Determining the Input Value to Produce the Same Output Value for Two Graphed Functions A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2). Use the graph to determine the input value for which f(x) = g(x) is true. x = 0.5 x = 1 x = 1.5 x = 2

Answer:

A

Step-by-step explanation:

substitute the values from the replacement set into the right side of the equation to find which values of x make the equation true.

x = - 32

[tex]\frac{-32}{4}[/tex] + 5 = - 8 + 5 = - 3 ← True

x = 8

[tex]\frac{8}{4}[/tex] + 5 = 1 + 5 = 6 ≠ - 3 ← False

x = 32

[tex]\frac{32}{4}[/tex] + 5 = 8 + 5 = 13 ≠ - 3 ← False

the solution is therefore x = - 32

Answer:

24

23fc

23

45jh4

66

35g

35

56

34

Answer:

Step-by-step explanation:

You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.

For some distance r and bearing angle θ, the (north, east) coordinates will be ...

  (north, east) = (r·cos(θ), r·sin(θ))

For the trip at hand, the final coordinates of the plane are ...

Distance north = (400 km)cos(25°) +(700 km)cos(80°)

  = 362.52 km +121.55 km = 484.07 km

B is about 484 km north of O.

Distance east = (400 km)sin(25°) +(700 km)sin(80°)

  = 169.05 km +689.37 km = 858.41 km

B is about 858 km east of O.

__

Additional comment

Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...

  (x, y) = (r·cos(θ), r·sin(θ))

You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.

Using the median concept and the quartiles, we have that:

In this problem, there are 12 elements, hence:

Thus, Q1 = 120, Q3 = 160 and the IQR is:

IQR = 160 - 120 = 40.

1.5 IQR is: 1.5 x 40 = 60.

The boundaries are:

There is a value less than 60 in the data set, hence the sentence that describes the outliers is: B: The outlier is less than the lower boundary.

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Answer:

Use the data to answer the questions.

What is 1.5 ∙ IQR? ✔ 60

What is the lower boundary? ✔ 60

What is the upper boundary? ✔ 220

Which sentence describes the outliers? ✔ The outlier is less than the lower boundary.

Step-by-step explanation:

edge 2023

Answer:

-∞ and -∞ both answers

Step-by-step explanation:

From the graph it is clear that as x becomes smaller and smaller, y gets smaller and smaller. So as x → -∞, y → -∞

On the positive x side, as x gets bigger and bigger, y gets smaller and smaller so
as x → +∞, y → -∞

The range of the salary will be the closed interval [23,200, 26,800].

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x |

A new hire at one organization may expect to get an average beginning pay of $25,000 per year. The absolute divergence from the real compensation is no more than $1800.

Let 'x' represent the actual salary. Then the inequality is given as,

|x - 25,000| ≤ 1800

- 1,800 ≤ x - 25,000 ≤ 1,800

25,000 - 1,800 ≤ x ≤ 25,000 + 1,800

23,200 ≤ x ≤ 26,800

The range of the salary will be the closed interval [23,200, 26,800].

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Answer:

  g(x) = 3x +5

Step-by-step explanation:

You want the function that results from translating f(x) = 3x upward by 5 units.

The y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.

The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:

  (x, f(x) +5) . . . . . graph translated 5 units up

Using the given definition of f(x), this becomes ...

  (x, 3x +5)

The translated function is defined as g(x), so we have ...

  (x, g(x)) = (x, 3x +5)

or ...

  g(x) = 3x +5

The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).

A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.

Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:

E'( - 9, - 8 )

When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:

F'( - 9, - 4 )

When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:

G'( - 2, - 4 )

When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:

D'( 8, 2 )

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Answer:

x=27 or x= -8

Step-by-step explanation:

rearrange the terms

convert the expression

simplify the expression

rewrite the equation

solve the equation

formulate new equations

I can't show the full steps since there's no image

Answer:

this is answers

scan and see

The measurement 9 feet is closest to 270 centimeters.

In this problem we have a case of unit conversions, in which we must find what measure in a unit offers the best approximation to other represented in other unit. Please notice that a centimeter equals 25 / 762 feet and 50 / 127 inches. Now we proceed to calculate the equivalent quantities in feet and inches by simple rule of three:

x = 270 cm × (25 / 762 feet / cm)

x ≈ 8.858 feet

x = 270 cm × (50 / 127 inches / cm)

x ≈ 106.299 inches

The measurement 9 feet is closest to 270 centimeters.

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Answer:

17

Step-by-step explanation:

Angle 2 and angle 4 are alternate exterior angles so they congruent angles which means they have same angle measurement.

To find the measure of angle 2 we first need to find the value of x.

And to do that we can write the following equation based on the information we have in hand:

6x + 8 = 4x + 11 transfer like terms to the same side of the equation

6x - 4x = 11 - 8 add/subtract like terms

2x = 3 divide both sides by 2

x = 1.5 now to find the measure of angle 2 replace x with 1.5

6×(1.5)+8 = 17

Answer:

The answer to your question is 588

Answer:

588

Hope this helps

The fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.

Here we want to simplify the fraction 24/56. To do so, we need to find the greatest common factor between 24 and 56, to find that, we need to write both of these numbers as a product of their prime factors.

We will get:

24 = 2*2*2*3

56 = 2*2*2*7

We can identify the greatest common factor between parenthesis:

24 = (2*2*2)*3

56 = (2*2*2)*7

So the greatest common factor is 2*2*2 = 8, then we can divide both numerator and denominator by 8, we will get:

24/8 = 3

56/8 = 7

Then the fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.

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Answer:

$150

Step-by-step explanation:

Given the following question:

Lucy paid 120 dollars for an item
The item was 20% off

What was the original price? To find the original price we will need to use the formula to calculate percentages.

20% of 150
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times150}{100}[/tex]
[tex]20\times150=3000[/tex]
[tex]3000\div100=30[/tex]
[tex]150-30=120[/tex]
[tex]=120[/tex]

Which means our original price is "$150."

Hope this helps.

The slope of a line that passes through the ordered pairs (0,1) and (3,5) would be m = 4/3.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal. Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

WE have been given line that passes through the ordered pairs (0,1) and (3,5).

Slope = m

Therefore,

[tex]m = \dfrac{y-q}{x-p}\\\\m = \dfrac{5 -1}{3-0}\\\\m = \dfrac{4}{3}[/tex]

Hence, the slope of a line that passes through the ordered pairs (0,1) and (3,5) would be [tex]m = \dfrac{4}{3}[/tex].

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The picture of the triangle ΔDEF is attached below.

A triangle can be defined as a basic polygon which has 3 sides.

In the given ΔABC we see that AC is the hypotenuse and the two sides AB and AC are the legs of the triangle.

m∠B=90°

The ΔDEF is drawn such that m∠E=90° and AB=DE and EF=BC .

Therefore we can say that the two triangles are congruent by SAS axiom of congruency.

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Answer:

Step-by-step explanation:

Let the initial salary be x.

Set equation and solve for x:

Answer:

The original salary is $11641.18.

Step-by-step explanation:

The equation will be,

→ x + (x × 2)/100 = 11874

Now the original salary will be,

→ x + (x × 2)/100 = 11874

→ x + 0.02x = 11874

→ 1.02x = 11874

→ x = 11874/1.02

→ x = 11641.1764706

→ [ x = 11641.18 ]

Hence, original salary is $11641.18.

Answer:

33

 messages

Step-by-step explanation:

If Partial Derivatives f(x,y) -8e^4x sin(7y) is 32 e^(4 x) sin(7 y) and

56 e^(4 x) cos(7 y)

Partial Derivatives

d/dx(8 e^(4 x) sin(7 y))

Factor out constants:

= 8 (d/dx(e^(4 x))) sin(7 y)

Using the chain rule, d/dx(e^(4 x)) = (d e^u)/(du) (du)/(dx), where u = 4 x and d/(du) (e^u) = e^u:

= e^(4 x) (d/dx(4 x)) 8 sin(7 y)

Factor out constants:

= 4 (d/dx(x)) 8 e^(4 x) sin(7 y)

Simplify the expression:

= 32 e^(4 x) (d/dx(x)) sin(7 y)

The derivative of x is 1:

= 32 e^(4 x) sin(7 y)

Simplify the expression:

32 e^(4 x) sin(7 y)

Part 2:

Partial Derivatives

d/dy(8 e^(4 x) sin(7 y))

Factor out constants:

= 8 e^(4 x) (d/dy(sin(7 y)))

Using the chain rule, d/dy(sin(7 y)) = (dsin(u))/(du). (du)/(dy), where u = 7 y and d/(du) (sin(u)) = cos(u):

= cos(7 y) (d/dy(7 y)) 8 e^(4 x)

Factor out constants:

= 7 (d/dy(y)) 8 e^(4 x) cos(7 y)

Simplify the expression:

= 56 e^(4 x) cos(7 y) (d/dy(y))

The derivative of y is 1:

=  56 e^(4 x) cos(7 y)

Simplify the expression:

56 e^(4 x) cos(7 y)

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Answer:

Final answer is 2

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

If you factor [tex]a^2-a-30[/tex] you get [tex]\left(a^2+5a\right)+\left(-6a-30\right)[/tex]

= [tex]a(a+5)-6(a+5)[/tex]

= [tex]a(a+5)(a-6)[/tex]

That's where the a comes in

Not sure if that answers your question

Answer: 30

Step-by-step explanation:

181+180+150=

361+150=511

541-511=30 18-24 year olds

**46 of 181 students that watched TV ate pizza and the same 46 students of  the 150 students that ate pizza watched TV.

By solving a system of equations we can see that there are 400 main-floor seats and 500 balcony seats.

Let's define the two variables:

We know that if all the seats are sold, then the total income is $5,200, we can write the equation:

x*$8 + y*$4 = $5,200

And if 25% of the main-floor and 50% of the balcony seats are sold, then we get an income of $1800, then we can write:

0.25*x*$8 + 0.5*y*$4 = $1,800

x*$2 + y*$2 = $1,800

So we have a system of equations:

x*$8 + y*$4 = $5,200

x*$2 + y*$2 = $1,800

If we subtract twice the second equation for the first one we get:

(x*$8 + y*$4) - (x*$2 + y*$2) = $5,200 - 2*$1,800

x*$4 = $1,600

x = $1,600/$4 = 400

So there are 400 seats on the main-floor.

Using the first equation we can find:

x*$8 + y*$4 = $5,200

400*$8 + y*$4 = $5,200

$3,200 + y*$4 = $5,200

y*$4 = $5,200 - $3,200 = $2,000

y = $2,000/$4  = 500

So there are 500 balcony seats.

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Answer:

574

Step-by-step explanation:

Answer: a=(V-4)/t

Step-by-step explanation:

V = 4 + at

V-4=at

a=(V-4)/t

Polynomial equation with integer coefficients that has roots x= -1 and

x = -6 is equal to x² +7x +6=0.

As given in the question,

Given roots for the polynomial equation with integer coefficient are

x = -1 ⇒ x + 1=0

x = -6 ⇒ x + 6 =0

Polynomial equation is

( x + 1) ( x + 6) =0

⇒ x² + 1x + 6x + 6 =0

⇒ x² + 7x + 6 =0

Therefore, polynomial equation with integer coefficients that has roots x= -1 and x = -6 is equal to x² +7x +6=0.

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