Worth 20 Points

The angle between 0 and 2\pi in radians that is coterminal with the angle (5)/(2)\pi in radians is

The points D(3,-5), E(3, 4), and F(-4, 3) form a triangle. Then 26.701 unit is the perimeter of the triangle.

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. The length of the shape's edge is measured by its perimeter. All of the shape's sides added together provide it. It just has one dimension and uses linear units to represent itself. In contrast, area quantifies how much space a form takes up.

The points D(3,-5), E(3, 4), and F(-4, 3) form a triangle.

DE = [tex]\sqrt{(3-3)^2+ (4 +5)^2}[/tex]

DE = 9 units

EF = [tex]\sqrt{(-4-3)^2+ (3-4)^2}[/tex]

EF = √50 units

DF = [tex]\sqrt{(-4-3)^2 + (3+5)^2}[/tex]

DF = √113 units

So, the perimeter of the triangle DEF = sum of all three sides

= 9 units +  √50 units + √113 units

= 26.701 unit

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Answer:

what is the question?

Answer to what?

There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: Useful if you simply need a broad answer or are certain that the intersection takes place at an integer location. To find where the two lines intersect, just plot them.

(2) The Substitution Approach: To begin, a linear equation for y must be resolved in terms of x. Substitute that expression for y in the other linear equation after that. A formula will be given to you in x. You'll know the intersection's x-coordinate if you can figure this one out. Insert x into either equation to get the equivalent y-coordinate.

(3) Using a linear combination: Add (or subtraction) a multiple of one equation to (or from) the other equation to make the x-terms or y-terms cancel out. Solve for x (or y, depending on which is left) before substituting to get the other coordinate.

(4) The Matrix Approach: This is actually just a streamlined notation of the Linear Combination approach.

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Answer:

Step-by-step explanation:

Answer:

7.8

Step-by-step explanation:

7 plus 0 is 7 and .5 plus .3 is .8.

Answer: The answer (when finding s) is 7.8

Step-by-step explanation: The equation is fairly straight-forward. The equation is asking you what the variable s is equal to. You simply add 7.3 and 0.5. Since 5 and 3 is 8 that gives you the decimal 0.8, and there is nothing being done to the 7 making the answer 7.8

Mean

Step-by-step explanation:

Use the mean to find the average price since the numbers are far apart.

Answer:

No

Step-by-step explanation:

[tex]s = 2(5)(3) + 2(3)(4) + 2(5)(4) \\ = 30 + 24 + 40 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: = 94 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

1

Step-by-step explanation:

Answer:

t = 16

Step-by-step explanation:

B and C are corresponding points.

D and E are also corresponding points.

Hence, BD = CE.

t + 90 = 10t - 54  ==> substitute t + 90 for BD and 10t - 54 for CE

t + 144 = 10t  ==> add 54 on both sides

144 = 9t  ==> subtract 9t on both sides

t = 16  ==> divide both sides by 9

Step-by-step explanation:

The length of mid segment of trapezoid is given by the equation (1)

[tex]length of mid segment = \frac{b1 + b2}{2} [/tex]

The given trapezoid ABCD has following properties

AD and BC are the bases of the trapezoid.

Mid segment of trapezoid = EF

AD = 4

EF = 2x + 8

BC = 5x + 5

b1 = AD

b2 = BC

[tex]EF = \frac{AD + BC}{2} [/tex]

[tex]2x \: + 8 = \frac{4 + 5x + 5}{2} [/tex]

[tex]4x + 16 = 5x + 9[/tex]

[tex]5x - 4x = 16 - 9[/tex]

[tex]x = 5[/tex]

so if we put in value of x in EF

we get,

EF = 2x + 8 = 2(2) + 8 = 4 + 8 = 12

According to the transformation as shown in the graph the equation of f(x) is

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations.

The approach include: reflection, rotation, translation and dilation

The Pre-Image is the object's original shape, while the transformed object's ultimate shape and location is termed the Image.

In the transformation, the movement is as follows

(x - 2)²: translation to the right by 2 units

(x - 2)² + 2: translation 2 units up

2(x - 2)² + 2: vertical stretch 2 units

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Answer:

160 cups are in 10 gallons

The circumference of a circle with given radius is 30.1 meters.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Also, it has rotational symmetry around the center for every angle.

Given the radius of the circle = 4.8 m

to find the circumference,

circumference of a circle is given by

C = 2πr

where r = radius = 4.m

C = 2π(4.8)

C = 2(3.14)(4.8)

C = 30.144 m

C = 30.1 m

Hence the circumference is 30.1 metres.

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====================================================

Explanation:

Let's find the slope.

[tex]A = (x_1,y_1) = (4,7) \text{ and } B = (x_2,y_2) = (2,3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{3 - 7}{2 - 4}\\\\m = \frac{-4}{-2}\\\\m = 2\\\\[/tex]

The slope is 2.

Then apply point-slope form

[tex]\text{y} - \text{y}_1 = \text{m}(\text{x} - \text{x}_1)\\\\\text{y} - 7 = 2(\text{x} - 4)\\\\\text{y} - 7 = 2\text{x} + 2(-4)\\\\\text{y} - 7 = 2\text{x} -8\\\\\text{y} = 2\text{x} -8+7\\\\\text{y} = 2\text{x} -1\\\\[/tex]

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

Check:

Plug in x = 4. We should get y = 7 as the output.

y = 2x-1

y = 2*4-1

y = 8-1

y = 7

This verifies point A(4,7) is on the line.

Plug in x = 2. We should get y = 3 as the output.

y = 2x-1

y = 2*2-1

y = 4-1

y = 3

This verifies point B(2,3) is also on the line.

The answer is fully confirmed. You can use graphing software like Desmos or GeoGebra as a quick way to confirm.

y =-1/2x+7 is the equation of the line that is parallel to 2x+4y=6 and passes through the point (6, 4).

Parallel to 2x+4y=6 and passing through(6,4) 2 x 4y = 6

Find the slope of this line and make y the subject 4y=-2x 6

By Dividing the equation by 4 we get:

y=-1/2 x + 3/2

Compare this equation with y=mx+b

slope m=-1/2

The slope of a line parallel to the above line will be the same

The slope of the required line will be - 1/2

m=-1/2,  at the point (6,4)

Finding b by plugging the values of m & the point in y=mx+b

4=-3+b

b= 7

m=-1/2

Plug value of the slope and b in y = mx +b

The required equation is y=-1/2x+7

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Answer:

Step-by-step explanation:

The hypotenuse of the triangle is equal to 14.14 feet, and thus the distance of the tree from the house is 14.14 feet.

Triangle is a three-sided, two-dimensional shape with three angles. It is one of the basic shapes in geometry and is formed by connecting three straight lines. Triangles can be classified based on their angles and sides. An equilateral triangle has all three sides equal in length and all three angles are equal. An isosceles triangle has two sides equal in length and two angles equal. An scalene triangle has all three sides and angles different in length and measure.

In order to determine the distance of the tree from the house, the Pythagorean theorem can be used. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse).

Looking at the diagram, the sides of the triangle are 10 feet, 10 feet, and 12 feet. If we label the sides as a, b, and c, then we can use the Pythagorean theorem to solve for c:

a2 + b2 = c2

102 + 102 = c2

100 + 100 = c2

200 = c2

√200 = c

Therefore, the hypotenuse of the triangle is equal to 14.14 feet, and thus the distance of the tree from the house is 14.14 feet.

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On solving the algebraic expression 4nm^0 × 2m^4n^3, the value is obtained as 10368.

What is algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

The given algebraic expression is -

4nm^0 × 2m^4n^3

The values for n and m is given as 2 and 3 respectively.

Substitute the values of n and m in the algebraic expression.

= 4nm^0 × 2m^4n³

= 4(2)(3)^0 × 2(3)^4(2)³

Use the exponents rule -

= 4(2)(1) × 2(81)(8)

Use the arithmetic operation of multiplication -

= 8 × 1296

= 10368

Therefore, the final value is obtained as 10368.

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If m=3 and n=2. What is 4nm^0 x 2m^4n^3 ?

The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

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1. The expression of Luke's weight loss over the three weeks is 13/4 x-1/2

2. The expression of Liam's weight loss over the three weeks = 21/4 x-9/2

3. Luke lost 2 pounds in the first week.

4. The number of pounds Luke and Liam each lost over the three weeks is 6 pounds.

In the given question, Luke started a weight loss program.

The first week, he lost X pounds.

The second week, he lost 3/2 pounds less than 3/2 Times do the pounds he lost the first week.

So the expression is:

3/2 x - 3/2

The third week, he lost 1 pound more than 3/4 of the pounds he lost the first week.

Now the expression is:

3/4x + 1

Liam started a weight loss program when Luke did.

The first week, he lost 1 pound less than 3/2 times The pounds Luke lost the first week.

3/2 x - 1

The Second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week.

5/2 x - 4

The third week, he lost 1/2 pounds more than 5/4 times the Pounds Luke lost the first week.

5/4 x + 1/2

Assuming they both lost the same number of pounds over the three weeks, then we have complete the following sentences.

1. We have to write the expression for Luke's weight loss over the three weeks.

The expression of Luke's weight loss over the three weeks = The weight lost in first week + The weight lost in second week + The weight lost in third week

The expression of Luke's weight loss over the three weeks = x + 3/2 x - 3/2 + 3/4x + 1

Now we simplify the expression.

The expression of Luke's weight loss over the three weeks = 13/4 x - 1/2

2. We have to write the expression for Liam's weight loss over the three weeks.

The expression of Liam's weight loss over the three weeks = The weight lost in first week + The weight lost in second week + The weight lost in third week

The expression of Liam's weight loss over the three weeks = 3/2 x - 1 + 5/2 x - 4 + 5/4 x + 1/2

Now we simplify the expression.

The expression of Liam's weight loss over the three weeks = 21/4 x - 9/2

3. Now we have to find the number of pounds Luke lost in the first week.

As given that they lost the same weight. So,

The expression of Luke's weight loss over the three weeks = The expression of Liam's weight loss over the three weeks

13/4 x - 1/2 = 21/4 x - 9/2

Add 9/2 on both side, we get

13/4 x + 4 = 21/4 x

Subtract 13/4 x on both side, we get

2x = 4

Divide by 2 on both side, we get

x = 2

Hence, Luke lost 2 pounds in the first week.

4. We have to find the number of pounds Luke and Liam each lost over the three weeks.

The expression = 21/4 x - 9/2

Now putting the value of x.

The expression = 21/4 × 2 - 9/2

The expression = 21/2 - 9/2

The expression = 12/2

The expression = 6 pounds

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There are 1e-6 cubic meters in a cubic centimeter.

A centimeter is a metric unit of measurement used for measuring the length of an object. It is written as cm. It can also be defined as the unit of length in the International System of Units (SI), the current form of the metric system. It is equivalent to 1/100 meters.

A meter has 100 centimeters.

10 millimeters make one centimeter.

The centimeter can be written as cm.

While calculating the surface area of an object, the unit of measurement becomes cm².

While measuring the volume of an object, the unit of measurement becomes cm³.

Thus, There are 1e-6 cubic meters in a cubic centimeter.

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Mackenzie owed $100 after -4 weeks. This means that after 4 weeks, the amount she owed was $100 less than it was at the start.

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When we say "solve for K" we mean to isolate K by itself on one side of the equal sign. You can do this by "moving" things from one side to the other using mathematical rules.

What does it mean to solve for K?

To isolate K by itself on one side of the equal sign is what we mean when we say "solve for K." Using mathematical principles, you can accomplish this by "moving" objects from one side to the other. The most crucial rule is that anything you do to one side of the equation must also be done to the other.

The K value, also known as the bending limit, of a cyclotron is the ratio between the obtainable energy and the charge-to-mass ratio, where is the particle's kinetic energy, m is the number of atoms, and k is the variational constant. By dividing the y-coordinate by the x-coordinate, we can calculate k when given any position because it is constant (the same for every point).

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Answer: y = -3x + 2

Step-by-step explanation:

ur welcome

It will take 3 hours and 40 minutes for a car to travel 200km at an average speed of 55km/hr.

200km / 55km/hr = 3.63 hrs

3.63 hrs x 60 minutes/hr = 218 minutes

218 minutes - 60 minutes = 158 minutes

158 minutes / 60 minutes = 2.63 hrs

2.63 hrs + 1.37 hrs (3.63 hrs - 2.26 hrs) = 3.40 hrs

To calculate how long it will take a car to travel 200km at an average speed of 55km/hr, you first need to divide the distance (200km) by the speed (55km/hr). This gives you 3.63 hours. To convert this to minutes, you need to multiply this by 60 minutes/hour, which gives you 218 minutes. Subtracting 60 minutes from this gives you 158 minutes. To convert this to hours, you need to divide by 60 minutes/hour which gives you 2.63 hours. Then, you need to add 1.37 hours (3.63 hours - 2.26 hours) to get a total of 3.40 hours. Therefore, it will take 3 hours and 40 minutes for a car to travel 200km at an average speed of 55km/hr.

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Answer:

X Y 6 1 8 3 10 5 7 2 14 9

Step-by-step explanation: X-5=Y

the length of the flag is 28.8.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

width to length ratio of 10:19

it is 18 inches wide

then, length = 18*19/10

                    =28.8

hence, the length of the flag is 28.8.

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Answer:

Step-by-step explanation:

The orthocenter

The length of the rectangular garden is 23 feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

Length of the rectangular garden is 5 feet longer than its width.

Let w be the width of the rectangle.

Then w + 5 is the length of the rectangle.

Area of a rectangle = Length × Width

Area is given as 414 square feet.

(w + 5) w = 414

w² + 5w - 414 = 0

Factorizing,

(w - 18) (w + 23) = 0

w - 18 = 0, then w = 18

w + 23 = 0, then w = -23

w = -23 is not possible for the width.

So w = 18 feet

Length of the rectangle = w + 5 = 18 + 5 = 23 feet

Hence 23 feet is the length of the rectangle.

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