Make x the subject of y=3+2^x+1​

Answer:

To find the factored form of the polynomial function, we start by using the zeros to write out the factors of the polynomial. If the zeros are a, b, c, d, then the factors are (x-a), (x-b), (x-c), and (x-d).

In this case, the zeros are -1, -3, 3, and 1, so the factors are (x+1), (x+3), (x-3), and (x-1). Multiplying these factors together gives the polynomial function:

f(x) = (x+1)(x+3)(x-3)(x-1)

To simplify this expression, we can use the distributive property to expand the factors:

f(x) = (x+1)(x^2 - 9)(x-1)

Next, we can multiply the remaining factors using the distributive property and combining like terms:

f(x) = (x^3 - 8x - 9)(x-1)

Finally, we can use the distributive property again to expand the remaining factor:

f(x) = x^4 - 9x^2 + 8x + 9x^3 - 8x - 9

Simplifying this expression gives the factored form of the polynomial function:

f(x) = (x+1)(x+3)(x-3)(x-1) = x^4 - 9x^2 + 8x - 9x^3 - 8x - 9.

Answer:

Step-by-step explanation:

1,2,3,4,6,8,12,16,24,48

hope i helped

Answer:

y = (3/2)x + 17/2

Slope: 3/2

Step-by-step explanation:

y + 2 = 3/2 (x+7)

y + 2 = (3/2)x + 21/2

y = (3/2)x + 21/2 - 2

y = (3/2)x + 21/2 - 4/2

y = (3/2)x +17/2

The calculated value of the perimeter of triangle ABD is 48 units.

Given that

A(1, 1), B(17, 1) and D(17, 13)

To find the perimeter of triangle ABD, we need to find the lengths of its three sides and add them up.

We can use the distance formula to find the lengths of the sides.

The distance between points A and B is:

AB = √((17 - 1)^2 + (1 - 1)^2) = √(256) = 16

The distance between points B and D is:

BD = √((17 - 17)^2 + (13 - 1)^2) = √(144) = 12

The distance between points D and A is:

DA = √((1 - 17)^2 + (1 - 13)^2) = √(256 + 144) = √(400) = 20

Therefore, the perimeter of triangle ABD is:

AB + BD + DA = 16 + 12 + 20 = 48

So, the perimeter of triangle ABD is 48 units.

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None of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:

e. None of the above.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To check whether the relation is functional, we need to make sure that each x-value is associated with only one y-value.

We can see that the pairs (6,7), (-2,9), (8,8), and (-4,9) all have different x-values, and therefore are associated with different y-values. This means that the relation is currently functional.

To determine which ordered pair could not be substituted so that the relation is functional, we need to find an x-value that is associated with two different y-values.

Let's look at each of the answer choices and see if they fit this criteria:

a. (9,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

b. (2,9): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

c. (7,8): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

d. (8,3): This pair does not already appear in the relation, so it's possible that it could be added without affecting the functionality of the relation.

Since none of the answer choices would result in an x-value being associated with two different y-values, the correct answer is:

e. None of the above.

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The amount she charges for each necklace is $7.50 (option B).

Profit is the total difference between total revenue and total cost. Total cost is the sum of fixed cost and variable cost.

Profit = total revenue - total cost

Profit = (price x quantity sold) - (fixed cost + total variable cost)

Profit = (price x quantity sold) - (fixed cost +(variable cost per unit x quantity sold)

P = 7.5n - (2.25n + 15)

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The collection of all points in a plane that are equally spaced from a given point, referred to as the circle's center, is referred to as a circle. The radius of the circle is the distance measured from any point on the circle to its center.

A circle is described as the collection of all points on a plane that is at the same distance, or radius, from a fixed point known as the circle's center.

Every location inside the circle is, therefore, closer to the center point than the radius, and any point outside the circle is farther away from the center point than the radius.

Therefore, a circle is made up of points that are spaced out by a particular amount, known as the radius, from the circle's center.

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Answer:

x = 360°/8 = 45°

y = 2 × 45° = 90°

The arc length generated by a radius r is S = 11πr

The formula for arc length is given by:

S = θr

where θ is the central angle in radians and r is the radius of the circle.

For a full revolution, a radius r revolves around the center of the circle at an angle of 2 radians. Therefore, the central angle for 5 1/2 revolutions would be:

θ = (5 1/2) * 2π radians

θ = 11π radians

So, the arc length generated by a radius r rotating 5 1/2 revolutions is:

S = θr

S = 11πr

Note that if the radius is not given, then the arc length cannot be determined.

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The required value of z such that 0.6318 of the area lies between −z and z is 0.89.

If 0.6318 of the area lies between −z and z, then the area outside of this range is (1-0.6318) = 0.3682.

Since the normal distribution is symmetric, the area to the left of −z is equal to the area to the right of z. So, the area to the right of z is (0.3682 / 2) = 0.1841.

Using a standard normal distribution table, we can find the z-score corresponding to an area of 0.1841 to the right of z:

z = invNorm(0.1841) ≈ 0.89

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The measure of arc BC is 40⁰.

The measure of angle BPE is 50⁰.

The measure of angle BAD is 55⁰.

The measure of angle AOP is 110⁰.

The measure of angle AFB is 70⁰.

The value of arc DE is 110⁰.

The measure of each angle is calculated as follows;

if arc BA = arc CD, then value of arc BC is calculated as follows;

BA + CD + BC = 180 (sum of angles of a semi circle)

arc CD = 70 (intersecting chord theorem)

70 + 70 + BC = 180

140 + BC = 180

BC = 180 - 140

BC = 40

Arc AE = 70⁰, since angle EOF = 70 (vertical opposite angles)

Arc AB = 180 - (AE + BC)

arc AB = 180 - (70 + 40)

arc AB = 70⁰

The value of angle P is calculated as follows;

arc EB = 70 + 70 = 140⁰

m∠BPE = ¹/₂ (140 - 40)

m∠BPE = 50⁰

m∠BAD = ¹/₂ (BC + CD) (intersecting chord theorem)

m∠BAD = ¹/₂ (40 + 70)

m∠BAD = 55⁰

m∠AOP =  (AB + BC) (intersecting chord theorem)

m∠AOP = (70 + 40)

m∠AOP = 110⁰

m∠AFB = (AB) (intersecting chord theorem)

m∠AFB = 70⁰

The value of arc DE is calculated as follows;

DE = 360 - (180 + CD) (sum of angles of a circle)

DE = 360 - (180 + 70)

DE = 360 - 250

DE = 110⁰

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The solutions are explained in the solution below.

1) t³ = 216

t = ∛216

t = ∛6×6×6

t = 6

2) a² = 15

a = √15

a = 3.87

3) m³ = 8

m = ∛8

m = ∛2×2×2

m = 2

4) c³ = 343

c = ∛343

c = ∛7×7×7

c = 7

e) f³ = 181

f = ∛181

f = 5.65

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We can see here that the best representation of the possible range of values for the third side, s is: 2 < s < 18.

An acute triangle is a type of triangle where all three angles are acute angles, meaning they are less than 90 degrees. In other words, an acute triangle is a triangle with all three angles being sharp or narrow.

The best representation of the possible range of values for the third side, s, can be determined using the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have two sides measuring 8 cm and 10 cm. Let's call the third side "s". Using the Triangle Inequality Theorem, we can write:

8 + 10 > s

18 > s and

8 + s > 10

s > 2

and

10 + s > 8

s > -2 (since a length cannot be negative)

Therefore, we know that s must be greater than 2 and less than 18.

The best representation of the possible range of values for s is: 2 < s < 18

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To find the simple interest earned on an investment, we use the formula:

I = P * r * t

Where:

I = simple interest earned

P = principal amount invested

r = annual interest rate (as a decimal)

t = time period of investment (in years)

In this case, we have:

P = $9,900

r = 7.8% = 0.078 (since the rate is given as an annual rate, we need to divide by 100 to get the decimal equivalent)

t = 24 months / 12 months/year = 2 years

Substituting these values into the formula, we get:

I = 9,900 * 0.078 * 2

= $1,545.60

Therefore, the simple interest earned on the investment is $1,545.60.

Yes, [tex]T(x_1,x_2,x_3)=(x_1+x_3,2x_2-x_3)[/tex] is a linear transformation.

A linear map is a mapping V to W between two vector spaces in mathematics, more specifically in linear algebra, that keeps the operations of vector addition and scalar multiplication. The more broader example of modules over a ring also uses the same terminology and definition are Module homomorphism.

The maps between algebraic objects are known as homomorphisms. Group homomorphisms and ring homomorphisms are the two basic categories. In Other words ,homomorphisms of modules, algebras, and vector space homomorphisms, which are also known as linear maps.

Two properties must be satisfied  if  T is a linear transformation:

T(x+ y)  = T(x) + T(y) for any x, y in [tex]R^3.[/tex]

homogeneity is T(ax) = a T(x). For all scalars a and x in [tex]R^3.[/tex].

let a consider

L.H.S,T(x+y)= T[tex]((x_1+y_1),(x_2+y_2),(x_3+y_3[/tex]))= [tex](x_1+y_1+x_3+y_3, 2x_2+2y_2-x_3)[/tex]

R.H.S. T(x) + T(y) =[tex](x_1+x_3, 2x_2-x_3) +(y_1+y_3, 2y_2-y_3) =(x_1+y_1+x_3+y_3, 2x_2+2y_2-y_3).[/tex]

L.H.S.=R.H.S.

So,The first property is satisfied i.e. T(x+ y)  = T(x) + T(y) for any x, y in [tex]R^3.[/tex]

For homogeneity,

let a consider ,

L.H.S. T(ax) = T[tex](ax_1,ax_2,ax_3) = (ax_1+ax_3, 2ax_2-ax_3).[/tex]

R.H.S. a T(x) = a T[tex](x_1,x_2,x_3) = a(x_1+x_3, 2x_2-x_3) = (ax_1+ax_3, 2ax_2-ax_3).[/tex]

L.H.S.=R.H.S.

So, T(ax) = a T(x). for all scalars a and all vectors x in  [tex]R^3.[/tex].are satisfied

A linear transformation from [tex]R^3[/tex]to[tex]R^2[/tex]  . is therefore represented by T.

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Answer:

A) 150%

B) 20.67 J

Step-by-step explanation:

A) To determine the efficiency of the engine, we can use the formula:

efficiency = (work output / heat input) x 100%

In this case, the engine does 62 J of work each cycle, so the work output is 62 J. We're also given that the engine absorbs 2 times as much heat as it discharges to the environment, so we can express the heat input as 2 times the heat discharged:

heat input = 2 x heat discharged

Therefore, we can rewrite the efficiency formula as:

efficiency = (62 J / (2 x heat discharged)) x 100%

Simplifying this expression, we get:

efficiency = 31 J / heat discharged

Now we need to determine the value of heat discharged. We know that the engine absorbs 2 times as much heat as it discharges, so the net heat input is 3 times the heat discharged:

net heat input = heat input - heat discharged = 2 x heat discharged - heat discharged = heat discharged

Therefore, we can express the net heat input as:

net heat input = 3 x heat discharged

Now we can use the first law of thermodynamics, which states that the net heat input is equal to the work output plus the heat discharged:

net heat input = work output + heat discharged

Substituting the given values, we get:

3 x heat discharged = 62 J + heat discharged

Solving for heat discharged, we get:

heat discharged = 20.67 J

Now we can calculate the efficiency:

efficiency = 31 J / 20.67 J = 1.50 or 150%

Therefore, the efficiency of the engine is 150%.

B) To determine the quantity of heat discharged to the environment each cycle in Joules, we can use the value we calculated above for heat discharged:

heat discharged = 20.67 J

Therefore, the quantity of heat discharged to the environment each cycle is 20.67 J.

Hope this helps!

Ian earned $500 in simple annual interest after 10 years, while Jackson earned $1,128.89 more in interest than Ian after 10 years due to compound interest.

Ian's account earns simple annual interest, which means that he earns 5% interest on his initial deposit every year. After 10 years, he will have earned

interest = principal x rate x time

interest = 1000 x 0.05 x 10

interest = $500

Jackson's account earns interest that is compounded annually, which means that he earns 5% interest on his initial deposit plus any interest that has already been earned every year. After 10 years, he will have earned

[tex]balance = principal x (1 + rate)^{time}[/tex]

balance = 1000 x (1 + 0.05)¹⁰

balance = $1,628.89

To find out how much more interest Jackson earned than Ian, we need to subtract the interest Ian earned from the balance in Jackson's account

$1,628.89 - $500 = $1,128.89

Therefore, Jackson earned $1,128.89 more in interest than Ian after 10 years.

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The coordinates of the vertices of rectangle are (-3,3),(6,3),(6,-3), (-3,-2).  the rectangle is 9 units long and 5 units wide.

In mathematics and computer science, a graph is a collection of vertices (also called nodes) and edges that connect pairs of vertices. Graphs are used to represent various types of relationships between objects, such as social networks, road networks, electrical circuits, and many others.

Vertices in a graph are typically represented by circles or points, while edges are represented by lines or arcs that connect pairs of vertices. A graph can be directed, where each edge has a direction, or undirected, where edges have no direction.

The coordinates of the vertices of rectangle are (-3,3),(6,3),(6,-3), (-3,-2).

To find the length and width of the rectangle, we need to determine the distance between the points on the x and y axes.

The length of the rectangle is the distance between points (-3,3) and (6,3) on the x-axis:

Length = 6 - (-3) = 9 units

The width of the rectangle is the distance between points (-3,3) and (-3,-2) on the y-axis:

Width = 3 - (-2) = 5 units

Therefore, the rectangle is 9 units long and 5 units wide.

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The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points .

A circle is a closed shape made up of all elements in a plane that are indistinguishable from a predetermined point known as the centre. The radius (r) of a circle is the separation between the circle's centre and any other point on the circumference.

given

These procedures can be used to graph the circle :

Determine the circle's centre. The point in this instance serves as the centre (5, 6).

Determine the circle's radius. The circle's diameter is 4/2, or two.

Place the circle's centre on the coordinate plane.

Plot points that are 2 units distant from the centre in all directions to form the circle.

The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points, and the points (5, 4) and (5, 8) are two points on the circle's y-axis.

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It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, 9) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x = -1.

In Mathematics and Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided, the vertex is located at point (2, 0), and this ultimately implies that the axis is represented by the vertical line x = 2 that passes through the vertex.

Additionally, the parabola would be bilaterally symmetric about the above axis, and the mirror image of the point (5, 9) would also be on this parabola.

Therefore, the mirror image would have the same y-coordinate of 9 while the x-coordinate is given by:

x = 2 - (5 -2)

x = -1.

In conclusion, the required point is (-1, 9).

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Complete Question:

The graph of a quadratic function has a vertex (2, 0). One point on the graph is (5, 9). Explain how to find another point on the graph. It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, _) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x=

Because the sine of angle ACB = 3/5, then the sine of angle ANM will be equal to 3/5 too.

A triangle is a shape with 3 sides. There are 3 types of triangle which are:

From the diagram, we can see that we have a small triangle inside a big triangle. From the principle of triangle, the angle C is equal to angle N.

Let us say angle C is 30° then the angle N will also be equal to 30*. Therefore the angle ACB = angle ANM = 3/5

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The total amount that Meihua pays for the 36 pencils is  9M - 36n

We know that a set of 4 pencils has a price M, then the price of each single pencil is:

P = M/4

And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:

P = M/4 - n

Now we know that she buys 36 of these, so the amount that she pays is given by the product:

amount  = 36*(M/4 - n)

amount = 9M - 36n

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Step-by-step explanation:

x^2 -6x - 72   =  ( x-12)(x+6)

If you can't do this 'in your head'  you can always use Quadratic Formula

  with  a = 1      b= - 6    and   c= -72

      to find roots   x = 12 and  -6      then write the equation as above

Answer: D

Step-by-step explanation:

Answer: #1

Step-by-step explanation:

In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]

Answer:

Linear relationship always produces a straight line and are without exponential.

2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

Step-by-step explanation:

Hope this helps! =D

The estimated value of the expression [tex]6/5/8 - 2/3/8[/tex] is approximately [tex]0.5082[/tex].

In Mathematics, fractions are defined as the parts of a whole. The whole can be an object or a group of objects

To estimate 6/5/8 - 2/3/8, we can convert the fractions to decimals and then perform the subtraction.

6/5/8 is equivalent to 6 ÷ 5.8, which is approximately 1.0345. 2/3/8 is equivalent to 2 ÷ 3.8, which is approximately 0.5263.

Therefore, 6/5/8 - 2/3/8 is approximately 1.0345 - 0.5263 = 0.5082.

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Answer:

160

Step-by-step explanation:

9 x 18 = 162

Since the last number is not 5 and is lower it rounds down to 160.

The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. The input values are often called the independent variable, while the output values are called the dependent variable. Functions are commonly denoted using functional notation, such as f(x), where x is the input and f(x) is the output. Functions are used to describe relationships between variables, such as in algebraic expressions or equations. They can take many forms, including linear, quadratic, polynomial, exponential, trigonometric, and logarithmic functions. Functions are fundamental to many areas of mathematics, science, engineering, and economics, and have many applications in real-world situations.

Here,

A. The function 2x+y=10 is not a linear function because it is not in the form of y=mx+b, where m and b are constants. In other words, the function is not a straight line, because y is not directly proportional to x. Instead, it is a linear equation in two variables x and y, where the graph of the equation is a straight line.

B. The function f(x) = 4x² is not a linear function because it does not have a constant rate of change. In a linear function, the rate of change of the function (slope) is always constant, meaning that for any two points on the line, the change in y over the change in x is always the same. However, in this case, the rate of change of the function depends on the value of x, and thus the graph of the function is not a straight line. Instead, it is a quadratic function, where the graph is a parabola.

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