Last week, the price of apples at the grocery store was $1.75 per pound This week, the price has decreased by 20%. What are the prices of apples this week?

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:

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

The term prime factorization refers to any number represented as the product of its prime factors.

For instance, the prime factors that make up the number 60 are listed as follows:

60=2×3×2×2×5

The idea behind prime factorization is to divide the provided whole numbers into their prime factors in order to find the largest common factor and least common multiple of each number.

Procedures for using prime factorization to find the greatest common factor (G.C.F.)

The given numbers should be written as their prime factors.

To find the G.C.F., multiply each of the given numbers by the product of the discovered common factors.

For instance, using the formula below, one may get the largest or greatest common factor between the values 50 and 20.

50 = 2 x 5 x 5

20 = 2 x 2 x 5

The highest common factor is found by multiplying the common prime factors of 50 and 20.

G.C.F = 2 x 5

The greatest common factor of the supplied numbers can then be computed using prime factorization.

Following these steps will help you use prime factorization to find the LCM:

In the form of their prime factors, write the given numbers.

Take the product of the numbers' rare prime factors and discovered common prime factors.

For instance, using prime factorization, the least common multiple of the numbers 50 and 20 can be calculated as follows:

Separately write the prime factors of 50 and 20.

50 = 2 x 5 x 5

20 = 2 x 2 x 5

Multiply the resulting common prime factors (2 and 5) with the remaining uncommon prime factors (2 and 5) to find the least common divisor.

L.C.M = 2 x 2 x 5 x 5

In this way, we can take advantage of prime factorization to compute the least common multiple of a given number.

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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

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

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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Answer:

25 and 12

Step-by-step explanation:

1/2 of 50 = can be rewritten as (1/2)*(50) = (50/2) = 25

1/3 of 36 = can be rewritten as (1/3)*(36) = (36/3)  =  12

Answer:

1/2 of 50 could also be re-written as 1

___ × 50

2

So to solve this we need to multiply 1 by 50

like this 50×1

which is equal to 50 i.e 50 × 1 = 50

the next step is to then divide by 2

i.e 50

___ = 25

2

this is so because there are simply 2 25s in 50

So i guess you should be able to do the second one

Jaane

If Plan B has a monthly charge of $24 plus an additional charge of $0.05 per minute. The number of minutes of monthly usage that both plans cost the same amount is 160 minutes.

Let x represent the number of minutes of monthly usage

Hence,

Formulate an equation

0.05x + 24 = 32

Combine like terms

0.05x = 32 -24

0.05x = 8

Divide both side by 0.05x

x = 8/0.05

x = 160 minutes

Therefore 160 is the number of minutes.

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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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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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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.

Answer:

12:18

Step-by-step explanation:

Yan te ok na ata yan

Answer:

12:18

Step-by-step explanation:

You have 12 banana muffins, and 18 squid ball's.

Put it in ratio form. so it's B:S in name form, so the final answer will be 12:18.

If you put it in this form S:B, then the answer will be 18:12.

Goodluck!

Answer:

4.7x²

Step-by-step explanation:

3.7x² + x² = 3.7x² + 1x² = 4.7x²

Answer: how do you do the question what the

Step-by-step explanation:

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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The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

From the question, we have

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry

This means that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

From the question, we understand that

The graph is a proportional graph

This means that the line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Remove one of the points

(x, y) = (0, 0) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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Answer:

The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

Step-by-step explanation:

I took the exam and got it right

Answer:

9

Step-by-step explanation:

(5)3-6(5)+4(3)2

(15-30)+4(3)2

-15+ 24

=9

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

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

3y = 6x + 5 ( divide through by 3 )

y = 2x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form

with slope m = 2

line 2

y - 2x = 1 ( add 2x to both sides )

y = 2x + 1 ← in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes

then line 1 and line 2 are parallel

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:

Step-by-step explanation:

Area of triangle equation:

Find the value of h, using given values:

Use Pythagorean and find the missing side s of the triangle:

Find the perimeter of this isosceles triangle:

The perimeter of the triangle is 70 ft.

A triangle is a polygon with 3 sides.

Given that, the area of the triangle is 168 square feet.

The formula for the area of a triangle with base b and height h is:

A = (1/2)×bh

Substitute A = 168 and b = 14 into the equation:

168= (1/2)×(14)h

168/14 = (1/2)h

12 = (1/2)h

12×2 = h

24 = h

Hence, the height of the triangle is 24 ft.

Let the length of the slant side of the triangle be s.

Use the Pythagorean theorem to find the value of s:

s² = b² + h²

Substitute b= 14 and h = 24 into the equation:

s² = 14² + 24²

s² = 196 + 576

s² = 772

s = √772

s ≈ 28

The length of both slant sides of the triangle is the same, therefore, the perimeter of the triangle is given by:

P = 14 + 28 +28

P = 70

Hence, the perimeter of the triangle is 70 ft.

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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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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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In linear equation,  the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

What are examples of linear equations?

The amount of water an Olympic-sized pool can hold is, 660,000 gallons.

The pool is 63% full at the moment.

The of water in the pool now is  

              63% of 660,000   = 415,800 gallons

If the pool is 90% full then the amount of water in the pool is

        90% of 660,000 = 594,000 gallons

The amount of water added by the pool maintenance is:

Amount of water added = 90% of 660,000 - 63% of 660,000

                      = 594000  -  415800

                       = 178200

Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.

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Answer:

e

Step-by-step explanation:

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

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 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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The best option for Taylor is d. Put in $5000 for your down payment, and choose a loan with a long term length

A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, or other entities in finance. The recipient (i.e., the borrower) incurs a debt and is typically required to pay interest on that debt until it is repaid, in addition to repaying the principal amount borrowed.

The document evidencing the debt (for example, a promissory note) will typically specify the principal amount borrowed, the interest rate charged by the lender, and the date of repayment.

In this case, choosing a long term repayment plan will make it easier to pay back.

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According to the given linear equation depth of the dive is 17.59 feet.

What is linear equation?

   A linear equation is also known as a one degree equation. The linear equation's highest power is 1. Linear equations are equations with variables on both sides that are multiplied by a constant.

Here the given linear equation is ,

=> y = 0.25+5.78t

Here t is time in seconds which is t=3 seconds.

Put t=3 sec into linear equation then,

=>y=0.25+5.78*3

=>y= 0.25+17.34

=>y=17.59.

Hence depth of the dive is 17.59 feet.

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