PLEASE HELP! PLEASE SHOW WORK
Use the following expression to answer this three part question:
f(x) = 2x2 + 4x − 6

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

Answer:

The equation of the line is, y = x

Step-by-step explanation:

The constraints of the required linear equation are;

The point through which the line passes = (2, 2)

The line to which the required line is parallel = y = x + 4

Two lines are parallel if they have the same slope, therefore, we have;

The slope of the line, y = x + 4 is m = 1

Therefore, the slope of the required line = 1

The equation of the required lime in point and slope form becomes;

y - 2 = 1 × (x - 2)

∴ y = x - 2 + 2 = x

The equation of the required line is therefore, y = x

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

Answer:

3

Step-by-step explanation:

We are going to be using cofunction identity cos(90-x)=sin(x).

Apply to either side but not both.

cos(22f − 1) = sin(7f + 4)

sin(90-[22f-1])=sin(7f+4)

90-[22f-1]=7f+4

Distribute

90-22f+1=7f+4

Combine like terms

91-22f=7f+4

Add 22f on both sides

91=29f+4

Subtract 4 on both sides

87=29f

Divide 29 on both sides

3=f

f=3 is between 0 and 90

Answer:

The answer is "3."

Step-by-step explanation:

Just submitted the test and got the answer correct!

Answer:

They are parallel so also -4/3

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]

[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]

[tex]y+2=\dfrac{12}{8}(x-1)[/tex]

[tex]y+2=\dfrac{3}{2}(x-1)[/tex]

Multiply both sides by 2.

[tex]2(y+2)=3(x-1)[/tex]

[tex]2y+4=3x-3[/tex]

[tex]2y-3x=-3-4[/tex]

[tex]-3x+2y=-7[/tex]

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

[tex]-3x+2y>-7[/tex]

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

[tex](-3x+2y)(-1)<-7(-1)[/tex]

[tex]3x-2y<7[/tex]

Therefore, the correct option is D.

Answer:

Hey, could you please add the number line to the question too

Answer:

-7

Step-by-step explanation:

63/9 but there is an odd number of negative numbers so negative answer

Answer:

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

Step-by-step explanation:

Given

[tex]\{(5, -9), (6, -6), (-3, 8), (9, -6)\}[/tex]

[tex]\{(-6, -4), (4, -8), (-6, 9), (1, -3)\}[/tex]

[tex]\{(1, -1), (-5, 7), (4, -9), (-9, 7)\}[/tex]

[tex]\{(8, -9), (-3, -6), (-4, 4), (1, -5)\}[/tex]

Required

Which is not a function

An ordered pair is represented as:

[tex]\{(x_1,y_1),(x_2,y_2),(x_3,y_3),..........,(x_n,y_n)\}[/tex]

However, for the ordered pair to be a function; all the x values must be unique (i.e. not repeated)

From options (a) to (d), option (b) has -6 repeated twice. Hence, it is not a function.

Answer:

the answer is -3

Step-by-step explanation:

0.7x - 1.4 = -3.5

add 1.4 to both sides of the equation

you're left with 0.7x = -2.1

then divide both sides by 0.7

you're left with your answer of -3

Hello!

8 × 3 + 10 - 13 × 2 =

= 24 + 10 - 13 × 2 =

= 24 + 10 - 26 =

= 34 - 26 =

= 8

Good luck! :)

Answer:

8

Step-by-step explanation:

According to bdmas rule

First multiply 8 and 3 or 13 and 2

Then, there will be 24 + 10 - 26

Then add 24 + 10, there will be 34

and again minus by 26

Then finally answer will be 8

Answer:

20

Step-by-step explanation:

f = 2f - 20

f - 2f = - 20

- f = - 20

f = 20

Answer:

x =  20

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, sum to 180°

5x + 4x = 180

9x = 180 ( divide both sides by 9 )

x = 20

Answer:

The value of x is 40⁰.

Step-by-step explanation:

5x + 4x = 360⁰

DUE TO THE SUM OF QUADRATIC ANGLE.

Answer:

(C) 0.3(10 + 4h) = 0.25(6h)

Step-by-step explanation:

Here's what we know about Fernando's fees:

$10 is the initial fee

$4 is the hourly fee (h)

Saves 30% (also written as 0.3) of the total cost (includes initial and hourly fee)

Here's what we know about Brenna's fees:

No initial fee

$6 is the hourly fee (h)

Saves 25% (also written as 0.25) of the total cost (just the hourly fee because she doesn't have an initial fee)

We want to find which hour Fernando and Brenna will have saved the same amount of money.

To do this, let's first set up an equation for Fernando and Brenna separately:

Fernando's equation:

0.3(10 + 4h) = how much money he saves from the total cost

Brenna's equation:

0.25(6h) = how much money she saves from the total cost

Now we set them equal to each other:

0.3(10 + 4h) = 0.25(6h)

There's your answer!

Hope it helps (●'◡'●)

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

A) 0.019

B) 0.563

Step-by-step explanation:

a) We will use Poisson distribution formula to solve this;

The formula is given as;

P(X = x) = ((e^-λ) × (λˣ))/x!

Mean is 1. Thus;

λ = 1 aircraft/hour.

Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)

Thus;

P(X > 3) = 1 - P(X ≤ 3)

Thus;

1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Solving through online calculator, we have;

P(X > 3) = 1 - 0.98101

P(X > 3) = 0.01899

To 3 decimal places, we have; P(X > 3)= 0.019

b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;

P(X ≤ 3) = 1 - P(X > 3)

P(X ≤ 3) = 1 - 0.01899

P(X ≤ 3) = 0.98101

Since there are 30 one-hour intervals, then we have;

Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;

(P ≤ 3) = (0.98101)³⁰

(P ≤ 3) = 0.5626

Approximating to 3 decimal places, we have;

(P ≤ 3) = 0.563

Answer:

l

Step-by-step explanation:

Answer:

2/60 = 1/30 = 3.3%

Step-by-step explanation:

Answer:

x = 27.5.

Step-by-step explanation:

There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.

So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.

With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.

Therefore, x = 27.5.

Answer:

In picture

Step-by-step explanation:

Brainliest please~

[tex](0,3)[/tex] and [tex](1,-2)[/tex]

Equation: (refer the image below)

Slope:

[tex]m=\frac{3+2}{0-1}[/tex]

[tex]m=-5[/tex]

Equation:

[tex]y=5x-b[/tex]

[tex]3=b[/tex]

Substitute (0,3)

Point: [tex](1,-2)[/tex]

Answer:

Traversable because it has exactly two odd nodes

Step-by-step explanation:

There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.

Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.

So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.

Answer:

The fraction of the pocket money she left is 1/8.

Step-by-step explanation:

Let the total pocket money is p.

Spent on Monday = p/2

Amount left = p - p/2 = p/2  

Spent on Tuesday = 2/3 of p/2 = p/3

Amount left = p/2 - p/3 = p/6

Spent on Wednesday = 1/4 of p/6 = p/24

Amount left = p/6 - p/24 = p/8

So, the fraction of the pocket money she left is 1/8.  

answer:

to test whether agraph is linear

Answer:

[tex]\rm\displaystyle 0,\pm\pi [/tex]

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

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

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]

factor out tanγ:

[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]

divide both sides by tanαtanβ-1 and that yields:

[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]

multiply both numerator and denominator by-1 which yields:

[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]

recall angle sum indentity of tan:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]

let α+β be t and transform:

[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]

remember that tan(t)=tan(t±kπ) so

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]

therefore when k is 1 we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]

when is 0:

[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]

likewise by Opposite Angle Identity we obtain:

[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]

isolate -α-β to left hand side and change its sign:

[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]

and we're done!

Answer:

-π, 0, and π

Step-by-step explanation:

You can solve for tan y :

tan y (tan a + tan B - 1) = tan a + tan y

Assuming tan a + tan B ≠ 1, we obtain

[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]

which implies that

y = -a - B + kπ

for some integer k. Thus

a + B + y = kπ

With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.

It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so

[tex]B=\frac{\pi }{2} - a + k\pi[/tex]

but with the given limitation we must have k = 0, because 0 < π/2 - a < π.

On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again

k = 0, so we obtain

[tex]\frac{\pi }{2} - a=-a[/tex]

a contradiction.

Answer:

x < 0.5

Step-by-step explanation:

Given

2(1 - x) > 2x ( divide both sides by 2 )

1 - x > x ( add x to both sides )

1 > 2x ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] > x , that is

x < [tex]\frac{1}{2}[/tex] OR x < 0.5

Answer:

the angle <ABC is equal to 65°

Answer:

8/15

Step-by-step explanation:

The ratio of perpendicular to base is tan B .

Here ,

=> tan B = 8 ft/ 15ft

=> tan B = 8/15

Step-by-step explanation:

Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)

= 200+625-1156 ÷ (2000)

= 1069 ÷2000

Cos A = 0.5345

A= cos inverse 0.5345

A = 57.7

Answer:

57.7

Step-by-step explanation:

took the test

Answer:

20

Step-by-step explanation:

3 (b + a) = c

3 (4 + 5) = 7

12 + 15 = 7

27 = 7

27 - 7

20

[tex]\huge\boxed{ \sf{Answer}} [/tex]

Given,

[tex]a = 5 \\ b = 4 \\ c = 7[/tex]

And the equation we need to solve is,

[tex]3(b + a) = c[/tex]

To find the answer, you need to substitute the values of a, b & c in the equation.

[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]

↦ The answer is 20.

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