#9: A college student's bank account is losing the same amount of
money each week since the beginning of the semester according to
the table shown below. Determine the equation of the function that
inputs the number of weeks since the beginning of the semester and
outputs the money in his bank account.
On Number 10, fill in the missing values on the table.
(Use the variables "m" and "w")

The graph of the exponential function y = (3/4)^x is given by the following option:

Option A.

The general format of an exponential function is defined as follows:

[tex]y = ab^x[/tex]

The meaning of the parameters a and b are given as follows:

In this problem, the function is given by:

y = (3/4)^x.

Hence the values of the parameters are:

a = 1, b = 3/4.

The parameter a = 1 means that the function crosses the y-axis at y = 1, hence options B and C are removed.

From the table given in the problem, at x = -2 the function is very close to 2, while it decreases to a value close to 0.5 at x = 2, hence option A is the correct option for the graph of the exponential function.

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The complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

From the question, we have the following equation:

f(x) = 3ˣ

From the table of values, we have the following x values

x = -2, -1, 0, 1 and 2

Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ

When x = -2

f(-2) = 3⁻² = 1/9

When x = -1

f(-1) = 3⁻¹ = 1/3

When x = 0

f(-1) = 3⁰ = 1

When x = 1

f(1) = 3¹ = 3

When x = 2

f(2) = 3² = 9

Hence, the complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

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The slope of line q is 3/7

The equation of line p is y=3/7x+9

The standard form of equation of a line is

y = mx + c

where m represents the slope of the line

Upon comparing the standard form with the given equation

y = 3/7 x + 9

we get that the slope of this line is 3/7

and the y intercept c is 9

When two lines are parallel to each other, then the slope of both the lines are same.

the slope of line q is same as the slope of line p as line q is parallel to line p

the slope of line q is 3/7

Therefore,  the slope of line q is 3/7

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In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of every binomial formula, such as (x + y)ⁿ.

Although it is much older, it bears the name of the French scholar Blaise Pascal from the 17th century. In the eleventh century, the Chinese mathematician Jia Xian created a triangular form for the coefficients.

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The slope of the line r is 3 and the y intercept is (0,15) .

We know that coordinates of the point (x,y) after dilation by factor k centered at (a,b) is  (k(x-a) + a , k(y-b) + b)  .

In the question ,

it is given that

the slope of the line p [tex]=[/tex] 3

and the intercept of the line p = (0,2)

So , the equation of the line p is y = 3x + 2 .

So , the coordinates of the point (0,2) after dilation by factor 3 centered at (0,0) is (3(0 - 0) + 0 , 3(5 - 0) + 0)

= (0 , 15)

Point (0,0) does not lie on the line, so the line r after dilation is parallel to the line p,

the slope of line r = 3 , the y intercept is 15 .

Therefore , The slope of the line r is 3 and the y intercept is (0,15) .

The given question is incomplete , the complete question is

In the coordinate plane, line p has slope 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r ?

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Keeping it short.

Differentiate each term with respect to [tex]x[/tex], then solve for [tex]y'.[/tex]

[tex]\frac{dy}{dx} =12\sin^3(3x)\text{cos}(3x)[/tex]

Thanks.

When the perimeter of the rectangle is 70 in, the length and width are 19 and 16 inches.

It should be noted that the perimeter of a rectangle will be calculated as:

= 2(Length + Width)

In this case, the length of a rectangle is 3in longer than it’s width and the perimeter of the rectangle is 70 in.

Therefore, width = w

length = w + 3

The perimeter will be:

2(w + w + 3) = 70

2(2w + 3) = 70

4w + 6 = 70

Collect like terms

4w = 70 - 6

4w = 64

Divide

w = 64 / 4

w = 16

Width = 16 inches

Length = w + 3 = 16 + 3 = 19 inches.

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Complete question

The length of a rectangle is 3in longer than it’s width. If the perimeter of the rectangle is 70 in, find the length and width.

Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.

The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²

f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of  .f(x) =x²-2x+1

Rewrite the given function f(x).

f(x) =  (x-1)²

Now, the graph is stretched vertically by a factor of 2.

= 2(-x-1)²

reflect the graph about the y-axis.

2(x+1)²

move to the left by 3 units.

= 2(x+3+1)²

=2(x+4)²

The function g(x) =2(x+4)²

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The price bid will be increased by 23% over the cost, according to the question.

What do you mean by percentage?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

According to data in the given question,

We have given data:

Cost on the product you make is $112 per unit.

Bid amount $138 per unit,

Cost over the bid= $138-$112 = $26

Now, we need to determine the Percentage increase,

Percentage increase[tex]= \frac{26}{112}*100 \\[/tex]

= 23%

Therefore, the price bid will be increased by 23% over the cost.

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Answer:

1,11,21,31,41,51,61,71,81,91,101..

Step-by-step explanation:

The distance between David's home and the airport is 210 miles.

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by 350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

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Answer:

e

Step-by-step explanation:

e is already irrational so if multiplied by 1/2 it will stay irrational

Answer:

y = 2x we need to solve when x= -3. Using elimination, we can solve this system of equations like this:

y = 2x

x = -3

*2  *2

simplify

y = 2x

-6 = 2x

subtract

y+6=0

-6    -6

y=-6

So, when x=-3, y=-6

Answer:

b² +5b + 4 = 0

b² + 5b -41= 5.702

3

Step-by-step explanation:

 1.1     Factoring  b2+5b-4 

The first term is,  b2  its coefficient is  1 .

The middle term is,  +5b  its coefficient is  5 .

The last term, "the constant", is  -4 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -4 = -4 

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   5 .

     -4   +   1   =   -3     -2   +   2   =   0     -1   +   4   =   3

The mass of the solid copper is 1479 g.

According to the question,

We have the following information:

The density of copper is 9.86 g/[tex]cm^{3}[/tex].

Measurements of the solid copper cuboid = 10 cm, 3 cm and 5 cm

We know that the following formula is used to find the volume of cuboid:

Volume = length*breadth*height

Volume = 10*3*5

Volume = 150 [tex]cm^{3}[/tex]

Now, we know that the following formula is used to find the density of an object:

Density = mass/volume

9.86 = mass/150

Using the cross multiplication method:

Mass = 150*9.86

Mass = 1479 g

Hence, the mass of the solid copper is 1479 g.

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After converting into a linear equation, we have the equation y = -3x

What is a linear equation?

A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.

Solution Explained:

From the question, we have
x = -1
y = 3
slope (m) = -3

Substituting these values in the equation,

y = mx + c

3 = (-3) x -1 + c

After simplyfing the equation, we get

c = 0

We again substitute the value of m and c in the equation,

y = mx + c

y = -3x + 0

y = -3x

Hence, the linear equation is y = -3x.

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The amount of money that is needed to pay after 5 years is 12762.9  .

In the question ,

it is given that ,

the amount borrowed(P) = $10000

the rate at which the amount is borrowed (r) = 5% = 0.05

the time for which the amount is borrowed (t) = 5 years

the number of times the interest is charge (n)  = 1 .

The final amount for the compound interest is calculated using the formula .

Amount = [tex]P\times(1+\frac{r}{n})^{nt}[/tex]

Substituting the value of P , r , n and t , in the formula ,

we get

Amount = 10000 (1 + 0.05)⁵

= 10000*(1.05)⁵

= (10000)*(1.2762815625)

= 12,762.815625

≈ 12762.9

Therefore , The amount of money that is needed to pay after 5 years is 12762.9  .

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Answer:

y - 1 = 6(x+7)

Step-by-step explanation:

point slope form is  y-y₁=m(x-x₁)

given m = 6 and the point is (-7,1)

plug in your values

remember that an ordered pair is (x,y)

y-y₁=m(x-x₁) ----> y-1 = 6(x+7)...............just plug in values

Sugar will i need to make enough cookies to feed my whole class is 11 cups.

Given:

A recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class.

2/3 cup of sugar = 3/4 of my class

Multiply by 12 on both sides

2*12/3 = 3*12/4

24/3 = 36/4

8 cups of sugar = 9 of my class.

if 3/4 = 9 whole class = 12.a

Add plus 3 on both sides

8 + 3 = 9 + 3

11 cups of sugar = 12 of my class.

Therefore Sugar will i need to make enough cookies to feed my whole class is 11 cups.

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The table of values on the given graph is for the polynomial y = -x+4.

The example we are using is a polynomial in one variable. It is to be represented graphically. The graph for it is given below.

From this graph, we can clearly see the coordinates of all points we have taken. In order to make the table of values, we need to find the x and y intercepts.

We see that the first point from the left is aligned to the -2 on the x-axis and to the 6 on the y-axis. Similarly, we can identify the following values from the given graph.

x = -2 and y = 6

x = -1 and y = 5

x = 0 and y = 4

x = 1 and y = 3

x = 2 and y = 2

This is the table of values that we found out through the graph.

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Yes, quadrilateral ABCD is a parallelogram.

What are the properties of parallelogram?

A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another.

Properties:

1. Opposite sides are congruent.

2. Opposite angels are congruent.

3. Consecutive angles are supplementary.

4. If one angle is right, then all angles are right.

5. The diagonals of a parallelogram bisect each other.

6. Each diagonal of a parallelogram separates it into two congruent

It is given that the coordinates of the vertices of quadrilateral ABCD are A (8, -3), B(-2, 1), C (-4,-4), and D(6, -8).

According to distance formula,

If A(a,b) and B(x,y) are two coordinates then

AB = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}}[/tex]

Now, using this distance formula in quadrilateral ABCD

AB = [tex]\sqrt{(-2-8)^{2}+(1+3)^{2}}= \sqrt{(-10)^{2}+(4)^{2}}=\sqrt{100+16}=\sqrt{116}[/tex]

CD = [tex]\sqrt{(6+4)^{2}+(-8+4)^{2}}=\sqrt{10^2+(-4)^2}=\sqrt{100+16}=\sqrt{116}[/tex]

Now, If we have two coordinates A(a,b) and B(x,y) then

Slope of AB = [tex]\frac{y-b}{x-a}[/tex]

Using this formula , finding slope of AB and CD of quadrilateral ABCD we get ,

Slope of AB = [tex]\frac{1+3}{-2-8}=\frac{4}{-10}=\frac{2}{-5}[/tex]

Slope of CD = [tex]\frac{-8+4}{6+4}=\frac{-4}{10}=\frac{-2}{5}[/tex]

As slope of both AB and CD is equal therefore, we can say that AB and CD are parallel.

As AB = CD and AB is parallel to Cd Therefore, ABCD is a parallelogram as opposite sides of parallelogram are equal and parallel.

Hence, quadrilateral ABCD is a parallelogram.

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The first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.

What is slope of the line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.

From the given table the points are, (0, 5) and (4, 9).

Since, for points [tex](x_1, y_1), (x_2, y_2)[/tex] the slope can be defined as,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex](x_1, y_1)=(0, 5)\\(x_2, y_2)=(4, 9)[/tex]

So, the slope is

[tex]m = \frac{9-5}{4-0}[/tex]

This is the first expression.

Therefore, the first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.

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Answer:

4.7x²

Step-by-step explanation:

3.7x² + x² = 3.7x² + 1x² = 4.7x²

Answer: 84m

Step-by-step explanation:

If one of the perimeters are 2m longer than the other that means on side can be expressed as x and the other expressed as x+2

So the equation for the area is [tex]x^{2} \\[/tex]+2x

Becasue the shaded area has an gap of in it we need to find the area of the gap to find the total area of the square

0.5x3x4=6

114+6

So the total area is 120

So we can use the area equation from before to figure out x

120=[tex]x^{2} \\[/tex]+2x

0=[tex]x^{2} \\[/tex]+2x-120

0=(x-10)(x+12)

Since its a measurement x must equal 10

Now we know that one side is 20m and the other is 22m

So the perimetre must be 84

Answer:

Step-by-step explanation:

. = 12\0.75

. = 16

Answer:

16

Step-by-step explanation:

12÷[tex]\frac{3}{4}[/tex] = [tex]\frac{12}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{48}{3}[/tex] = 16

The approximate area of the regular pentagon is 342cm²

Using the Pythagorean theorem, we can calculate the apothem of the pentagon.

We have then:

a = √(12² - (14.1/2)²)

a = 9.7

Then, the area of the pentagon is given by:

Area = 5 (1/2) x l x a

Where,

L: side of the pentagon

a: apotema

Substituting values:

area = 5(1/2) x 14.1 x 9.7

area = 341.925 cm²

Rounding the nearest whole we have: 342 cm²

Hence, the approximate area of the regular pentagon is 342cm²

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Answer: y < 3 - 2x

Step-by-step explanation:

6x + 3y < 9

3y < 9 - 6x (after subtracting both sides by 6x)

y < 3 - 2x (after dividing both sides by 3)

Answer: how do you do the question what the

Step-by-step explanation: