A system of equations is graphed on the set of axes below.


The solution of this system is:
A.
(4, 3)
B.
(3, 4)
C.
(2, 0)
D.
(0, ‒8)

The solution of the equation is (-2, 3) and to eliminate x we have to multiply equation(i) by 3 and multiply equation(ii) by 4.

System of equation can be solved using different method such as elimination method, substitution method and graphical method,

Let's use elimination method to solve the system of equation.

Therefore,

4x + 5y = 7

3x - 2y = - 12

Multiply equation(i) by 3 and equation(ii) by 4 to eliminate x.

Hence,

12x + 15y = 21

12x - 8y = - 48

Subtract the equations

23y = 69

y = 69 / 23

y = 3

Hence,

4x = 7 - 5y

4x = 7 - 5(3)

4x = 7 - 15

4x = -8

x = -8 / 4

x = -2

Therefore, the solution is (-2, 3)

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Answer:

35

Step-by-step explanation:

18+17=35

Population in 2011 is 361.606 million, Population in 2025 is 438.094 million, Year when population will be 2 billion is 2136

What is Function?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given the function of the population = P(t) = 3111(1+0.0138)^t

1. Population of Indonesia in 2011

= P(11) = 311 (1.0138)^11

= P(11) = 361.606 million

2. Population of Indonesia in 2025

= P(25) = 311 (1.0138)^25

= P(25) = 438.094 million

3. Year when population is 2 billiion

2000 million= 311(1.0138)^x

x = 136 years approx. i.e. 2136

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The equation of the line perpendicular to the line 3x - 6y = - 8 is y = - 2x - 15 and of line parallel to the line 3x - 6y = - 8 is y = x/2.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a line 3x - 6y = - 8.

We have -

3x - 6y = - 8

3x = 6y - 8

6y = 3x - 8

y = x/2 - 4/3

For a parallel line -

slope = 1/2

y = x/2 + c

for the point (- 6, - 3), we can write -

-3 = -6/2 + c

-3 = -3 + c

c = 0

Equation : y = x/2

For a perpendicular line -

y = - 2x + c

for the point (- 6, - 3)

- 3 = - 2 x - 6 + c

- 3 = 12 + c

c = - 15

Equation : y = - 2x - 15

Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y = - 2x - 15 and of line parallel to the line 3x - 6y = - 8 is y = x/2.

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The slope of the line in the graph is -3/4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the line;

The slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula;

m = 0 - 3 / 4 - 0

Slope = -3/4

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Answer:

x is 13 and y is 10

Step-by-step explanation:

Multiply the second equation by 3

Answer:

 D. Multiply the second equation by 3. The solution is x = 12, y = 10.

Step-by-step explanation:

You want the multiplier for the elimination of the y-variable in the system of equations x +3y = 42; 2x -y = 14.

The coefficients of y are +3 and -1, so multiplying the second equation by 3 will make it the opposite of the former. Then their sum is zero, which is what you want when eliminating the y-variable.

Multiplying the second equation by 3 and adding the first gives ...

  3(2x -y) +(x +3y) = 3(14) +(42)

  7x = 84 . . . . . . . . . simplify. Note the y-variable has been eliminated.

  x = 12 . . . . . . . . . divide by 7

  2(12) -y = 14 . . . . substitute for x in the second equation

  24 -14 = y = 10 . . . . add y-14

The solution is (x, y) = (12, 10).

Answer:

20

Step-by-step explanation:

add 1 to both sides

3/4x=15

multiply both by 4

3x=60

divide by 3

x=20

The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3  .

In the question ,

it is given that ,

the required line passes through the points (-3,5) and (6,5) ,

we need to find equation of line ,

to find the equation , we first need to calculate the slope (m) .

slope(m) = (6-5)/(6-(-3))

= 1/9

So , the equation of the line passing through the point (6,5) with slope 1/9 in point slope form is

(y - 5) = 1/9(x - 6)

9(y - 5) = 1(x - 6)

9y - 45 = x - 6

9y = x - 6 + 45

9y = x + 39

y = x/9 + 39/9

y = x/9 + 13/3

Therefore , The equation of the line passing through the points (-3,5) and (6,5) is y = x/9 + 13/3  .

The given question is incomplete , the complete question is

What is the equation of the line in the point slope form passing through the points (-3,5) and (6,5) ?

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Inequality which shows the number of phone calls in order to make Plan 1 more economical is, x> 375.

It means if customer calls for more than 375 times Plan 1 is more economical for him/her.

Given that Plan 1 offers unlimited calls against $29 per month.

and Plan 2 offers each call against $0.04 and with an adiditional charge $14 per month.

Let if there are x calls in a month then Plan 1 is more economical.

Plan 1 is more economical means Plan 1 costs the customer less than the Plan 2.

So for x calls the bill according to Plan 2 = 14 +0.04x

And the charge $29 fixed for Plan 1.

So the required inequality is,

14+0.04x > 29

Solving the inequality we get,

0.04x > 15

.x > 375

So the calls should be more than 375.

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The probability an athlete plays golf or tennis but not both = 0.75  

The ratio of favorable outcomes to all possible outcomes of an event is known as probability.  

The formula to calculate the probability of an event is given by

Probability(E) = Favorable Outcomes/Total Outcomes  

Here we have 40 athletes,  

Number of athletes who plays both tennis and golf = 5

Number of athletes who plays tennis = 30

=> Number of athletes who plays only tennis = 30 - 5 = 25  

Number of athletes who plays golf = 10  

Number of athletes who plays only golf = 10 - 5 = 5

From the above calculations,

Number of athletes who plays tennis or golf but not both = 25 + 5 = 30

Probability that athletes play golf or tennis but not both = 30/40 = 0.75

Therefore,

The probability an athlete plays golf or tennis but not both = 0.75

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Ratio of the sundae with nut to total number is 2:3.

The ratio will be written as numerator and denominator seperated by colon. The numerator will be number of sundae with nut and denominator will be total number of sundae. So, writing the numbers in mentioned description of ratio.

Ratio of the number of sundae with nut to the total number of sundae = 4 : 6

The ratio can be further simplified by dividing both numerator and denominator by 2.

Ratio of the number of sundae with nut to the total number of sundae = 2 : 3

Thus, the required ratio fo sundae is 2:3.

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Answer:

1:38

Step-by-step explanation:

i think that is the answer

Answer: Its started driving through the neighborhood at 1:37

Step-by-step explanation:

Answer:

4. d = 4

5. d = 8.8

6. d = 6

7. d = 10

8. d = 3

9. d = 1

Step-by-step explanation:

4. (-5, 2), (-5, 6)

    (x₁, y₁)  (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5 - (-5))² + (6 - 2)²

d = √(-5 + 5)² + (4)²

d = √(4)²

d = √16

d = 4

5. (4.5, -3.3), (4.5, 5.5)

       (x₁, y₁)      (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4.5 - 4.5)² + (5.5 - (-3.3)²

d = √(0)² + (5.5 + 3.3)²

d = √(8.8)²

d = √77.44

d = 8.8

6. ((5(1/2), (-7(1/2)) and ((5(1/2), (-1(1/2))

         (x₁,     y₁)                   (x₂,     y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(11/2) - (11/2)² + (-3/2) - (-15/2))²

d = √(d)² + ((-3/2) + (15/2)²

d = √(6)²

d = √36

d = 6

7. (-2(1/4)), -8) and (7(3/4), -8)

        (x₁,   y₁)               (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(31/4) - (-9/4))² + (-8 - (-8))²

d = √(31/4) + (9/4))² + (-8 + 8)²

d = √(10)²

d = √100

d = 10

8. (5(1/4)), (-3(1/4) and ((5(1/4), (-6(1/4))

         (x₁,     y₁)                    (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(21/4) - (21/4))² + (-25/4) - (-13/4))²

d = √(-25/4) + (13/4))²

d = √(-3)²

d = √9

d = 3

9. (-1(1/2)), (-6(1/2) and ((-2(1/2), (-6(1/2))

          (x₁, y₁)                        (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5/2) - (-3/2))² + (-13/2) - (-13/2))²

d = √(-5/2) + (3/2))²

d = √(-1)²

d = √1

d = 1

I hope this helps!

Answer:

64 milliliters of 25% juice

96 milliliters of 50% juice.

Step-by-step explanation:

Answer:

96 mL of the 50% juice

64 mL of the 25% juice

Step-by-step explanation:

Declaration

Let the number of mL of 25% juice = x

Let the number of mL of 50% juice = y

Equations

25/100 * x + 50/100 y = 40/100 * 160        Combine

x + y = 160 mL

Solution

0.25x + 0.5y = 0.4 * 160

0.25x +0.5y = 64                            Multiply this equation by 4

0.25*4x + 0.5*4y = 64*4                Combine

x + 2y = 256                                   Put the first equation underneath and subtract

x + 2y = 256

x + y = 160                                    Subtract

     y = 96                                       mL of 50% fruit juice

x + y = 160

x + 96 = 160                                    Subtract 96 from both sides.

x + 96 - 96 = 160-96

x = 64                                              mL of the 25% fruit juice.

If 15% of 500 is equal to 7.5% of the number, the number is equals to 1000.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

Therefore, let's find the number if 15% of 500 is equal to 7.5% of the number.

Let

x = the number

Hence,

15% of 500 = 7.5% of x

15 / 100 × 500 = 7.5 / 100 × x

75 = 7.5x / 100

cross multiply

7500 = 7.5x

divide both sides by 7.5

x = 7500 / 7.5

x = 1000

Therefore, the number is 100.

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Answer:

11x^2 - x + 15

Step-by-step explanation:

x^2-x+8+10x^2+7 =

= 11x^2 - x + 15

Answer:

x=-1

Step-by-step explanation:

5x+6=1

5x=-5

x=-1

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The Number of Associates and Number of Partners assigned to the case by the law firm is 5 and 9 respectively. We can solve this by using the concept of Linear Equation.

Given that,

Daily rate charged to the client for each Associate = $ 800

Daily rate charged to the client for each Partner = $ 1700

Let number of Associates assigned to case = X

And number of Partners assigned to case = Y

So, According to Question

X + Y = 14    ----(1)

800X + 1700Y = 19300        ---(2)

From the equation (1) , Y = 14 – X

Substituting the value of Y into equation (2) we get,

800X + 1700(14-X) = 19300

800X + 23800 – 1700X = 19300

23800 – 900X = 19300

23800 – 19300 = 900X

4500=900X

4500/900 = X

X = 5

Put the value of X into equation (1),

5 + Y = 14

Y = 14 -5

Y = 9

So we let the number of Associates assigned to case X and number of partners assigned to case Y and the value of X is 5 and Y is 9 .

Hence the number of Associates assigned to the case is 5 and the number of Partners assigned to the case is 9.

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The difference between lagging strand and leading strand based on DNA replication is.

What is DNA?

DNA stands for deoxyribonucleic acid.

Main body:

The major difference between a lagging and leading strand is that the lagging strand replicates discontinuously forming short fragments, whereas the leading strand replicates continuously. Find out more such differences between a lagging and leading strand, in the table below.

Lagging Strand  

Description:                                                      

Leading Strand

Description:                

Therefore the difference between lagging strand and leading strand are as follows.

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If A = 21 bh, b= 16, and A= 40, then value of h is 0.1190.

∴ A= 21 bh, b = 16, A= 40

Putting the values in A = 21 bh, we get

A= 21 bh

⇒ 40 = 21×16×h

⇒h = 40/21×16

⇒h = 0.1190

So the value of h is 0.1190.

Answer:

Step-by-step explanation:

(4i)·(-8i)·(5+5i) = 160+ 160i

We take into account that (i)²  = -1

1)

(4i)·(-8i) = (-32)·i² = (-32)·(-1) = 32

2)

32·(5 + 5i) = 32·5 + 32·(5i)  = 160 + 160 i

At the 0.05 level of confidence, there is enough data to say that Gentle Ben's blood glucose is higher than 85 mg/100 ml.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph. Data are symmetrically distributed and skew-free in a normal distribution. As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.

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The value of b after solving the expression 45= |b-12| is 57 or -33

Given,

The algebraic expression; 45= |b-12|

Algebraic expression;

An algebraic expression is an equation made up of variables and arithmetic operations like multiplication and division.

We are aware that the encoding of a modulus sign as a rand absolute value with two values a value, either positive or negative.

Here,

45= |b-12|

45 = ± (b - 12)

Solve for;

b = 45 + 12

b = 57

Solve for;

b = - 45 + 12

b = - 33

Therefore,

The value of b after solving the expression 45= |b-12| is 57 or -33

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Answer:

A

Step-by-step explanation:

40% = 40/100 = 4/10 = 2/5

2/5 * 2/5 = 4/25 = 0.16

Answer:

9 = 20

7 = 10

Step-by-step explanation:

We list the operations done between two functions below:

In this problem we find three functions, two of them defined by quadratic equations (f(x), g(x)) and the other defined by a linear equation (h(x)). There are five operations that can be used b two functions:

Now we proceed to determine the result of each operation:

Case 1:

g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3)

Case 2:

h(x) - g(x) = (2 · x - 3) - (4 · x² + 2 · x - 1)

h(x) - g(x) = - 4 · x² - 2

Case 3:

h(f (x)) = 2 · (3 · x² + 2) - 3

h(f (x)) = 6 · x² + 1

Case 4:

f(x) + g(x) = (3 · x² + 2) + (4 · x² + 2 · x - 1)

f(x) + g(x) = 7 · x² + 2 · x + 1

Case 5:

h(f(x)) = 6 · x² + 1

h(f(2)) = 6 · 2² + 1

h(f(2)) = 25

Case 6:

f(h(x)) = 3 · (2 · x - 3)² + 2

f(h(x)) = 3 · (4 · x² - 12 · x + 9) + 2

f(h(x)) = 12 · x² - 36 · x + 29

f(h(3)) = 12 · 3² - 36 · 3 + 29

f(h(3)) = 29

Case 7:

g(x) + h(x) = (4 · x² - 12 · x + 9) + (2 · x - 3)

g(x) + h(x) = 4 · x² - 10 · x + 6

g(2) + h(2) = 4 · 2² - 10 · 2 + 6

g(2) + h(2) = 2

Case 8:

2 · f(x) - g(x) = 2 · (3 · x² + 2) - (4 · x² + 2 · x - 1)

2 · f(0) - g(2) = 2 · (3 · 0² + 2) - (4 · 2² + 2 · 2 - 1)

2 · f(0) - g(2) = 4 - 19

2 · f(0) - g(2) = - 15

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Answer:

  C.  all real numbers

Step-by-step explanation:

You want the domain of the function F(x) = 1.

The domain of a function is the set of values of the independent variable for which the function is defined. The function F(x) is defined for all possible values of x, so its domain is all real numbers.

For each pair of fractions, following fraction is larger

a) 5/6 > 5/7

b) 2/9 < 5/9

c) 3/4 < 9/10

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given,

Fraction:

a) 5/6 or 5/7

Taking LCM,

LCM = 42

5/6 × 7/7

35/42

5/7 × 6/6

30/42

5/6 > 5/7

b) 2/9 or 5/9

They have same denominator,

So,

2/9 < 5/9

c) 3/4 or 9/10

Taking LCM:

LCM = 20

3/4 ×5/5

15/20

9/10 × 2

18/20

3/4 < 9/10

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