The area of a right Triangle is 30 sq.cm and it’s perimeter is 30cm. If it’s hypotenuse is 13cm, what are the lengths of the other two sides?

In given expression constant term is 4, degree of expression is 2, coefficient of second term is 5 and at x=-1 value of expression is 6.

The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial.

The degree denotes the polynomial's highest exponential power.

A term in an equation with a fixed value that is unaffected by variations in the variable.

A constant is typically represented as c to reflect a fixed value when written as a variable.

The usage of the word "variable" in this terminology may be perplexing, but all it really implies is that c is a variable that may stand in for any fixed value.

Given: p(x)=7x²+5x+4

(a) Constant term is coefficient of [tex]x^{0}[/tex].

So constant term in given equation is 4.

(b) Degree of expression is highest power of x in the expression. For our expression we have two as our highest power.

So, degree of expression is 2.

(c) Coefficient of second term is 5.

(d) On substituting value of x as -1, we get

7× (-1)² +5(-1) +4 = 7-5+4 = 6

So, value of expression at x=-1 is 6.

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The data set of favorite sports among 9th graders is univariate and numerical.

Univariate data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In bivariate two different variables in this kind of data. The analysis of this kind of data focuses on linkages and causes, and it seeks to understand the causal connection between the two variables.

Given, A set of data of the favorite sports among 9th graders.

Baseball or Softball, Basketball, Lacrosse, Soccer and Field hockey

and the percentage of 9th graders who plays a certain type of sport.

This is a univariate and numerical type of data set not bivariate,

An example of bivariate data is temperature and ice cream sales in the summer season as the sales of ice cream must be related to the temperature.

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An equation to represent the other lengths, X, of the triangle is 2X+7=23.

An isosceles triangle is one that has two equal-length sides in geometry. The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception. The faces of bipyramids and a few Catalan solids are examples of isosceles triangles, as are the isosceles right triangle, the golden triangle, and others.

Isosceles triangles have been the subject of mathematical research since the time of the Babylonians and the Egyptians.

Given,

Perimeter of an isosceles triangle=23 meters

The base of a triangle=7 meters

P=2X+b

2X+7=23

Therefore, an equation to represent the other lengths, X, of the triangle is 2X+7=23.

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Answer:

Add together

Step-by-step explanation:

Look all you do is add them all together!

The equation of the line passing through points (5, 18) and (8, 9) will be y = - 3x + 33.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(5, 18) and (8, 9)

The points (5, 18) and (8, 9) will satisfy the equation y = mx + c, then the equations are given as,

18 = 5m + c          ...1

9 = 8m + c           ...2

From equations 1 and 2, then we have

18 - 9 = 5m - 8m

3m = - 9

m = -3

Then the value of 'c' is given as,

9 = 8(-3) + c

9 = - 24 + c

c = 33

The equation is written as y = -3x + 33.

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Answer:

1:2

1 to 2

These are the other notations for 1/2

Answer:

You're welcome. :)

Step-by-step explanation:

Hope you're able to understand it.

No, the ordered pair (0, 4) is not a solution of the inequality y ≤ x − 3

The solution of the inequality is checked by substituting the value in the ordered pair

If the given function helps in finding the each of the numbers that makes up the ordered pair then it is a solution

The substitution is as below

y ≤ x − 3

substituting x = 0

y ≤ x − 3

y ≤ 0 − 3

y ≤ -3

y is 4 and 4 is not less than or equal to -3, this means that the ordered pair is not a solution

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21.8 cm  is length of rectangle .

What is the name of the rectangle shape?

A rectangle may also be referred to as an equiangular quadrilateral. This is so because a rectangle is a quadrilateral (4-sided form) with parallel sides that are equal to one another and corners with 90o angles on each side.

             An equiangular quadrilateral is another name for a rectangle shape because all of the angles are 90 degrees.

L=5+6W

156 = 2L + 2w

2(5+6W) + 2W = 156

10+ 12W +2W =50

   14W = 40

    W = 40/14

      W = 2.8 CM

W =5 cm

L= 5+6( 2.8 ) = 21.8 cm

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The number of students travelled by bus and train are 38.

Given that, the Marching Band is traveling from Minnesota to Florida to perform in a national competition

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x = Students traveling by train

Let y = Students traveling by bus

Now equations to represent the situation is

150x+120y=4,800 and 15x+20y=720

30(5x+4y)=4,800

5x+4y=160 ----------(I)

15x+20y=720

3x+4y=144 ----------(II)

Subtract equation (II) from (I), we get

5x+4y-(3x+4y)=160-144

⇒ 2x=16

⇒ x=8

Substitute x=8 in equation (I), we get

5(8)+4y=160

⇒ 4y=120

⇒ y=30

Number of students =38

Therefore, the number of students travelled by bus and train are 38.

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Answer:

Step-by-step explanation:

7y = -3x + 7

y = -3/7x + 1

Answer:

Step-by-step explanation:

-3.45

From the given 2D graph:

1. It took 20 minutes for Alec to get to his first friend's house.

2. Alec stayed for 40 minutes at his first friend's house.

3. It took 10 minutes for Alec to ride his bike from his first friend's house to his second friend's house.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

4. Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for 115 minutes.

1. From the given graph we can observe that part A of the graph is the time taken by Alec to reach his first friend's house which is 20 minutes.

2. From the given graph we can observe that part B of the graph is the time that Alec stayed at his first friend's house.

3.  From the given graph we can observe that part C of the graph is the time that Alec took to ride his bike from his first friend's house to his second friend's house.

4. Alec stayed at his first friend's home for 40 minutes, and he stayed at his second friend's home for 30 minutes, therefore Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.

5. In part E of the graph Alec is riding his bike toward his home.

6. In part A of the graph Alec is traveling the fastest.

7. Alec was away from his house for part(A+B+C+D+E)=20+40+10+30+15=115 minutes.

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They took 1.53 hrs long before they are 1000 nautical miles apart.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Here, we have

A plane leaves Charlotte at 9:00 AM and flies north at 400 knots. At the same time, another plane flies south from Charlotte at 250 knots

The speeds are added when going in opposite directions = 400 + 250knots =  650 knots

We apply here distance formula,

Distance = rate × time

t = d/r

= 1000/650 hours

= 1.53 hours

Hence, they took 1.53 hrs long before they are 1000 nautical miles apart.

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The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Now,

Since, The synthetic division problem is,

⇒ - 3/ 2 4 -4 6

Hence, The divisor of the synthetic division problem is,

⇒ x - (- 3) = x + 3

And, There are four leading coefficient.

Hence, The dividend of the polynomial must be degree of 3.

So, By the leading coefficient are;

⇒ 2, 4, - 4, 6

Hence, We get;

⇒ 2x³ + 4x² - 4x + 6

Thus, The value of divisor and the dividend for the synthetic division problem will be;

⇒ (x + 3) and 2x³ + 4x² - 4x + 6

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Answer:

-10x = -51 + 5

-10x = -46

x=-46/-10

x=46/10

x=4.6

Answer:

x=23/5

Step-by-step explanation:

-10x-5=-51

-10x=-51+5

-10x=-46

10x=46

x=46/10

x=23/5

Answer:

I think its these:

(0,3)

(1,4)

(2,5)

Step-by-step explanation:

Having sides that are parallel to one another, a parallelogram is a two-dimensional geometric shape. It is a sort of four-sided polygon (sometimes known as a quadrilateral) where each parallel pair of sides is the same length.

In addition, AB = CD and AD = BC.

A = C & B = D are also true.

Therefore,

∠A + ∠D = 180

∠B + ∠C = 180

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When  (a, b) appears on a graph, it is said to be symmetric around the x-axis if (a ,b) also appears there at the same time. A graph that is symmetric around the x-axis is shown in the following illustration. A graph is said to be symmetric around the y-axis if and only if (a ,b) and (a, b) are both present on it.

We replace all the x's with -x and check to see if we get an equivalent formula to determine algebraically whether a graph is symmetric with regard to the y axis. Example: A) To make y = x2 symmetric with regard to the y axis, we substitute y = (-x)2 = x2 for y = x2.

Ordered pairs (x, y) and and exist in equations or functions that are symmetric to the origin (-x, y). The original equation is symmetric with respect to the origin if you swap -x for x and -y for y in the equation and simplify.

If we reflect a function's graph about the y-axis, we will get the same graph since some functions might be symmetrical about the y-axis. We may reflect various functions about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as even and odd functions.

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45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

Two or more expressions with an Equal sign is called as Equation.

Given,

Salad 'n Scoops is a food truck that sells salads for $4 and scoops of ice cream for $2

On a hot July day, they had 118 customers and earned $326.

Let x be the number of scoops of ice cream sold and y be the number of salads sold that day.

From the given information

4x+2y=$326...(1)

x+y=118

x=118-y..(2)

Substitute 2 in 1

4(118-y)+2y=326

472-4y+2y=326

472-2y=326

Subtract 472 on both sides

-2y=-146

Divide both sides by 2

y=73

Plug in y value in equation 2'

x+y=118

x+73=118

x=118-73

x=45

Hence, 45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.

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Answer: they are complementary

Step-by-step explanation:

they are complementary because they both add up to 90°

Answer:

yes, because there is a constant of proportionality

Step-by-step explanation:

pages = 4h

If h = 1 ; pages = 4

if h = 2 ; pages = 8

4 / 1 = 4

8 / 2 = 4

The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.

What is line tangent?

A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Given g(x)=f(2x)

Differentiate it on both side with respect to x.

[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]

Slope =-10

Here x coordinate = -4

g(-4)=f(-8)=-4 = y coordinate

Thus point of tangency on function g is (-4,-4)

Thus equation of tangent is

y + 4= -10(x+4)

y + 10x + 44 =0

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Answer:

  y = 8x -11

Step-by-step explanation:

You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.

The equation of the tangent line at x=1 can be written ...

  y = g'(1)(x -1) +g(1)

The necessary function values are ...

  g(1) = f(2·1 -6) = f(-4) = -3

and

  g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)

  g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8

Then the equation of the line is ...

  y = 8(x -1) +(-3) = 8x -8 -3

  y = 8x -11 . . . . . . tangent to g(x) at x=1

__

Additional comment

The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).

The graph of f(x) = x in a straight line passing through the origin (0,0) and  at an angle of 45 degrees to the x axis. It increases from left to right.

What is graph?

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

A simple graph is one in which no two vertices are connected by more than one edge, and no edge begins or finishes at the same vertex. In other terms, a simple graph is one that doesn't have loops or many edges.

Reflection in the x axis  will convert all positive values of f(x) to negative values of f(x)  and vice versa.  

g(x)  = - x     and is a straight line passing through origin  at angle of 45 degrees but the slope descends from left to right.

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The vertex of the graph for the given equation is (-1, -8).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

Its geometrical aspect is the slope of the tangent at a given point.

The given equation is y = 2x² + 4x - 6.

The vertex is a point at the graph where the slope becomes zero. It can be found by equating the differentiation of the equation to zero as below,

y = 2x² + 4x - 6

=> y' = 4x + 4 = 0

=> x = -1

At x = -1 the value of y can be found as,

y = 2 × -1² + 4 × -1 - 6

  = 2 - 4 - 6

  = -8

Thus, the vertex is given as (-1, -8) which is only valid for option (b).

Hence, the key points to be used by sandy to draw the graph are x-intercept (1, 0), y-intercept (-3, 0) and vertex (-1, -8).

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The equation in point slope form will be -

y - 2 = 2(x - 3).

The general equation of a straight line is -

Other possible equations of lines are -

We have some equations of line as given in the question.

The point slope form is -

(y - y₁) = m(x - x₁)  

The points are -

(3, 2) and (5, 6)

So -

m = (6 - 2)/(5 - 3)

m = 4/2

m = 2

Equation will be -

y - 2 = 2(x - 3)

Therefore, the equation in point slope form will be -

y - 2 = 2(x - 3)

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Answer:

8x ≤ 53 - 10

8x ≤ 43

x ≤ 43/8

X is smaller or equal to 43/8 (5.375)

Answer:

39.512195122

Step-by-step explanation:

You divide 162 by 4.1, you can use a calculator to help solve. If needed to be rounded it is 40