Answer:
y=8(x+1)²-2
Step-by-step explanation:
Completing the square is a method of factorising. x²+bx+c=0 becomes x²+bx+([tex]\frac{1}{2}[/tex]b)²-([tex]\frac{1}{2}[/tex]b)²+c=0. This then gets converted to make an equation of (x+[tex]\frac{1}{2}[/tex]b)²+(-([tex]\frac{1}{2}[/tex]b)²+c)=0.
Vertex form is y=a(x-h)²+k.
8x²+16x+6=0 must first be divided by 8 to 8(x²+2x+[tex]\frac{6}{8}[/tex])=0 (as there cannot be a coefficient for x²).
This will become 8(x²+2x+[tex]\frac{2}{2}[/tex]²-[tex]\frac{2}{2}[/tex]²+[tex]\frac{3}{4}[/tex])=0.
From there, using the method above, we can convert it to 8[(x+1)²-1+[tex]\frac{3}{4}[/tex]]=0.
Solving this gets 8[(x+1)²-[tex]\frac{1}{4}[/tex]]=0.
With 8 as a, 1 as -h, and 8×-[tex]\frac{1}{4}[/tex] (-2) as k, we can input this into vertex format to get the result of y=8(x+1)²-2.
**This equation involves completing the square and vertex form, which you may wish to revise. I'm always happy to help!
calculate 7.5cm in km
Answer:
7.5e-5
Step-by-step explanation:
What is the volume of the cylinder below? 6 7 4
A. 96pie units³
B. 168pie units³
C. 84pie units³
D. 112pie units³
Answer:
I believe the answer is A
Step-by-step explanation:
What is the solution to the system of equations
Answer:
Y = 2
X = 3
Step-by-step explanation:
Substitution:
6(4y-5) - y = 16
24y-30-y=16
23y=46
Y = 2
So then:
6x-2 = 16
6x = 18
X = 3
What is cosθ = _____ based on this image
a)-3/5
b)-4/3
c)-4/5
d)-3/4
What is the value of X in the figure below? In this diagram ∆ABD is similar to ∆CAD.
Answer:
F. 45/4Step-by-step explanation:
Corresponding sides have same ratio:
AB/AC = BD/ADFind AB:
AB = [tex]\sqrt{20^2-15^2} = 5\sqrt{7}[/tex]Find AD:
AD = √15²-x²Now the ratio:
5√7/15 = (20 - x)/√(15²-x²)√7 *√(225-x²)= 3(20 - x)7(225 - x²) = 9(20 -x)²7*225 - 7x² = 9(400 - 40x + x²)1575 - 7x² = 3600 - 360x + 9x²16x² - 360x + 2025 = 0(4x)² - 2*4x*45 + 45² = 0(4x - 45)² = 04x - 45 = 04x = 45x = 45/4Correct choice is F
3) -7x - 3x + 2 = -8x - 8
A bag of cereal contains 12 blue marsh mellows, 16 red marshmellows , and 8 orange marsh mellows.If a marshmellow is picked from the bag at random, what is the probability that it is a red marsh mellow? Answers have been rounded to the tenths place.
Answer:
0.4 (decimal)
4/9 (fraction)
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
Probability a red marshmallow is picked = number of red marshmallows in the bag / sum of marshmallows in the bag
sum of marshmallows in the bag = 12 + 16 + 8 = 36
Probability a red marshmallow is picked = 16/36
To transform to the simplest form. divide both the numerator and the denominator by 4
= 4/9
to convert to decimal, divide 4 by 9 = 0.4444
0.4 to the nearest tenth
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Please give me the answer and show me how you solved it
on number 5 question the answer is 4,5,9
Step-by-step explanation:
it is because a right triangle is composed of 3 different sides (hypothenus, opposite angle and adjacent angle)
Answer:
5) B. 10, 24, 26
6) k = 8.5
Step-by-step explanation:
5) The a and b in context of the triangle have to be greater than the hypotenuse. It can’t equal the hypotenuse. 10 + 24 = 34, 34 > 26 Therefore our answer.
6) Our equation: c = sqrt of a^2 + b^2
C = sqrt of 3^2 + 8^2
*A= 3 B = 8*
C = sqrt of 9 + 64
C = square root of 73
C = 8.54 or 8.5
Giving our answer:
You could always check by listing the values of each side:
A=3 B=8 C=8.5
3, 8, 8.5
And up A and B: 3 + 8 = 11
11 > 8.5
Proving this is a right triangle!
Btw sqrt means square root! ;)
Hope this helps, good luck! :)
can someone pls help for brainlest
Answer:
12.56 in ^2
Step-by-step explanation:
First find the area of a circle with radius 4
A = pi r^2
A = (3.14) 4^2
A =50.24
Since it is 1/4 of a circle, multiply by 1/4
1/4 ( 50.24)
12.56
Answer:
Quarter circle's area is 12.56 inches².
Step-by-step explanation:
Concept:- Firstly, we need to find the area of circle and Since, it is quarter of circle we need to multiply the area of circle by 1/4. and we get answer
✯ Solution ✯Finding area of circle
Using Formula
Area of circle = π × r ²
Where,
r ,is the radius of circleAnd we have given
Radius, r of circle is 4 in.Value of π is 3.14Substitute the value into the formula
Area of circle = 3.14 × ( 4 in. )/²
now,
Area of circle = 3.14 × 16 in ².
multiply , we get
Area of circle is 50.24 nches ²
As have to find the quarter circle's area ,
and we know that quarter is the one fourth of the circle .
Quarter circle's area = Area of circle × 1/4
Multiply , we get
Quarter circle's area = 50.24 × 1/4
Therefore, quarter circle's area is 12.56 inches².
Use substitution to solve the
following system of equations.
2x + 4y = 12 AND x=y - 3
Answer:
The solution is (0, 3)
Step-by-step explanation:
First, reduce 2x + 4y = 12 to x + 2y = 6, for easier calculations.
Next, substitute y - 3 for x in the other equation:
y - 3 + 2y = 6, or
3y = 9
Then y = 3. Since x = y - 3 in general, x = 3 - 3 = 0 when y = 3.
The solution is (0, 3)
5) A certain stock opens with a price of $0.59. Over the first three days the stock value increases at an average rate of 50% per day. If this trend continues, how much will the stock be worth in 12 days?
Answer:
In 12 days the stock will be worth $ 76.55.
Step-by-step explanation:
Given that a certain stock opens with a price of $ 0.59, and over the first three days the stock value increases at an average rate of 50% per day, to determine, if this trend continues, how much will the stock be worth in 12 days the following calculation must be performed:
Initial value x rate of increase ^ number of years = X
0.59 x 1.5 ^ 12 = X
0.59 x 129.74 = X
76.55 = X
Therefore, in 12 days the stock will be worth $ 76.55.
find the measure of angle c
Answer:
add 7+5 and 3+9 and then subtract both answers together and the answer you get should be the answer if the degree
What’s the answer Answer???
Answer:
B.
Step-by-step explanation:
I might have gotten this wrong but my mind was telling me it was B hope this helped.
Thanks for your time.
(>.<) <3 Kris
convert 1/2 by decimal
Answer:
1/2
= 0.5
Step-by-step explanation:
this is very easy
what is the answer when you round 4186.666666666667 to nearst hundredth.
answer fast please in hurry needed. dont give explanation exact answer beeded.
Which of these mappings is a function? (PLEASEEE HELP MEEE)))
Step-by-step explanation:
creo..... que es la z ...
45
24
K K
AM
51
이
15
17
15
이
8
15
O
8
17
음
Hope this help!!!
Have a nice day!!!!
A ball is launched from 8 feet off the ground at an initial vertical speed of 64 feet per second. It is aimed across a field at a target also 8 feet off the ground. The height of the ball at time, t, in seconds, is given by the function, h = –16t 2 + 64t + 8. It will take the ball
seconds to hit its target.
Answer:
a
Step-by-step explanation:
because
Answer:The equation that is given, h = –16t 2 + 64t + 8, represents the general formula of the motion which is h(t) = h0 + v0t - 16t² where h0 is the initial height (8 feet), v0 is the initial velocity (+64 ft/s) and t is time in seconds. To determine the time when the ball is at the maximum height, we need to determine the vertex of the parabola which is done as follows:
vertex = time at maximum height = -b/2a = -64 / 2(-16) = 2 seconds
The maximum height can be calculated by substituting the time we obtained to the function.
h = –16t 2 + 64t + 8
h = –16(2)^2 + 64(2) + 8 = 72 feet
Step-by-step explanation:
Look at the number line below. Write the letter for each fraction in the correct box.
Answer:
DCAB
I arranged in increasing order
Answer:
DCAB
Step-by-step explanation:
[tex]A = \frac{2}{5} = 0.40\\\\B= \frac{2}{3} = 0.66\\\\C= \frac{1}{4} = 0.25\\\\D =\frac{1}{10} = 0.10[/tex]
So moving from least to highest DCAB
5. The points (2, 4) and (6,7) lie on a line. What is the slope of the line? A. 2 B. 1 C. 4/3 D. 3/4
A motorboat takes five hours to travel two hundred miles going upstream. The return trip takes four hours going down stream. What is the rate of the boat in Stillwater and what is the rate of the current?
Answer: [tex]45\ mph[/tex], [tex]5\ mph[/tex]
Step-by-step explanation:
Given
A motorboat takes 5 hours to travel 200 miles upstream and 4 hours to go downstream
Suppose the speed of motorboat in still water and rate of current be x and y respectively.
during upstream
[tex]\Rightarrow 5=\dfrac{200}{x-y}\\\\\Rightarrow x-y=40\quad \ldots(i)[/tex]
During downstream
[tex]\Rightarrow 4=\dfrac{200}{x+y}\\\\\Rightarrow x+y=50\quad \ldots(ii)[/tex]
Add (i) and (ii) we get
[tex]\Rightarrow 2x=90\\\Rightarrow x=45\ mph[/tex]
[tex]\therefore y=5\ mph[/tex]
Thus, the speed of boat in still water is [tex]45\ mph[/tex] and rate of current is [tex]5\ mph[/tex]
How many minutes will it take to bake 24 tortillas
Answer:
72 mins
Step-by-step explanation:
12 mins = 4 tortillas
1 tortilla = 3 mins
3x24=72
72 mins
Answer:
72 minutes
1 hour and 12 minutes
Step-by-step explanation:
[tex]\frac{4}{12}: \frac{24}{y}[/tex]
4 × y = 12 × 24
4y = 288
4y ÷ 4 = 288 ÷ 4
y = 72
a bicycle travels at a velocity of -2.33m/s and has a displacement of -58.3m how much time did it take??
Answer:
25.02 s
Step-by-step explanation:
velocity = distance/time
rearrange for time:
time = distance/velocity
time = -58.3m/-2.33 m/s
time = 25.02s
Mrs. Archer is doing a painting project with her art class. She uses a large jug with 28.5 ounces of blue paint to fill 6 smaller bottles. If she divides the paint evenly, how much paint will be in each bottle?
Answer:
4.75
Step-by-step explanation:
Divide 28.5 evenly with 6 because thee are 6 bottles. Then you receive 4.75
Hope this helps
please help me answer this!!
Answer:
(x, y) = (10, 290)
Step-by-step explanation:
From the table
Total fees = fixed + variable
Fixed:
When number of times Ahmed mowed, x = 0
y = 40
When x = 2, y = 65
Rate of change = y2 - y1
= 65 - 40
= 25
y = 40 + 25x
Where,
y = total fees charged
40 = fixed fee
25x = variable fee
Total amount Ahmed will make for mowing 10 times
when x = 10
y = 40 + 25x
y = 40 + 25(10)
= 40 + 250
= 290
y = 290
(x, y) = (10, 290)
Explain how to solve this problem in your own words.
Answer:
3 m^8
Step-by-step explanation:
We know that a^b / a^c = a^( b-c) so using the quotient rule for exponents
3 * m^( 7 - -1)
3 *m^(8)
is 69,370 divisible by 8,4,6, or 10
Answer: 69370 is divisible by 10 only
Answer:
10
Step-by-step explanation:
if u divide by 8,4,6 you get decimal answer
helpppppppppppp!!!!!!!!!!!!!!
Answer:
480N
Step-by-step explanation:
answer is in photo above
Select the correct answer.
How would you write this expression as a sum or difference?
[tex]log_{3} (^{5\sqrt{x}} X y )[/tex]
Answer:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
Step-by-step explanation:
Given
[tex]\log_{3} ({5\sqrt{x}} * y )[/tex]
Required
Write as sum or difference
Using addition law of logarithm, the equation becomes:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5\sqrt{x}) +\log_{3}( y )[/tex]
Expand
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5 * \sqrt{x}) +\log_{3}( y )[/tex]
Apply addition law
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
Math question. Genius, please answer correctly.
Answer:
16-31 20, 18,25,28,31,23,19,27,22,25,20 11
32-47 33,42,36,41,47 5
48-65 65,52,61,50 4
Step-by-step explanation: