find an equation for the perpendicular bisector of the line segment whose endpoints are (-1,-1) and (9,-5)​

Hence, if one trigonometric function of x is tangent, the value of x is arctan [tex]\frac{1}{\sqrt{5} }[/tex]. We can start solving this equation by isolating one of the trigonometric functions.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is a fundamental part of geometry, and is also used in other areas such as physics, engineering, and navigation.

Trigonometry functions such as sine, cosine and tangent are used to describe the ratios between the sides of a right angled triangle, These functions are periodic and defined for all real numbers.

Since the tangent and cotangent functions are reciprocals of each other, we can multiply both sides of the equation by the reciprocal of the tangent function:

[tex]\frac{1}{tan(x)}[/tex] = [tex]\frac{1}{2} * \frac{1}{cot(x)}[/tex]

Now we can use the fact that the cotangent function is the reciprocal of the tangent function to write:

[tex]\frac{1}{tan(x)}[/tex] =[tex]\frac{1}{2} * \frac{1}{\frac{1}{tan(x))} }[/tex]

Solving for tan(x) we get:

tan(x) = [tex]\frac{1}{\sqrt{5} }[/tex]

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Answer:

a = 23

c= 13

this is the answer

4 is the value of x ,on solving that  m and n are in perpendicular lines. calculating  the slope of AB is explained below,

in  order to find the slope of AB. the formula is used as

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

on substituting we get,

m=(8-6)/(4-(-2))

m=2/6

m=1/3

Calculating CD  in which it is perpendicular to AB

hence, it should contains the negative reciprocal of the slope of AB, mathematically as ,

m1 * m2= - 1  ,condition is applied when m and n  lines to be perpendicular

hence,

m/3=-1

m = - 3    

therefore  CD will have a slope of -3

in which CD  can be expressed as part of the each  line:

y=-3x+b, on solving  for b using point C, (8,12)...

12 = - 3(8) + b

12= - 24 + b

36=b

hence, the line of CD is :

y = - 3x + 36  

the x coordinate is calculated  for (x,24),

hence,

y=24

24=-3x+36

3x+24=36

3x=12

x=4

therefore the value of x = 4 when the 2 lines are in parallel lines .

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1000 cubic millimeters are in a cubic centimeter.

'What is cubic centimeter?'

There are 1000 cubic millimeters in one cubic centimeter (cm³) (mm³). Add 1000 to the cubic cm number to convert it to cubic mm.

For instance, multiplying 10 by 1000 results in 10000 mm3, or how many cubic mm there are in 10 cubic cm.

The volume of small items is measured in cubic centimeters, a tiny unit of measurement. Discover standard units of measurement, the definition of cubic centimeters, how to convert them, and how to measure volume using cubic centimeters. A little cube with sides that are 1 cm long occupies the same amount of space as a cubic centimeter.

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Answer:

Volume= πr^2h

Step-by-step explanation:

if you plot the values in above given formula

V≈0.058m³

V≈3562.57in³

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=7 \end{cases}\implies 7\theta =180(7-2) \\\\\\ 7\theta =900\implies \theta =\cfrac{900}{7}\implies \theta =128\frac{4}{7}\implies \theta \approx 128.57^o \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underset{in~degrees}{\textit{sum of all exterior angles}}\\\\ n\beta = 360 ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \beta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=7 \end{cases}\implies 7\beta=360 \\\\\\ \beta=\cfrac{360}{7}\implies \beta=51\frac{3}{7}\implies \beta\approx 51.43^o[/tex]

Answer:

31 levels

Step-by-step explanation:

Zoey already has 25 points

So she needs at least 850-25 more points to beat the high score

850-25 = 775

So Zoey needs at least 775 points more

Since she earns 25 points for each level, if she has to play L levels to beat the high score, she will need at least 25L points and that should be greater than or equal to 775

Therefore the inequality is
25L ≥ 775

Dividing by 25 on both sides of the inequality gives:

L ≥ 775/25

which simplifies to L ≥ 31

So Zoey needs at least 31 levels before she can break the record

The diagonal of a rhombus is a line lump that joins any two non-adjacent apexes of a rhombus.

A rhombus has two diagonals that cut each other at right angles, thus, they form 4 right-angled congruent triangles.

When the opposing vertices of a rhombus are joined, they form the diagonals of a rhombus. A rhombus has two diagonals that oppose each other at 90 degrees. Observe this rhombus to identify its diagonals and their properties listed in the following section.

The diagonals of a rhombus are line segments that are unavoidable between the opposite vertices of the rhombus. The quality of the diagonals of the rhombus are listed below.

The diagonals of a rhombus cut each other at right angles.

The diagonals of a rhombus may not be fundamentally equal.

The two diagonals cleave the rhombus into four congruous right-angled triangles.

The length of the diagonals can be calculated by different methods like using the Pythagoras theorem or by using the area of the rhombus.

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Answer:

[tex] x 2 + 4x + 4[/tex]

Step-by-step explanation:

yes

The graph of function g is a reflection of the graph of function f in the x-axis. This means that the transformation that took place to produce function g was a reflection in the x-axis.

Transformation is the process of changing something into a different state or form. It can refer to physical, emotional, spiritual, or psychological changes. It can involve transformation of an object, person, or situation. Transformation is often associated with growth and development and can require significant effort and dedication. Transformation can be used to make positive changes in our lives and ultimately lead to a better future. It is a process of self-discovery and can be a powerful tool for personal growth and development.

This means that for each x-value in function f, the corresponding y-value in function g is the negative of the y-value in function f.

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Answer: The markup percentage for the shirts is 22%. This means that the store makes a profit of 22% on the shirts, based on the cost price.

Step-by-step explanation:

To find the percent markup of the shirts in this case, we can use the following formula:

Markup percentage = (selling price - cost price) / cost price x 100%

Given that the cost price of the shirts is $9,000 and the selling price is $20 per shirt, we can substitute these values into the formula and calculate the markup percentage:

Markup percentage = ($20 - $9,000) / $9,000 x 100%

= (11,000 - 9000) / 9000 x 100% = 2000/9000 x 100% = 0.22 x 100% = 22%

- C

On solving the provided question, we can say that - the perimeter chest won't fit next to her bed, thus the answer is no.

The perimeter of a form is determined by the length of its contour. A rectangle or square's perimeter is determined by adding the widths of its four sides. In this instance, the rectangle's length and breadth are represented by x and y, respectively. The surface of a form is used to compute its area.

Given here is: In her room, it is 86 inches wide. The width of the bed is 76 inches.

She also wants to accommodate a chest of drawers that is 72 centimeters broad, which equals inches.

=> 90 cm = 24.6546536565 inches

and the space left in her room = 86-76=10 inches

thus, the chest will not fit next to her bed

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Where the properties of the triangle are given, by angle sum property the value of x in the expression (2 x + 10) +  (6 x + 1) +79 =180  is 11.25

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 °.

2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles.

The top angle of the triangle is (2 x + 10) °. The bottom right angle of the triangle is 79°.

The exterior angle to the bottom left angle is (6 x + 1) °.

By angle sum property

(2 x + 10) +  (6 x + 1) +79 =180

8x+11 + 79 =180

8x+11=180-79

8x+11 =101

8x = 90

x = 11.25

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a. The probability of guessing exactly three answers correctly is 0.0879.

b. The probability of guessing at least three answers correctly is 0.1035.

c. The probability of guessing less than three answers correctly is 0.8965.

Total number of questions = 5

Possible answer = 4

Therefore, the probability that the question is correct = 1/4 = 0.25

By using the Binomial Probability distribution

P(X=x) = ⁿCₓ * p^x * (1-p)^n-x

a) P(X = 3) = ⁵C₃ * (0.25)^3 * (1-0.25)^5-3

P(X = 3) = 0.0879

Therefore, the probability of guessing exactly three answers correctly is 0.0879.

b) P(X ≥ 3) = 1 - P(X ≤ 2)

P(X ≥ 3) = 1 - P(X = 0) + P(X = 1) + P(X = 2)

P(X ≥ 3) = 1 - (0.2373 + 0.3955 + 0.2637)

P(X ≥ 3) = 1 - 0.8965

P(X ≥ 3) = 0.1035

Therefore, the probability of guessing at least three answers correctly is 0.1035.

c) P(X < 3) = P(X ≤ 2)

P(X < 3) = 0.8965

Therefore, the probability of guessing less than three answers correctly is 0.8965.

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x²+√2x+3  and x²+√2x+6  are expressions that are not polynomial. (Option a and Option b)

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.

For the algebraic expression to be called a  polynomial, the exponents in the algebraic expression should be non-negative integers. Also if an algebraic expression has a radical in it then it can not be called a polynomial.

a) x²+√2x+3. This expression is not a polynomial as the polynomial expression does not contain any radicals. √2 here is a radical root.

      ⇒   Hence, option a is not a polynomial expression.

b) x²+√2x+6.This expression is also not a polynomial expression as it has a radical √2 present in the expression.

      ⇒   Hence, option b is not a polynomial expression.

c) x³+3x²-3. This expression can be termed as a polynomial expression since all of the variables have positive integer exponents.

     ⇒    Hence, option c is a polynomial expression.

d) 6x+4​. This expression is also a polynomial expression as all of the variables have positive integer exponents.

      ⇒   Hence option d is a polynomial expression.

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The point where the triangle's three altitudes connect is known as the orthocentre.

The circumcentre is the center of a triangle's circumcircle. It can be found as the point of intersection of the perpendicular bisectors of the triangle.

The letter H is frequently used to denote the orthocentre.

The kind of triangle determines where the orthocentre is.

The orthocentre will be located inside an acute triangle.

The orthocentre will be outside of an acute triangle.

Finally, the orthocentre will be the vertex at the correct angle if the triangle is right.

Thus, The point where the triangle's three altitudes connect is known as the orthocentre.

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The polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is f(x)=5(2x+3)(x+4) (x − 2)

The roots we can find by using 2x+3=0, x+4=0 and x-2=0

x=-3/2

x+4=0

x=-4

and x=2 are the roots of function.

Roots are nothing but zeros of the polynomial.

The function has exactly 3 zeros.

Hence, the polynomial function f(x)=5 (2x+3)(x+4) (x − 2) has exactly 3 zeros. So statement A is correct.

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Answer:

ii. (5x – 6) (5x – 4)

= 5x(5x - 4) - 6(5x - 4)

= 25x^2 - 20x - 30x + 24

= 25x^2 - 50x + 24

iii. (8m – 3n) (8m + 6n)

= 8m(8m + 6n) - 3n(8m + 6n)

= 64m^2 + 48mn - 24mn - 18n^2

= 64m^2 - 18n^2

iv. (4a – 6) (4a + 6)

= 4a(4a + 6) - 6(4a + 6)

= 16a^2 + 24a - 24a - 36

= 16a^2 - 36

v. 98 × 102

= (100 - 2)(100 + 2)

= 10000 - 400

= 9600

vi. 104 × 103

= (100 + 4)(100 + 3)

= 10000 + 300 + 400 + 12

= 10,712

Step-by-step explanation:

The solution of the inequality −2(−3x+4) − 5 > −3(x+7) − 19 is x > -3.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality as follows:

−2(−3x+4) − 5 > −3(x+7) − 19

let's open the brackets on both sides

−2(−3x+4) − 5 > −3(x+7) − 19

6x - 8 - 5 > -3x - 21 - 19

6x - 13 > -3x - 40

add 13 to both sides of the inequality

6x - 13 > -3x - 40

6x - 13 + 13 > -3x - 40 + 13

6x > -3x - 27

add 3x to both sides of the inequality

6x + 3x > -3x + 3x - 27

9x > -27

divide both sides by 9

x > -27 / 9

Hence,

x > -3

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Answer:

see below

Step-by-step explanation:

1st polynomial = 4q + 3b + 2c

2nd polynomial= -6a +4b -2c -2

Subtracting 2nd from 1st ,

= 4a -3b +2c - (-6a +4b -2c -2)

= 4a - 3b + 2c +6a -4b +2c +2

group like terms ,

=(6a +4a)-(4b +3b) +(2c+2c)+2

= 10a -7b +4c +2

since the highest degree of any variable is 1 so its degree is 1.

And we are done!

-Rishabh

Answer:

Step-by-step explanation:

d = dogs

c = cats

10 : 4 = 5 : d

d = 4 * 5 : 10

d = 2

5 : 2 = c : 32

c = 5 * 32 : 2

c = 80

Using a system of equations, if the summer soccer camp paid a total of $1,046 for the purchase of 84 soccer balls and t-shirts for $25 and $9.50 each, the number of each item ordered was 16 soccer balls and 64 t-shirts.

A system of equations is described as two or more equations solved concurrently.

It is also called simultaneous equations.

The total number of soccer balls and t-shirts ordered = 84

The cost per soccer ball = $25

The cost per t-shirt = $9.50

The total payment for the two items = $1,046

Let soccer balls = s and t-shirts = t

s + t = 84 ... Equation 1

25s + 9.5t = 1,046 ... Equation 2

Multiply Equation 1 by 25 to eliminate s:

25s + 25t = 2,100 ... Equation 3

Subtract Equation 2 from Equation 3:

25s + 25t = 2,100

-

25s + 9.5t = 1,046

= 15.5t = 1,054

t = 68

s + t = 84

s + 68 = 84

s = 16

Check:

25s + 9.5t = 1,046

25(16) + 9.5(68) = 1,046

400 + 646 = 1,046

Thus, the camp ordered 16 soccer balls and 64 t-shirts.

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The speeds of each train are 355.4 miles per hour and 365 miles per hour

From the question, we have the following parameters that can be used in our computation:

This means that

Train 1 + Train 2 = 720.4

Train 2 = 9.6 + Train 1

Substitute Train 2 = 9.6 + Train 1 in Train 1 + Train 2 = 720.4

Train 1 + 9.6 + Train 1 = 720.4

So, we have

2Train 1 = 710.8

Divide both sides by 2

Train 1 = 355.4

Recall that

Train 2 = 9.6 + Train 1

So, we have

Train 2 = 9.6 + 355.4

Evaluate

Train 2 = 365

Hence, the speeds are 355.4 and 365

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The required equation of the lines in the slope-intercept form can be obtained as y = -0.5x + 3, y = 2.5x + 1, y = -4x - 5, y = -x + 2, y = 2/3x - 4 and y = x.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The  equation of the lines given in the graph can be written as,

(4) Slope of the line is m = (3 - 0)/(0 - 6)

⇒ m = -0.5

And, y-intercept is 3

Then, the slope-intercept equation can be written as y = -0.5x + 3.

(5) Slope of the line is m = (1 - (-4))/(0 - (-2))

⇒ m = 5/2 =2.5

And, the y-intercept is 1.

Then, the slope-intercept equation can be written as y = 2.5x + 1.

(6) Slope of the line is m = (-5 - 3)/(0 - (-2)) = -4

And, the y-intercept is -5.

Then, the slope-intercept equation can be written as y = -4x - 5.

(7) Slope of the line is m = (2 - 0)/(0 - 2) = -1.

And, the y-intercept is 2.

Then, the slope-intercept equation can be written as y = -x + 2

(8) Slope of the line is m = (-4 - 0)/(0 - 6) = 2/3

And, the y-intercept is -4.

Then, the slope-intercept equation can be written as y = 2/3x - 4.

(9) Slope of the line is m = (6 - 0)/(6 - 0) = 1.

And, the y-intercept is 0.

Then, the slope-intercept equation can be written as y = x.

Hence, the equations of the lines can be obtained as y = -0.5x + 3, y = 2.5x + 1, y = -4x - 5, y = -x + 2, y = 2/3x - 4 and y = x.

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Answer: the answer is D. The panels already on the garage produce 600 watts of energy

Step-by-step explanation:

any starting energy would be above zero with there already being solar panels! So that leads to a y-intercept! Whatever the line starts at will tell you the amount of energy you get from the starting panels:) I hope this is helpful!

To solve a complex fraction with a whole number, you will need to first simplify the fraction by dividing the numerator and denominator by the same number.

A complex fraction is a fraction that contains another fraction within its numerator or denominator. To solve a complex fraction with a whole number, you will need to first simplify the fraction. This can be done by dividing the numerator and denominator of the fraction by the same number. Once the fraction has been simplified, you can further reduce the fraction as much as possible by cancelling out common factors. Finally, you can divide the numerator by the denominator of the fraction to find the answer as a whole number. It is important to note that the answer can also be in the form of a mixed number, depending on the result of the division.

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You must first simplify the fraction by dividing the numerator and denominator by the same amount in order to solve a complex fraction with a whole number.

A fraction that includes another fraction in either the numerator or denominator is referred to as a complicated fraction. You must first simplify the complex fraction in order to solve it with a whole number.

To achieve this, divide the fraction's numerator and denominator by the same number. After the fraction has been made simpler, it can be further decreased as much as feasible by removing frequent elements.

To find the solution as a whole number, divide the fraction's numerator by its denominator. It is significant to remember that, depending on how the division turned out, the solution could possibly take the shape of a mixed number.

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Step-by-step explanation:

the solution of a system of 2 equations (lines or other forms of functions) is the set of all intersection points.

that is where the equations are equal, share the same "behavior".

for 2 lines it is only possible to have

in our case here we see that most points are different.

so, the lines are not identical.

and there is one point they have in common : (0, 2).

that is the solution, the one intersection point.

since they have a point in common, they cannot be parallel.

Answer:

Maps show height in a number of different ways: Spot heights and triangulation pillars This map extract shows exact heights by a black dot with a number next to it

Step-by-step explanation:

The scale factor is 8 : 1 ( option A)

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2. The new sides will be 4cm and 8cm. Therefore the scale factor is 2

To calculate scale factor we divide the new shape size by original shape .

The new shape is 24m and the original shape is 3m.

scale factor = 24m/3m = 8/1

therefore scale factor = 8 : 1

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Answer:

8:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

when you divide you get 43. something but you can't have half of a chair so you should get another one making it 44 chairs

if wrong i'm sorry.