Find all the whole number solutions to the equation a+b+c+d=15

Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Answer:

Fraction is 180/900, or 1/5

Step-by-step explanation:

Price (Zeds)      Sold          Sold

    10                   X                  X

    15                 (1/5)*900       600

    30                (2/3)*900      120

Total                  900               900    

X + 600 + 120 = 900

X = 180

Fraction is 180/900, or 1/5

The equation of line that passes through the point (6, -1) & is parallel to the line represented by 8x + 3y = 15, in standard form is: 8x + 3y = 45.

Equation of a line in standard form is:

Ax + By = C

where A, B & C are constants.

As the required line is parallel to the given line, that is 8x + 3y = 15, the slope of the required line will be same as that of the given line.

Slope intercept form of a line is:

y = mx + b

where, m is slope of the line, b is a constant.

Re-writing the equation of the given line in slope-intercept form:

⇒ 3y = -8x + 15

⇒ y = (-8/3)x + 5

⇒ slope = m = -8/3

Now as the required line is parallel to the given line, hence its slope-intercept form will be

y = (-8/3)x + b

As the line passes through the point (6, -1),

⇒ -1 = (-8/3)×6 + b

⇒ b = 15

Hence, the slope-intercept form of the required line is

y = (-8/3)x + 15

Re-writing it in standard form, the equation comes out to be

8x + 3y = 45

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Answer:

One solution, x = 8/9

Step-by-step explanation:

One way to solve this is to take one equation and substitute into the other and then solve. So, take y=5(x-4) and put that into the other equation.

4x + 12 = -y

4x + 12 = -(5(x-4))       <--- substitution here

4x + 12 = -5(x-4)

4x + 12 = -5x + 20     <-- simplifying

4x + 5x = 20 - 12

9x = 8

x = 8/9

Answer:

6 duh!

you can do this by yourself lol

The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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Answer:

$15.27

Step-by-step explanation:

80.00 - 64.73

Take -1 from each digit until all digits are subtractable

7-6 = 1

9-4 = 5

9-7 = 2

10-3 = 7

15.27

Natasha get $15.27 in change.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Natasha bought a pair of boots for $64.73.

Natasha  gave the cashier $80.00.

So, she get

= 80- 64.73

= $15.27

Hence, Natasha get $15.27 in change.

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On a 7.5-minute quadrangle map, the spacing of UTM grid lines is typically 1,000 meters (1 kilometer) apart. To determine the contour interval if it is not provided in the map margin, one can examine the elevation markings on the map and identify the vertical distance between consecutive contour lines. Contours differ between a steep slope and a shallow slope in terms of their spacing. On a steep slope, the contour lines are closer together, indicating rapid changes in elevation. On a shallow slope, the contour lines are spaced farther apart, indicating gradual changes in elevation.

On a 7.5-minute quadrangle map, the UTM (Universal Transverse Mercator) grid lines are typically spaced at intervals of 1 kilometer. These grid lines provide a coordinate system that allows for accurate location referencing on the map.
If the contour interval is not explicitly stated in the map margin, one can determine it by examining the elevation markings. By identifying two adjacent contour lines and noting the elevation difference between them, one can calculate the contour interval. For example, if the elevation difference between two consecutive contour lines is 20 meters, then the contour interval is 20 meters.
Contours on a map represent lines of constant elevation. On a steep slope, the contour lines will be closer together, indicating a rapid change in elevation over a short distance. This signifies a steep or rugged terrain. On the other hand, on a shallow slope, the contour lines will be spaced farther apart, indicating a gradual change in elevation over a longer distance. This suggests a gentle or gradual terrain with a less pronounced change in elevation. The spacing of contour lines provides visual cues about the steepness or shallowness of the terrain.

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The given equation is y = 4^(x2–2x+5).To find the tangent line to the curve at x = 4, differentiate the given function with respect to x and find the slope of the tangent at x = 4.

Given function is y = 4^(x2–2x+5). In order to find the equation of the tangent line to the curve at x = 4, we need to differentiate the given function with respect to x and find the slope of the tangent at x = 4. Then we use the point-slope form of the equation to find the equation of the tangent line.The process of finding the equation of the tangent line to the curve is by first differentiating the given function.

We differentiate the given function as follows:d/dx(y) = d/dx[4^(x2–2x+5)] => d/dx(y) = 4^(x2–2x+5) * d/dx[x2–2x+5]

=> d/dx(y) = 4^(x2–2x+5) * [2x - 2]When x = 4,d/dx(y) = 4^(42–2*4+5) * [2*4 - 2]

=> d/dx(y) = 4^(5) * [6]

=> d/dx(y) = 6 * 1024

The slope of the tangent at x = 4 is: m = 6 * 1024

The point is: (4, y)We substitute the values in the point-slope form of the equation of the line:y - y1 = m(x - x1)

=> y - y1 = m(x - 4)

=> y - y1 = 6 * 1024 (x - 4)

Where x1 = 4, y1 = 4^(42–2*4+5)

=> y1 = 4^(5)

=> y1 = 1024

Therefore, the equation of the tangent line to y = 4^(x2–2x+5) at x = 4 is y - 1024 = 6 * 1024 (x - 4).

Therefore, we can conclude that the equation of the tangent line to y = 4^(x2–2x+5) at x = 4 is y - 1024 = 6 * 1024 (x - 4).

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The value of the card in 2002 ​is $12.00. Hence, relationship between x and y is not proportional to each other in this case.

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

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The number of years between 1996 to 2002 would be:

= 2002 - 1996

= 6 years

The relationship that is relating the value of the card y in dollars and the number of years x the player has been in retirement can be expressed as an equation in the form of the following;

y = 5.54 + 1.06x

where x = 6 years

y = 5.54 + 1.06(6)

y = 5.54 + 6.36

y = $12.00

The value of the card in 2002 ​is $12.00.

The relationship between x and y is not proportional to each other in this case.

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Answer:

The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.

To find the zeros of the function f(x) = 4x^2 - 10x - 6, we need to solve the equation f(x) = 0. 4x^2 - 10x - 6 = 0
Dividing both sides by 2, we get: 2x^2 - 5x - 3 = 0

Using the quadratic formula: x = (-(-5) ± √((-5)^2 - 4(2)(-3))) / (2(2)) x = (5 ± √49) / 4 x = (5 ± 7) / 4 Therefore, the zeros of the function f are: x = (5 + 7) / 4 = 3 x = (5 - 7) / 4 = -1/2 The zeros of the function f(x) = 4x^2 - 10x - 6 are 3 and -1/2.
To find the zeros of the function f(x) = 4x^2 - 10x - 6, follow these steps: 1. Set f(x) equal to 0: 0 = 4x^2 - 10x - 6 2. Use the quadratic formula, where a = 4, b = -10, and c = -6 x = (-b ± √(b^2 - 4ac)) / 2a 3. Plug the values into the formula: x = (10 ± √((-10)^2 - 4(4)(-6))) / 2(4) 4. Simplify the expression inside the square root: x = (10 ± √(100 + 96)) / 8 5. Calculate the square root: x = (10 ± √196) / 8 6. Simplify further: x = (10 ± 14) / 8 7. Find the two possible values of x: x₁ = (10 + 14) / 8  24 / 8 = 3 x₂ = (10 - 14) / 8 = -4 / 8 = -1/2 So, the zeros of the function f(x) = 4x^2 - 10x - 6 are x = 3 and x = -1/2.

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Using the quadratic formula, the zeros of the function f(x) = 4x^2 - 10x - 6 can be found as: x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the coefficients a = 4, b = -10, and c = -6, we get: x = (10 ± sqrt(100 + 96)) / 8

x = (10 ± sqrt(196)) / 8

x = (10 ± 14) / 8

x1 = 3/2 and x2 = -1Therefore, the zeros of the function f(x) are x1 = 3/2 and x2 = -1.

The quadratic formula is a standard method to find the zeros of any quadratic equation of the form ax^2 + bx + c. In this case, the function f(x) = 4x^2 - 10x - 6 is a quadratic function, and its zeros represent the x-values where the function intersects the x-axis.  In this case, the zeros are x1 = 3/2 and x2 = -1, which means that the function intersects the x-axis at these two points.

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The major methods of recording unstructured observational data are Narrative Description, Field Notes, Audio or Video Recording, Photography, Diagrams or Maps.

The major methods of recording unstructured observational data are:

1. Narrative Description: This method involves writing a detailed, chronological account of the observed events or behaviors, capturing the context and interactions as they occur naturally.

2. Field Notes: In this method, the observer takes brief, concise notes during the observation, focusing on key events, behaviors, or interactions. These notes can be expanded and organized later for further analysis.

3. Audio or Video Recording: Using audio or video equipment, the observer captures the events and interactions in their entirety. This allows for a more accurate record and the ability to review and analyze the data multiple times.

4. Photography: Taking photographs during the observation can provide a visual record of the events and behaviors. These images can supplement other data collection methods and help to illustrate specific aspects of the observation.

5. Diagrams or Maps: Drawing diagrams or maps of the observation setting can help capture the spatial relationships between individuals and objects, as well as the overall layout of the environment.

These methods can be used individually or in combination, depending on the research question and the specific needs of the study. Remember to always respect participants' privacy and obtain informed consent when necessary.

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Answer:

\(( - 1,2 \frac{1}{2} )\)

Step-by-step explanation:

\(\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}\)

Thus, midpoint

\( = ( \frac{4 - 6}{2} , \frac{8 - 3}{2} ) \\ = (\frac{ - 2}{2} , \frac{5}{2} ) \\ = ( - 1,2 \frac{1}{2} )\)

Answer: (-2,3)

Step-by-step explanation: To figure out where the missing point, D, would go, you have to figure out which side DE is congruent to and what side is missing. I saw that DE is correlates to the base of the triangle because that's the only one of that length. From there, I counted up from the center of the base, DE, to find a good place for the vertex, and made sure it was the same exact distance from DE as C is from the base of the first triangle.

a. the factors of equation is \(f(x)=(x-1)(x-10)(2x-3)\)

b. the factors of equation is \(f(x)=(x-1)(x^2+x+4)\)

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, with non-negative integer exponents.

a. Given function,

\(f(x)=2x^3 -25x^2 + 53x - 30\)

By using trial and error method, put values of x =1, x= 10, and x= 3/2 are satisfied values for above function,

\(f(x)=(x-1)(x-10)(2x-3)\)

therefore, the factors of equation is (x-1) (x-10) (2x-3)

b. Given function,

\(f(x)=x^3 +3x - 4\)

Similarly using trial and error method,

\(f(x)=(x-1)(x^2+x+4)\)

therefore, the factors of equation is (x-1) (x² + x + 4)

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Factor of given polynomials are a. (x-1)(x-10)(2x-3), b. (x-1)(x² + x + 4) .

In mathematics, a polynomial is an expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by a variable. The variables in a polynomial can only have non-negative integer exponents.

Polynomials can have different degrees, which is the highest power of the variable in the expression. For example, the polynomial 3x² - 5x + 2 is a quadratic polynomial, since its highest power of x is 2. If the degree of a polynomial is n, then it has at most n roots, which are the values of x that make the polynomial equal to zero.

Polynomials are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze many different types of phenomena, such as motion, population growth, and electrical circuits.

Polynomials can also be added, subtracted, and multiplied together to form new polynomials. Additionally, polynomials can be factored, which involves breaking them down into simpler polynomials that multiply together to give the original polynomial.

a) f(x)= 2x³ - 25x² + 53x - 30
⇒(x-1)(x-10)(2x-3)

b) f(x)= x³ + 3x - 4
⇒(x-1)(x² + x + 4)

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The complete question is:

Answer:

you're answer would be 6 tomatoes in all

The measure of arc XZ is 115 degrees and  measure of arc XYZ is 245 degrees

The given circle has a centre W

The measure of central angle is 115 degrees

We have to find the measure of the arc XZ

The central angle is equal to measure of the arc

115 = measure of arc XZ

Arc XZ =115 degrees

We know that the circle has a measure of 360 degrees

So the remaining angle is 360-115 = 245 degrees

The measure of arc XYZ is 245 degrees

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Answer:

r = 20 km

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Circumference of a Circle Formula: C = 2πr

Step-by-step explanation:

Step 1: Define

Identify variables

C = 125.6 km

Step 2: Solve for r

Answer:

197.29

Step-by-step explanation:

Multiple the circumfernece by 3.14 and then divide that number by 2.

Answer:

Step-by-step explanation:

5w + 4 = 2w + 19

3w + 4 = 19

3w = 15

w = 5

The translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

In geometry, a translation is a transfer that occurs either horizontally to a left or right as well as vertically up or down. It may also consist of a mix of the two.

Given data:

Parent function- y = x²

New function -  y = (x - 2)² +1

Thus, the translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

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Complete question:

1. Which of the following most accurately describes the translation of the graph from y = x² to y = (x - 2)² +1?

A.  shift of 2 units right and then shift of 1 unit up.

B.   shift of 2 units left and then shift of 1 unit up.

Answer: 0

Step-by-step explanation:

The slope of the line y = -1/5 is zero because it is a horizontal line.

Parallel lines have the same slope, so the answer is also 0.

The person can buy a total of 36 distinct systems from three models of the basic unit, three models of keyboard, and four models of printer.

Given, a person buying a personal computer system is offered a choice of three models of the basic unit, three models of keyboard, and four models of printer.

we have to find the number of distinct systems that can be purchased.

Using the concept of Permutations and Combinations, we get

Choose One model of basic unit from three models, Choose one model of keyboard from three models of keyboards and also choose one model of printer from four models of printers.

C(3 , 1)×C(3 , 1)×C(4 , 1)

= 3×3×4

= 36

So, the total of 36 systems can be purchased.

Hence, the total of 36 systems can be purchased.

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Answer: The answer is C

Step-by-step explanation:

Answer:

x = -6

Step-by-step explanation:

The triangle in the picture is an isoceles triangle in which the measure of top vertex angle is given and one of the base angles is also given.

According to angle sum property of triangle , sum of measure of all the angles of traingle is 180°. Also, in isosceles triangle , the base angles are always equal to each other .

So,

\(34 + (x + 79) + (x + 79) = 180\)

\( = > 2x + 158 + 34 = 180\)

\( = > 2x +192 = 180\)

\( = > 2x = 18 0 - 192 = - 12\)

\( = > x = \frac{12}{ - 2} = - 6\)

If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.

Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.

It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

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The initial equation is:

So if we use the distribution propertie, we have to multiply the 4 for all term in the parenthesis so:

and then we simplify:

So is option D)

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)