Solve the following quadratic equations by any method. The solutions are:

f (x) = x 2 − 12x + 32
a.

(X - 4)(X - 8) this means that X = 4 and -8
b.

(X - 4)(X - 8) this means that X = -4 and -8
c.

(X - 4)(X - 8) this means that X = +4 and +8
d.

(X - 4)(X - 8) this means that X = -4 and +8

k must be greater than or equal to 22.75 to have two different zeros.

Second order polynomials are algebraic expressions that observe the following form:

[tex]p(x) = a\cdot x^2 + b\cdot x + c[/tex]   (1)

Where:

For polynomials of the form p(x) = 0, we can infer the nature of their roots by applying the following discriminant:

d = b² - 4 · a · c   (2)

According to (2), there are three cases:

Now we have the following discriminant case:

-(3 + 2 · k)² - 4 · (1) · (4) ≠ 0

-(9 + 6 · k + 4 · k²) - 16 ≠ 0

-9 - 6 · k - 4 · k² - 16 ≠ 0

4 · k²+ 6 · k +25 ≠ 0

This characteristic polynomial has two conjugated complex roots, then we conclude that all values of k must positive or negative, but never zero. By graphng tools we find that k must be greater than or equal to 22.75 to have two different zeros.

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[tex]y = - x {}^{2} + 6x - 15[/tex]

[tex]y {}^{ \gamma } = - 2x + 6[/tex]

[tex]y {}^{ \gamma } = 0[/tex]

[tex] - 2x + 6 = 0[/tex]

[tex] - 2x = - 6[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

[tex]y = - (3) {}^{2} + 6(3) - 15[/tex]

[tex]y = - 9 + 18 - 15[/tex]

[tex]y = - 9 + 3[/tex]

[tex]y = - 6[/tex]

[tex]==============================[/tex]

In order to find the vertex of a parabola, we use the following formula:

[tex]\mathfrak{\displaystyle\frac{-b}{2a} }[/tex]

Please remember that a parabola looks like this:

[tex]\tt{y=ax^2+bx+c}[/tex]

Now you know what a and b stand for.

In this case, a = -1, and b is 6:

[tex]\mathfrak{\displaystyle\frac{-6}{2(-1)} }[/tex]

Simplify:

[tex]\mathfrak{\displaystyle\frac{-6}{-2}}[/tex]

[tex]\mathfrak{3}\\=======================================[/tex]

[tex]\mathcal{DiAmOnD}\\\tt{A~Creative~Helper}}}}[/tex]

11.9 - last one

Step-by-step explanation:

Adjacent + hypotenuse = Cos / Cah

Cos32 = x/14

x14

11.87... = x

So, 11.9 to nearest tenth

Hope this helps!

16.5/3 = 5.5

Step-by-step explanation:

becuase he needs to walk 16.5 miles. and he can walk 3 miles per x(hour)

you need to devide distance by speed to get time.

Step-by-step explanation:

line equation

y = ax + b

a is the slope, b is the y-intercept.

a slope perpendicular to another slope flips x and y upside down and flips the sign.

so, the slope perpendicular to 2/7 is -7/2.

so, our desires line function looks like

y = -7/2 × x + b

to get b we use the given point (and it's x and y coordinates = values).

-8 = -7/2 × 8 + b = -7×4 + b = -28 + b

b = 20

so, the full line equation is

y = -7/2 × x + 20

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

x + 2y = –1

(-3) + 2y = -1

-3 + 2y + 3 = -1 + 3

2y = 2

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

Answer:

147

Step-by-step explanation:

4/7 people in chairs

7/8 of chairs, rest are standing

8 empty chairs

empty chairs = 1/8

full chairs = 8 x 8

7/8 = 64.

4/7 = 64

1/7 = 64 / 4

1/7 = 21

7/7 = 21 x 7

7/7 = 147

There are 147 people in the room.

There are 147 people in the room.

The given is,

Four-sevenths of the people in a room are seated in seven-eighths of the chairs.

The rest of the people are standing.

there are 8 empty chairs, how many people are in the room in a room are seated in seven-eighths of the chairs.

The rest of the people are standing.

We have to determine there are 8 empty chairs, how many people are in the room.

Four-sevenths of the people.

4/7 people in chairs.

7/8 of the chairs, rest are standing

The 8 empty chairs,

The empty chairs = 1/8

The full chairs = 8 x 8

7/8 = 64.

4/7 = 64

1/7 = 64 / 4

1/7 = 21

7/7 = 21 x 7

7/7 = 147

There are 147 people in the room.

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Answer:

11x-3

11

Step-by-step explanation:

and that's the answer

Answer:

Step-by-step explanation:

Divide the circle into 10 parts and color 2 parts black and 8 parts red.

Explanation:

A direct proportion is of the form y = kx

To find k, pick any row to divide the y over x value

No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.

Therefore, we go from y = kx to y = 2x

Answer:

Probably 81.

Maybe 18.

See explanation below.

Step-by-step explanation:

(6 + 3)² = 9² = 9 × 9 = 81

(6 + 3) × 2 = 9 × 2 = 18

I think you mean the first expression in which 2 is an exponent, but since it's not clear, I solved it both ways.

Answer:

[tex]\frac{dx^{2} (x+1)S^{2} }{2(x^{2} +6x+3)^{2} }+ C[/tex]

Step-by-step explanation:

Answer:

isn't the answer 12/20

add the number of pets to make 20

then there are 12 cats

as a fraction

12/20

Answer:

  3

Step-by-step explanation:

The "initial value" of a function is the value when the independent variable is zero.

  f(0) = 3(5/4)^0 = 3×1 = 3

The initial value of the function is 3.

Δ = (-5)² - 4*1*6 = 25 - 24 = 1 = 1²

x' = (5 + 1) / (2*1) = 6/2 = 3

x" = (5-1) / (2*1) = 4/2 = 2

2 solutions : 2 and 3

x² - 5x + 6 = (x - 2) (x - 3)

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

Let y represent the population after x years.

Given that the growth rate is 4.5% per year and the current population is 1500.

Hence a = 1500, b = 100% + 4.5% = 104.5% = 1.045

y = 1500(1.045)ˣ

After 6 years:

y = 1500(1.045)⁶ = 1953

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

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answer:

148ft²

explanation:

to solve this problem, we must set up a proportion.

[tex]\frac{side (L)}{area(L)} = \frac{side(S)}{area(S)} \\\frac{15}{185} = \frac{12}{x}[/tex]

15x=2220

x=148ft²

--

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Answer:

  (d)  k = 8

Step-by-step explanation:

The value k in the equation ...

  g(x) = f(x) +k

represents a vertical translation by k units.

__

The vertex coordinates for f(x) and g(x) are ...

  f(x): vertex = (-3, -3)

  g(x): vertex = (-3, 5)

This means ...

  f(-3) = -3

  g(-3) = 5 = f(-3) +k = -3 +8   ⇒   k = 8

_____

Additional comment

Translations of various kinds are often most easily seen by comparing points where the graph has a distinctive feature. On this graph, that is the vertex.

Answer:

D. 48 feet

Step-by-step explanation:

Ladder (50 ft) = hypotenuse

Floor distance (14 ft) = b

Wall (unknown) = a

[tex]a^2+b^2=c^2[/tex]

[tex]a^2+14^2=50^2[/tex]

[tex]a^2+196=2500[/tex]

[tex]a^2=2500-196[/tex]

[tex]a=\sqrt{2304}[/tex]

[tex]a=48[/tex]

Hope this helps!

Answer:

48 feet

Step-by-step explanation:

Here,

c = 50 ft

b = 14 ft

To find : the height of the wall that the ladder reaches ( a ) = ?

Formula : -

a² + b² = c²

a² = c² - b²

= 50² - 14²

= ( 50 x 50 ) - ( 14 x 14 )

= 2500 - 196

= 2304

= 48 x 48

a² = 48²

a = 48 feet

Answer:42 is the third quartile

Step-by-step explanation:

1,200 divide by 600 = 2 students

2 students multiply by 50% is 100 students.

So, approximately 100 students ride their bicycles home.

(If not correctly, I am truly sorry)

Answer:

Line LM

Step-by-step explanation:

     A ray has a point at one end, this figure does not.

     A line goes out forever in both ends, this is shown by the two arrows. Line LM describes this figure.

     Points LM are going to be two separate points, this figure does not have points.

     Plane LM will have three points to show a plane, this is a single line.

     Using these definitions and facts we know, we can figure out this is best described as Line LM.

The measure of the arc of the sinkhole that falls within the restaurants property is -21°

Let x be the angle at the dollar store at the intersection

Now the angle of the grocery store at the intersection, y is 2/3 that of the dollar store. So, y = 2x/3

Since both x and y are supplementary,

x + y = 180°

x + 2x/3 = 180°

5x/3 = 180°

x = 180° × 3/5

x = 36° × 3

x = 108°

The gas station has the same angle at the intersection but has 88° more of the sinkhole edge to stabilize. So, the angle the gas station store subtends at the sinkhole is z = x + 88°

Also, since the grocery stores property has 2/3 of the angle in the intersection at the dollar store has, but has 5° more of the sinkhole edge to stabilize. The angle the grocery store subtends at the sinkhole is k = y + 5° = 2x/3 + 5°

Let k' be the angle subtended by the restuarant at the sinkhole.

Since the sinkhole is a circle, we have that

x + z + k + k' = 360°

x + x + 88° + 2x/3 + 5° + k' = 360°

8x/3 + 93° + k' = 360°

8x/3 + k' = 360° - 93°

8x/3 + k' = 267°

So, making k' subject of the formula, we have

k' = 267° - 8x/3

Substituting the values of the variables into the equation, we have

k' = 267° -  8 × 108°/3

k' = 267° - 288°

k' = -21°

So, the measure of the arc of the sinkhole that falls within the restaurants property is -21°

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Answer:

  k = 3

Step-by-step explanation:

The value of k is the amount by which the function f(x) is translated upward to give the function g(x). We can compare y-intercepts to see that the y-intercept of g(x) is 5 -2 = 3 units more than the y-intercept of f(x). This means ...

  g(x) = f(x) +3

Comparing to ...

  g(x) = f(x) +k

we see that k = 3.

Answer:

Here,

n(A)={0,1,3,5,6}

n(B)={1,2,3,7}

n(AUB)=?

we know that,

AUB={0,1,2,3,5,6,7}

Step-by-step explanation:

is it okay ?

hopefully it works <3 ❣️

Answer:

her balance aka ADB would be 372.08