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BaLLatris [955]
3 years ago
8

Y=x² + 16x + 64

Mathematics
1 answer:
motikmotik3 years ago
8 0

I'll do the first one to get you started

The equation y = x^2+16x+64 is the same as y = 1x^2+16x+64

Compare that to y = ax^2+bx+c and we see that

a = 1

b = 16

c = 64

Use the values of 'a' and b to get the value of h as shown below

h = -b/(2a)

h = -16/(2*1)

h = -8

This is the x coordinate of the vertex.

Plug this x value into the original equation to find the corresponding y value of the vertex.

y = x^2+16x+64

y = (-8)^2 + 16(-8) + 64

y = 0

Since the y coordinate of the vertex is 0, this means k = 0.

The vertex is (h,k) = (-8, 0)

---------------------

So we found that a = 1, h = -8 and k = 0

Therefore,

f(x) = a(x-h)^2 + k

f(x) = 1(x-(-8))^2 + 0

f(x) = (x+8)^2

is the vertex form

---------------------

<h3>Final answer to problem 1 is f(x) = (x+8)^2 </h3>
You might be interested in
3/2 x 1/4 x 5/3 = v.
jekas [21]

Answer: 5/8 or 0.625

Step-by-step explanation:

3/2x1/4= 3/8

Then, 3/8x5/3= 15/24

15/24 simplified equals 5/8. 5/8 in decimal form is 0.625

3 0
3 years ago
I need help with this can you explain how to do this so I can understand please ASAP!!
Ratling [72]

Answer: 1.64     2.100

Step-by-step explanation:

The reason for this is squaring something is simply mulyiplying the number by itself. for example

8 squared

there is a 2 above the 8 which means we will do 8x8.

8x8= 64

Hope this helps!!!!

7 0
3 years ago
280 in the ratio 3:5
Sonja [21]

Answer:

105:175

Step-by-step explanation:

3+5 = 8

3/8 of 280 is 105.

5/8 of 280 is 175.

the ratio is 105:175

next we have to simplify it:

divide both sides by 5:

21:35 divide both sides by 7=

3:5

7 0
3 years ago
Guys please help me to do these!!!! im tryin’ my best but it’s so hard
Eduardwww [97]

Answer:

Step-by-step explanation:

1.

∠ACB=6 x°

∠DCE=30°

6x=30°-----------------divide both sides by 6

x=30°/6= 5°

∠BCE=180°-30°=150°----------------sum of angles on a straight line

2.

∠ABD=(4+5x)°

∠CBD=(x+2)°

(4+5x)°+(x+2)°=180°-----------sum of angles on a straight line

4+5x+x+2=180°----------------collect like terms

6x+6=180°

6x=180°-6°

6x=174°------------divide by 6 both sides

x=174°÷6= 29°

∠ABD=4+5x=4+(5*29)= 4+145=149°

∠CBD= x+2=29°+2°=31°

3.

BE bisects ∠ABE=(3x+1)°

m∠DBA=(8x-14)°

1/2 (m∠DBA)° = m∠ABE

1/2(8x-14)°=(3x+1)°

(4x-7)°=(3x+1)°

4x-7=3x+1

4x-3x=7+1-------------collecting like terms

x=8°

m∠ABE=(3x+1)°=(3*8+1)=24+1=25°

m∠DBA=(8x-14)°= (8*8-14)°=(64-14)=50°

4.

∠ADE=∠CDG

50+3x-y=x+2x-16------------collect like terms

50+16-y=x+2x-3x

66-y=3x-3x

66°=y

∠ADC +∠ADB+∠BDE

90°+50°+(3x-y)°=180°

140°+(3x-y)°=180°

3x-66°=180°-140°

3x=40°+66°

3x=106°-----------divide both sides by 3

x=106°÷3= 35.33°

∠FDG=(2x-16)°= (2×35.33° - 16° )= 54.67°

∠BDE = (3x-y)°= (3×35.33°-66°)= 105.99-66=39.99°

5.

∠ABD+∠DBC=90°

(6x+4)°+32°=90°

(6x+4)°=90°-32°

6x+4=58°

6x=58°-4°

6x=54°

x=54°÷6=9°

∠ABD= (6x+4)°+32°

∠ABD= (6×9 +4)°+32°

∠ABD= (54°+4°) + 32°

∠ABD=58°+32°=90°

6.

∠AED=∠CEB

(3x+5)°=(4y-15)°------------------form equation of equality

3x+5=4y-15

5+15=4y-3x

20=4y-3x------------------------------(1)

∠AEC=∠DEB

(y+20)°=(x+15)°

y+20=x+15

20-15=x-y

5°=x-y

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

Use equation (2) in equation (1)

20=4y-3x

20=4y-3(5+y)

20=4y-15-3y

20+15=4y-3y

35°=y

Solve for x

x=5+y=5°+35°=40°

∠AED=(3x+5)°=(3×40 +5 )=120+5=125°

∠AEC= (y+20)°= 35° + 20° =55°

8 0
3 years ago
Please help me. <br> What is 70% of 20?
Gnom [1K]

Answer:

14

Step-by-step explanation:

20 x 0.7 = 14

8 0
3 years ago
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