Math question pre algebra

Answer:

Step-by-step explanation:

Roots:  set y = x^2 + 8x + 12 = 0 and solve for x:  x + 6 = 0, so x = -6 is one root.  The other is x = -2.  The corresponding points are (-6, 0) and (-2, 0).

y-intercept:  Let x = 0.  Then y = 12.  The y-intercept is (0, 12).

Axis of symmetry:  x = -b / (2a) => x = -8/(2*1) = -4:  x = -4

Vertex y-value:  evaluate y at x = - 4:  (-4)^2 + 8(-4) + 12 = -4:    (-4, -4)

Arbitrarily chosen x value:  x = 1 => 1^2 + 8(1) + 12 = 21:     (1, 21)

The five points are:  (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21).  The vertex is (-4, -4).  The parabolic graph opens UP.

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = x² + 8x + 12

Conver the equation into a vertex form. Then we have

y = x² + 8x + 12

y = x² + 8x + 16 - 16 + 12

y = (x + 4)² - 4

The vertex of the parabolic equation y = x² + 8x + 12 will be at (-4, -4).

The graph is given below.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

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Answer:

A) The solution is x = 2 and y = 2

B) The graphs would intersect at the point (2, 2).

Step-by-step explanation:

A)

We start with the system of equations:

y = 6*x - 10

y = 2*x - 2

To solve this, the first step is to isolate one of the variables in one of the equations.

Here we can see that the variable "y" is already isolated in both equations, so we can skip that step.

Now we can "replace" the "y" in one of the equations for the correspondent expression in the other.

we can write:

(6*x - 10) = y

and for the second equation, we know that y = 2*x - 2

So replacing that, we get:

6*x - 10 = 2*x - 2

Now we can solve this for x.

6*x - 2*x = - 2 + 10

4*x = 8

x = 8/4 = 2

Now to find the value of y, we can just input this value of x in any one of the two equations:

y = 6*2 - 10 = 12 - 10 = 2

y = 2*2 - 2 = 4  - 2 = 2

So the solution of the system is:

x = 2, y = 2

B) Because the solution of the system is the ordered pair (2, 2), this means that the ordered pair belongs to the graph of both lines, then we can conclude that these lines will intersect at that point (the one that is common to both lines). Actually, when we have a system of equations, graphing both equations and finding the points where the graphs intersect is one method to estimate the solution of the system.

Answer:

C

Step-by-step explanation:

do that with pithagoras:

20² + 4,5² = x²

400 + 20,25 = x²

420,25 = x²

x = [tex]\sqrt{420,25}[/tex]

x ~ 20,5

Letter C: 20,5 feet

The required length of the ladder is given as 20.5 feet. Option C is correct.

In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.

Here,
The height of the building is 20 feet,
base length from the bottom of the building to the bottom of the ladder is 4.5 feet,
Let the hypotenuse length of the ladder be x,
Applying the Pythagoras theorem,
x² = 4.5² + 20²
x = √[420.25]
x = 20.5 feet

Thus, the required length of the ladder is given as 20.5 feet. Option C is correct.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

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Answer:

D

Step-by-step explanation:

I hope you get this right

Answer:

58.5 square feet

Step-by-step explanation:

Answer:approximately 2.718

Step-by-step explanation:The exponential constant is an important mathematical constant and is given the symbol e. Its value is approximately 2.718. ps. i got this from someone

Answer: X-

Step-by-step explanation:

Answer: A  Rhombus has 4 congruent sides .

Answer:

3.26 hours

Step-by-step explanation:

speed = distance / time

595 = 1940 / t

t = 1940 / 595  = 3.26 hours

or

I think the answer is 2 percent

hope this is answer

Answer:

The answer would be 90° seeing that it is a right angle triangle

Answer:

This is called a Trapezoidal prism

Number of faces: 5

Number of edges: 9

Number of vertices: 6

Hope this helps!!

Answer:

3 to the power 9 is the answer

Answer:

[tex] 3^9 [/tex]

Step-by-step explanation:

[tex] 3^8 \times 3 = 3^8 \times 3^1 = 3^{8 + 1} = 3^9 [/tex]

Answer:

24,000 for 20 years

Step-by-step explanation:

Because 4% of 100K=4K

Add them is 24K

Answer:

5^8

Step-by-step explanation:

(5^4)^2 = 390625

5^8 = 390625

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

2 + 2 = 4

5 + 5 = 5

4/5

Answer:

1. 23

2. 8

Step-by-step explanation:

1. 180-157 = 23

2. 15²+x²=(9+x)²

225 +x²=81+18x +x²

225-81=18x

144 = 18x

x = 144/18 = 8

Answer:

y=12

Step-by-step explanation:

y is inversely proportional to x

y=k/x

k is a constant of proportionality

k=yx

y1x1=y2x2

8(9)=y2(6)

y2=8(9)/6

y2=12

Answer:

f(-4) is basically just saying that you need to use the function given while x = -4.

The function given:

f(x) = -8(5-x)

We see that f(-4) means that x has to be -4, so we can substitute it in:

f(-4) = -8(5-(-4))

f(-4) = -8(9)

f(-4) = -72

Therefore, f(-4) is -72.

Add :

→ (√5 + 2√2) & (√2 - 5√3)

→ (√5 + 2√2) + (√2 - 5√3)

Removing the brackets.

→ √5 + 2√2 + √2 - 5√3

→ √5 + (2 + 1)√2 - 5√3

→ √5 + 3√2 - 5√3

Therefore, the required answer is √5 + 3√2 - 5√3.

Answer:

[tex]\dfrac{-1}{2}[/tex]

Step-by-step explanation:

We need to find ration numbers between -1 and 1.

Multiplying and dividing both -1 and 1 by 2.

[tex]\dfrac{-1\times 2}{2}=\dfrac{-2}{2}[/tex]

and [tex]\dfrac{1\times 2}{2}=\dfrac{2}{2}[/tex]

Now, the rational number between -2/2 and 2/2 is [tex]\dfrac{-1}{2}[/tex].

Wait… what lesson? I am confused :/

Answer:

The diameter is 1 unit.

Step-by-step explanation:

The formula for circumference of a circle of diameter d is C = (3.14)d, where 3.14 is a close approximation of π (pi).

Here the circumference is given and is 3.14 units.  Because C = 3.14d,

the diameter of this circle is 3.14/3.14, or simply 1 (unit).

Answer:

Option A

Step-by-step explanation:

From the question given in the picture attached,

Directrix of the parabola → y = 2

Focus of the parabola → (-5, 0)

Since, focus is below the directrix, parabola will open open downwards.

Equation of the parabola will be in the form of,

y - k = -4p(x - h)²

Here, (h, k) is the vertex of the parabola

p = Distance between vertex and focus or distance between vertex and directrix

Since, distance between vertex and focus = Distance between vertex and directrix

Therefore, vertex of the parabola → (-5, 1)

Now distance (p) between vertex (-5, 0) and focus (-5, 1) = 1 unit

By substituting these values in the equation,

y - 1 = -4(1)[x - (-5)]²

y - 1 = -4(x + 5)²

y = -4(x + 5)² + 1

Option A will be the answer.

Answer:

18.84feet

Step-by-step explanation:

Length of an arc = rtheta

radius r = 9feet

theta = SR= 120°

Convert theta to radians

theta = 120π/180

theta= 2π/3

Length of the arc = 9 * 2π/3

L = 18π/3

L = 6π

L = 6(3.14)

L = 18.84feet

Hence the length of the arc is 18.84feet

While this may look like it's a lot to keep track of, its not too bad. We have 7 copies of (-8) in total. The 7 copies due to the exponent of 7. Nice work on getting the correct answer for the second part.

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A further detailed breakdown:

(-8)^3 is the same as (-8)(-8)(-8) so we have three copies here

(-8)^4 is the same as (-8)(-8)(-8)(-8) and we have four copies

Overall, we have 3+4 = 7 copies total.