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1. Use vertical line test to determine if
the graph is a function. Why or why not?
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Total number of postage stamp having total mass 1 kg = 50000 stamps

Unitary Method: What is it?

The unitary method involves first establishing the value of a single unit, followed by the value of the required number of units. What can be numbers and units?

Let's say you go to the store to purchase six apples. You are told by the shopkeeper that he is selling 10 apples for Rs 100. In this example, the value and the units are the cost of the apples. Understanding the units and values is crucial when using the unitary technique to a problem.

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

Given That :

1 postage stamp is = 1 cg

now we will convert cg into g

1 cg = 0.01g

1 postage stamp is = 0.02g

now we will convert g into kg

1 g = 0.001 kg

0.01g = 0.00001kg

1 postage stamp is = 0.00002kg

so now

total number of stamp in 1 kg = 1/0.00002 = 50000

Hence the ans is 50000 stamps

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The value of g(x) is √2x.

What is a composite function?

A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.

Here, we have

g(f(x)) =x√6.

f(x) = 3x²

By applying a composite function

g(f(x)) =√6x

g(3x²) = x√6

g(x) must be √(2x)

because if we  substitute  x = 3x² in this we get

= (√2(3x^2))

= √2√3√(x²)

= √6 x

Hence, the value of g(x) is √2x.

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The total fencing material required to fence the playground and both flower beds is

Information from the question

The boundary of a park is shaped like a circle

The length of the rectangular playground is / and its width is w

The length of each side of the square flower beds is a

The problem is asking for the perimeter of a rectangle and 2 squares

perimeter of a rectangle is 2( /  + w)

perimeter of a square is 4a

If there was no over lap the expression will have no reduction and hence the quantity of material required for the fencing is equal to their respective perimeters

The flower beds are two so the perimeter will be multiplied by 2 to give 8a

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By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:

392

For a set of N elements, the number of different sets of K elements that can be formed is:

C(N, K) = N!/(K!*(N - K)!)

Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women

Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:

for men:

C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56

for women:

C(7, 6) = 7!/(6!*(7 - 6)!) = 7

Then the total number of different committees is:

C = 56*7 = 392

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Answer:

-2x^2  - 43x - 343 - 2393/x-7

Answer:

B

Step-by-step explanation:

the two angles lies on the same lines and they have the same vertex

A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

example :

y=4+2x+x

y = 3x + 4

y = 3x + 4 is a polynomial that has exponent equal to 1.

Therefore A polynomial is a function which involves only non-negative integer powers or only positive integers exponents the variable of any polynomial is the highest power present in it in the  quadratic equation, cubic equation, polynomial function.

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Answer:

A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).

Step-by-step explanation:

shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.

8×2 = 17

15×2 = 30

17×2 = 34

After solving the equation of vector, the value obtained is equal to one, which shows that vectors are orthogonal.

A vector is a quantity with both magnitude and bin physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector has magnitude and the direction, but no position. As soon as a vector's length remains unchanged, it is consequently untouched by movement perpendicular to itself.

In contrast to vectors, scalars are normal variables having a magnitude but no direction. Displacement, velocity, and acceleration are all vector quantities, unlike speed, time, or weight, which are scalar variables.

uw = -6 + 10- 3

uw = 1.

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Answer:

the perimeter is 129 inches

Step-by-step explanation:

4x² + 8x + 3x² - 5x + 20 + 7x + 30 + 31 =

= 7x² + 10x + 81

x = 2

= 7(2²) + 10(2) + 81

= 7(4) + 20 + 81

= 28 + 101

= 129

Answer: 129 in.

Answer:

The rate of change is -2

Step-by-step explanation:

formula we will use: G(x)= [tex]\frac{f(b)-f(a)}{b-a}[/tex]  [-1,2]

g(x)= [tex]x^3[/tex]-5x

g(-1)=[tex]-1^3[/tex]-5(-1)

g(-1)=-1+5

g(-1)=4

g(2)=[tex]2^3[/tex]-5(2)

g(2)=8-10

g(2)=-2

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

g(x)= [tex]\frac{-6}{3}[/tex]

g(x)=-2

The mistakes that Claire made in solving the equation are;

1) She did not use distribution property correctly in step 1 as 2(8) = 16 and not 10.

2)  - (2+5x) should have been simplified to -2 - 5x and not -2 + 5x

3) 10 + 56x = 8x - 2 should have been 12 = -64x and not 12 = 64x

We want to solve the equation 8(2 + 7x) = 3x - (2 + 5x)

Step 1; Expand the bracket on the left hand side and right hand side to get; 16 + 56x = 3x - 2 - 5x

Step 2; Simplify the right hand side to get;

16 + 56x = -2x - 2

Step 3; Rearrange to get;

16 + 2 = -58x

Step 4; Add up the left hand side to get;

18 = -58x

Step 5; Divide both sides by -58 to get;

x = -9/29

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Complete question is;

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. It

turns out Clare's work has three mistakes!

find all three mistakes explain the below

8(2 + 7x) = 3x - (2+5x)

10 + 56x = 3x - 2 + 5х

10 + 56x = 8x - 2

10 = 64x - 2

12 = 64x

x = 3/16

An equation of this line shown in the graph in slope-intercept form is y = 0.75x + 5 or 3x/4 + 5.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following parameters:

Point (x, y) = (60, 50)

Point (x, y) = (20, 80)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (80 - 50)/(20 - 60)

Slope, m = 30/40

Slope, m = 3/4 or 0.75

At point (60, 50), the intercept is given by:

y = mx + c

50 = 0.75(60) + c

50 = 45 + c

Intercept, c = 50 - 45

Intercept, c = 5.

Now, we can write the equation of this line in slope-intercept form as follows:

y = 0.75x + 5 or 3x/4 + 5.

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The total cost for the appliances plus interest is 4330.

What is an interest rate?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.

Here, we

Cost of the appliance = $3725

Neema paid $700 so amount financed = $3725 - $700 = $3025

Interest rate on the loan = 3025*0.05*4 = $605

Total cost of the appliance = $3725 + 605 = $4330

Hence, the total cost for the appliances plus interest is 4330.

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Answer:

5 yds

Step-by-step explanation:

i am assuming that 4 yd and 3 yd are the legs

so

to find the hypotenuse you square both legs add them and then take the square root of that

so

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

the final side is 5

89.81% of 2.16 million is 1.94 million.

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. After dividing a number by its whole, multiply it by 100 to determine its percentage. As a result, the percentage refers to a component per 100. The word "percent" denotes a percentage of 100.

To calculate a group's share of the total in terms of 100, use the percentage formula. Using this method, you may represent a number as a fraction of 100. You'll see that the approach below may be used to rapidly calculate each of the the percentages:

(Value/Total Value) x 100 = %

According to the question,

(x/100) 2.16 = 1.94

x = 1.94 (100)/ 2.16

x = 194/ 2.16

x = 89.81 %

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Answer:

p < -15

Step-by-step explanation:

[tex]4 - \frac{1}{6} (p - 3) > 7[/tex]

[tex] - \frac{1}{6} (p - 3) > 3[/tex]

[tex]p - 3 < - 18[/tex]

[tex]p < - 15[/tex]

The speed of the current is 9 miles per hour

Given that: the motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning.

Total time = 5.5 hours

Let s = speed of the current

speed downstream relative to land =  11 + s

speed upstream relative to the land = 11 - s

speed = distance/time

time = distance/speed

upstream time + downstream time = total time

10/11-s  + 10/11+s = 5.5      (find LCM of 11-s and 11+s)

10(11+s) + 10(11-s) /(11-s)(11+s)  = 5.5

110+10s+110-10s /(11-s)(11+s)  = 5.5

220 = 5.5(11-s)(11+s)

220 = 5.5(121 - 11s + 11s - s²)

220 = 5.5(121 - s²)

220 = 665.5 - 5.5s²

5.5c² = 665.5 - 220

5.5c² = 445.5

s² = 445.5/ 5.5

s² = 81

s = √81 = 9

Therefore, the speed of the current is 9 miles per hour

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Answer:

1024

Step-by-step explanation:

8 times 2 to the 7th power

2 by the 7th power 128 times 8 1024

By graphing, the solution of the system of equations is: (-4, 1).

The solution to the system of equations can be solved by graphing both lines of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.

Given the following equations:

y = 1/4x + 2

y = -2x - 7

The graph for y = 1/4x + 2 will intercept the y-axis at 2 and also has a slope of 2. The line for this equation is the red line.

The graph of y = -2x - 7 will also have a slope of -2. Its y-intercept would be -7. The line of the equation is the blue line.

The graph below shows the lines of both equations which intersect at (-4, 1), The solution is, (-4, 1).

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Kurt spent a total amount of $22.68 a month on movie streaming services.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.

These operations are used from the unit rates, as when we have an amount over some time, then the amount per unit of time is the total amount divided by the total time.

We have been given the important parameters are;

The total amount = is $96.39.

The time is a mixed number, 4 and 1/4 months, hence it will be 4.25 months,

Therefore, his monthly spending is given by the unit rate as;

96.39/4.25 = $22.68 a month.

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Answer:

The answer should be 13.928

Step-by-step explanation:

You do A square + B square = C square

The bookcases that Deion will be able to paint is 16.

It should be noted that a fraction is a part of a whole number that has a numerator and denominator.

In this case, Deion has 3 1/5 gallons of paint and all of the bookcases are the same size and each requires 1/5 gallon of paint.

The number of bookcase needed will be:

= Total gallons / Gallons for each

= 3 1/5 ÷ 1/5

= 16/5 ÷ 1/5

= 16/5 × 5/1

= 16

He can paint 16 cases.

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Equation of the line in standard form is 6x + y + 4 = 0.

Slope-intercept form of equation -> y = mx + c

Given in question,

Slope = m = -6

y-intercept = c = -4

Putting values of m and c in Slope-intercept form of equation,

y = -6x - 4

Standard form :

6x + y + 4 = 0

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A possible perimeter for the rectangular table that was built by Irene is 50 inches.

My thinking was gotten by getting the dimensions and then using the perimeter formula to solve it.

From the information given, it should be noted that the area of the rectangle is given as 114 square inches. A dimension that can give this is 19 inches and 6 inches

The perimeter of a rectangle is calculated as:

= 2(Length + Width)

= 2(19 inches + 6 inches)

= 2(25 inches)

= 2 × 25

= 50 inches

The perimeter is 50 inches.

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Answer:

                             y = (-1/4)x + 9/4

Step-by-step explanation:

i got u

If function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

The function is

f(x) = (x+3)(3x-5) - 4

We have to find the value of f(3) - f(-2) ,to find that find the value of f(3) and f(-2) separately.

The function is

f(x) = (x+3)(3x-5) - 4

Substitute the values in the equation

f(3) = (3+3)(3×3 - 5) - 4

= (6) × (9-5) - 4

= 6 × 4 -4

= 24 - 4

= 20

The value of f(3) = 20

f(-2) = (-2+3)(3×-2 - 5) - 4

= 1 × (-6-5) -4

= 1 × (-11) - 4

= -11 - 4

= -15

The value of f(-2) = -15

Then,

f(3) - f(-2) = 20 - (-15)

= 20 + 15

= 35

Hence, if function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

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