What is the area of the triangle

Solution :

Given data :

[tex]c_{in}[/tex] = 1 g/L

[tex]r_{in}[/tex] = 5 L/min

[tex]r_{out}[/tex] = 5 L/min

[tex]$v_0$[/tex] = 250 L

[tex]A_0[/tex] = 20 g

∴ [tex]r_{net} = r_{in}- r_{out}[/tex]

         = 5 - 5

          = 0

[tex]c_{out} = \frac{A}{250} \ g/L[/tex]

Now, [tex]\frac{dA}{dt}=(r_{in} \times c_{in}) - (r_{out} \times c_{out})[/tex]

[tex]$\frac{dA}{dt} = 5-5\left(\frac{A}{250}\right)$[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5 \text{ with} \ A_0 = 20[/tex]

Integrating factor = exp(5 t/250)

Therefore,

[tex]A \times \exp (5t \ /250) = \text{integral of}\ 5 \times \exp (5t / 250) + C[/tex]

Put [tex]A_0=250+C[/tex]

C = -230

[tex]A \times \exp(5t/250) = 250 \exp(5t/250) + (-230)[/tex]

[tex]A(t) = 250-230 \exp(-5t/250)[/tex]

[tex]A(t) = 250-230e^{\left(\frac{-t}{50}\right)} \ g[/tex]

Answer:

210

Step-by-step explanation:

7:5

First add the ratios

7+5=12

Put each ratio over the denominator 12 then multiply each by the total

7/12×1260= 735

5/12 × 1260 = 525

To find how many more winners than losers

735-525= 210

Answer:

<V = 40

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

20x = 60+7x+5

Combine like terms

20x = 7x+65

Subtract 7x from each side

20x -7x = 7x+65-7x

13x = 65

Divide each side by 13

13x/13 = 65/13

x = 5

<v = 7x+5 = 7*5+5 = 35+5 = 40

answer:

it's U = 60°

V = 50°

T = 70°

Answer:

(0, -6)

Step-by-step explanation:

Given the following systems of linear equations;

3x - 2y = 12 ...... equation 1

16x - 4y = 24 ........ equation 2

We would solve for the solution using the elimination method;

Multiplying eqn 1 by 2, we have;

2 * (3x - 2y = 12)

6x - 4y = 24

16x - 4y = 24

Subtracting the two equations, we have;

(6x - 16x) + (-4y -[-4y]) = (24 - 24)

-10x - 0 = 0

-10x = 0

x = -0/10 = 0

Next, we would find the value of y;

3x - 2y = 12

3(0) - 2y = 12

0 - 2y = 12

-2y = 12

y = -12/2

y = -6

Check:

3x - 2y = 12

3(0) - 2(-6) = 12

0 - (-12) = 12

12 = 12

Note: the options provided for this questions are incorrect or inappropriate.

Answer:

78 miles

Step-by-step explanation:

Given that:

Original length, L = 47 miles

Additional length (miles) added per day, = 1 mile

Representing as an equation :

L(D) = original length + additional length per day * number of days

Let, D = number of days

L(D) = 47 + D

Length after 31 days :

L(31) = 47 + 31

= 78 miles

Answer:

x = 2√2

Step-by-step explanation:

Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.

Now, since we see that it is also a right angled triangle, it means one angle is 90°.

Let the equal angles be a.

Thus;

a + a + 90 = 180 (since sum of angles in a triangle is 180)

2a + 90 = 180

2a = 180 - 90

2a = 90

a = 90/2

a = 45°

Now, using sine rule, we can find x. Thus;

x/sin 45 = 4/sin 90

sin 90 = 1

sin 45 = 1/√2

Thus;

x = (4 × 1/√2)/1

x = 4/√2

Let's rationalize the denominator to get;

x = (4/√2) × √2/√2

x = (4√2)/2

x = 2√2

Answer:10

Step-by-step explanation:

10 because 10 minus 8 would be 2

Answer:

Step-by-step explanation:

82

Answer:

Step-by-step explanation:

.5(half) x 14(base) x 16(height)=112cm

Answer:

614

Step-by-step explanation:

This pattern is being multiplied by 2

keep multiplying by two till you get to the 11th term

6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144

6144 is the 11th term.

Answer:

5

Step-by-step explanation:

The median is the middle when the numbers are lined up from smallest to largest

3,4,4,6,7,15

There are 6 number so the middle is the  between the 3rd and 4th number

3,4,4,    6,7,15

Take the 3rd and 4th numbers and average

(4+6)/2 = 10/2 = 5

Answer:

median = 5

Step-by-step explanation:

Arrange the data in ascending order :

3 , 4 , 4 , 6 , 7 , 15

Choose the middle number.

Here there are even number of data. Take the average of the middle

numbers .

4 and 6 are the middle number. average of 4 and 6 = ( 4 + 6 ) /2 = 5

Therefore , median = 5

Answer:

C

Step-by-step explanation:

Since Carrie walked 6 miles her day, the function that best suits this relationship is given by [tex]y=6x[/tex] where [tex]x[/tex] is the number of days she walked and [tex]y[/tex] is the number of miles.

Table C represents this function [tex]y=6x[/tex] because all y values are exactly 6 times the x value.

Answer:

The answer is C.

Step-by-step explanation:

18 ÷ 3 = 6 miles a day

36÷6 = 6 miles a day

54÷9 = 6 miles a day

72÷12 = 6 miles a day

Answer:

$68.97

Step-by-step explanation:

The equation you have to use is I=p(1.45)

If you have a 45% increase to 100, the original price was $68.97.

Answer:

The answers are given below.

Step-by-step explanation:

The computation is shown below:

1.a.

Profit Margin = Net Income ÷ Sales × 100

= $374 ÷ $6,900 ×100

= 5.4%

1-b:

Average Assets = (Beginning Assets + Ending Assets) ÷ 2

= ($3,200 + $3,600)  ÷ 2

= $3,400

Now  

Return on Assets = Net Income ÷ Average Assets

= $374 ÷ $3,400

= 11%

1-c

Average Equity = ($700 + $700 + $320 + $270) ÷ 2

= $995

Now  

Return on Equity = Net Income ÷  Average Equity *100

= $374 ÷ $995

= 37.59%

2:

Dividends Paid = Beginning Retained Earnings + Net Income – Ending Retained Earnings

= $270 + $374 - $320

= $324

Answer:

q.12

angle ACB=180-123

therefore ACB=57

again 5x-15+7x+6+57=180

or,12x+48=180

or,x=132/12

or x=11

Answer:

[tex]\frac{5}{2}[/tex] or 2.5

Hope that this helps!

Answer: GIVEN : f(x)= -3x+1

f(x)= -5

REQUIRE:  x=?

CALCULATION:

f(x)= -3x+1

As, given f(x)= -5.

Hence,

-5= -3x+1

OR

-3x+1= -5

-3x= -5-1

-3x=-6

x= -6/-3

x= 2

Answer:

There was a 45% increase in furniture sales.

Furniture sales rose by 9 percentage points.

Step-by-step explanation:

absolute difference = new - old

29-20= 9 percentage points

absolute difference / initial value = 9/20 = .45 * 100 = 45%

Two statements which are true about furniture sales are  [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and  [tex](f)[/tex]  Furniture sales rose by [tex]9[/tex] percentage points.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]

We have,

Sales of furniture in [tex]2015=20\%[/tex]

Sales of furniture in [tex]2016=29\%[/tex],

So,

Change in Percentage [tex]=29-20=9\%[/tex]

i.e.

Sales rise by [tex]9\%[/tex] points,

And,

Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]

Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.

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Answer:

I don't know for sure, but I'm pretty sure its 1,640.

Step-by-step explanation:

80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

According to question, The price at which it was sold is equal to :

The car was sold at $ 6560

Now, loss is equal to :

Answer:

Below:

Step-by-step explanation:

A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)

B) 0.45

C) 0.40

A) the total probability has to equal 1.

To find the probability of rat subtract the other animals from1:

Rat = 1 - 0.35-0.4-0.1 = 0.15

Rat = 0.15

B) probability of cat or hamster equals the sum of their probabilities:

Cat = 0.35 + hamster = 0.1 = 0.45

Answer = 0.45

C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16

Answer = 0.16

Answer:

354.

Step-by-step explanation:

De acuerdo a la sucesión 11,18,25,32..., para encontrar el término que se ubica en la posición 50​ se debe realizar el siguiente razonamiento lógico-matemático:

32 - 25 = 7

25 - 18 = 7

18 - 11 = 7

Así, los números van subiendo de 7 en 7. Por lo tanto, para determinar el número que se ubica en la posición 50 debe realizarse el siguiente cálculo:

(7 x 49) + 11 = X

343 + 11 = X

354 = X

Por lo tanto, el término que se ubica en la posición 50 es 354.

Answer:

Volume = 111.33 in.³

Step-by-step explanation:

The volume of the shape = volume of the rectangular prism part + volume of the triangular prism part

✔️volume of the rectangular prism part:

V = L*W*H

Where,

L = 5.1 in.

W = 3.4 in.

H = 5.9 in.

V = 5.1*3.4*5.9

V = 102.306 in.³

✔️volume of the triangular prism part:

V = ½*b*h*l

b = 6 - 5.1 = 0.9 in.

h = 5.9 in.

l = 3.4 in.

V = ½*0.9*5.9*3.4

V = 9.027 in.³

✅Volume of the shape = 102.306 + 9.027

= 111.333 in.³

≈ 111.33 in.³ (approximated to 2 decimal places)

Answer:

x=0

Step-by-step explanation:

0/3 = 0

0+5=5

Answer:

y = defence

Step-by-step explanation:

x^2 + ( 47y (7 + 6) + 18.1)  is a starter point

x^2 +  (47y (7+6) + 3(6+ 1/30))  

x^2 + (611y + 3(6+1/30))

x^2 + (611y + 18.1)

x^2 + 629.1y

With x representing x billion and y representing y billion for defence

The budget for defense can be represented by the algebraic expression $ (x + 629.1) billion.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.

Let x represents the budget for education.

Given that the budget for defense exceeded the budget for education by $629.1 billion.

The budget for defense can be represented by (x + 629.1).

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Answer:

use photo math. it will help

Answer:

this is the correct answer

Answer:

B) 720 in

Step-by-step explanation:

1 yard is equal to 36 inches.

So, we just have to multiply 20 by 36:

20 × 36 = 720

20 yards is 720 inches.

Answer:

-27

Step-by-step explanation:

a = 7 and c = -4

- a + 5 c

- ( 7 ) + 5 ( - 4 )

- 7 - 20

- 27

Step-by-step explanation:

51 and 51

maybe

Step-by-step explanation:

[tex]4 {x}^{2} \times 2 {x}^{3} = 8 {x}^{5} [/tex]

Answer:

Step-by-step explanation:

4x^2 * 2x^3

(2)^2 *x^2 *2*x^3

(2)^2+1 *x^2+3

(2)^3 *x^5

8*x^5

8x^5

another method

4*x^2*2*x^3

multiply 4 and 2

8*x^2+3

8x^5

in multiplication if the bases are same we add their power(exponent).In division if the bases are same we subtract their power(exponent).