What is the equation of the following line written in general form?

Answer:

a = - 2, b = - 6

Step-by-step explanation:

Substitute the values of the zeros into the polynomial and equate to zero.

x² +(a + 1)x + b

x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is

4 - 2a - 2 + b = 0

2 - 2a + b = 0 ( subtract 2 from both sides )

- 2a + b = - 2 → (1)

x = 3 → 3² + 3(a + 1) + b = 0, that is

9 + 3a + 3 + b = 0

12 + 3a + b = 0 ( subtract 12 from both sides )

3a + b = - 12 → (2)

Subtract (1) from (2) term by term to eliminate b

5a = - 10 ( divide both sides by 5 )

a = - 2

Substitute a = - 2 into either of the 2 equations and evaluate for b

Substituting into (2)

3(- 2) + b = - 12

- 6 + b = - 12 ( add 6 to both sides )

b = - 6

Thus a = - 2 and b = - 6

Answer:

d

Step-by-step explanation:

The most efficient step to finding the solution to the given inequality is, to subtract 4 from both sides. Option D is correct.

Given that,
To determine which step is the most efficient way to find the solution of x + 4 > -8.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
Given inequality,
x + 4 > -8
Subtract 4 from both sides,
x + 4 - 4 > - 8 - 4
x > -12

Thus, the most efficient step to finding the solution to the given inequality is, to subtract 4 from both sides. Option D is correct.

Learn more about inequality here:

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Answer:

200 cc

Step-by-step explanation:

Volume of the prism = Area of base * height

= 40*5

= 200 cubic cm

Answer:

1/2 probably

Step-by-step explanation:

Answer:

- 3, - 11, - 35, - 107

Step-by-step explanation:

Using the recursive formula with f(1) = - 3 , then

f(2) = - 2 + 3f(1) = - 2 + 3(- 3) = - 2 - 9 = - 11

f(3) = - 2 + 3f(2) = - 2 + 3(- 11) = - 2 - 33 = - 35

f(4) = - 2 + 3f(3) = - 2 + 3(- 35) = - 2 - 105 = - 107

Thus the first four terms are

- 3, - 11, - 35, - 107

Answer:

There are no x-intercepts

Step-by-step explanation: This is because the parabola does not pass through the x-axis at all.

Answer:

no x intercept

Step-by-step explanation:

The x intercept is the value where it crosses the x axis.

This functions does not cross the x axis

There is no x intercept

Answer:

C.) 2x+3 = 12

Step-by-step explanation:

x+x=2x

2x-(-3) is 2x+3

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Answer:

2) Exact

3) Exact

4) Exact

5) Approximation

Step-by-step explanation:

How much does it cost to buy 10 computer mice (not the living thing :) ) that are $24.75 each.

10(24.75)=247.5

It will cost $247.5

It would be $247.50

Step-by-step explanation:

24.75 x 10

Answer:

3,400 people

Step-by-step explanation:

First, find how many minutes are between noon and 1:30 pm

This is an hour and 30 minutes, so it will be 90 minutes

Then, multiply 90 by 35, since 35 people enter per minute

90(35)

= 3150

Then, add the 250 people that were already in it

3150 + 250

= 3400

So, there will be 3,400 people in the stadium

Answer:

3400

Step-by-step explanation:

250+35m=noon

Step-by-step explanation:

Hey there!

Here,

The equation is:

[tex]7 \sqrt{3 \: } {x}^{2} + 10x - \sqrt{3 } = 0[/tex]

Comparing the equation with ax^2+bx+c=0. We get;

[tex]a = 7 \sqrt{3} [/tex]

[tex]b = 10[/tex]

[tex]c = \sqrt{3} [/tex]

Now,

Discriminant= ?

We have,

[tex]discriminant = {b}^{2} - 4ac[/tex]

Put all values.

[tex]discriminant = {10}^{2} - 4 \times 7 \sqrt{3} \times \sqrt{3} [/tex]

[tex]discriminant = 100 - 4 \times7 \times 3[/tex]

[tex]discriminant = 100 - 84[/tex]

Therefore the discriminant = 16.

Hope it helps...

Answer:

Shalini = 12

Poonam = 60

Step-by-step explanation:

Let p = poonams age

Let s = shalini's age

p = 5s

p+s = 72

Substitute the first equation into the second equation

5s+s = 72

Combine like terms

6s= 72

Divide by 6

6s/6 = 72/6

s = 12

p = 5s =5*12 = 60

Shalini = 12

Poonam = 60

Answer:

c

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 24 when x = - 15, then

24 = - 15k ( divide both sides by - 15 )

k = [tex]\frac{24}{-15}[/tex] = - [tex]\frac{8}{5}[/tex] = - 1.6 , thus

y = - 1.6x ← equation of variation

When y = 16, then

16 = - 1.6x ( divide both sides by - 1.6 )

x = - 10 → c

Answer:

y = -3 ÷ 2x - 3

Step-by-step explanation:

As it can be seen that the line is passed by y-axis at -3.

Now we have to determine the slope

For this, use the following formula

= (x2 - x1) ÷ (y2 - y1)

At

(-2, 0), (0, -3)

So,

= (-3-0) ÷ (0+2)

= -3 ÷ 2

Now

Put in the following equation

y = mx + b.

where,

m = slope

b = y-intercept

So,

y = -3 ÷ 2x - 3

Answer: a plane

Step-by-step explanation: A flat surface made up of points that extends infinitely in all directions. There is exactly one plane through any three points that are not on the same line. Two dimensions with length (infinite) and width (infinite).

Answer:

y = 8x - 26

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (3, - 2) and (x₂, y₂ ) = (4, 6)

m = [tex]\frac{6+2}{4-3}[/tex] = 8 , thus

y = 8x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 6) , then

6 = 32 + c ⇒ c = 6 - 32 = - 26

y = 8x - 26 ← equation of line

Answer:

chips 1.50 cents hot dogs 2 dollars

Step-by-step explanation:

Hot do is 2 dollars because the same chips were put but 1 extra dog is 2 dollard and you divide from there and get 1.50 for chips

Answer:576cm

Step-by-step explanation:

Multiply length width

And height

Answer:

[tex] \boxed{ \bold{ { \boxed{ \sf{576 \: cubic \: centimeters}}}}}[/tex]

Step-by-step explanation:

Given,

Length of the rectangular prism ( l ) = 16 cm

Height of the rectangular prism ( h ) = 4 cm

Width of a rectangular prism ( w ) = 9 cm

Finding the volume of the rectangular prism. having length of 16 cm , width of 9 cm and height of 4 cm

[tex] \boxed{ \sf{volume \: of \: a \: rectangular \: prism = lwh}}[/tex]

[tex] \longrightarrow{ \sf{volume \: = 16 \times 9 \times 4}}[/tex]

[tex] \dashrightarrow{ \sf{576 \: {cm}^{3} }}[/tex]

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:

Put (-6,0) and (0,3) into a table of values

form of the equation: mx+b

x -6 0

y 0 3

3/-6=-0.5 (m)

3=b (the value of y when x=0)

equation: y=0.5x+3

Answer:

integers

they include all whole numbers and their negative counterpart

Answer:

Step-by-step explanation:

the correct name for the set of numbers is integers numbers.

Answer:

The pattern is that each time, 8 is added. The next 2 numbers are 47, 55.

Step-by-step explanation:

7+8=15

15+8=23

23+8=31

31+8=39

39+8=47

47+8=55

Answer:

1/8^5 is the simplified answer  

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

3/10 - 1/4

First, convert the fractions to a common denominator:

3/10 *2/2 = 6/20

1/4 * 5/5 = 5/20

Now put them back into the equation and solve:

6/20 - 5/20 = 1/20

Another way to do this:

3/10 - 1/4

Convert the fractions into decimals:

3/10 = 0.3

1/4 = 0.25

substitute back into the equation and solve:

0.3 - 0.25 = 0.05

convert back into fractions:

0.05 = 1/20

Answer:

k=3/12

k=.25

Step-by-step explanation:

we need to get k by itself

because 12 is over k we need to get rid of it by moving it to the other side (multiplying) because it is 12/k we need to multiply it by 1/12

This eliminates 12 and leaves us with k=3/12