How do I solve part A

Answer:

Your last step ( step 5 ) :

[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{c}{a} + \frac{ {b}^{2} }{4 {a}^{2} } [/tex]

Step 6:

[tex]{ \boxed{x + ( \frac{b}{2a}) = ± \frac{ \sqrt{ {b}^{2} - 4ac } }{ \sqrt{4a^2} } }}[/tex]

Step-by-step explanation:

[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{4ac}{4 {a}^{2} } + \frac{ {b}^{2} }{4 {a}^{2} } \\ \\ {x}^{2} + \frac{b}{a} x = \frac{4ac}{4a {}^{2} } \\ \\ {x} = \sqrt{ \frac{ - 4ac + b {}^{2} }{4a {}^{2} } } [/tex]

.,............. ..... ..nnkkjk

Answer:

0.06

Step-by-step explanation:

Total number of marbles:

6 + 10 + 5 + 1 = 22 marbles

Probability of picking 1 red marble:

red marbles / total marbles

6/22

Probability of picking a green marble:

green marbles / total marbles

5/22

Now, multiply the probabilities:

6/22 • 5/22 = 15/242 = 0.06

Answer:

2304 cubic inches

Step-by-step explanation:

Volume = Width x length x height

Green cube:

[tex]12*12*6=864[/tex]

Blue cube:

[tex]10*18*8=1440[/tex]

Add them together:

[tex]1440+864=2304[/tex]

Answer:

y = -x + 4

Step-by-step explanation:

(x₁,y₁)= (5, - 1)    & (x₂,y₂)= (2 , 2)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]\frac{2-[-1]}{2-5}\\\\=\frac{2+1}{-3}\\\\=\frac{3}{-3}\\\\= -1[/tex]

m = -1

Equation of the line y - y₁ = m(x - x₁)

y  - [-1] = (-1)*(x - 5)

y + 1 = -x + 5      {-1 is distributed}

y = -x + 5 - 1

y = -x + 4

Answer:

Step-by-step explanation:

Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

(x^2)^2-6x^2-7=0

y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots)    x^2=7 x=sqrt7 or x=-sqrt7

2 roots

Your Answer Is in this attachment.

Answer:

D-212 Degrees

Step-by-step explanation

i got it right on edge

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = [tex]3^{x}[/tex] , then

f(x + 1) = [tex]3^{x+1}[/tex] = [tex]3^{x}[/tex] × 3

Then

f(x) + f(x + 1)

= [tex]3^{x}[/tex] + 3. [tex]3^{x}[/tex] ← factor out [tex]3^{x}[/tex] from each term

= [tex]3^{x}[/tex] (1 + 3)

= 4. [tex]3^{x}[/tex]

= 4f(x)

Answer:

big area/small area = (big length/small length)^2

24/small area = (6/3)^2

24/sa = 4

sa= 6

Answer:

y=-3x

Step-by-step explanation:

3>2. It doesn't matter if some or all of the numbers are negative.

Answer:  y = -3x has the steeper slope

==========================================

Explanation:

Any linear equation is of the form y = mx+b, where m is the slope.

For y = -2x, the slope is -2. For y = -3x, the slope is -3.

We just look at the number to the left of x to find the slope.

To figure out which slope is steeper, we simply look to see which slope value is furthest from 0 on the number line. A slope of 0 itself is completely horizontal and flat. As the slope value moves away from zero, in either positive or negative direction, then the slope gets steeper and steeper.

In short, a slope of -3 is more steep compared to a slope of -2. Therefore, y = -3x is the answer.

The graph below helps visually confirm that y = -3x is indeed steeper. We drop one extra unit down each time we move to the right one space.

Answer:

n means number

Step-by-step explanation:

Answer:

The value of n is 54......

The remainder theorem says that dividing a polynomial f(x) by a 1st-degree polynomial g(x) = x - c leaves a remainder of exactly f(c).

(a) With f(x) = px ³ + 4x - 10 and d(x) = x + 3, we have a remainder of 5, so

f (-3) = p (-3)³ + 4(-3) - 10 = 5

Solve for p :

-27p - 12 - 10 = 5

-27p = 27

p = -1

(b) With f(x) = x + 3x ² - px + 4 and d(x) = x - 2, we have remainder 8, so

f (2) = 2 + 3(2)² - 2p + 4 = 8

-2p = -10

p = 5

(you should make sure that f(x) was written correctly, it's a bit odd that there are two x terms)

(c) f(x) = 2x ³ - 4x ² + 6x - p, d(x) = x - 2, R = f (2) = 18

f (2) = 2(2)³ - 4(2)² + 6(2) - p = 18

12 - p = 18

p = -6

The others are done in the same fashion. You would find

(d) p = 14

(e) p = -4359

(f) p = 10

(g) p = -13/2 … … assuming you meant f(x) = x ⁴ + x ³ + px ² + x + 20

Answer:

y(x)=12*(5)^x

Step-by-step explanation:

y=ab^x, y(0)=12. 12=a.

y=12*b^x, y(2)=300. 12*b^2=300. b^2=25. b=5

Answer:

Round 874.902237102

874.9

Rounded to the nearest  Tenths Place.

hope this would help

Answer:

See below.

Step-by-step explanation:

1.) 5√6

2.) 6√2

3.) 3√7

To solve this without the use of a calculator, split the given number into a series of products (numbers multiplied) and look for pairs.

Look at the attached example of Problem 1 to get a better idea of what I mean.

9514 1404 393

Answer:

  33 11/16 m² = 33.6875 m²

Step-by-step explanation:

The volume of a prism is given by ...

  V = Bh

where B is the area of the base, and h is the height. Solving for B, we find ...

  B = V/h

  B = (539 m³)/(16 m) = 33 11/16 m² = 33.6875 m²

Answer:8-8 and 12 and 6

Step-by-step explanation:

The system of equations based on the given information is represented by y = 8x³ - 8x² , y = 12x³ - 6x² .

Let's set up the equations based on the information:

x be the width of the fish tanks (in cm),

y be the volume of the fish tanks (in cubic cm).

For the first fish tank:

Height = 2x - 2 (2 cm less than twice the width)

Length = 4x (4 times the width)

Volume (V) of a rectangular prism = Length × Width × Height

V = (4x) × x × (2x - 2)

V = 4x² × (2x - 2)

V = 8x³ - 8x² (equation 1)

For the second fish tank:

Length = 2x - 1 (1 cm less than twice the width)

Height = 6x (6 times the width)

Volume (V) of the rectangular prism = Length × Width × Height

V = (2x - 1) × x × (6x)

V = (2x² - x) × 6x

V = 12x³ - 6x² (equation 2)

So, the system of equations representing the situation is:

V = 8x³ - 8x²

V = 12x³ - 6x²

Therefore, the correct answer is a system of equations are

y = 8x³ - 8x²

y = 12x³ - 6x²

learn more about system of equations here

brainly.com/question/32645146

#SPJ2

Answer:

9.) y=-2x-4

10.)y=2/3x

Step-by-step explanation:

Parallel lines have the same slope, different intercepts

9.) The slope is -2x

To find the parallel line

y-(-4)=-2(x-0)

y+4=-2x

y-4=-2x-4

y=-2x-4

10.) You must first put the equation in slope-intercept form.

-2x+2x+3y=2x+12

3y=2x+12

Divide by 3

3y/3=2x/3+12/3

Simplify

y=2/3x+4

Slope = 2/3x

y-2=2/3(x-3)

y-2=2/3x-6/3

y-2=2/3x-2

y-2+2=2/3x-2+2

y=2/3x

Answer:

$40.5

Step-by-step explanation

10% comes from selling biscuit:$ 9

remaining money: $81

50% of the remaining money comes from chocolate cakes: 81*50%=$40.5

Answer:

No. of children Frequency

0. 5

1. 7

2. 11

3. 5

4. 6

5 3

6 3

Answer:

(4,0)

Step-by-step explanation:

1. X= (4,0) the coordinates of x

Answer:

5

Step-by-step explanation:

when 13 is subtracted from 5 we get 8

again when 8=2m

8/2=m

4=m

.

9514 1404 393

Answer:

  a) $554

  b) y = 138.50x

  c) see attached

Step-by-step explanation:

a) The cost is the product of the number of hours and the cost per hour.

  cost = (4 h)($138.50 /h) = $554.00 . . . . for a 4-hour course

__

b) As above, the cost (y) is the product of the number of hours (x) and the cost per hour ($138.50).

  y = 138.50x . . . . tuition for x credit hours.

__

c) As in part (b), the tuition is hours times 138.50. That means hours are tuition divided by 138.50.

Answer:

I think the answer for this question is 2.24cm

Answer:

The answer is A: 120yd^2

Step-by-step explanation:

Volume = Width x length x height

Volume = 8 x 3 x 5

Volume = 120

Answer:

120

Step-by-step explanation:

8*3*5

Answer:

4536

Step-by-step explanation:

Answer:

630 students passed the exam and 126 students failed the exam

Answer:

27 1/2 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5 * 5 1/2

Change to an improper fraction

A = 5 * (2*5+1)/2

A = 5*11/2

A = 55/2

Change back to a mixed number

A = 27 1/2