The standard form of the equation of a parabola is y = 7x2 + 14x + 4. What is the vertex form of the equation?

What is the common ratio of the following geometric sequence 5/12, 1/4,3/20,9/100,27/500

suter [353]

Answer:

3/5

Step-by-step explanation

Ratio =second term divided inti first term a2/a1

a1=5/12 a2=1/4

1/4: 5/12 is the same as 1/4*12/5 =12/20 = 3/5

5/12*3/5 = 15/60 = 1/4

1/4* 3/5 =3/20

3/20*3/5 =9/100

9/100 *3/5 = 27/500..........

5 0

3 years ago

Of Canada's total area of 9,976,140 km² , 755,170 km² is water. To the nearest tenth of percent, what part of Canada is water?

algol13

Answer:

755170/9976140 x 100

= 7.56976 %

= 8 % or (to the nearest 10th 10%) of Canada

Step-by-step explanation:

5 0

3 years ago

OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS- PLSS TELL ME WHA

denpristay [2]

Answer:

The answer to this question is $14,916

Step-by-step explanation:

18,469 - 3,553 = 14916

As he already has money for the car.

A bar model is shown in the linked picture.

7 0

3 years ago

Tell me what each angle is in the following triangle: angle 1 is 8x, angle 2 is 2x+3, angle 3: 30 degrees. give me the two answe

9966 [12]

Answer: 117.6° ; 32.4° .
_________________________
Explanation:
_______________________________________________________
Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
_____________________
We are given the following:
_______________________
We have a triangle.

Angle 1: m∡1 = (8x) ;

Angle 2: m∡2 = (2x + 3) ;

Angle 3: m∡3 = 30.
______________________________________
We are asked to find: "m∡1" and " m∡2" .
______________________________________
Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
________________________________________
So, " m∡1 + m∡2 + m∡3 = 180 " .
________________________________________
Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
___________________________________________

 m∡1 + m∡2 + m∡3 = 180 ;
___________________________________________
8x + (2x + 3) + 30 = 180 ;
___________________________________________
8x + 2x + 3 + 30 = 180 ;
___________________________________________
Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
____________________________________________________________
+8x + 2x = +10x ;
___________________________________________
+3 + 30 = +33 ;
___________________________________________
Rewrite the entire equation, as:
___________________________________________
10x + 33 = 180 ;
___________________________________________
Now, subtract "33" from EACH SIDE of the equation:
___________________________________________
10x + 33 − 33 = 180 − 33 ;
___________________________________________
to get:
___________________________________________
10x = 147 ;
____________________________________________
Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
____________________________________________
10x / 10 = 147 / 10 ;
____________________________________________
to get:
____________________________________________
x = 14.7 ;
___________________________________________
Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m∡1" and "m∡2"; as follows:
________________________________________________

Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
________________________________________________
Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
________________________________________________
These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
____________________________________
Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m∡3 = 30°); all add up to 180° ?
___________________________________________
Let us check:
_______________________________
m∡1 + m∡2 + m∡3 = 180 ;
_______________________________
Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
______________________________________________
→ 117.6 + 32.4 + 30 = ? 180 ??
______________________________________________
→ 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes!
______________________________________________

4 0

4 years ago

In a home theater system, the probability that the video components need repair within 1 year is 0.02, the probability that the

earnstyle [38]

Answer:

(a) The probability that at least one of these components will need repair within 1 year is 0.0278.

(b) The probability that exactly one of these component will need repair within 1 year is 0.0277.

Step-by-step explanation:

Denote the events as follows:

A = video components need repair within 1 year

B = electronic components need repair within 1 year

C = audio components need repair within 1 year

The information provided is:

P (A) = 0.02

P (B) = 0.007

P (C) = 0.001

The events A, B and C are independent.

(a)

Compute the probability that at least one of these components will need repair within 1 year as follows:

P (At least 1 component needs repair)

= 1 - P (No component needs repair)

$=1-P(A^{c}\cap B^{c}\cap C^{c})\\=1-[P(A^{c})\times P(B^{c})\times P(C^{c})]\\=1-[(1-0.02)\times (1-0.007)\times (1-0.001)]\\=1-0.97216686\\=0.02783314\\\approx 0.0278$

Thus, the probability that at least one of these components will need repair within 1 year is 0.0278.

(b)

Compute the probability that exactly one of these component will need repair within 1 year as follows:

P (Exactly 1 component needs repair)

= P (A or B or C)

$=P(A\cap B^{c}\cap C^{c})+P(A^{c}\cap B\cap C^{c})+P(A^{c}\cap B^{c}\cap C)\\=[0.02\times (1-0.007)\times (1-0.001)]+[(1-0.02)\times 0.007\times (1-0.001)]\\+[(1-0.02)\times (1-0.007)\times 0.001]\\=0.02766642\\\approx 0.0277$

Thus, the probability that exactly one of these component will need repair within 1 year is 0.0277.

7 0

3 years ago