If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?

An expression is defined as a set of numbers, variables, and mathematical operations. A simplified expression for the length of the garage in terms of x is 2x-19.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given the width is x + 15, and the length is 49 less than 2 times the width. Therefore,  a simplified expression for the length of the garage in terms of x is,

Length = 2(x+15) - 49 = 2x + 30 - 49 = 2x-19

Hence,  a simplified expression for the length of the garage in terms of x is 2x-19.

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Using a linear function, it is found that the costs are given as follows:

A linear function is modeled by:

y = mx + b

In which:

Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:

C(r) = 20 + 4r.

Hence, for 6 rides, the cost is given by:

C(6) = 20 + 4 x 6 = $44.

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If quadrilateral JKLM were in third quadrant then the coordinates will be (-1,0),(-4,-1),(-4,-2)(-1,-2)

Given Quadrilateral JKLM is in fourth quadrant and coordinates (1,0),(4,-1),(4,-2)(1,-2)

We know that the coordinates of x used to negative in third quadrant and positive in fourth quadrant. Coordinates of y used to negative in third and fourth quadrant.

So in order to change the coordinates from fourth to third we need to change the coordinates of x axis to negative and the coordinates will be :

Coordinates of J will change from (1,0) to (-1,0)

Coordinates of  K will change from(4,-1) to (-4,-1)

Coordinates of L will change from (4,-2) to (-4,-2)

Coordinates of M will change from (1,-2) to (-1,-2).

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Coordinates are numerical lengths or angles that uniquely identify locations on two-dimension. The missing coordinates are coordinates 3 and 4.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

Location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ).

Mathematics, scientists, and engineers frequently employ a variety of coordinate systems.

Hence the missing coordinates are coordinates 3 and 4.

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Answer:

A

Step-by-step explanation:

First, simplify the numerator:

[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]

Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]

Finally, evaluate the denominator by multiplying them together.

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]

Simplify:

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]

And done! :)

The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

The given polynomial equation below is:

0 = 3x⁵ − x⁴ − 5x² + 1

3x⁵ − x⁴ − 5x² + 1 = 0

The given polynomial equation is a polynomial of degree 5.

The simplest method is to solve it graphically using a graphing program.

Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.

We may now locate the roots of the equation using the graph.

Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots

Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.

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Step-by-step explanation:

a=110. x,55

y=180-(x+75)=50

w,75

b,110

x,40

y,30

Shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

As given,

Shapes F and G are similar

Perimeter of shape F=180mm

Area of shape F=2196mm²

Perimeter of shape G=300mm

Let xmm²be the area of shape G

Square of ratio of perimeter of similar shape =Ratio of area of similar shape

⇒(180 /300)² =(2196/x)

⇒9/25=2196/x

⇒x=(2196×25)/9

⇒x=6100mm²

Therefore, shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

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Transformation involves changing the position and size of a shape.

The true statements are:

The complete question is as follows:-

The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).

The process of changing the location of the image on the coordinate system will be known as the translation.

The coordinates of the triangle are:

L =(-1,2)

M = (-1,-1)

N = ( 2,-1)

The transformation rule is given as:

do 0.75 (x,y) 2 (x,y)

The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.

Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:

∠l≅∠l''

∠m≅∠m''

∠n≅∠n''

Δlmn⇒Δl'm'n'

The above highlights mean that:

The angles of both triangles are congruent

The triangles are similar

Next, we apply the rule on the coordinates of the triangle

L'' = 0.75 x 2 x (-1,2)

L'' = ( -1.5,3)

M'' = 0.75 x 2 x (-1,-1)

M'' = ( -1.5 , -1.5)

N'' = 0.75 x 2 x (2,-1)

N'' = (3 , -1.5)

Hence, the true statements are: The coordinates of n" are.

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The significance of 160,000 in the function is the initial population at the time of the estimation.

The correct option is (C)

A collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Given:

As per the table attached below:

F(x) signify the total population when the time was x hour.

So,  160,000 in the function signifies that the population at starting i.e., initial point.

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Answer:

y = -x

Step-by-step explanation:

Breaking down the equation

[tex]y=e^x-x[/tex] can be written as [tex]y=e^x + (-x)[/tex], making it more clear that this function is composed of two functions:

asymptotes of the parts

The regular exponential function normally has an asymptote at y=0, a horizontal line because as "x" gets more and more negative, e^(x) gets closer and closer to zero (see blue graph).  This asymptotic behavior perhaps can be more easily understood by recognizing that [tex]e^{-x}[/tex] is equivalent to [tex]\dfrac{1}{e^x}[/tex], so that as the x values get more and more negative, it is effectively dividing 1 by a larger and larger number, thus getting closer and closer to zero.

In this situation, that exponential function is added to "-x", which is a linear function with a slope of negative 1.

As the left end of the exponential function gets closer and closer to zero, the exponential part contributes almost nothing to the sum, whereas as the "x" gets more and more negative, the linear function "-x" gets more and more positive (linearly).  Since the exponential piece adds almost nothing to it (when moving to the left), the combined function is essentially "-x" (although it is ever so slightly greater than it, just as it was ever so slightly greater than zero) (see pink graph, with dashed asymptote).

Clarifications

To be clear, on the right side of the graph, the exponential part of the function completely overwhelms the linear piece, and the function behaves much more like an exponential function, nearly completely masking the behavior of the linear piece.  Since an exponential function is unbounded, and the domain of both the exponential and linear functions are all real numbers, on the right side of the graph, there is no asymptotic behavior.

The simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical expression:

= 6543549² × 4³ ÷ 8

Using BODMAS

= 6543549² × 8

= 3.4254×10¹⁴

Thus, the simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴

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Answer:

f(4) = 5

Step-by-step explanation:

The notation used for a point is (x,y). The first number is the x and the second number is the y.

In function notation, you have f(x) = y.

The input number, x, is in the parenthesis beside the f. The output, y is all by itself on the other side of the equal sign.

For the point (4,5), 4 is the x so it goes by the f. 5 is the y so it goes by itself on the other side of the equal sign.

f(4) = 5

The solution is :  f(4) = 5, the equation must be true.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

The notation used for a point is (x,y).

The first number is the x and the second number is the y.

In function notation, you have f(x) = y.

The input number, x, is in the parenthesis beside the f. The output, y is all by itself on the other side of the equal sign.

For the point (4,5), 4 is the x so it goes by the f.

5 is the y so it goes by itself on the other side of the equal sign.

f(4) = 5

Hence, The solution is :  f(4) = 5, the  equation must be true.

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Answer:

AB and CD have the same midpoint, therefore they bisect each other.

Step-by-step explanation:

Find the midpoint of AB. Then, find the midpoint of CD. They are the same. The segments bisect each other. See image.

The height of the shorter cone is 6.81cm

A cone is hollow three-dimensional shape with side lengths that tappers from the base to a point at the vertex.

Analysis:

Let the radius of the first cone be = r

radius of shorter cone = R

height of first cone = h

height of shorter cone = H

if volume of the two cones are same

1/3π[tex]r^{2}[/tex]h = 1/3π[tex]R^{2}[/tex]H

[tex]r^{2}[/tex]h = [tex]R^{2}[/tex]H

H =  [tex]r^{2}[/tex]h /  [tex]R^{2}[/tex]

H = [tex](8.5)^{2}[/tex]x 10 / [tex](10.3)^{2}[/tex] = 6.81cm

In conclusion, the height of the shorter cone is 6.81cm

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The value of the variable x and y will be 1  2/3 and 4  2/3. Then the correct option is C.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = 4x − 2  ...1

y = x + 3    ...2

Subtract equation 1 from 2, then we have

 0 = 3x – 5

3x = 5

 x = 5/3

 x = 1  2/3

Then the value of y will be

y = 5/3 + 3

y = 14 / 3

y = 4  2/3

Then the correct option is C.

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Step-by-step explanation:

Given:

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

To find the x-intercepts set y to 0 and solve for x which is done below:

Therefore x-intercepts:(3,0),(-2,0)

To figure out the y-intercept , substitute 0 for x and simplify

Hence, The y-intercept is (0,-6)

(skipped the steps as you've already figured it out)

Likewise A:

X-intercepts:

Therefore,x-intercepts:(3,0),(-2,0)

Y-intercept:

⇒y=-0²+0+6

⇒y=6

Therefore, y-intercept (0,6)

The vertex:(0.5,6.25)

The difference between the two parabolas is that The blue parabola is the result of reflection over x-axis of the red one.

Answer:

a.

The x-intercepts are 3 and -2

The y-intercept is -6

The vertex is (1/2 , -25/4)

b.

The two parabola are symmetric across the x-axis

Step-by-step explanation:

x² - x - 6

[tex]=x^{2}-2\times \frac{x}{2} +\frac{1}{4} -\frac{1}{4}-6[/tex]

[tex]=(x-\frac{1}{2} )^{2} -(\frac{1}{4}+6)[/tex]

[tex]=(x-\frac{1}{2} )^{2} -\frac{25}{4}[/tex]

The x-intercepts :

(x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² - 0 - 6 = -6

b.

we notice that :

-x² + x + 6 = -(x² - x - 6)

Then

-x² + x + 6

[tex]=-(x-\frac{1}{2} )^{2} +\frac{25}{4}[/tex]

The x-intercepts :

[tex]-(x-\frac{1}{2} )^{2} +\frac{25}{4}=0[/tex]

⇔ (x-1/2)² = 25/4

Then

x - 1/2 = 5/2 or x - 1/2 = -5/2

Then

x = 3 or x = -2

The y-intercepts :

We get the y-intercept by replacing x by 0 in the trinomial :

0² + 0 + 6 = 6

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

baseline and height must be at a right angle with each other.

so, in our case

6 × 11 / 2 = 3 × 11 = 33 cm²

Answer:

Area = 33 cm²

Step-by-step explanation:

[tex]\textsf{Area of a triangle}=\sf \dfrac{1}{2}bh[/tex]

where:

If we turn the triangle counterclockwise, so that the side that measures 6 cm is the base, we will see that the length that measures 11 cm is the height of the triangle (see attached).

Therefore:

Substitute the found values into the formula and solve for A:

[tex]\implies \sf A=\dfrac{1}{2}(6)(11)[/tex]

[tex]\implies \sf A=\dfrac{1}{2}(66)[/tex]

[tex]\implies \sf A=33[/tex]

Therefore, the area of the triangle is 33 cm²

Answer:

x=y-p+q

Step-by-step explanation:

y=x+p-q

x=y-p+q

the answer I knew but I forgot at ate

Answer:

The choice A ;

[tex] \frac{1}{ {7}^{8} } [/tex]

Step-by-step explanation:

[tex] \frac{ {7}^{ - 6} }{ {7}^{2} } = \frac{ {7}^{ - 6 - 2} }{1} = {7}^{ - 8} = \frac{1}{ {7}^{8} } \\ \\ \\ or. \: \frac{ {7}^{ - 6} }{ {7}^{2} } = \frac{1}{ {7}^{ 2 + 6} } = \frac{1}{ {7}^{8} } [/tex]

Hii!

Answer:

Step-by-step explanation:

Use the rule of exponents.

If we divide two numbers with the same bases, we subtract the exponents.

7^-6/7^2=7^-6-2=7^-8

Now, if we have a negative exponent, we flip over the number.

7^-8=1/7^8

Great job!

—

Hope that this helped.

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

Assuming the dilation is centered at the origin, the scale factor is 1/3.

This means the coordinates of the point (8,4) are [tex]\boxed{\left(\frac{8}{3}, \frac{4}{3} \right)}[/tex]

Answer:

Hey, You don't need to buy supplies. Just use your at home!

Step-by-step explanation:

Brainlest?

Answer: Algebra: 3 sub. spiral notebook, pencil pouch to hold colored pencils and ... Algebra 2: 2 or 3 subject spiral notebook (can use folder instead of binder).

Step-by-step explanation:

An equation is formed of two equal expressions. The solution is (-9,-2).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the equation x + 3y = -15 and -3x + 2y = 23,

Step 1- Multiply the equations to make the coefficients match in either the x- or y-variable.

x + 3y = -15

3x + 9y = -45

Step2- After you multiply, add or subtract the two equations.

3x + 9y -3x + 2y = -45 + 23

Step 3- Then solve for the variables that is left.

11y = -22

y = -2

Step4- Substitute the value of y in any one of equations to solve for x.

x + 3(-2) = -15

x - 6 = -15

x = -9

Hence, The solution is (-9,-2).

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Answer:

oh soooooooooooooooo sorry

Step-by-step explanation:

sorry

Answer:

12.5N

Step-by-step explanation:

See attached image.

Answer:

The answer is tanx

Step-by-step explanation:

This is because, when you graph the trigonometric functions, which can be reresented as: a*(trig sign)*bx + K, the period of the function for sin, cos, csc, and sec are all 2pi divided by "b". However, the formula to find the function of tan or cot graphs is pi divided by b. And, since we don't see any values being multilied to the x in the choices, and we calculate the period for each of them, it concludes that tanx, has a period of pi