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3 years ago

Using a graphical method, solve the simultaneous equations x+y =4 and y=2x+1

Mathematics

1 answer:

adoni [48]3 years ago

7 0

Answer:

(1, 3)

Step-by-step explanation:

Given the expression

x+y = 4 ... 1

y = 2x+1 ....2

Substitute equation 2 into 1

x + (2x+1) = 4

3x + 1 = 4

3x = 4-1

x = 3/3

x = 1

Since y = 2x + 1

y = 2(1) + 1

y = 3

Hence the solution to the equation is (1,3). This means that the coordinate point on the graph where both lines intersect will be at (1, 3)

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1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classe

Juli2301 [7.4K]

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) $\$68.76$

Part 4) $\$12\ per\ hour$

Part 5) The equation that can be used is $27x=242.73$ and the cost of one print is $\$8.99$

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is $m=\$10\ per\ class$

The y-intercept is $b=\$100$

$y=10x+100$ ----> equation A

Non-Members

The slope is $m=\$15\ per\ class$

$y=15x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$10x+100 < 15x$

Solve for x

subtract 10 x both sides

$100 < 15x-10x$

$100 < 5x$

Divide by 5 both sides

$20 < x$

Rewrite

$x > 20$

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

The sum of 8 and 3 times a number is 23 is the same that

$8+3x=23$

solve for x

subtract 8 both sides

$3x=23-8$

$3x=15$

Divide by 3 both sides

$x=5$

Part 3) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is $m=\$0.42\ per\ mile$

The y-intercept is $b=\$36$

$y=0.42x+36$

For x=78 miles

substitute in the linear equation and solve for y

$y=0.42(78)+36$

$y=\$68.76$

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

The linear equation that represent this situation is

$40x+10(1.5x)=660$

solve for x

$40x+15x=660$

$55x=660$

Divide by 55 both sides

$x=\$12\ per\ hour$

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

The linear equation is equal to

$27x=242.73$

solve for x

Divide by 27 both sides

$x=\$8.99$

Part 6) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is $m=\$7\ per\ class$

The y-intercept is $b=\$120$

$y=7x+120$ ----> equation A

Non-Members

The slope is $m=\$11\ per\ class$

$y=11x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$7x+120 < 11x$

Solve for x

subtract 7x both sides

$120 < 11x-7x$

$120 < 4x$

Divide by 4 both sides

$30 < x$

Rewrite

$x > 30$

therefore

The number of classes must be greater than 30

4 0

3 years ago

If johnny gets 2 apples every 5 minuets how much apples does johnny have in 8 hours.

hodyreva [135]

Answer:

192

Step-by-step explanation:

5 0

2 years ago

Find all real and imaginary zeros 1.) 343x^3-8=0 2.) 64x^3=0

puteri [66]

1. 343x³ - 8 = 0
343x³ + 98x² - 98x² + 28x - 28x - 8 = 0
343x³ + 98x² + 28x - 98x² - 28x - 8 = 0
  7x(49x²) + 7x(14x) + 7x(4) - 2(49x²) - 2(14x) - 2(4) = 0
7x(49x² + 14x + 4) - 2(49x² + 14x + 4) = 0
  (7x - 2)(49x² + 14x + 4) = 0
  7x - 2 = 0 or 49x² + 14x + 4 = 0
+ 2 + 2 x = -(14) ± √((14)² - 4(49)(4))
7x = 2   2(49)
7   7 x = -14 ± √(196 - 784)
x = ²/₇   98
x = -14 ± √(-588)
-98
x = -14 ± 14i√(3)
-98
x = -14 + 14i√(3) or x = -14 - 14i√(3)
-98 -98
x = ¹/₇ - ¹/₇i√(3) or x = ¹/₇ + ¹/₇√(3)
x = ¹/₇ ± ¹/₇i√(3)
Solution Set: {¹/₇ ± ¹/₇i√(3), ²/₇}

2. 64x³ = 0
64 64
x³ = 0
∛(x³) = ∛(0)
x = 0
Solution Set: {0}

6 0

4 years ago

Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.n=800, p=0.6a) Determine the mean of t

Leno4ka [110]

Answer:

Standard deviation of the binomial distribution

= $\sqrt{n p q} = \sqrt{192} = 13.856$

Step-by-step explanation:

Explanation:-

Given size 'n' = 800

The population proportion 'p'=0.6

Let 'X' be the random variable of the binomial distribution

a) mean of the binomial distribution = n p = 800 ×0.6

μ = 480

b) variance of the binomial distribution

= n p q

= 800 X 0.6 ×0.4

σ² = 192

Standard deviation of the binomial distribution

σ = $\sqrt{n p q} = \sqrt{192} = 13.856$

6 0

3 years ago

Understand multiplying

taurus [48]

Answer:

Step 1 : 1000 * 2 * 9

Step 2 : 1000 * 18

Step 3 : 18000

Step-by-step explanation:

Step 3

2000 * 9 = y ⇒ 18000

y = 18000

Step 1

Solving for this, we have:

Let a be the unknown variable

a * 2 * 9 = 18000

18a = 18000

a = 1000

Therefore, when we multiply 1000 by 2 & 9, we have 18000

Step 2

Solving for this, we have:

Let a be the unknown variable

a * 18 = 18000

18a = 18000

a = 1000

Therefore, when we multiply 1000 by 18, we have 18000

We therefore see that the value of the unknown variables (a, y) is shown above & the product of all the steps (step 1 - 3) is 18000

3 0

4 years ago