Calculations:
The relationship between the slopes
of the parallel sides is...

The relationship between the lengths of
the non-parallel sides is...

The area of the triangle JKL is  11/2  units² = 5.5 units².

What are the vertices of a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The coordinates of the vertices of the triangle JKL are J(-2,1), K(0,3), and L(3,-4).

The formula for the area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is A = 1/2[x₁ (y₂ - y₃) + x₂( y₃ - y₁) + x₃ (y₁  - y₂)]

In the question:

x₁ = -2, y₁ = 1, x₂ = 0, y₂ = 3, x₃ = 3, y₃ = -4:

The area of the given triangle is:

A = |1/2[-2 (3 - (-4)) + 0(-4 - 1) + 3(1  - 0)]|

A = |1/2[ -2 × 7 + 0 + 3]|

A = |1/2[ -14 + 3]|

A = |-1/2(11)|

A = 11/2 square units.

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Answer:

Each student would get 25 sheets of paper.

Step-by-step explanation:

Mr. Perez starts out with 500 sheet.  He puts 1/4 in the printer.  That leaves 3/4 that he did not put in the printer.

3/4 x 500 = 375.

He take 2/3 of the 375 sheets and stores them.  This leaves 1/3 of 375 sheet to hand out to students.

1/3 x 375 = 125

He has 125 sheets to share among 25 students.

125/5 = 25

Therefore , When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expression is  as 12x2 - 8.

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

Here,

Given :

smartboard of side length is ( 2x-1) and ( 4x + 5 )

perimeter of small board = 2( l+ b)

2( 2x-1 + 4x + 5  )

2( 6x - 4)

When the side lengths are (2x-1) and (4x + 5), the smartboard's perimeter is expressed as 12x2 - 8.

The diagram can be imagined as a big whiteboard of shape of rectangle.

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98,329.16 is the Growing Ordinary Annuity's Future Value (FV). Given a predetermined rate of return or discount rate, the present value of an annuity is the entire cash worth of all of your future annuity payments.

A sequence of equal-spaced payments constitutes an annuity. There are a lot of real-world examples of financial transactions involving annuities, including. • an automobile loan with a set repayment schedule of equal monthly payments.

Calculating the present value of an annuity is done by multiplying the dollar amount of each payment by the following formula:[tex]P = PMT \times [1- [ (1 / 1+r)^n] / r][/tex]  where P is the present value of your annuity stream. PMT is short for payment method type.

A set of periodic payments that will be received in the future at the start of each period or at its conclusion is referred to as a "annuity." The formula used to determine annuity payments and annuities due is based on the PV of annuities due, the effective interest rate, and the number of periods.

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The line with slope 1 passing through the point (5, 3) is y = x - 2.

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

The letter m is frequently used to represent slope; the reason for this is unclear, but it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888,

who wrote it as

                                             y = mx + c

To Graph the line with slope 1 passing through the point (5, 3) we need to find the slope intercept form

The slope formula =  y - y₁ = m(x -x₁)

⇒  y - 3 = 1(x -5)

⇒  y = x -5 + 3

⇒  y = x - 2

Now putting the value on graph we get [See attachment]

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The fraction of Polygon P's area, that is Polygon Q's area, given the scale factor, is 1 / 4.

The fact that Polygon Q is a scaled copy of Polygon P using 1 / 2 as a scale factor means that Polygon Q is half the size of Polygon P.

This means that in terms of area, Polygon Q in relation to Polygon P would be :

= 1 /2 x 1 / 2

= 1 / 4

For example, a square with sides 6 would have an area of :

= 6 x 6

= 36 units ²

The scaled shape would have sides of 3 because of the scale factor of 1 / 2 :

= 3 x 3

= 9 units ²

The fraction of the smaller shape's area is:

= 9 / 36

= 1 / 4

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The percent value of 7th grade students enrolled in French or German is given as 64%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

As per the table given the following data can be concluded as,

Total number of students in 7th grade is 11 + 13 + 5 + 15 = 44

And, the number of students of 7th grade in french or german is,

Number of students in French + Number of students in German

⇒ 13 + 15 = 28

Then, the percent value can be calculated by the operation given below as,

⇒ 28 ÷ 44 × 100 = 63.63%

Which is approximately 64%.

Hence, the percent value of 7th graders in French or German is obtained as 64%.

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Answer:

A. -6 is the correct answer.

Answer:

So the remainder when 3 is synthetically divided into the polynomial -2x² + 7x - 9 is -6. The correct answer is therefore A.

Answer:

like 10 or 15 grams because theare is glass of juice

200 ml of juice will contain 20.4 g of  sugar.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: 250 ml of juice contains 29.5g carbohydrate, 25.5g sugar , 0.3 g protein.

Now 250 ml of juice contains 25.5 g of sugar

therefore 1 ml of the juice will contain 25.5/250=0.102 g

Thus 200 ml of juice will contain 0.102×200=20.4 g

Hence, 200 ml of juice will contain 20.4 g of  sugar.

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Answer: 1/7^3

Step-by-step explanation:

When dealing with negative integers, you divide instead of multiplying and you write it as a fraction. Therefore, 1/7 to the 3rd power is the same as 3 to the power of -7. Hope this helps!

Answer:

the percentage profit of the company is 63.9%.

Step-by-step explanation:

Cost of making pins= £1.10

Number of pins= 1000

Total cost for making the pins

= Cost of each pin × Number of pins

= £1.10 × 1000

= £1110

Percentage of pins sold in charities

= 35% of 1000 pins

= (35/100) × 1000

= 350 pins

Left pins= 1000-350 = 650 pins

Number of pins sold at £3.00:

= 60% of 650

= (60/100) × 650

= 390

Selling price of these 390 pins

= 390 × £3.00

= £1170

Number of pins sold at £5.00 for 2:

= 40% of 650

= (40/100) × 650

= 260

These 260 pins were sold in pairs for £5.

Therefore, number of pairs sold

= 260/2

= 130 pairs

Selling price of these 130 pairs of pins

= 130 × £5.00

= £650

Therefore, total selling price

= £1170 + £650

= £1820

Profit by company

= Selling price - Cost price

= £1820 - £1110

= £710

Profit percentage

= Profit × 100 / Total cost price

= 710 × 100 / 1110

= 71000/1110

= 63.9%

Probability that people picked from this group at random is either drinking punch or eating fish is 42/100.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of people = 100

Number of people drinking punch = 19

Number of people eating fish = 23

Probability of people drinking punch = 19/100

Probability of people eating fish = 23/100

Probability that people picked from this group at random is either drinking punch or eating fish = P(people drinking punch) + P(people eating fish)

                                                = (19/100) + (23/100)

                                                = 42/100

Hence the probability of people drinking punch or eating fish is 42/100.

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Answer: 8

Step-by-step explanation: make it x = 1/3 times 24.

Also, try inserting 8 in the blank.

The surface area of the label would be 30.48 square centimeters.

Surface is the outermost layer of a body, such as the skin, the crust of a planet, or the outermost layer of a liquid. Surface can also refer to the top of an object, such as the surface of a table or a lake. The term can also be used to describe a general area, such as the surface of the moon. In terms of physics, surface is any area where two materials meet.
The surface area of the label can be determined by multiplying the three

Measurements of the box together. In this case, the label is 2 inches in length, 4 inches in width, and 1.5 inches in height. Multiplying these three numbers together results in a surface area of 12 square inches. To find the surface area in a different unit of measurement, such as centimeters, the measurements must first be converted to the appropriate unit. For example, if the measurements were converted to centimeters, the surface area of the label would be 30.48 square centimeters.

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Answer:

$1825 is paid each quarter

Step-by-step explanation:

$6500 for PPO

+ 546 for Dental

+ 244 for vision

= 7300 ÷ 4 (there are 4 quarters in each year)

= $1825 each quarter

Answer:

3π/2 radians

Step-by-step explanation:

Its 3 quadrants. That's 3/4 of 2π radians, or 3π/2 radians.

Answer:

15 + 4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

the leading coefficient is the number in front of the variable with the largest exponent.

here, the largest exponent is 3 in 2x³ and the corresponding coefficient for that is 2

Answer:

no solution

Step-by-step explanation:

4x + 10 + x = 2.5(2x - 4) ← distribute parenthesis

5x + 10 = 5x - 10 ( subtract 10 from both sides )

5x = 5x - 20 ( subtract 5x from both sides )

0 = - 20 ← not possible

this indicates the equation has no solution

Answer:

A balanced

Step-by-step explanation:

A reaction in which the number of each type of atom on one side of the equation is equal to the number of the same kind of atoms on the other side of the equation is called a balanced chemical equation.

It is a chemical equation that has the same number of atoms of each element on both sides of the equation. This is important because the law of conservation of mass states that matter can't be created or destroyed, so the number of atoms on one side of the equation must be equal to the number of atoms on the other side of the equation.

It is also important for calculating the stoichiometry of a reaction, determining the amount of reactants and products needed for a reaction, and to make sure that the chemical equation is in accordance with the laws of thermodynamics.

From the given figure c+d  = 70 and the value of a+b could be 70 .

What is triangle ?

triangle is defined as a plane figure in which it has three sides and three angles.

In the given triangle, in which it contains angle c and d

let another angle could be z .

so c + d + z = 180

as the sum of all three angles in a triangle is 180 degrees.

c+d = 70

so,

z = 180 - (c+d )

z = 180 - 70

z =110

in another traingle which is opposite to angle z.

let angles in that triangle be x , y , f .

x+y+f = 180

180- a + 180 - b + f = 180

180 = a+b+f

angle f = angle z as vertically opposite angles are always equal.

hence

a+b+f = 180

a+b = 180-f

a+b = 180-z

a+b = 180-110

a+b = 70

Hence the value of a+b is 70

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M) At least one factor must equal zero.

Factors of production are, land, labor, capital, and entrepreneurship

Factors of production is an economic term that describes the inputs that are used in the production of goods or services in order to make an economic profit.

In order for a product of factors to be equal to zero, at least one of the factors must be equal to zero. This is because any number multiplied by zero is equal to zero. So, if (b - 3)(3b + 8)(2b + 5) = 0, then at least one of the factors (b - 3), (3b + 8), or (2b + 5) must equal zero. It is not necessary for all three factors to be equal to zero, as long as one of them is.

Hence, M) At least one factor must equal zero.

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The zeros of the polynomial f(x)= x³ + (b-a)x² - abx for the positive real numbers a and b  are 0, a, and -b.

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.

Given:

f(x) = x³ + (b-a)x² - abx

Take x common on the right side as shown below,

f(x) = x [x² + (b - a)x - ab]

Factorize the term as shown below,

f(x) = x (x - a)(x + b)

Plug the zero on the left side to find the zeros,

0 =  x (x - a)(x + b)

x = 0,

x - a = 0,

x = a

x + b = 0,

x = -b

Thus, the zeros are 0, a, and -b.

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The perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}

Given is a pentagon JKLMN .

The perimeter of a figure is the sum of the length of its sides. So, we can write the perimeter of the pentagon as -

{P} = {JK} + {KL} + {LM} + {MN} + {NJ}

Therefore, the perimeter of the triangle would be -
{P} = {JK} + {KL} + {LM} + {MN} + {NJ}

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Answer:

  6.0 cm²

Step-by-step explanation:

You want the area of ∆DEF with sides e=1.4 cm, f=9.1 cm, and angle D=109°.

The area of the triangle is given by the formula ...

  A = 1/2ef·sin(D)

  A = 1/2(1.4 cm)(9.1 cm)sin(109°) ≈ 6.37·0.94552 cm² ≈ 6.023 cm²

The area of triangle DEF is about 6.0 square centimeters.

An equation is a mathematical expression that shows the relationship between two variables

Since Claire traveled 382 miles. She drove 82 miles every day. On the last day of her trip she only drove 52 miles.

Let d represent the number of days Claire travelled.

Since Claire travelled 82 miles per day, the number of miles she travels in d days is D = 82 × d = 82d

Also, since she travels 52 miles on the last day, the total distance she travels is D' = 82d + 52

Now, since the total distance Claire travels is 382 miles, we have that

D' = 382 miles

So,

82d + 52 = 382

So, the required equation is 82d + 52 = 382

Solving the equation for d, we have

82d + 52 = 382

82d = 382 - 52

82d = 330

d = 330/82

d = 4.02 days

d ≅ 4 days

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The number of Cones needed in the first, second, and third cases will be 7, 4, and 3, respectively.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

Let πr³ = x. Then the volume of a cylinder is given as,

V₁ = πr³

V₁ = x

The volume of a sphere is given as,

V₂ = (4/3)πr³

V₂ = 4x/3

The volume of a cone is given as,

V₃ = (1/3)πr³

V₃ = x/3

The number of Cones needed, along with 1 Sphere to equal the volume of one Cylinder will be given as,

⇒ (4x/3 + x) / (x/3)

⇒ (7/3) × (3)

⇒ 7

The number of Cones needed to equal the volume of one Sphere will be given as,

⇒ (4x/3) / (x/3)

⇒ (4/3) × 3

⇒ 4

The number of Cones needed to equal the volume of one Cylinder will be given as,

⇒ (x) / (x/3)

⇒ 1 × 3

⇒ 3

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Answer:

B

Step-by-step explanation:

The coefficient of friction between the ring and the rod is approximately 0.408.

friction = (force parallel to the surface) ÷ (force perpendicular to the surface)

       F_horizontal = friction

       F_horizontal = µ × F_perpendicular

       8 N = µ × m × g

      where m is the mass of the ring and g is the acceleration due to gravity.

       8 N = µ × 0.2 kg × 9.8 m/s²

           µ = 8 N ÷ (0.2 kg * 9.8 m/s²)

            µ = 0.408

So the coefficient of friction between the ring and the rod is approximately 0.408.

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