the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.

Answer:

y =  x - 2

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 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (0, - 2 )

m = [tex]\frac{-2-2}{0-4}[/tex] = [tex]\frac{-4}{-4}[/tex] = 1

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = x - 2 ← equation of line

Answer:

The equation is 21x+4y<3150

Step-by-step explanation:

This question can be understood by the concept of inequalities.

Let x be the number of stocks of software company and y be the number of stocks of robotics company purchased.

Money invested in 1 stock of software company = $42

Money invested in 1 stock of robotics company = $8

Total expenditure on software company stock = 42*x

Total expenditure on robotics company stock = 8*y

So the total expenditure should be less than 6300

Hence the equation is

42x+8y<6300

21x+4y<3150

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The value of integers a and b is 1 and 2 and the value of a/b is 1/2.

According to the statement

we have  a given a expression 4k+8 / 4 and we have to simplify this expression in the form of ak+b and find the value of a/b where a and b are the integers.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Here 4k+8/4 becomes

4k/4 +8/4  -(1)

and general form is

ak+b  -(2)

Now, compare these equations then we get

a = 1 and b = 2.

Now we find the value of a/b

then

a/b = 1/2.

So, The value of integers a and b is 1 and 2 and the value of a/b is 1/2.

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Answer: 15 square units

Step-by-step explanation:

[tex]A=(5)(3)=15[/tex]

The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

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Richard Travel 40 feet on the zip line in 1 sec

The diagram is missing and hence the diagram.is shown below

Distance is the total movement of an object without any regard to direction.

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis

According to given Diagram

120 - 80 = 40 feet

On the Zip line

80-40=40

So the richard travels 40 feet on the zip line in 1 sec

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Answer:

37°

Step-by-step explanation:

Subtract angle IJL from angle IJK.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

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Answer:

  II only

Step-by-step explanation:

The positive leading coefficient and even degree of f(x) tell you its graph is U-shaped and opens upward.

If there is an interval where the function is negative, it must lie between the two x-intercepts. The graph will be above the x-axis (f(x) > 0) for x-values outside that interval.

The only reasonable answer choice is ...

  II  (-1, 4) . . . . only

the minimum surface area for the box is 4800 cm².

Forming the Equation of SurfaceArea

It is given that the given rectangular box is square-based and top is open. hence, it consists of  square and 4 rectangles.

Let the side of the square be a, and height of the box be h.

Then, the total surface area of the box will be given by,

S = a² + 4ah _________ (1)

Also, it is given that the volume of the box is, V = 32000 cm³

The volume of the rectangular box, V = a² h

Eliminating One of the Variables From the Equation

The volume of the rectangular box, V = a² h

⇒ a² h = 32000

⇒ h = 32000/a² _______ (2)

Substituting this value of h in equation (1), we get,

S = a² +4a(32000/a²)

S = a²+128000/a

Minimizing the Surface Area Equation

To find the minima, put, dS/da = 0

dS/da = 2a-128000/a²

⇒ 2a-128000/a² = 0

Multiplying the whole equation with a², we get,

2a³-128000 = 0

⇒ 2a³ = 128000

⇒ a³ = 128000/2

⇒ a³ = 64000

⇒ a = 40 cm

Calculating the Minimum Surface Area

From, equation (2), h = 32000/(40)²

h = 32000/1600

h = 20 cm

Now, substituting the computed values of a and h in equation (1), we get,

S = (40)² +4(40)(20)

S = 1600 +3200

S = 4800 cm²

∴ The minimum surface area of the box is 4800 cm².

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line above

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{4}}} \implies \cfrac{3 +2}{-1 -4}\implies \cfrac{5}{-5}\implies \cfrac{1}{-1}\implies -1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{-1}} ~\hfill \stackrel{reciprocal}{\cfrac{-1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{-1}{1}\implies 1}}[/tex]

Answer: 88%

Step-by-step explanation: So, to convert the decimal into a percentage, multiply .88 by 100. And BOOM! you have 88% as your answer.

We spent 88% of your allowance this week.

Since  we know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

To find out what percentage of your allowance you spent,

Divide the amount you spent by your total allowance,

then multiply by 100 to get the percentage.

Here are the steps:

1.  Identify the amount you spent: 0.88

2. Identify your total allowance: 1.00 (assuming your allowance is $1.00) 3. Divide the amount spent by the total allowance,

⇒ 0.88 ÷ 1.00 = 0.88 4.

Multiply the result by 100 to get the percentage,

⇒ 0.88 x 100 = 88%

Therefore, we spent 88% of your allowance this week.

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The situation in which the quotient of -24 divided by 3 be used to answer the question is;

Check all options:

A. The temperature of a substance decreased by 24∘C per minute for 3 minutes. What was the overall change of the temperature of the substance?

Temperature decrease = 24°C per minutes × 3 minutes

= 72°C decrease in temperature

B. A football team lost 24 yards on one play, then gained 3 yards on the next play. How many total yards did the team gain on the two plays?

Loss = -24 yards

Gain = 3 yards

Total gain = -24 + 3

= -21 yards

C. Julia withdrew a total of $24 from her bank account over 3 days. She withdrew the same amount each day. By how much did the amount in her bank account change each day?

Amount withdrawn per day = -$24 / 3

= -$8 per day

Change in her account per day = $8

D. A cookie jar contains 24 cookies. Each child receives 3 cookies. How many children are there?

Number of children = 24 cookies / 3 cookies

= 8 cookies per children

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The quotient of the polynomials [tex]2x^{3} +3x^{2} -5x-6[/tex] divided by (x+1) is [tex]2x^{2} -x-6[/tex].

Given two polynomials [tex]2x^{3}+3x^{2} -5x-6[/tex] and (x+1).

We have to determine whether [tex]2x^{3}+3x^{2} -5x-6[/tex] is divisible by (x+1).

Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.

Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.

We have to first find the factors of polynomial [tex]2x^{3}+3x^{2} -5x-6[/tex].

[tex]2x^{3}+3x^{2} -5x-6[/tex]=[tex]2x^{3}+3x^{2} -4x-x-6[/tex]

=[tex]x^{2}[/tex](2x+3)-2(2x+3)-x

=[tex](x^{2} -x-2)[/tex](2x+3)

=([tex]x^{2}[/tex]-x-2)(2x+3)

=[[tex]x^{2}[/tex]-2x+x-2](2x+3)

=[x(x-2)+1(x-2)](2x+3)

=(x+1)(x-2)(2x+3)

Because (x+1) is a factor of [tex]2x^{3}+3x^{2} -4x-x-6[/tex],so it is divisible by (x+1).

Hence using factor theorem we can say that [tex]2x^{3}+3x^{2} -4x-x-6[/tex]is divisible by (x+1).

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Answer:

(0,8)

Step-by-step explanation:

[tex]g(0)=4f(0)=4(2)=8[/tex]

Answer:

The sum of all 2 digit multiples of 6 is 810

Step-by-step explanation:

12+18+24+30+36+42+48+54+60+66+72+78+84+90+96 = 810

Answer:

810

Step-by-step explanation:

2 digit multiples of 6 are 12,18,24...90,96

You can just add them on your calculator.

An example of a rational expression is 2x+3/x-2.

The complete question wasn't found. Therefore, a overview will be given. It should be noted that a rational expression simply means quotient of two polynomials.

A rational expression is a fraction whose numerator and denominator are polynomials.

In this case, an example of a rational expression is 2x+3/x-2

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Answer: D. the y-intercept is (0,1)

Step-by-step explanation:

For all exponential functions without a vertical shift, the y-intercept is (0,1).

The correct option is C. find the real range, find the interval width, and construct the frequency distribution.

To make the information easier to understand, frequency distributions are textured look which organise and present frequency counts. Absolute frequencies as well as frequency distributions, such as percentages or ratios, can be displayed in frequency distributions.

The real range is find by the following method-

The interval width is find by the following method-

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The correct question is-

The three steps for constructing a simple frequency distribution are -

Group of answer choices

A. find the observed range, find the interval width, and construct the frequency distribution

B. find the real range, count the scores, and construct the frequency distribution

C. find the real range, find the interval width, and construct the frequency distribution

D. all of the above

The correct property of the quadratic parent function is given by:

B. Its vertex is at the origin.

The quadratic parent function is modeled by:

y = x².

It has the vertex at the origin and increases to the left and to the right, into quadrants I and II, forming a function that is graphed by a parabola.

Hence the correct option regarding a property of the quadratic parent function is given by:

B. Its vertex is at the origin.

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Answer:no but maybe

Step-by-step explanation:if you distribute the 3 and multiply the 3 with box the 2 and 1 you would get 6x+3 which is not equal to 5x+4 but if you take one from the 6 and add it to the 3 it would be even so i dont know but maybe

Answer:

It was difficult reading the question, as written.  Check my assumptions.

Step-by-step explanation:

"five more than the product of two and a number,

decreased by seven"

---

Let the "number" be a.

We are told "five more than . ." means +5,

"the product of two and a number" means 2a,

"decreased by seven" mean -7

Put the statements together to obtain:

+5+2a-7

Simplify to 2a-2

Evaluate when a = 8:

2a-2

2(8)-2

16-2

= 14

The sequence that shows a pattern where each term is 1.5 times the previous term is option D

Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.

Let us test each option one by one.

Option A

1.5 x -4 = -6

But the next number in the series is 6

Option B

1.5 x 10 = 15

1.5 x 15 = 22.5

But the next number in the series is 25

Option C

1.5 x 98 = 147

But the next number in the series is 99.5

Option D

1.5 x -200 = -300

1.5 x -300 = -450

1.5 x -450 = -675

Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D

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Answer: D (-200,-300,-450,-675,...)

Step-by-step explanation:

Recognizing the pattern in a sequence is used to write the function that represents it.

Answer:

54

Step-by-step explanation:

6 bars of soap = $1

x bars of soap = $9

We need to multiply both sides of the equation by the same amount so that $9 is on the right.

$1 x 9 = $9

6 x 9 = 54

So, you can buy 54 soaps with $9.

Hope this makes sense. Feel free to ask further if need be.

Answer:

a)

Surface Area: 172 cm^2

Volume: 112 cm^3

b) Surface Area

c) Volume

Step-by-step explanation:

Answer:

I think it's (B) and (D)

Step-by-step explanation:

As to what I have studied

Third option Base angles theorem is the correct answer as it contains the information that statement 4 is missing.

About The Base Angle Theorem

The two base angles in an isosceles triangle that are opposite the congruent sides must be identical in measure or congruent, according to the base angle theorem.

As a result, JKL and MLK are the base angles of the recognized isosceles triangle. Thus, the two angles, ∠JKL and ∠MLK are congruent or equal to each other by the means of the base angles theorem, and third option -   base angles theorem - the missing justification for statement 4.

About the other options

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Answer: option c

Step-by-step explanation:

The best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

A class can be defined as a user-defined blueprint (prototype) or template that is typically used by software programmers to create objects and define the data types, categories, and methods that should be associated with these objects.

In object-oriented programming (OOP) language, a class that is written or created to implement an interface in a software would most likely implement all of that interface's method declarations without any coding error.

In this scenario, the best object-oriented program design for this car dealership's software program is to use a single class Car, with three instance variables (fields):

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Complete Question:

A car dealership needs a program to store information about the cars for sale. For each car, they want to keep track of the following information: number of doors (2 or 4), whether the car has air conditioning, and its average number of miles per gallon. Which of the following is the best design?

(A) Use four unrelated classes: Car, Doors, AirConditioning, and MilesPerGallon.

(B) Use a class Car with three subclasses: Doors, AirConditioning, and MilesPerGallon.

(C) Use a class Car, with fields: numDoors, hasAir, and milesPerGallon.

(D) Use a class Car, with subclasses of Doors, AirConditioning, and MilesPerGallon.

(E) Use classes: Doors, AirConditioning, and MilesPerGallon, each with a subclass Car.

Answer:

a=5

b=6

c=3

d=4

surface area: 105.24

Answer:

Area of the right triangular prism = 84 cm²

Step-by-step explanation:

A  is the width of the right side rectangle = 4 cm

B is the length of the rectangle =  6 cm

C is the base of the triangle = 3 cm

D is width of the middle rectangle =  5 cm

b) Area of rectangle = length *width

 [tex]\sf Area \ of \ triangle = \dfrac{1}{2}*base *height\\\\Area of 2 triangles = 2 *\dfrac{1}{2}*base * height = base * height[/tex]

Surface area of the right triangular prism =   area of 2 triangle + area of left rectangle + area of middle rectangle + area of right rectangle

              =  3 * 4  + 3*6 + 5 * 6 + 4 *6

              = 12 + 18 + 30 + 24

              = 84 cm²

Answer:

False

Step-by-step explanation:

Prisms can have more than one base.