f(x)=x^2+12x+26
Vertex form of f(x) = a(x-h)^2 +k
We change f(x) into vertex form using completing the square method
We take half of square of middle term
middle term is 12
Half of square of 12 is then 6^2 = 36
Add and subtract 36 to complete the square
The vertex form
Answer:
He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.
Step-by-step explanation:
Given
Required
Determine Ming's error
Ming's error is from here
He calculated the unit rate as pound per dollar.
So, after calculating the unit rate, the unit should be:
But instead, he solved as:
<em>Hence, (a) is correct</em>
Answer:
The quadratic equation form is x² - 9 x + 14 = 0
Step-by-step explanation:
Given in the question as ,
The solution of quadratic equation are x = 2 and x = 7
The constant K is a non-zero number
Now , let the quadratic equation be , ax² + bx + c = 0
And sum of roots =
product of roots =
So, 2 + 7 =
Or, 2 × 7 =
I.e = 9 ,
= 14
Or, b = - 9 a And c = 14 a
Put this value of b and c in standard form of quadratic equation
I.e ax² + bx + c = 0
Or, ax² - 9 ax + 14 a = 0
Or , a ( x² - 9 x + 14 ) = 0
∴ a = 0 And x² - 9 x + 14 = 0
Hence , The quadratic equation form is x² - 9 x + 14 = 0 Answer
Answer: The length of segments between this point and the vertices of greater base are and 18.
Step-by-step explanation:
Let ABCD is the trapezoid, ( shown in below diagram)
In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7
Let P is the point where The extended legs meet,
So, according to the question, we have to find out : AP and BP
In Δ APB and Δ DPC,
∠ DPC ≅ ∠APB ( reflexive)
∠ PDC ≅ ∠ PAB ( By alternative interior angle theorem)
And, ∠ PCD ≅ ∠ PBA ( By alternative interior angle theorem)
Therefore, By AAA similarity postulate,
Let, DP =x
⇒
⇒ 33 +11x = 18x
⇒ x = 33/7=
Thus, PD=
But, AP= PD + DA
AP=
Now, let PC =y,
⇒
⇒ 77 + 11y = 18y
⇒ y = 77/7 = 11
Thus, PC= 11
But, PB= PC + CB
PB= 11+7 = 18
Answer:
Length of package can be = 22 inches
Step-by-step explanation:
Given:
For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches
To find length of package when girth of package is = 63 inches
Solution:
Let length of package be = inches
Let girth length of package be = inches
Sum of length and girth of package = inches
To qualify for a certain postage rate the sum of length and girth should not exceed 85 inches.
Thus, the inequality representing the situation can be given as:
We are given girth of package is = 63 inches
So, inequality to find length would be:
Subtracting both sides by 63.
inches
So, length should not exceed 22 inches in order to qualify.
Thus, the maximum length of package to qualify for the postal rate must be = 22 inches