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Marina CMI [18]
1 year ago
11

Pls help me it’s due today!!

Mathematics
1 answer:
prohojiy [21]1 year ago
3 0

Answer: the number of times the cricket could be expected to chirp in one minute if it’s 75 degrees Fahrenheit

Step-by-step explanation:

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) () = 2 − 6 + 13 Translate f(x) 7 units to the left and down 5 units. Write your new function in vertex form
Mariulka [41]

Answer:

y= (x -4)^2 - 1

Vertex = (4,-1)

Step-by-step explanation:

Given

f(x) = x^2 + 6x+13

Required

7 units left and 5 units down

First, we have: [7 units left]

The rule is:

(x,y) \to (x-7,y)

So, we have:

f(x) = (x - 7)^2 + 6(x -7)+13

Next, we have: [5 units down]

The rule is:

(x,y) \to (x,y-5)

So, we have:

f'(x) = (x - 7)^2 + 6(x -7)+13 - 5

f'(x) = (x - 7)^2 + 6(x -7)+8

Rewrite as:

y = (x - 7)^2 + 6(x -7)+8

Expand

y = x^2 - 14x + 49  + 6x -42+8

Collect like terms

y = x^2 - 14x   + 6x -42+8+ 49

y = x^2 -8x +15

To write in vertex form, we have

Subtract 15 from both sides

y -15= x^2 -8x

Divide (-8) by 2; Add the square to both sides

y -15+ (-8/2)^2= x^2 -8x + (-8/2)^2

y -15+ 16= x^2 -8x + 16

y +1= x^2 -8x + 16

Expand

y +1= x^2 -4x - 4x + 16

Factorize

y +1= x(x -4) -4(x - 4)

Factor out x - 4

y +1= (x -4)(x - 4)

Rewrite as:

y +1= (x -4)^2

Make y the subject

y= (x -4)^2 - 1

The vertex is:

Vertex = (4,-1)

8 0
3 years ago
One positive number is 5 less than twice a second number, and their product is 117. Find the two numbers.
FrozenT [24]

x,y - the numbers

one positive number is 5 less than twice a second number

(1)    x - 5 = 2y

their product is 117

(2)    xy = 117

(1)     x - 5 = 2y     <em>add 5 to both sides</em>

x = 2y + 5   <em>substitute it to (2)</em>

(2y + 5)y = 117     <em>use distributive property</em>

(2y)(y) + (5)(y) = 117

2y² + 5y = 117      <em>subtract 117 from both sides</em>

2y² + 5y - 117 = 0

2y² + 18y - 13y - 117 = 0

2y(y + 9) - 13(y + 9) = 0

(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0

y + 9 = 0    <em>subtract 9 from both sides</em>

y = -9

2y - 13 = 0     <em>add 13 to both sides</em>

2y = 13     <em>divide both sides by 2</em>

y = 6.5

<em>substitute the values of y to (1)</em>

x = 2(-9) + 5 = -18 + 5 = -13 < 0

x = 2(6.5) + 5 = 13 + 5 = 18

<h3>Answer: x = 18 and y = 6.5</h3>
3 0
3 years ago
Which of the following gives all of the coefficients of the algebraic expression -2x2 + 17 -15x + 7xy?
Stels [109]
The answer is -15, -2,7
3 0
3 years ago
Read 2 more answers
In rectangle ABCD, point L lies on diagonal
iVinArrow [24]

Answer:

  ab/(a+b)

Step-by-step explanation:

Without loss of generality, we can put point C at the origin and define line BD by the equation ...

  x/a +y/b = 1

Points (x, y) fall on the line BD, and we have point L where x=y. That value of x, the square's side length, will satisfy ...

  x/a +x/b = 1 . . . . . fill in x=y in the equation

  x(a+b)/ab = 1 . . . .factor out x, add 1/a+1/b

  x = ab/(a+b) . . . . solve for x

The length of the side of the square is ab/(a+b).

5 0
3 years ago
I need help ASAP plz
Korvikt [17]

Answer:

24

Step-by-step explanation:

Mrk me brainliest

5 0
3 years ago
Read 2 more answers
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