Draw the following triangle after a 90 degrees counterclockwise rotation about the origin.

Answer:

Step-by-step explanation:

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we can use points A(4, 5) and B(9, 7):

slope = (7 - 5) / (9 - 4) = 2 / 5

So, the slope of line AB is 2/5.

On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.

Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.

M+D = 82 marbles

[tex]M= 82- D[/tex]

[tex]D= 4M+2[/tex]

[tex]D= 4(82-D) +2[/tex]

[tex]D= 328 - 4D+2[/tex]

[tex]5D = 330[/tex]

[tex]D= 66[/tex]

Therefore, Don has 66 and Mark has 82-66 = 16

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Answer: A = 15 units²

Step-by-step explanation:

The figure has 1 pair of parallel sides and is therefore a trapezium.

The area (A) of a trapezium is calculated as

A =  h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ are bases

here h = 3, b₁ = 3 , b₂ = 7 , then

A =  × 3 × (3 + 7) = 1.5 × 10 = 15 units²

The coordinates of point C in the given right triangle ABC is (2, 2√3-2)

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).

Now, AB=4-(-4)=8

AC=AB×sin60°= 8×√3/4√3

In right triangle ACD

AD=AC×cos30°

= 4√3×√3/2

= 6

Xc=6-4=2

Yc=AC×sin30°-2

= 4×3×1/2-2

= 2√3-2

The coordinates of point C(2, 2√3-2)

Therefore, coordinates of C(2, 2√3-2).

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The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]

A rhombus is a quadrilateral that has four congruent sides.

The specified shape of the quadrilateral MATH = A rhombus

The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;

The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;

The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]

The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4

The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7

The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]

Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]

The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)

The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;

y - 2.5 = (-4/7)·(x - 2)

y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14

y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14

y = [tex]3\frac{9}{14}[/tex] - 4·x/7

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Answer:

51°

Step-by-step explanation:

180°-129°=51°

I hope it helps you

Answer:

5/6

Step-by-step explanation:

The number of gallons of paint that the painter should buy is; 4 gallons

The parameters given are;

Side length of cube = 20 ft

Area that a gallon of paint can cover = 400 square feet

Since the room is shaped like a cube, then it will have 4 equal wall areas.

Area of one wall = 20 * 20 = 400 square feet

Area of 4 walls = 4 * 400 = 1600 square feet

Since 400 sq.ft  is covered by 1 gallon, then;

1600 sq.ft = (1600 * 1)/400

= 4 gallons

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The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The given function is:

y = 5(2)ˣ

The value of y from x= 0 to x = 3 is:

y = 5(2)⁰ = 5

y = 5(2)¹ = 10

y = 5(2)² = 20

y = 5(2)³ = 40

The most rapid rate of change as x increases beyond 0 is:

y = 7ˣ

This is observed as the graph increases rapidly with change in value of x.

3. y = (1.20)ˣ

The constant 1.20 is greater than 1 thus, the function is exponential growth.

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The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.

The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.

On this note, the x-intercepts of the polynomial function which is as described in this scenario are;

x - 2 = 0; x = 2.

x - 3 = 0; x = 3.

x + 5 = 0; x = -5.

Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.

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Answer:

[tex] \frac{1}{2} \times 25 \times 10 = 125 [/tex]

[tex] \frac{1}{2} \times breath \times perpedicular \: hight[/tex]

Answer:

  b = 30

Step-by-step explanation:

You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).

The equation y = 20x +b can be solved for b:

  b = y -20x . . . . . . . . subtract 20x

Using the given point (x, y) = (6, 150), you have ...

  b = 150 -20(6) = 150 -120

  b = 30

The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.

A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

From the polynomial expression given:

[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]

The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.

The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.

The diameter of a circle is 2 times the radius of the circle.

The area of a circle is expressed as: A = πr²

The circumference of a circle is expressed as: 2πr

For question 1)

Radius r = 2

Diameter = 2 × radius = 2 × 2 = 4

Area = πr² = π( 2 )² = 4π

Circumference = 2πr = 2 × π × 2 = 4π

For question 2)

Radius r = 4

Diameter = 2 × radius = 2 × 4 = 8

Area = πr² = π( 4 )² = 16π

Circumference = 2πr = 2 × π × 4 = 8π

For question 3)

Diameter d = 2

Radius = diameter / 2 = 2/2 = 1

Area = πr² = π( 1 )² = 1π

Circumference = 2πr = 2 × π × 1 = 2π

For question 4)

Diameter d = 16

Radius = diameter / 2 = 16/2 = 8

Area = πr² = π( 8 )² = 64π

Circumference = 2πr = 2 × π × 8 = 16π

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Answer:

Step-by-step explanation:

The cost of renting a car for "d" days can be represented by the following function:

c(d) = 75d + 30

where "c" is the total cost of the car rental and "d" is the number of days the car is rented for. The first term, 75d, represents the daily rental fee of $75 per day. The second term, 30, represents the flat fee for the full tank of gas that can be returned either full or close to empty.

Answer:

The answer is 100, see Step-by-step explanation:

Step-by-step explanation:

If anyone looks at the verified answer, its wrong and so are the comments under it. In the answer above it says "Sci-fi = 100-24-22-20-14=20" that is correct but the answer is not. 20 percent of 500 is 100 not 72 or 20, I don't know how anyone got those answers.

Answer:

Note that 0.01 is the decimal form of 1%, so 0.01 multiplied by 7 yields 7%. So, if we were to find 1% of 250, which is 2.5, we can multiply the value by 7, which is 17.5.

Therefore, 7% of 250 is 17.5

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.

Each package of cups costs $3.50

The teachers need to buy 12 cups

So the total cost of cups is = 12 cups × ($3.50 per package) = $42

Now let's do the same thing for the napkins:

Each package of napkins costs $4.25

The teachers need to buy 10 napkins

So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50

To find out how much more money the teachers will need to buy cups and napkins,

= $42 + $42.50 - $25
= $59.50 - $25 = $59.5

Therefore, the teachers will need $59.5 more to buy cups and napkins.

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The difference between the median rating for each company is approximately 0.3 times the interquartile range.

Generally speaking, the median for 20 observations is the average of the 10th and 11th number:

Median rating of Company A = (4 + 4)/2

Median rating of Company A = 8/2

Median rating of Company A = 4.

Median rating of Company B = (3 + 3)/2

Median rating of Company B = 6/2

Median rating of Company B = 3.

Difference in median = 4 - 3

Difference in median = 1

For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:

1 = 3x

x = 1/3.

x = 0.3

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The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The interest is given as,

I = PRT / 100

Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,

x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200

0.06x + 8,000 - 0.08x = 7,200

-0.02x = -800

x = 40,000

The amount in the second bank is given as,

⇒ 100,000 - 40,000

⇒ 60,000

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

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The measure of the side AE would be 70 units.

We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

In the given triangle B, D, F are the midpoints of the triangle.

AC=50, CE=60,

BD=35

Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).

⇒ BD ≅ FE= 1/2 AE

AE = 70 units

Then, the length of line segment AE = 70 units

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No, it is impossible to construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm as the dimensions defy the triangle inequality theorem.

It follows from the triangle inequality theorem that the sum of any two side lengths of a triangle must be greater than the third side length and also, the difference of two side lengths of a triangle must be less than the third side lengths.

However, in this case, since QR + PR = PQ, it can be inferred that the two side lengths cannot possibly be used to construct a triangle.

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Answer:

...here is the answer...

Answer:

2489

Step-by-step explanation:

it would be 30+ 1,000+29+30+400+1,000+ 2489

I really hope this helps

Proverbs 4:6-7

Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)

Answer:

2489

Step-by-step explanation:

Answer:

∠ a = 30° , ∠ b = 90°

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , that is

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

------------------

the sum of the 3 angles in a triangle = 180° , that is

∠ b + ∠ a + 60° = 180°

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

Answer:yes

Step-by-step explanation:

The degree of the polynomial is; 6.

The leading coefficient of the polynomial is; 1.

The maximum number of real zeroes is; 6.

As evident in the task content; the given polynomial is;

f (x) = 2x⁵ - x³ + x⁶ - 4.

By observation, the term with the highest power of x is; x⁶.

Therefore, the degree is; 6.

The leading coefficient is the coefficient of x⁶ which is; 1.

The maximum number of real zeroes possible is dependent on the degree of the polynomial and is; 6.

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The measure of angle A is given as follows:

<A = 60º.

The three trigonometric ratios are defined as follows:

For the angle A, we have that:

Applying the sine ratio, the angle measure is given as follows:

sin(A) = 13/15

A = arcsin(13/15)

A = 60º.

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The magnitude of the vector is 25.5 metres.

The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

| N | = √22.2² + 12.6²

| N | =  √492.84 + 158.76

| N | =  √651.6

| N | = 25.5264568634

| N | = 25.5 metres

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