Translate the following sentence into an equation using n to represent the unknown number. Then solve the equation for n.
six more than twice a number is 16

Answer:

x^4 - 2x^3 - 29x^2 - 42x

Step-by-step explanation:

Equal all the zeros to x then move them over.

x=7,x=-3,x=0,x=-2

x-7,x+3,x+0,x+2

Then multiply each factor

(x-7)(x+3)(x)(x+2)

x^4 - 2x^3 - 29x^2 - 42x

The piecewise function for f(x) is f(x) = x - 2, x ≥ 2; -x + 2, x < 2, So the correct answer is option C.

In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element of another set (called the range). Functions are a fundamental concept in mathematics and are used to describe relationships between variables, as well as to model and solve a wide range of mathematical problems.

A function is typically denoted using a letter such as "f", and is defined by an equation or formula that specifies how the input (or domain) values are transformed into output (or range) values. For example, the function "f(x) = 2x + 1" assigns each input value "x" to an output value equal to twice the input value plus one.

The absolute value function f(x) = |x - 2| can be written as a piecewise function by separating it into two cases:

Case 1: x - 2 ≥ 0 or x ≥ 2

In this case, the expression inside the absolute value bars becomes x - 2, so f(x) = x - 2.

Case 2: x - 2 < 0 or x < 2

In this case, the expression inside the absolute value bars becomes -(x - 2) = -x + 2, so f(x) = -x + 2.

Therefore, the piecewise function for f(x) is:

f(x) =

x - 2, x ≥ 2

-x + 2, x < 2

So the correct answer is option C.

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Answer: Hope this helps ;)

Step-by-step explanation:

Answer =

Equations:

Quantity Eq. : h + c = 375

Quantity Eq. : c = 3h

----------------------------

Substitute to solve for "h":

h + 2h = 375

3h = 375

h =  125 (# of hamburgers)

----------

Substitute to solve for "c":

125 + c = 375

c = 250 (# of cheeseburgers)

Answer:

$1

Step-by-step explanation:

If you have x dimes, you have 8x nickels.

So, this means x + 8x = 18.

This means you have 2 dimes and 16 nickels, which have a combined value of 2(0.10)+16(0.05)=$1.

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 2x² + x - 3

The rate of change of the function for the interval between 0 to 2 is calculated as,

Average rate = [f(2) - f(0)] / [2 - 0]

Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2

Average rate = 10 / 2

Average rate = 5

The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.

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Answer:

38 remander 8

Step-by-step explanation:

Answer:

the answer is D just did the quiz hope this helps!!!!!

Step-by-step explanation:

b)

We need to find the equation when the population increases by 2 percent a year.

Then, the equation must be an exponential function:

The population increases by 5% = 0.05 year

Hence, p= initial value + (1 + 0.05)^t

Replacing the values:

If circle with center N with m∠MNP=124 ∘ and MN=13,  the area of sector MNP is approximately equal to 194.86 square units.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360°) x πr²

Where r is the radius of the circle.

In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:

Area of sector = (124/360) x π(13)²

Area of sector ≈ 194.86

Therefore, the area of sector MNP is approximately equal to 194.86 square units.

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Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

Plants have chlorophyll and can produce it on their own, whereas fungi must obtain their nutrition from other living things. Because of this, there are significant differences between plants and fungus.

Multicellular eukaryotic heterotrophic (unable to create their own food) organisms that play key roles in the nutrient cycle in ecosystems are members of the kingdom of fungi (plural: fungus).

Plants reproduce through seeds and pollen while fungi do so through spores. Plants have roots, stalks, and leaves. Fungi only contain the filaments that attach to the host. Plants are the producers and fungi are the decomposers in the eco system. Cellulose makes up the walls of plant cells, whereas chitin makes up the walls of fungal cells.

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Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer:

Step-by-step explanation:

The formula for determining the surface area of a cuboid or box is expressed as

Surface area = 2lw + 2lh + 2wh

Where l, w and h represents length, width and height of the box respectively.

2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,

Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².

The cost would be

0.25 × 47 = $11.75

Therefore,

Yes, she should have only added the area of five of the six faces.

Answer:

its A

Step-by-step explanation:

The solution of expression 3(x+4)(x+1)/(x+2)(x-2) at x=4 is 10.

An expression is a combination of numbers, symbols, variables, indeterminates, function. It is usually not present in equal to form. It expresses some relationship between variables.

The expression which is given as 3(x+4)(x+1)/(x+2)(x-2) and we have to find the value at x=4.

To find the value of expression at x=4 we have to put the value of x=4 in the expression.

at x=4, 3(4+4)(4+1)/(4+2)(4-2)

=(3*8*5)/6*2

=120/12

=10

Hence the value of expression 3(x+4)(x+1)/(x+2)(x-2) at x=4 is 10.

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Given the following question:

Check = $60.67

Ari wants to leave a 20% tip

To find the answer we have to find 20% of $60.67

The tip is $12.13

The total cost = tip + check

The total costs = $72.8

Answer:

V = l x w x h

V = 2m x 1.5m x  1m

V = 3 cubic meter

The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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Answer:

Since the slope is undefined, this is a vertical line. Vertical lines have no y-intercept. No y-intercept.

Step-by-step explanation:

hope this helped:)

Answer:

To write the equation of a line in slope-intercept form, we need to first find the slope of the line. The slope is a measure of the steepness of the line, and is calculated as the rise over the run between two points on the line. In this case, we can use the points (-6,-3) and (6,-7) to calculate the slope.

To find the slope, we first need to find the difference between the y-coordinates of the two points, which is -3 - (-7) = 4. We then need to find the difference between the x-coordinates of the two points, which is 6 - (-6) = 12. The slope is then calculated as the rise over the run, which is 4/12 = 1/3.

Once we have the slope, we can use the point-slope formula to write the equation of the line in slope-intercept form. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, we can use the point (-6,-3) and the slope 1/3 to write the equation of the line.

The equation of the line in slope-intercept form is then y - (-3) = 1/3(x - (-6)), which simplifies to y + 3 = 1/3x + 2. This is the equation of the line that passes through the points (-6,-3) and (6,-7) in slope-intercept form.

Therefore, the correct answer is y + 3 = 1/3x + 2.

Step-by-step explanation:

Answer:it’s the same distance traveled each way

Step-by-step explanation:

U go 5 steps to 5 and you go 5 steps to -5. Since it doesn’t ask HOW you r walking and only about the distance then they r both the dame

We want to find the value of x and y that satisfy both equations:

2x + 3y = 7

x + y = 3

We are going to solve it using the Elimination Method.

We want to find an equation with only one variable based on both given equations.

We are going to add both sides of them.

In that addition we want that the term with x is 0.

In order to do it we transform the second equation multiplying it by -2, because

2x - 2x = 0x

Step 1: transforming the second equation

We multiply both sides of the second equation by -2:

x + y = 3

↓

-2(x + y) = -2 · 3

↓ since -2(x + y) = -2x - 2y and -2 · 3 = -6

-2x - 2y = -6

Then we have the equations:

2x + 3y = 7

x + y = 3

↓

2x + 3y = 7

-2x - 2y = -6

Step 2: adding both equations

Now we add each side of both equations:

2x + 3y = 7

-2x - 2y = -6

_________

0x + 1y = 1

Then, simplifying the result:

y = 1

Step 3: finding x value

We replace y by 1 on any of both original equations:

x + y = 3

↓ since y = 1

x + 1 = 3

↓ taking 1 to the right side

x = 3 - 1

x = 2

Step 4: ordered pair

In an ordered pair we wirte first the x value and then the y value:

(x, y)

↓

(2, 1)

The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.

Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;

y^ = 180.8 + 15.2x

Now, for 2 tablespoons of sugar , we have x = 2. Thus;

y^ = 180.8 + 15.2(2)

y^ = 212.4 hours

Residual for 204 hours is;

Residual = 204 - 212.4 = -8.4 hours

Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

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Complete question is;

Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.

Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.

Answer:

The kinetic energy will increase.

Step-by-step explanation:

1/2*80*9=360J .After the acceleration, it will increase to 1/2*80*36=1440J

Answer:

Less than 1

1/2=6/12

6/12+5/12=11/12

11/12<1

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Make it brainliest ty

Answer:

w = 18

Step-by-step explanation:

Step 0: Set up the equation

=> -3w - 4 + 5w = 32

Step 1: Move the same variable together

=> -3w + 5w = 32 + 4

Step 2: Add up and simplify

=> 2w = 36

Step 3: Divide both by 2

=> w = 18

Answer:

W=18

Step-by-step explanation:

-3w-4+5w=32

-3w+5w-4=32

2w-4=32

2w=32+4

2w=36

W=18

The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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Answer:

  (c)  Factor

Step-by-step explanation:

The constituents of a product are its factors.

Dividing a product by one of its factors will not leave a remainder.

__

A term is a constant or product of one or more variables and a constant. For example, -4 and 24xy are both terms.

A multiple is a product with one factor being an integer. For example, 3×1.5 = 4.5 is a multiple of 1.5.

A variable is a symbol for an unknown value. Commonly, a variable is a single letter, but may also be a blank (__) or a question mark (?). Sometimes a word or phrase is used as a variable. For example, ...

  3 + x = 5

  3 + __ = 5

  3 + ? = 5

  3 + (some number) = 5

Answer:

7. -21-15g

8. x+3y+7

Step-by-step explanation:

use multiplication for number 7

number 8 is just rearranging the numbers

number 9 is confusing since i don't know if it's a point or another symbol