Find an equation of the line of symmetry of triangle ABC.

The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and

<k = 125 degree.

When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.

Given:

As, from the Figure

<h + 135 = 180 (Linear Pair)

<h = 180 - 135

<h = 45

and, <g = 135 (Vertical Opposite Angle)

Now, <m + 125 = 180 (Linear Pair)

<m = 180 - 125

<h = 55

and, <k = 125 (Vertical Opposite Angle)

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The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars

The mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.

How to solve for the mean of Y

Y = exp(Y)

= 60 * EXP(X) - 5

the expected value of x is 1.8

= 60 * 1.8 - 5

= 103 dollars

then we have to solve for the standard deviation of Y

standard deviation of x = 1.08

= 60 * 1.08

= 64.8 dollars

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Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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The volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters is 400π m³.

Volume is the amount of space occupied by an object in three dimensions. It is a measure of how much space is contained within a solid shape, such as a cube, sphere, or cylinder. The unit of volume can vary based on the system of measurement being used, but common units include cubic meters, cubic centimeters, liters, and gallons. Volume is calculated by multiplying the area of the base of the object by its height or depth, depending on the shape of the object.

The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.

In words, the volume of a right circular cylinder is equal to the area of the circular base (πr²) multiplied by the height (h). This formula holds true regardless of the dimensions of the cylinder, as long as it has a circular base and straight sides that are perpendicular to the base.

The volume of a right circular cylinder is given by the formula V = πr²h, where r is the radius of the circular base and h is the height of the cylinder.

Since the diameter of the circular base is 10 meters, the radius is half of that, or 5 meters. The height of the cylinder is 16 meters.

Substituting these values into the formula, we get:

V = π(5)²(16) = 400π

Therefore, the volume of the cylinder is 400π cubic meters.

So the answer is 400π m³.

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The height of the triangular prism will be 100mm.

The three-dimensional object has a base of triangular shape and has some height is called a triangular prism.

Given that the height and the base of the triangular shape of the triangular prism are 8 mm and 6.9 mm respectively. The volume of the prism is V = 2760 cubic mm.

The height of the triangular prism will be calculated as:-

Volume = 1/2 x b x h x H

2760 = 1/2 x 8 x 6.9 x H

H = 100 mm

Therefore, the height of the prism is 100mm.

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The shipping charge of an item on the purchase $56 is $2.52.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The percentage of a number is the value of the number out of 100.

For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.

A company charges  shipping fee = 4.5% of the purchase price for all items,

Cost of an item =$56

So, shipping fee = 4.5% of 56

= 4.5/100 × 56

= 0.045 × 56

= $2.52

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The solution of the expression for the value of k is [tex]\dfrac{8}{3^{15}}[/tex].

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

The given expression is,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

The given expression will be solved as below,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

Apply the properties of exponents which say that the number with the same base its exponents will be added.

[tex]\dfrac{3^{16}}{8}\times k = 3[/tex]

Now cross-multiply the number 3 by the ratio of 8 and the 3¹⁶ and solve for the value of k,

[tex]k = \dfrac{8}{3^{15}}[/tex]

Therefore, the value of k will be calculated as the ratio  [tex]\dfrac{8}{3^{15}}[/tex].

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Answer:

it's like this the answer

Step-by-step explanation:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Answer:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Step-by-step explanation:

Step-by-step explanation:

oh, come on ! we are dealing with rectangles.

and you know how to get the perimeter and the area of a rectangle. upper elementary school students can do that.

remember, the perimeter is the distance when you walk all around the rectangle.

so, 2 times the length and 2 times the width.

and the area is simply length × width.

but your teacher was very lazy and careless with some phrasing about what is needed.

the original room is 8 ft × 3 ft.

1.

the length of border needed is exactly the perimeter.

so,

2×8 + 2×3 = 16 + 6 = 22 ft

2.

the area of the floor is

8×3 = 24 ft²

this is the amount of floor panels to be bought. we buy them in ft².

3.

the new room is (8+3) ft × (3-2) ft. = 11 ft × 1 ft.

that is a very strange room. no human can live in such a room.

I think your teacher meant (8-2) ft × (3+3) ft = 6 ft × 6 ft.

but let's stick with the original information.

the border for this room (perimeter) is

2×11 + 2×1 = 22 + 2 = 24 ft

4.

the floor area is

11 × 1 = 11 ft²

if we consider my correction of the room size, it is

6×6 = 36 ft²

5.

"difference in size" is not clear. regarding the dimensions (side lengths and correspondingly the perimeter) or regarding the floor size ?

if we consider the perimeter, the difference is

24 - 22 = 2 ft

the new room's perimeter is 2 ft less.

if we consider the floor area, the difference is

24 - 11 = 13 ft²

the new room is 13 ft² smaller.

or for my size correction, the difference is

36 - 24 = 12 ft²

the new room is then 12 ft² larger.

Answer:

see explanation

Step-by-step explanation:

A segment joining the midpoints of two sides of a triangle is

parallel to the third side

∠ 1 and 144° are same- side interior angles and sum to 180° , so

∠ 1 + 144° = 180° ( subtract 144° from both sides )

∠ 1 = 36°

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

∠ 2 and 56° are corresponding angles and are congruent , so

∠ 2 = 56°

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

∠ 3 and 56° are a linear pair and sum to 180°

∠ 3 + 56° = 180° ( subtract 56° from both sides )

∠ 3 = 124°

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

the sum of the 3 angles in a triangle = 180° , then

∠ 1 + ∠ 2 + ∠ 4 = 180° , that is

36° + 56° + ∠ 4 = 180°

92° + ∠ 4 = 180° ( subtract 92° from both sides )

∠ 4 = 88°

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

∠ 5 and ∠ 1 are corresponding angles and are congruent , so

∠ 5 = 36°

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

Answer:

m∠1 = 36° , m∠5 = 36° , m∠4 = 88°  , m∠3 = 124° , m∠2= 56°

Step-by-step explanation:

m∠1 and 144° are Co-Interior angles, or the angles which are on the same side of the transveral

m∠1 + 144°  = 180°

m∠1 = 36°

angle 5 and 144° are in a linear pair-
144 °+ angle 5 = 180°

m∠5 = 36°

angle 5 + 56° + angle 4 = 180°        because addition of angles of a triangle is 180°

36° + 56° + angle 4 = 180°
angle 4 = 180° - 92°
angle 4 = 88°

56° and angle 3 are in a linear pair

56° + angle 3 = 180°
angle 3 = 124°

angle 3 and angle 2 are Co-Interior angles

angle 3 + angle 2 = 180°
124° + angle 2 = 180°
angle 2 = 56°

Hope it helped and you understood it :)

The mean cost for a pint of strawberries is $2.20, with a standard deviation of $0.50. The value of the variance will be 0.25.

The variance (σ2) is a measure of how ways each value inside the information set is from the mean.

A standard deviation (or σ) is a measure of the way dispersed the records are in terms of the suggested.

The formula for standard deviation is given, the square root of variance by determining each data point's deviation relative to the mean.

Standard deviation = $0.10

Variance = (standard deviation)²

Variance = ( 0.50 )^2 = 0.25

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Answer:

Step-by-step explanation:

The surface area of a cuboid is 600 cm².

The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.

Given that, a cuboid whose 6 faces have 10 cm.

We know that, surface area of a cuboid = 2(lb+bh+hl)

= 2(10×10+10×10+10×10)

= 2(100+100+100)

= 2(300)

= 600 cm²

Therefore, the surface area of a cuboid is 600 cm².

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Answer:

change the 2w value

Step-by-step explanation:

first, check the equation:

14w + 21 = 14w + 20

when subtracting the 14w from both sides you can see that

21 is NOT EQUAL to 20, making the answer NS.

now, reread the question... create a new equation with ONE solution.

to fix this, we need to change the amount of W's, NOT the amount of constant.

let's try out another number in place of 2w

7 ( 3w + 3 ) = 14w + 20

21 w + 21 = 14w + 20

7 w = -1

w = -1/7

so now it is clear. to change the outcome of the equation, try out another value instead of 2w. Maybe try 3w, 3.5w, or maybe even 1w, or 1.5w .

Answer:

change the 2w

Step-by-step explanation:

=> 7 ( 3w + 3 ) = 14w + 20

=> 21 w + 21 = 14w + 20

=> 7 w = -1

=> w = -1/7

So everything is now evident. Change the value of 2w to anything else to alter the equation's result. Try 3w, 3.5w, or even 1w or 1.5w if you can.

Hope it have been helpful.

Answer:

j≥19

hope this helpss :))

Yes, providing additional information affect responses to a survey question. The difference in the proportion of shoppers who admitted to texting and driving in the two groups is 0.2.

To calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups, we need to first determine the number of shoppers in each group who admitted to texting and driving.

Let's assume that in Group A, 10 shoppers admitted to texting and driving, while in Group B, 5 shoppers admitted to texting and driving.

Then, we can calculate the proportion of shoppers who admitted to texting and driving in each group by dividing the number of shoppers who admitted to texting and driving by the total number of shoppers in each group:

Proportion in Group A = 10/25 = 0.4

Proportion in Group B = 5/25 = 0.2

The difference in proportions is then:

Difference = Proportion in Group A - Proportion in Group B

Difference = 0.4 - 0.2

Difference = 0.2

Therefore, the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B) is 0.2 or 20%.

This suggests that providing additional information about the potential consequences of texting and driving may reduce the proportion of people who admit to engaging in this behavior. However, it's important to note that this study has a small sample size and there may be other factors that influence people's responses to survey questions about texting and driving.

Correct Question :

Does providing additional information affect responses to a survey question? Two statistics students decided to investigate by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked Version A and the other half were asked Version B. Version A: A lot of people text and drive. Are you one of them? Version B: About 6000 deaths occur per year due to texting and driving. Knowing the potential consequences, do you text and drive? Calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B).

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In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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The cost of each pizza is $14 and the cost of each cool drink is $3.

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.

Given that, John told Serena that when he ordered from Tony's last week, he paid $34 for two 16-inch pizzas and two drinks.

Let the cost of each pizza be x and the cost of each cool drink be y.

Now, 2x+2y=34

x+y=17 -------(i)

Jodi told Serena that when she ordered one 16-inch pizza and three drinks, it cost $23.

x+3y=23 -------(ii)

Subtract equation (i) from (ii), we get

x+3y-(x+y)=23-17

2y=6

y=3

Substitute y=3 in equation (i), we get

x=14

Therefore, the cost of each pizza is $14 and the cost of each cool drink is $3.

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Answer:

70

Step-by-step explanation:

Let x be the number of kangaroos adopted last year.

Twice the number adopted last year is 2x.

So, the number adopted this year is 2x - 24.

Equating this to the given number of kangaroos adopted this year, we have:

2x - 24 = 116

Adding 24 to both sides, we get:

2x = 140

Dividing both sides by 2, we get:

x = 70

So, the number of kangaroos adopted last year was 70.

Answer:

-94.94

Step-by-step explanation:

f(x)=23.2x+2.5

Let x = -4.2

f(4)=23.2(-4.2)+2.5

    =-97.44+2.5

    =-94.94

Answer:

Since x = -4.2, just fill it in the equation and solve:

23.2 * -4.2 + 2.5 =

23.2 * -4.2 = -97.44

-97.44 + 2.5 = -94.94

f(x) = -94.94

Step-by-step explanation:

Hope it helps! =D

Hope it ain't wrong either. If so, I'm sorry.

Answer:

68 people choose meat over pork

Step-by-step explanation:

subtract 17 from 85

Answer:

3w² = 243

Step-by-step explanation:

Answer:

12 ways

Step-by-step explanation:

the mother and father can either stand at the front/back or back/front respectively (2 ways)

that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6

6 ways for the children * 2 ways for the parents = 12 ways

Answer:

I think a is the right answer

The quadratic equation that represents the parabola is y - 2 = - x².

In this problem we find a table representing a quadratic equation, whose definition can be found by using two points and the vertex form of the parabola equation:

Vertex form

y - k = C · (x - h)²

Where:

First, determine the coordinates of the vertex of the parabola by table:

(h, k) = (0, 2)

Second, find the vertex constant:

C = (y - k) / (x - h)²

C = (1 - 2) / (1 - 0)²

C = - 1

Third, write the equation of the parabola:

y - 2 = - x²

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Answer:

ABCD forms a rhombus

Step-by-step explanation:

When you graph it out on a graph, the points make a rhombus

Step-by-step explanation:

9-3 =6

So we have 6 dollars for 3 bracelets

Which means each bracelet costs 2 dollar each

So 9x-3x=6x

Note that the lenght of segment LN = 55.14 (Option D)

This is arrived at using the Chord Bisector Theorem and the  lengths of the sides of a right-angled triangle.

According to the theorem, the line that goes through the circle's center and is perpendicular to the chord also bisects it.

This means that LK (as per the attached image) is the same as MK.

The Right Angle Postulate also means that:

LX = √[KX² - LK²]

LX = √[29² - 9²]

LX = √(841  81)

LX = √760

LX = 27.57

Since LN = LX *2
LN = 27.57 * 2

LN = 55.14

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The slope between the points is same, hence the points lie on the same line. The point (2, 3) does not lie on the graph of y = 3x - 4.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The given points are, (1,3) (4,2) (-2,4):

Calculate the slope of the line formed by the points.

The slope of the line is given by:

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

For (1,3) (4,2):

m = (2 - 3) / (4 - 1) = -1/3

For (4,2) (-2,4):

m = (4 - 2) / (-2 - 4) = 2/ -6 = -1/3

The slope between the points is same, hence the points lie on the same line.

The equation of the graph is:

y = 3x - 4

The given point is (2, 3):

Substituting the point in the equation:

3 = 3(2) - 4

3 = 6 - 4

3 = 2

False.

Hence, the point (2, 3) does not lie on the graph of y = 3x - 4.

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