Your class earned $120.00 Saturday afternoon by washing cars to raise money for the class trip. This is 1/4 of the money needed for the trip. What is the total amount needed?

The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.

A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.

Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.

Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.

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The graph which could be the graph of the polynomial f( x) with roots-8,-5, 1, and 2 is Graph 4.

What is Polynomial function?

A polynomial function is a function that involves onlynon-negative integer powers or only positive integer expounders of a variable in an equation like the quadratic equation, boxy equation, etc. For illustration, 2x 5 is a polynomial that has exponent equal to 1.

Given that;

Root of polynomial = 4.

This means that the polynomial f( x) has 4 roots.

Now, when f( x) = 0, we're told that the 4 roots are;

x = -8

x = -5

x = 1

x = 2

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Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

How to find their elevation?

To find out after how many minutes Marsha and Kristen will be at the same elevation, we can set their elevation equations equal to each other:

-24 - 12t = -8 - 16t

Then, we can solve for t by adding 8 to both sides and dividing by 4:

t = 4

So, Marsha and Kristen will be at the same elevation after 4 minutes.

To find out what elevation they will be at that time, we can substitute 4 into either one of the elevation equations and solve for the elevation:

-24 - 12(4) = -24 - 48 = -72

So, Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

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Answer:

Option 3

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

After dilation of with a scale factor of 0.25 the pre image coordinates

V (1,  1), W (2, -2) T ( 4, 2) and U(3, 3) transformed to

V' (0.25, 0.25)

W' (0.5, -0.5)

T' (1, 0.5)

U' (0.75, 0.75)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

In dilation, transformation rule is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar the rule for r = 0.25 we have

preimage                                       image

V (1,  1)   → (0.25 * 1, 0.25 * 1)  →   V' (0.25, 0.25)

W (2, 2)   → (0.25 * 2, 0.25 * -2) →  W' (0.5, -0.5)

T (4, 2)   → (0.25 * 4, 0.25 * 2) →   T' (1, 0.5)

U (3, 3)   → (0.25 * 3, 0.25 * 3) →   U' (0.75, 0.75)

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The measure of the same side interior angle made by track T and track U is; 79 degrees

Same side interior angles are defined as two angles that are on the interior of or between the two lines and particularly on the same side of the transversal. The same-side interior angles usually sum up to 180 degrees. Finally, when two parallel lines are intersected by a transversal line they will form 4 interior angles.

Now, we are told that the train track U creates an interior angle of 101 with track S.

Thus, using same side interior angles definition, the measure of the same side interior angle made by track T and track U is;

same side interior angle = 180 - 101

= 79 degrees

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As per the given tax percentage, the sales tax is $3 and the total amount paid by the group including the tip is $47.25

Here we have given that the bill before sale tax and tip is $37.50.

Here we have know that there was a tax of 8%.

And the there was a tip of 18%.

As we all know that the tip is after the tax, then it's not going to affect it, and we can essentially ignore it.

Therefore here the real question here is just what is 8% of $37.50.

Now, here we have to find the percent of something, then first you need to put the percent as a decimal.

Then we get the 8% in decimal form is 0.08 where as 18% as 0.18

Now, we have to multiply the percent in decimal form by the number.

Then we get,

=> 37.50 dollars × 0.08 = 3 dollars.

=> 37.50 dollars × 0.18 = 6.75 dollars.

And the total amount pair is calculated as,

=> 37.50 + 3 + 6.75

=> 47.25

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Every 10 degrees higher in temperature, the slope would be around -3 so draw a line from (40,20) to (80,8) .

How steep a line is defined by its slope. Gradient overflow is a term used to describe a gradient-based mathematical equation (the change in y divided by the change in x). The slope is calculated by dividing the horizontal change (run) between two points by the vertical change (rise) between the same two points. The slope-intercept form of an equation is used to express the equation of a straight line, which is written as y = mx + b. The line's y-intercept is situated where the slope is m, b is b, and (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 (0, 7).

givenI won't use (40,2) because it is an extreme case.

If I were to draw a line from those points, I would roughly estimate that it would have the same number of dots above and below the line, indicating that it is a line of best fit.

Every 10 degrees higher in temperature, the slope would be around -3 so draw a line from (40,20) to (80,8) .

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Answer:

1000$

Step-by-step explanation:

1000$

Answer:

A and B

Step-by-step explanation:

to determine which pairs are solutions , substitute the x and y coordinates into the left side of the equation and if equal to the right side then solution.

A (- 6, - 14 )

7(- 6) - 5(- 14) = - 42 + 70 = 28 ← true , so solution

B (- 1, - 7 )

7(- 1) - 5(- 7) = - 7 + 35 = 28 ← true , so solution

C (4, 10 )

7(4) - 5(10) = 28 - 50 = - 22 ≠ 28 , not a solution

D (7, 9 )

7(7) - 5(9) = 49 - 45 = 4 ≠ 28 , not a solution

The lengths 5, 13 and 12 can form a right angled triangle as they follow Pythagoras theorem.

The lengths can form a right triangle if they follow Pythagoras theorem. The longest side will be hypotenuse which is 13. Remaining will be base and height.

Pythagoras theorem -

Perpendicular² = Base² + Height²

Keep the values in formula

13² = 12² + 5²

Taking square on each side of the equation

169 = 144 + 25

Performing addition on Right Hand Side of the equation

169 = 169

Thus, the righ triangle can be formed based on the mentioned dimensions.

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So, the answer after simplifying the given square root equation is 8√5 + 3√30.

A square has four equal sides, and four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

Solving,

√5 (8+3√6)

= √5 * 8 + √5 * 3√6

= 8 * √5 + √5 * 3√6

= 8√5 + 3√5*6

= 8√5 + 3√30

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Answer: The interval in which the greatest number of scores would occur is between (20 - 2.6) and (20 + 2.6), which is approximately 17.4 and 22.6 respectively. This interval is also known as the "bell curve" or the "normal distribution curve" and it is centered at the mean (20) and covers approximately 68% of all possible scores. Most of the data points would fall within one standard deviation of the mean, hence the greatest number of scores would occur in this interval.

Step-by-step explanation:

The length of the vegetable garden as a function of its length will be given as: y = 3x + 2

The expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

Let the length of the garden be y

Let the length of the tomato patch be x

If Melissa wants the length of  the garden to exceed three times the length of the tomato patch by 2 feet, the length of the vegetable garden as a function of its length will be given as:

y = 3x + 2

Therefore, If she also wants the garden's width  to exceed the width of the tomato patch by 5 feet,  the expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

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The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

Vertical Stretch/Compression by a factor of 3: The coefficient in front of the x^2 term is 1/3, which stretches or compresses the graph vertically by a factor of 3.

Horizontal Stretch/Compression by a factor of 24: The exponent on the x term is 24, which stretches or compresses the graph horizontally by a factor of 24.

Reflect over the x-axis: The coefficient in front of the x^2 term is positive, so the graph is reflected over the x-axis.

Shift up or down: The constant term is not present, so the graph does not shift up or down.

Shift left or right: The constant term is not present, so the graph does not shift left or right.

Rotation: The graph does not rotate as it is a parabola in the standard form y=ax^2 + bx + c, it does not have any trigonometric function in it.

Therefore, The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

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A perpendicular line is one that is perpendicular or 90 degrees to another line. In order to draw a perpendicular line in Class 7, it is important to understand the formula and calculation associated with it.

The formula associated with perpendicular lines is that the product of the slope of the two lines must be equal to -1. This means that if one line has a slope of m1, then the slope of the perpendicular line must be -1/m1.

In order to calculate the slope of a line, we must use the formula m = (y2-y1)/(x2-x1), where m is the slope, (x1,y1) is the first point, and (x2,y2) is the second point. With this information, we can use the formula to calculate the slope of the line we want to draw a perpendicular line to, and then use the formula m = -1/m1 to calculate the slope of the perpendicular line.

Finally, with the slope of the perpendicular line, we can use the point-slope form of the equation of a line, y-y1=m(x-x1), to plot the equation of the line and draw it on the graph. This formula can be used to draw a perpendicular line in Class 7.

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Centroid​, Incenter, Circumcenter,Orthocenter are the name of its center

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Answer:

Maria chose C. 2682

Step-by-step explanation:

Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.

In the study of mathematics, a variety of subjects are studied, including numbers, figures, logic, quantity, equations, and arrangements. Through the use of numerical variable computations, math enables students to find answers to issues.

Here,

Thus the 6 main branches of pure mathematics are

1) Algebra

2) Geometry.

3) Trigonometry.

4) Calculus.

5) Probability and

6)statistics.

the solution of the given problem is Algebra , geometry , trigonometry , calculus , probability and statistics.

Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.

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Answer:N= 10 fo sho m -14 maybe

Step-by-step explanation:

this triangle is an isosceles triangle because of the 90 45 45 angles. This means that the two side lengths are equal and 10 is equal to n. to calculate m is maybe square root of 2 times 10 because this image.

=================================================

Explanation:

Matrix C has 3 rows and 2 columns. The size or dimensions can be written in shorthand as 3x2.

Matrix D has dimensions 2x1, aka 2 rows and 1 column.

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

Write "3x2" and "2x1" side by side in that exact order.

Notice the inner '2's match up. This is important. We need the inner numbers to match so that matrix multiplication is possible. The outer values '3' and '1' will help form the dimensions of the final answer matrix. The final answer matrix will have dimensions 3x1

Luckily we don't need to compute the value of CD. We just need to use the justification mentioned in the previous paragraphs to conclude that matrix CD is possible.

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

Something like BC is not possible because B is 3x2 and C is 3x2. We don't have a match of inner values this time. We can then rule out the answer choice "BC". The answer choices "DC" and "CB" are ruled out for similar reasoning.

Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.

An equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.

Here,

Given : 4x-3y = 6

-4x + 2y =8

=> y = 4/5x + 4

=> 4/5x + 2y = 6

Thus ,

From the above following equations we get ,

4x-3y = 6

as a standard equation in all the above options.

Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.

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On solving the provided question, we can say that the equation that cab be formed the data is as 8 > 3x => x>2.6666666667

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation that cab be formed the data is as

eight more than three times the sum of a number

let the number be x.

8 > 3x

x> 8/3

x>2.6666666667

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The inverse function is used to find the temperature in Celsius,

the temperature in celsius is  -12.22°C and 32.22°C.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator).

Given expression for temperature calculation

Original function: F =  9/5​C + 32

Inverse function: C = (F − 32)5/9

where C is temp. in Celsius and F is temp. in Fahrenheit,

so when the temperature is given in Fahrenheit we have to use the inverse function formula to calculate the temperature in degree celsius,

because it will be easy to calculate.

temperature = 10°F

C = (F − 32)5/9

C = (10 - 32)5/9

C = -22 x 5/9

C =  -12.22°C

when temperature = 90°F

C = (90 - 32)5/9

C = 32.22°C

Hence the temperature is  -12.22°C and 32.22°C.

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Examining the function  -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0

The sign of the x2 coefficient determines whether a parabolic curve opens upward or downward in this scenario.

In this function, the coefficient of x2 is a and is -9.

Rising downwards results from a negative coefficient, while opening upwards from a positive coefficient

The intercept of y

-9x² + 7x = 0

x(-9x + 7) = 0

x = 0

-9x + 7 = 0

-9x = -7

x = 7/9

Therfore, Examining the function  -9x² + 7x ,  0 and 7/9 is the y intercept.

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Answer:

8, 15, 16

Step-by-step explanation:

8, 15, 16 is not a Pythagorean triple because it doesn't satisfy the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

When we plug this set of numbers into the theorem:

[tex]8^2 + 15^2 \stackrel{?}{=} 16^2[/tex]

[tex]289 \neq 256[/tex]

we get an inequality, not an equality which would make this set of numbers a Pythagorean triple.

Note that all of the other given triples satisfy the Pythagorean Theorem.

The  area of the triangle is equal to: Area = (|A| x |B| x sin(θ))/2

To calculate the area of a triangle with 3 vectors, we will use the vector triple product formula. This formula states that the area of the triangle is equal to the magnitude of the cross product of two of the vectors divided by two.

Let's say we have three vectors A, B, and C. The area of the triangle is then equal to the magnitude of the cross product of vector A and B, divided by two.

The magnitude of the cross product of A and B can be calculated as follows:

Magnitude of (A x B) = |A| x |B| x sin(θ)

Where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

Therefore, the area of the triangle is equal to:

Area = (|A| x |B| x sin(θ))/2

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