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2 years ago

Prove algebraiclly that the straight line with equation x = 2y + 5

Mathematics

1 answer:

Semmy [17]2 years ago

6 0

<h2>Answer and step by step explanation</h2>

x = 2y + 5 (1)

x^2 + y^2 = 5 (2)

Sub (1) into (2) to find the y intersection of these functions

(2y + 5)^2 + y^2 = 5 simplify

4y^2 + 20 y + 25 + y^2 = 5

5y^2 + 20y +20 = 0 divide through by 5

y^2 + 4y + 4 = 0 factor

(y + 2)^2 = 0 take the square root of both sides

y + 2 = 0

y = -2

And x = 2(-2) + 5 = 1

So....(1, -2) is the tangent point because it is the only point that makes both equations true

1 = 2(-2) + 5 is true and

(1)^2 + (-2)^2 = 5 is also true

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Match the fractions that are equivalent to each other?

MrRissso [65]

Answer:

1&a 2&b 3&c 4&d

Step-by-step explanation:

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4 0

3 years ago

Read 2 more answers

Consider the vector x: x <- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Opti

Nookie1986 [14]

<u>Completed Question</u>

Outputs to be matched to the functions are:

1,2,3,4,5
1,5,3,2,4
1, 4, 3, 5, 2
2, 18, 27, 43, 96

Answer:

sort(x): 2, 18, 27, 43, 96
order(x): 1, 5, 3, 2, 4
rank(x) : 1, 4, 3, 5, 2
none of these : 1, 2, 3, 4, 5

Step-by-step explanation:

Given the vector x: x <- c(2, 43, 27, 96, 18)

In R, the sort(x) function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.

Therefore, the output that matches the sort function is:

sort(x): 2, 18, 27, 43, 96

The rank function returns a vector with the "rank" of each value.

x <- c(2, 43, 27, 96, 18)

2 has a rank of 1
43 has a rank of 4
27 has a rank of 3
96 has a rank of 5
18 has a rank of 2

Therefore, the output of rank(x) is: 1, 4, 3, 5, 2

<u>Order</u>

When the function is sorted, the order function gives the previous location of each of the element of the vector.

Using the sort(x) function, we obtain: 2, 18, 27, 43, 96

In the vector: x <- c(2, 43, 27, 96, 18)

2 was in the 1st position
18 was in the 5th position
27 was in the 3rd position
43 was in the 2nd position
96 was in the 4th position

Therefore, the output of order(x) is: 1, 5, 3, 2, 4

7 0

2 years ago

Evaluate the expression for f = -6 and g = -1.<br> fg - f =

Arlecino [84]

Answer:

Step-by-step explanation:

Given the information from the question:

$fg - f = f \times g - f$

Next we can use the order of operations to find the value of the expression.

$fg - f = - 6 \times - 1 - ( - 1) \\ = 6 - ( - 1) \\ = 6 + 1 \\ = 7$

5 0

1 year ago

Multiply (x-2) (2x+4)

Bas_tet [7]

Answer:

$2x {}^{2} - 8 = 0$

Step-by-step explanation:

$(x-2) (2x+4) = 0\\ 2x {}^{2} + 4x - 4x - 8 = 0 \\ 2x {}^{2} - 8 = 0$

5 0

3 years ago

Twin brothers, Billy and Bobby, can mow their grandparent’s lawn together in 63 minutes. Billy could mow the lawn by himself in

Pepsi [2]

Answer:

<h2>140 minutes</h2>

Step-by-step explanation:

this problem focuses on the combined work rate

both can finish the work under 63 minute

let bobby mow the lawn in x minute

Billy will then mow the lawn in x-25 minutes

Let the completed job = 1 (a mowed lawn)

we can now apply the combined work formula for the two boys as

$\frac{63}{x}+\frac{63}{x-25}=1$

multiplying through by x(x-25 )we have

$63(x-25)+63x= x(x-25)$

open bracket we have

$63x-1575+63x= x^2-25x$

rearranging and collecting like terms we have

$0=x^2-25x-63x-63x+1575 \\\\0=x^2-151x+1575 \\\\x^2-151x+1575=0$

we can now use the quadractic formula

$x=\frac{-b\frac{+}{} \sqrt{b^2-4ac} }{2a}$

a= 1

b= -151

c= 1575

$x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}$

$x=\frac{-(-151)\frac{+}{} \sqrt{22801-6300} }{2} \\\\x=\frac{-(-151)\frac{+}{} \sqrt{16501} }{2} \\\\x=\frac{-(-151)\frac{+}{} 128.45}{2} \\\\$

$x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27$

the first answer x= 139.72 approximately 140 minutes mins is correct for Bobby's time

let us check

$\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1$

we can see that the solution approximates to 1

8 0

3 years ago