a² + b² = c²
52 + 122 = c²
[?] + [ ] = c²
4
Find the value of 52.
5
12
K
C
C=

The value of x in the solution set of 3x 4 ⥠5x 2 is x = -2.

3x 4 ⥠5x 2

3x 4 - 5x 2 = 0

3x - 5x = -2

-2x = -2

x = -2

The solution set of 3x 4 ⥠5x 2 is the set of all values of x that when substituted into the equation, make it true. To find the value of x, we must start by rearranging the equation to make the variable x the subject, or the thing that we are trying to find. To do this, we subtract 3x 4 from both sides of the equation, leaving us with 5x 2 = 0. We then subtract 5x from both sides of the equation, leaving us with -2x = -2. To solve for x, we divide both sides of the equation by -2, which gives us the answer x = -2. Therefore, the value of x in the solution set of 3x 4 ⥠5x 2 is x = -2.

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The area of trapezoid abcd is 164 cm2 with an altitude is 8cm, ab is 10 cm, and cd is 17 cm and bc=10cm

The area of a trapezoid can be calculated if the length of its parallel sides and the distance between them are given. The formula for the area of a trapezoid is expressed as,

A = ½ (a + b) h

where (A) is the area of a trapezoid, 'a' and 'b' are the bases and 'h' is the height.

Given that Area of trapezoid A=164 and the altitude is 8 cm, ab is 10 cm, and cd is 17cm.

Substitute these values in the formula:

164=8(BC+AD)/2

8(BC+AD)=328

BC+AD=41

Drop perpendiculars from B to AD and from C to AD and let them hit AD at E and F respectively. Note that each of these perpendiculars has a length of 8.

From the Pythagorean Theorem, AE=6 and DF=15 thus AD=BC+21. Substituting back into our original equation we have

BC+BC+21=41

2BC=20

BC=10cm.

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X = - (y + 2)/3 dividing the difference in the -coordinates by the difference in the -coordinates is a gradient of line.

The gradient of a line is a measure of how steep a straight line is. A line’s gradient might be positive or negative and does not have to be a whole integer.

Y=-3x-2

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

Y+2=-3x-2+2

Y+2=-3x

-3x= y +2

3x/3=-y+2/3

X = - (y + 2)/3

A line’s gradient is computed by dividing the difference in -coordinates by the difference in -coordinates. This is also known as the vertical divided by the horizontal, or the change in divided by the change in. Choose two points on the graph for a straight-line graph. Line gradient = (change in y-coordinate)/(change in x-coordinate). Of course, we can use this to determine the equation of the line. Because the line crosses the y-axis at y = 3, the graph’s equation is y = 12x + 3.

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The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,

[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\ [/tex]

[tex]\longrightarrow m =\dfrac{4-0}{0-(-2)}\\ [/tex]

[tex]\longrightarrow m =\dfrac{4}{2}\\ [/tex]

[tex]\longrightarrow m = 2 [/tex]

Now we may use point slope form of the line as ,

[tex]\longrightarrow y - y_1 = m(x-x_1)\\ [/tex]

[tex]\longrightarrow y - 4 = 2(x-0)\\ [/tex]

[tex]\longrightarrow y -4 = 2x \\ [/tex]

[tex]\longrightarrow \underline{\underline{ y = 2x +4}}[/tex]

And we are done!

Answer:

The given line passes through points (0,4) and (-2,0) . So firstly we can find the slope of the line as ,

Now we may use point slope form of the line as ,

And we are done!

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

Total number of students = 113

we require to find the number of students who like both hockey and rugby.

number of students who like game = total number of students - students who doesn't like either one

= 113 - 18 = 95 = A ∪ B

So equation become

A ∪ B = A + B - A ∩ B

95 = 60 + 45 - A ∩ B

A ∩ B = 105-95 = 10.

The set of all real numbers constitutes the range and all positive real numbers constitute the domain of a logarithmic function

All real numbers make up the domain, and all positive real numbers make up the range of an exponential function.

The set of all real numbers constitutes the range of a logarithmic function.

As a result, x > 0 (or) (0, ∞) is the domain of the log function y = log x. The set of all real numbers is the range of any log function belonging to R.

All real numbers make up the domain, and all positive real numbers, or (0, ∞) in interval notation, make up the range.

An exponential function is a mathematical function of the following form: f(x) = ax. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values. The y values are those.

The domain of a function is the set of all input values (sometimes referred to as independent variables) for which the function is defined and produces an acceptable result (also called dependent variable). Most often, the domain is represented by a collection of numbers or a range of numbers.

The term "range" refers to the entire set of potential output values (dependent variable) that a function can produce for any set of valid input values inside its domain. Usually, a group of numbers or a range of numbers is used to represent the range.

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Answer:

The rate of change, or slope, between two points on a graph is the change in the y-coordinate (rise) divided by the change in the x-coordinate (run). The formula for the slope between two points (x1, y1) and (x2, y2) is:

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

Given the points (-4,-2) and (1,-7) we can plug in the coordinates into the formula:

slope = (-7 - (-2)) / (1 - (-4)) = (-5) / (5) = -1

So the rate of change, or slope, between the two points (-4,-2) and (1,-7) is -1.

This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1.

Answer:

Step-by-step explanation:

it’s 3-1

Answer:   -36

Step-by-step explanation:

so when a variable and a number are together you multiply, 8 times c, c is found equal to -6, so 8 x -6 would be -48 so then its -48 minus d d is found equal to -12 so -48 minus -12 would equal -36               hope this helped ^^

The quadratic equation's answer is found by completing the square: x= 7/4, x = -1.

x ax2+bx+c=0, a quadratic polynomial in a single variable, is a quadratic equation. a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that there is at least one solution. There are both straightforward and complex solutions. A quadratic equation is a quadratic equation. This suggests that it contains at least one word that has to be squared. One of the commonly used answers to quadratic equations is "ax2 + bx + c = 0." where the unknown variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

4x^2 -3x-7 =0

4x^2 - 7x + 4x -7 = 0

x(4x-7) +1(4x-7) = 0

(4x-7 )(x+1) = 0

The quadratic equation's answer is found by completing the square: x= 7/4, x = -1.

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Please have a look at the diagrams of a quadrilateral and a trapezoid in your textbook.

Ans--- A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Let v is the rate of cyclist 1 and v + 6 is the rate of cyclist 2.

Equation: d = (v + v + 6) * t

Solving for v and v+6

d = (v + v + 6) * t

120 = (2v + 6)3

40 = 2v +6

2v=34

v = 17 km/h ………… is the rate of cyclist 1

v + 27 = 23 km/h…….. is the rate of cyclist 2

Answer: 17 and 23.

Explanation: Let the rate of the slower cyclist be x.

After 3 hours, the total distance between the both will be of:

3x (distance from the slower cyclist from the starting point) + 3(x + 6) (distance from the faster cyclist from the starting point) = 120.

Solving by x, 17 = x. Since x is the rate of the slowest cyclist, x + 6 = 23, is was the rate of the faster cyclist.

Answer:

A scale model of a house uses a scale of 14 inches = 3 feet, this means that for every 14 inches in the model, it represents 3 feet in the actual house.

If the model is 4.25 inches tall, we can use this proportion to find the actual height of the house:

4.25 inches / 14 inches = x / 3 feet

To find the actual height of the house, we can cross-multiply and then divide:

(4.25 inches * 3 feet) / 14 inches = x

x = 1.5 feet

So the actual height of the house is 1.5 feet

The solution to the system of equation y = 9x + 2 and 7y = 63x + 14 is x = -1 and y = -7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

y = 9x + 2

multiply the equation by 7:

7y = 63x + 14

-63x + 7y = 14          (1)

And:

-2x + 7y = -47     (2)

To solve by elimination method, subtract equation 2 from 1 to get:

-61x = 61

x = -1

Put x = -1 in the equation:

y = 9x + 2

y = 9(-1) + 2 = -9 + 2 = -7

The solution to the equation is x = -1 and y = -7

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Answer:

ffggggggggggytdcuihgr

the answer is 7x I'll save you some time by not explaining

The solution of the equation  [tex]\frac{z}{z+15}[/tex]= [tex]\frac{4}{9}[/tex]  is 12.

 [tex]\frac{z}{z+15}[/tex]= [tex]\frac{4}{9}[/tex]

9z=4z+60 (cross multiplication)

9z-4z=60

5z=60

z=60/5

z=12

quadratic equation:

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is an unknown variable. It is called a quadratic equation because the highest power of x is 2. Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula. The solutions to a quadratic equation are the values of x where the equation equals to zero.

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The equation that can be used to find the total area of the figure is 168 = (18)(3x) + (6)(x).

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The given figure can be divided into two segments.

A rectangle having the dimensions of length = 12 and width = 3x, and second rectangle with the dimensions of length = (18 - 12) = 6 and width = x.

The area of the figure is:

A = Area of segment 1 + area of segment 2

168 = (18)(3x) + (6)(x)

Hence, the equation that can be used to find the total area of the figure is 168 = (18)(3x) + (6)(x).

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Answer:

201=21 x X + 16 x 3X

Step-by-step explanation:

The HCF of the polynomials x6 - 3x4 + 3x2 - 1 and x3 + 3x2 + 3x + 1 as calculated from the data given is found to be as (x + 1)3.

We will solve the given functions, to get their HCF.

   f(x) = x6 - 3x4 + 3x2 - 1  

⇒ x6 - x4 - 2x4 + 2x2 + x2 - 1

⇒ x4(x2 - 1) - 2x2(x2 - 1) +1(x2 + 1)

⇒ (x2 - 1)(x4 - 2x2 + 1)

⇒ (x + 1)(x - 1)(x4 - 2x2 + 1)

⇒ (x + 1)(x - 1)(x2 - 1)2

⇒ (x + 1) (x - 1) (x + 1)2 (x - 1)2

⇒ (x + 1)3(x - 1)3    

Similarly ,

g(x) = (x + 1)3      

Therefore,

The HCF of f(x) and g(x) is the common factor of equations obtained by solving these functions which is , (x + 1)3.

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A) Kristine have enough money to make the purchase.

B) She have left over $10.25 after the purchase.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Kristine has $150 to spend on school clothes.

The store is having a sale for 25% off.

Coupon= 10% off

So, Cost of three shirts = 3 x 35 = 105

Cost of pair of jeans = $40

Cost of pair of shoes = $70

So, She have to spend total = 105 + 40 + 70 = $215

After discount she have pay = 215 - 215 x 0.35

                                                = $139.75

Thus, Kristine have enough money.

Now, She would left with = 150- 139.75 = $10.25.

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Answer:[tex]a=4jk\\isolate J: divide 4 and k\\= \frac{a}{4k} =J[/tex]

Step-by-step explanation:

Answer:

[tex]a = 4jk \\ akj = a \\ \frac{akj}{4k} \: = \frac{a}{ak} \\ j = \frac{a}{4k} \\ [/tex]

Here ur ans.

By:- Utsav Xettri

Function f is represented by f(x)=5(x+11), the value of x such that fix)-90 is true; x = -29.

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

f(x) = 5(x + 11)

or, f(x) = 5x + 55

now, putting the value of f(x) = -90

-90 = 5x + 55

or, 5x = - 145

or, x = - 29

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Half of the data points, or a straight line, are on either side of a line of best fit.

A line is a geometric object that is defined as being straight, thin, one-dimensional, zero width, and extending in both directions to infinity. An uncurved line is simply what a straight line is. We can also state that every line that connects any two specific places on the same plane will be distinct.

A student who doesn't study for the test is expected to receive a test score of 38, according to this line of best fit.

It is equivalent to doing no homework to not study for an exam (doing homework is considered studying).

Half of the data points, or a straight line, are on either side of a line of best fit.

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Answer: 15 laps in 12 seconds

Step-by-step explanation:

15 divided by 12 is 5/4 which is also 1.25

12 divided by 10 is 6/5 which is also 1.2

1.25 is greater then 1.2

Therefore ,light of this, the solution to the triangle issue given is ABC, which is equivalent to XYZ.

A triangular is a polygon since it has number of sides and three vertices. This geometric form is essential. Triangle ABC is still a triangles whose corners are located at points A, B, then C. In geometric shapes, a single planar and triangle are produced when four components are not coherent. Due to their three sides and top right corner, triangles are included in polygons.

Here.

Given :

ABC and XYZ are the same, hence ∠ A = ∠ X.

∠ B and ∠ Y mean the same thing.

"∠ Z" = "∠ C," and

The value of line ab matches that of xy.

Both line bc and yz can be substituted.

XZ corresponds to line ac.

To come up with a solution, Cpct was used.

Triangle segments that match each other are congruent.

The solution to the triangle problem is ABC is equal with XYZ as a result.

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The factored form of the given equation as calculated from the data is found to be as 3x( x -2 )  , and on further solving we get the roots of the equation to be as x- 0 and 2.

The expression given is 3x²- 6x, in order to get it's factored form we will factorize this expression ,

Let ,  3x²- 6x =0

therefore,

3x( x -2 ) = 0

which means,

3x = 0 and x - 2 = 0

hence ,

x = 0 and x = 2.

A statement that supports the equality of two expressions and is equated using the equals sign "=" is called as an equation.

For instance,  3x²- 6x = 13 , here  3x²- 6x and 13 are expressions which are separated by the "=" is the sign that connects these two expressions.

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Answer:

  A. Discrete

Step-by-step explanation:

You want to know the sort of domain (discrete, continuous) of the equation 2x +3y = 24, or y = -2/3x +8, when x and y are numbers of hot dogs and hamburgers, respectively.

A set is described as "discrete" if it consist of particular values, and those only. Here, the numbers describing the numbers of hot dogs and hamburgers will be whole numbers. Fractions and irrational numbers are not allowed. (You cannot purchase √2 hot dogs, for example.)

That means the domain of this equation is "discrete."

If fractions and irrational numbers are allowed in a given expression or formula, the domain is "continuous." Lengths of string, for example, tend to be values that do not fall into a specific set of values. ("Nominal" length may be discrete (50', 100', and so on), but actual length likely will not be, especially when one considers that it stretches.)

__

Additional comment

Quantum physics seems to be telling us that many things in the universe are quantized (discrete) at the lowest levels. In the practical world, the effect of numerous quantized values added together has the effect of making any particular measurement appear to be continuous.

Answer:

Step-by-step explanation:

The lowest number that is a multiple of two or more numbers is known as the least common multiple (LCM). To calculate the LCM of a, b, and c, we must first determine the greatest power of each prime number that appears in any of the integers.

Assume a = 23x3, b = 2x3x5, and c = 32x5.

As a result, the LCM of a, b, and c is 23x32x5.

Given that the LCM [a,b,c] = 2x32x5,

So, n= 2x3²x5

n=180

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Given that the height of the tower is 168 foot, and the angle is 30 degrees.

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse.

To find the hypotenuse, we use the trigonometric ratios as follows:

Sin 30 = 168 / Hypotenuse

0.5 = 168 / Hypotenuse

Hypotenuse = (168)(0.5)

Hypotenuse = 84.

Hence, the wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

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The Y intercept of a straight line is simply where the line crosses the Y axis. In the above diagram the line crosses the Y axis at 1. The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero

Now, According to the question:

Y-Intercepts:

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Is the y-intercept 0 or 1?

The Y intercept of a straight line is simply where the line crosses the Y axis. In the above diagram the line crosses the Y axis at 1. The Y intercept is equal to 1 and the point is written as (0,1). Notice that for the y-intercept the x-coordinate of the point is always zero.

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