Which equation has a solution of r = 1/3

Answer:

$ 30,000

Step-by-step explanation:

0.15(50,000 - x) - 0.1x = 2,500

7,500 - 0.15x - 0.1x = 2,500

7,500 - 2,500 = 0.15x + 0.1x

5,000 = 0.25x

5,000/0.25 = x

x =20,000

50,000 - 20,000 = 30,000

0.15 * 30,000 = $4,500

0.1 * 20,000 = $2,000

$4,500 - $2,000 = $2,500

Using the fundamental counting theorem, it is found that 107,016 different choices are possible.

Fundamental counting theorem:

States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem:

Then, applying the theorem:

[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]

107,016 different choices are possible.

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Answer:

1. 3x

2. 2xy+13y

3. -2x^2+4y+2

4. -2a^3+3a^2

5. -2pq^2-7p^2q

Answer:

Option B

Step-by-step explanation:

[tex]PV = nRT\\\rule{150}{0.5}\\\rightarrow \frac{PV = nRT}{nR}\\\\\rightarrow \boxed{\frac{PV}{nR} = T}[/tex]

Hope this helps.

The equation for T will be;

⇒ T = PV/nR

Where, P, V, and T represent pressure, volume, and temperature, n represents the number of moles of gas, and R is a constant for the ideal gas.

Option B is true.

What is Linear equation?

When in an equation the highest power of variable is one then its called Linear equation.

Given that;

The equation for the ideal gas law is,

PV = nRT

Where, P, V, and T represent pressure, volume, and temperature,

n represents the number of moles of gas, and R is a constant for the ideal gas.

Now,

Solve the equation for T as;

PV = nRT

Divide both side by 'nR' we fet;

PV/nR = nRT/nR

PV/nR = T

T = PV/nR

Thus, The equation for T will be;

⇒ T = PV/nR

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Answer:

bt.ly/d97sjdu8 there is your answer!

Step-by-step explanation:

Answer:

x-intercept is 0

Step-by-step explanation:

(0, 24) (4,0)

(x, y)

0/4=0

The length of time it would take the given principal to become Php 8,000 is 8 years.

The formula that would be used to determine the length of time it would take Php 20000 to accumulate an interest of Php 8000 can be determined using this formula:

Time = Interest earned / (principal x interest rate)

8000 / (20,000 x 0.05)

= 8 years

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Answer:

The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.  The solution is the ordered pair(s) common to all lines in the system when the lines are graphed.

Lines that cross at a point (or points) are defined as a consistent system of equations. The place(s) where they cross are the solution(s) to the system.

Parallel lines do not cross. They have the same slope and different y-intercepts. They are an example of an inconsistent system of equations. An inconsistent system of equations has no solution.

Two equations that actually are the same line have an infinite number of solutions. This is an example of a dependent system of equations.

Step-by-step explanation:

Solve the system of equations graphically.

3x + 2y = 4

−x + 3y = −5

Solution

Graph each line and determine where they cross.

The lines intersect once at (2, −1).

A graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. At times the point of intersection will need to be estimated on the graph. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination.

Substitution Method

To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.

Example

Solve the following system of equations by substitution.

x + 3y = 18

2x + y = 11

Solution

Solve for a variable in either equation. (If possible, choose a variable that does not have a coefficient to avoid working with fractions.)

In this case, it's easiest to rewrite the first equation by solving for x.

x + 3y = 18

x = −3y + 18

Next, substitute (−3y + 18) in for x into the other equation. Solve for y.

2(  3y + 12x + y = 11

2(−3y + 18) + y = 11-------Substitute -3y + 18 in for

   −6y + 36 + y = 11-------Distribute.

2(3y −5y + 36 = 11-------Combine like terms.

2(3y +  18−5y = −25-----Subtract 36 from both sides

2(3y + 18) +  y = 5----   -Divide both sides by -5.

Then, substitute y = 5 into your rewritten equation to find x.

x = −3y + 18

x = −3(5) + 18

x = −15 + 18

x = 3

Identify the solution.   A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).

Elimination Method

Another way to solve a system of equations is by using the elimination method.  The aim of using the elimination method is to have one variable cancel out. The resulting sum will contain a single variable that can then be identified. Once one variable is found, it can be substituted into either of the original equations to find the other variable.

Example

Find the solution to the system of equations by using the elimination method.

x − 2y = 9

3x + 2y = 11

Solution

Add the equations.

 x −  2y = 9

3x +  2y = 11

4x +  2y = 20

Isolate the variable in the new equation

4x = 20

 x = 5

Substitute x = 5 into either of the original equations to find y.

 x − 2y = 9

(5) − 2y = 9

     −2y = 4

        y = −2

Identify the ordered pair that is the solution.   A check in both equations will show that (5, −2) is a solution.

It may be necessary to multiply one or both of the equations in the system by a constant in order to obtain a variable that can be eliminated by addition. For example, consider the system of equations below:

3x + 2y = 6

 x − 5y = 8

Both sides of the second equation above could be multiplied by −3. Multiplying the equation by the same number on both sides does not change the value of the equation. It will result in an equation whereby the x values can be eliminated through addition.

Special Cases

In some circumstances, both variables will drop out when adding the equations. If the resulting expression is not true, then the system is inconsistent and has no solution.

4x + 6y = 13

6x + 9y = 17

3(4x + 6y = 13)

2(6x + 9y = 17)

12x + 18y = 39

12x + 18y = 34

             0 = 5

The equation is false.  The system has no solution.

If both variables drop out and the resulting expression is true, then the system is dependent and has infinite solutions.

6x + 15y = 24

4x + 10y = 16

2(6x + 15y = 24)

3(4x + 10y = 16)

12x + 30y = 48

12x + 30y = 48

             0 = 0

The equation is true.  The system has an infinite number of solutions.  (Notice that both of the original equations reduce to 2x + 5y = 8.  All solutions to the system lie on this line.)

Answer:

234

Step-by-step explanation:

The answer to your question is 7.65.

Answer:

Step-by-step explanation:

(6)10x + 4y = 14(6)

4(15x + 6y) = 21(4)

60x + 24y = 84

60x + 24y = 84

It has infinite, as if this were to be graphed the lines would overlap.

Answer:

Step-by-step explanation:

the answer  is . (5xy² + 3x² - 7) + (3x²y² - xy² + 3y² + 4). hope this helps

9514 1404 393

Answer:

  a. Z: 30,000; T: 50,000

  b. Z: 37.5%; T: 62.5%

Step-by-step explanation:

a. The "ratio units" add up to 3+5 = 8, so we can find the investment amounts by multiplying the ratio by 10,000

  Z : T = 3 : 5 = 30,000 : 50,000

__

b. Zoe's investment amount is 3/8 of the total, or ...

  3/8 × 100% = 37.5%

Toria's percentage is the rest of it:

  100% -37.5% = 62.5%

  Zoe invested 37.5% of the total; Toria invested 62.5% of the total.

Answer:

Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.

Given the three events, which of the following statements is true?  

Select all that apply.

Event A: The mother or father carries the recessive gene.

Event B: The father carries the recessive gene.

Event C: The baby is at risk for Cystic Fibrosis.

Select all that apply:

Event A and Event B are mutually exclusive.

Event B and Event C are mutually exclusive.

Event A and Event C are not mutually exclusive.

Event A and Event C are mutually exclusive.

Event A and Event C are not mutually exclusive.

Remember that in general, A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.

In this question, note that if the mother or father carries the recessive gene for cystic fibrosis, the baby is at risk. So here, A and C are not mutually exclusive, and B and C are not mutually exclusive.

A and B are not mutually exclusive because they share an outcome: the father carrying the recessive gene.

Step-by-step explanation:

The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.

Reasons:

The area of the triangle, A = 0.5·x·y

Where;

x and y are the values of the line at the intercepts

The equation of the line is; (y - 7) = m·(x - 8)

At the y-intercept, x = 0, therefore;

(y - 7) = m·(0 - 8) = -8·m

At the y-intercept, y = 7 - 8·m

At the x-intercept, y = 0, therefore;

(0 - 7) = m·(0 - 8) = -8·m

At the x-intercept, -7 = m·x - 8·m

8·m - 7 = m·x

[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]

Therefore;

[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]

When the area is minimal, we have;

[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]

m² × 0 = 24.5 - 32·m²

[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]

[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]

[tex]\displaystyle m = \pm \frac{7}{8}[/tex]

The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;

(y - 7) = m·(x - 8)

[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]

[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]

[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]

[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]

The x and y intercept of the above line are 0

When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;

[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]

Which gives;

[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]

[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]

The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;

[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]

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Answer

your equation in part c is wrong

Step-by-step explanation:

part c

y=mx+c

11=2m+c-----------(1)

15=3m+c----------(2)

(2)-(1)

15-11=(3m+c)-(2m+c)

4=3m-2m+c-c

m=4

substitute in (1)

2m+c=11

2*4+c=11

8+c=11

c=3

so equation should be y=4x+3

Answer:

I am almost completely sure its 4.

Step-by-step explanation:

I dont mind brainiests by the way

Answer:f(x)=1.5-x + 8

Step-by-step explanation:

Answer:

x=68 and y = 112

Step-by-step explanation:

angles of a triangle must equal 180, so

52°+60°+x°=180

112+x=180 <-- subtract 112 to get x on one side.

x=68

To solve for y, a straight line = 180 so

68+y=180 --> just subtract 180-68

y=112

Answer:

As 1 feet = 12 inches

Therefore, 4 feet = 48/12

= 4

Answer = 4 feet

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Steps are in the attachment.

________

Hope it helps :)) ⚜

Answer:

a

Step-by-step explanation:

a

Answer:

11

Step-by-step explanation:

yeah-ya............ right?

Check the picture below.

Answer:

Yes, Kathy does  have enough juice.

Step-by-step explanation:

Kathy does have enough because quarts are a little bigger than liters, so the 3 quarts she has will cover the liters.

Answer:

919,800

Step-by-step explanation:

To round up, the tens place would have to be either 5 or higher. Since the number in the tens place is 2, which is under 5, it will stay the same.

The 2 points marked on the graph are :-

(2, 3) & (-7, -4)

Here,

=》x₁ = 2

=》y₁ = 3

=》x₂ = -7

=》y₂ = -4

Using distance formula....

√(x₂ - x₁)² + (y₂ - y₁)²

= √(-7 - 2)² + (-4 - 3)²

= √(-9)² + (-7)²

= √81 + 49

= √130 (in radical form)

= 11.4 (approx......in standard form)

♧ The distance between the 2 points is √130 units.

______

Hope it helps ⚜

Answer:

-39a - 16 is not the answer, it's -5/6a - 5/8

Step-by-step explanation:

Took the test and got it incorrect.

Answer:

-5/6a - 5/8

Step-by-step explanation:

There is a massive difference between -2/3a & -23a.

Same goes for 1/8 & 18, -1/6a & -16a, and -3/4 & -34.

My earlier answer, -39a - 16, IS correct for the question you wrote. What was incorrect was the question.

It is important to write the question properly because

−23a+18−16a−34

and

−2/3a+1/8−1/6a−3/4

will have very different answers.

In conclusion, make sure you write your question correctly. It's unfair to others genuinely trying to help who then are blamed for supplying the "wrong answer" by others who also copied and pasted from their school work.

If you had written, −2/3a+1/8−1/6a−3/4, then the answer would be -5/6a - 5/8.

Step-by-step explanation:

earbuds

we have a 1in : 0.2in scale of drawing to reality.

0.2 = 2/10 = 1/5

so, 1in in the drawing is actually 1/5in in reality.

how long are the 4in in the drawing ?

well, 4 times the 1in thing.

4×1/5 = 4/5 = 0.8in long

again the similar triangles

similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.

so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?

27 × x = 9

x = 9/27 = 1/3

and that is the scale factor.