Identify the domain of the function shown in the graph.

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Answer:

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

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No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

9514 1404 393

Answer:

  (g·h)(-3) = 2.8

Step-by-step explanation:

Given:

  g(x) = (x +1)/(x -2)

  h(x) = 4 -x

Find:

  (g·h)(x) = g(x) × h(x)   for x = -3

Solution:

  g(-3) = (-3+1)/(-3-2) = -2/-5 = 2/5

  h(-3) = 4 -(-3) = 4 +3 = 7

Then the product is ...

  g(-3)·h(-3) = (2/5)(7) = 14/5 = 2.8

  (g·h)(-3) = 2.8

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Answer:

Carmen:27

Abdul:17

David=34

Step-by-step explanation:

Carmen+Abdul+David = 78

Carmen-Abdul=10

David=2Abdul

Carmen=Abdul+10

Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78

4Abdul=68

Abdul = 68/4=17

Carmen = 17+10=27

David = 2 * 17 = 34

27+17+34=78

Answer:

45 days

Step-by-step explanation:

Based on the giving information, 30*15/10.

Reduce the fraction by canceling the greatest common factor: 3*15 = 45

Answer:

ask in English then I can help u

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.

The percentage that is over 50 is 15.6%:

The data on the bar graph can be represented as:

Under 17 [tex]\to[/tex] 25

18 - 24 [tex]\to[/tex] 35

25 - 34 [tex]\to[/tex] 40

35 - 50 [tex]\to[/tex] 35

Over 50 [tex]\to[/tex] 25

So, the total customer surveyed are:

[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]

[tex]Total = 160[/tex]

The percentage over 50 are:

[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]

[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]

[tex]\%Over\ 50 = 0.15625* 100\%[/tex]

[tex]\%Over\ 50 = 15.625\%[/tex]

Approximate

[tex]\%Over\ 50 = 15.6\%[/tex]

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Answer:

A

Step-by-step explanation:

(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)

[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

Answer:

Step-by-step explanation:

CD/6.5 = 2.6/4.9    This is the result of the angle bisector theorem.

The theorem basically says that the side opposite the angle being bisected is divided  the ratio of the sides enclosing the angle.

Multiply both sides of the proportion by 6.5

CD = 2.6 * 6.5 / 4.9

CD = 3.4489

CD = 3.4 rounded.

Answer: -21/2

Concept:

Usually, when doing mathematics operation, it goes by the PEMDAS order:

However, since the question asks to solve the order of operation from left to right, then we would be doing [addition] --> [Divison]

Solve:

Given

(-5/2) + 3/4 ÷ 1/6

Operate with addition

=(-10/4) + 3/4 ÷ 1/6

=(-7/4) ÷ 1/6

Operate with division

=(-7/4) × 6/1

=-42 / 4

=-21 / 2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

13

Step-by-step explanation:

If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144= c^2

169 = c^2

Take the square root of each side

sqrt(169) = sqrt(c^2)

13= c

Answer:

The length of the hypotenuse is 13.

Step-by-step explanation:

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

[tex]a^2 = 12^2 + 5^2[/tex]

[tex]a^2 = 144 + 25[/tex]

[tex]a^2 = 169[/tex]

a=[tex]\sqrt{169}[/tex]

a= 13

Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which  [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.

HOPE THIS HELPED

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

You need to re copy and paste it, I can’t see the full possible answers/question.

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Answer:

  1/63

Step-by-step explanation:

There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:

  4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63

The larger fraction is 1/63 unit larger than the smaller fraction.

Answer:

$2046

Step-by-step explanation:

Add 1947 and 99 because he is depositing, as in adding, 99 dollars

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

3x - 5 = 37

Step 2: Solve for x

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º

Answer:

24

Step-by-step explanation:

24-16=8

The solution to the equation is g = 24.

To solve the equation g - 16 = 8 and find the value of g.

we need to isolate the variable g on one side of the equation.

Starting with the given equation:

g - 16 = 8

To isolate g, we can add 16 to both sides of the equation:

g - 16 + 16 = 8 + 16

g = 24

Therefore, the solution to the equation is g = 24.

To learn more on Equation:

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Answer:

a=3

Step-by-step explanation:

Given points (a, b) and (c,d), the midpoint of the points will be at

((a+c)/2, ((b+d)/2)

Therefore, given (9, 2) and (a,2a), our midpoint is at

((9+a)/2, (2+2a)/2) = (6,4)

Matching the x values to their corresponding x values and doing the same with the y values, we get

(9+a)/2 = 6

(2+2a)/2 = 4

First, we have

(9+a)/2 = 6

multiply both sides by 2 to remove the denominator

9+a = 12

subtract 9 from both sides to isolate a

a = 3

2a = 2 * a = 6

Confirming this, we have

(2+2a)/2 = 4

(2+6)/2 = 4

8/2=4

The value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).

It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

Point M is the midpoint of CD.

The coordinate of the C is (a, 2a)

The coordinate of the M is (6, 4)

The coordinate of the C is (9, 2)

Using bisection formula:

(a + 9)/2 = 6

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. I

a + 9 = 12

a = 12 - 9

a = 3

Or

(2a + 2)/2 = 4

a + 1 = 4

a = 3

Thus, the value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).

Learn more about the order double here:

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Answer:

only 4 is incorrect...

1,450,000 = 1.45 x [tex]10^{6}[/tex] NOT

1,450,000 = 1.45 x [tex]10^{7\\}[/tex]

Step-by-step explanation:

Answer:

there would be 21 girls and 14 boys

Step-by-step explanation:

I split the kids down in half and then added seven to the girls and when added up 21+14=35 and that’s is 7 more girls then boys

Answer:

(x-7) and (x+12) are the factors and the rest are non factors...

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

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Explanation:

A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.

A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.

Producing these at home can be an interesting project. A circle can be made using a compass.

An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.

A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.

A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.

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The general form equation for a conic is ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0

Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,

In standard form, the equations for figures centered at the origin are ...

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The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.

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Answer:

  A

Step-by-step explanation:

The function f(x) is required in the numerator, eliminating choices C and D.

The restriction is that function g cannot be zero, so we cannot have ...

  3x +2 = 0

  3x = -2

  x = -2/3 . . . . . eliminates choice B; confirms choice A

(1) D

[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]

Integrate by parts, taking

[tex]u = t \implies \mathrm du=\mathrm dt[/tex]

[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]

Then

[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]

(2) A

[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]

[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]