n}}[/tex], we can input our new values.

This gives us our answer of [tex]9.78[/tex] ± [tex]\frac{10.45}{\sqrt{60}}[/tex]

TL;DR

I took the test and the answer was right

The interval in which the population mean $98.75 with standard deviation of $10.45 with a sample size of 60 is given by its lower and upper limit as given by: 98.75 ± 10.45/(√(60))

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%[/tex]

where we had  where mean of distribution of X is [tex]\mu[/tex]  and standard deviation from mean of distribution of X is [tex]\sigma[/tex] (assuming X is normally distributed).

Suppose X has has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], then, the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with mean equal to the mean of X, and standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]

Symbolically, we write it as:

[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]

(for large enough samples, n > 30)

For this case, we're specified that:

Then, the distribution of the sample mean is approximately normal distribution with mean $98.75 and standard deviation approximately [tex]10.45/\sqrt{60}[/tex]

Symbolically, we get:

[tex]X \sim N(98.75, 10.45/\sqrt{60})[/tex]

Then, using empirical rule, we find the limits for sample mean for which we're 68% sure that the sample mean will lie in that interval as one standard deviation (of the sample mean) away from its mean.

[tex]P\left( 98.75 - 10.45/\sqrt{60} < \overline{X} < 98.75 + 10.45/\sqrt{60}\right) \approx 68\%[/tex]

So, limits are:

[tex]98.75 \pm \dfrac{10.45}{\sqrt{60}}[/tex]

Thus, the interval in which the population mean $98.75 with standard deviation of $10.45 with a sample size of 60 is given by its lower and upper limit as given by: 98.75 ± 10.45/(√(60))

Learn more about empirical rule here:

https://brainly.com/question/13676793

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