car a leaves the grand canyon at noon. it travels at 80 mph, but stops at 3 pm for an hour. car b leaves the grand canyon at 2 pm and travels at 90 mph without stopping on the same route as car a. when does car b catch up with car a?

The perimeter of the trapezoid ABFE and the prove that the triangle ΔABC is an isosceles are as follows;

First question;

The perimeter of the trapezoid ABFE is 100 units

Second question;

The sides AB and BC in the triangle ΔABC are congruent, therefore, triangle ΔABC is an isosceles triangle

An isosceles triangle is a triangle that has two sides that have the same lengths.

The specified parameters are;

The segment joining the midpoints of the side [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex] of the equilateral triangle ΔABC = EF

EF = 2·x + 8 and AB = 7·x - 2

The midsegment theorem applied to the triangle ΔABC indicates that we get;

EF = (1/2) × AB

Therefore; 2·x + 8 = (1/2) × (7·x - 2)

(1/2) × (7·x - 2) = 2·x + 8

7·x - 2 = 2 × (2·x + 8)

7·x - 2 = 4·x + 16

7·x - 4·x = 16 + 2 = 18

3·x = 18

x = 18/3 = 6

x = 6

EF = 2·x + 8

Therefore; EF = 2 × 6 + 8 = 20

EF = 20

AB = 7·x - 2

Therefore; AB = 7 × 6 - 2 = 40

AB = 40

AB = AC = BC (Definition of an equilateral triangle)

Therefore;

AC = BC = AB = 40 (symmetric property)

The midpoints E and F, indicates that we get;

AE = CE and BF = CF

AC = AE + CE and BC = BF + CF (segment addition property)

Therefore; AC = AE + AE = 2 × AE

40 = 2 × AE

AE = 40/2 = 20

BC = 2 × BF

40 = 2 × BF

BF = 40/2 = 20

The perimeter of the trapezoid ABFE, P = AB + BF + EF + AE

P = 40 + 20 + 20 + 20 = 100

Second question

The coordinates of the vertices of the triangle are;

A(1, 2), B(-5, 3), and C(-6, -3)

The lengths of the sides of the triangle found using the distance formula are;

AB = √((-5 - 1)² + (3 - 2)²) = √(37)

BC = √((-6 - (-5))² + (-3 - 3)²) = √(37)

AC = √((-6 - 1)² + (-3 - 2)²) = √(74)

The lengths of the sides AB and BC in the triangle ΔABC are the same, therefore, the triangle ΔABC is an isosceles triangle.

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The measure of ∠VWX in this triangle VWX is, 68.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The cosine rule of triangles,

Here, cosW = (VW² + XW² - VX²)/2(WX×WV).

cosW = (36² + 23² - 35²)/2(36×23).

cosW = 600/1656.

W = cos⁻¹(0.36).

∠W = 68.9°.

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Answer:

95+B=180. ( linear pair)

95+105=180

180=180

hence proved

Therefore , the solution of the given problem of coordinates comes out to be the image of point B(7/3, 5/4) after dilation with center (0,0) and scale factor 1/2 is B'(7/6, 5/8).

A reference frame is a geometrical technique that uses one or so more values or locations to better be able to observe points and any other topological entities on a spectrum, including such Euclidean space. A point or object's coordinates on a double planes are a pair of numbers. The x and y values of a point on a two - dimensional plane are two integers that identify its location. a collection of integers that represent exact coordinates .

Here,

The image of a point B(x, y) after a dilation with center (0,0) and scale factor k is given by the point B'(kx, ky).

In this case, the center of dilation is (0,0) and the scale factor is 1/2.

So, the image of point B(7/3, 5/4) after dilation is given by:

B'(kx, ky) = B'(1/2 * 7/3, 1/2 * 5/4)

B' = (7/6, 5/8)

Therefore, the image of point B(7/3, 5/4) after dilation with center (0,0) and scale factor 1/2 is B'(7/6, 5/8).

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Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).

What is the Law of Sines?

The Law of Sines, also known as the sine rule, is a trigonometric formula used to find unknown sides or angles in a triangle.

To solve this problem, we can use the Law of Sines, which states that for any triangle ABC,

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths opposite the corresponding angles A, B, and C, respectively.

Using this formula, we can set up the following proportion:

b/sin(B) = a/sin(A)

Plugging in the values we know, we get:

b/sin(36°) = 6/sin(121°)

Solving for b, we get:

b = (6 sin(36°))/sin(121°)

Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).

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Answer:

see explanation

Step-by-step explanation:

the inscribed angle ADB is half the arc that subtends it , AB , then

AB = 2 × ∠ ADB = 2 × 46° = 92°

the central angle BOC is equal to the arc that subtends it, BC , so

BC = 22°

Then

ABC = AB + BC = 92° + 22° = 114°

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

BD is a diameter of the circle , so BAD = 180° THEN

AD = 180° - AB = 180° - 92° = 88°

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

the sum of the arcs on a circle = 360° , so

ADC = 360° - ABC = 360° - 114° = 246°

Using trigonometric identity, cos(2θ-1) / cos(2θ+1) is equal to [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

We can use the trigonometric identity:

cos(2θ) = 1 - 2sin^2(θ)

to rewrite the expression as follows:

cos(2θ-1) = cos(2θ)cos(1) + sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)

Similarly,

cos(2θ+1) = cos(2θ)cos(1) - sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) -  2sin(θ)cos(θ)sin(1)

Dividing these two expressions, we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)] / [(1 - 2sin^2(θ))cos(1) - 2sin(θ)cos(θ)sin(1)]

Now, we can use the identity:

tan(θ) = sin(θ) / cos(θ)

to simplify the expression. Specifically, we can express sin(θ) in terms of tan(θ) and cos(θ) as follows:

sin(θ) = tan(θ)cos(θ)

Substituting this into the expression for cos(2θ-1) / cos(2θ+1), we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

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The width W of the island will be 3.75 ft by given scaling factor.

What exactly is scaling factor?

The Scale Factor is used to scale shapes in various dimensions. Geometry teaches us about various geometrical shapes in both two and three dimensions. The scale factor is a statistic for figures that seem similar but have different scales or measures. Imagine two circles have the same appearance but different radii.

The scale factor specifies how much larger or smaller a figure is than the original figure. With the use of a scale factor, you may design an expanded or smaller version of any original form.

Now,

Here given that 1 inch=1.5 ft

and as w=2.5 inches then the actual width W will be =2.5*1.5

=3.75 ft

and we can find scaling factor by  length of the actual object divided by length of scale drawing i.e.

S=length of object/length of drawing

hence,

          The width W of the island will be 3.75 ft.

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Since we want the equation in the form y = kx, we need to find the value of k that will make this equation fellow to the bone we just wrote.

We can rewrite the equation as

y = ( m/ x) x b

Now, we can see that if we set k = m/ x, the equation will be in the form y = kx.

So, the equation that describes the relationship between the number of square yards( x) of ground to be covered and the number of scoops( y) of bean seed demanded is y = kx

where k = m/ x, and m and b are constants that depend on the specific situation.

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Answer:

x = 28

Step-by-step explanation:

Since the e interior angles formed by the sides of a quadrilateral have measures that sum to 360°

we get 2x° + 2x° + 124° + 124° = 360°

4x° + 248° = 360°

4x° = 360° - 248 °

4x° = 112°

x = 112/4 = 28

Step-by-step explanation:

hence proved...

The answer mentioned in above pdf.

missing part is (. OC is correct option of cubic formula)...

The illustration of 10 sided polygon is attached below.

Polygons are closed geometric figures made up of line segments that are connected end-to-end. The number of sides of a polygon determines the polygon's name.

In mathematical terms, a decagon is a 10-sided polygon with 10 vertices and 10 angles.

To draw a decagon, we need to start by drawing a circle. We can use a compass to draw a circle of any size we want. The radius of the circle will determine the size of the decagon.

Next, we need to draw a horizontal line through the center of the circle. This line will be the base of the decagon, and it will divide the circle into two equal halves.

Since a decagon has 10 sides, we need to divide the circle into 10 equal parts.

We can then use these lines as guides to draw the sides of the decagon. We start at one of the points where the lines intersect the circle, and draw a line segment to the next point.

We can label the vertices of the decagon with numbers, starting with 1 and going clockwise, as shown in the diagram.

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The context that represents linear growth is:

A sunflower was growing at a rate of 2.5 inches per week.

A constant rate of change in a quantity over time is referred to as linear growth. The sunflower in this instance is expanding linearly at a pace of 2.5 inches each week, which is constant.

The other contexts listed do not represent linear growth:

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Therefore, the lateral surface area of the cube is 35/2 square inches.

In mathematics, area is the measure of the size of a two-dimensional region or surface. It is usually measured in square units, such as square meters, square feet, or square centimeters. The area of a shape or surface is determined by the amount of space it covers in a plane or on a flat surface. Areas are commonly used to describe the size of objects or spaces in a variety of contexts, including geometry, architecture, engineering, and physics. They are also used in everyday life, such as calculating the amount of carpet needed to cover a floor or the amount of paint needed to cover a wall.

Here,

Since the package is a cube, all of its faces are identical squares. Therefore, the area of one face is equal to the length of one side squared.

Let x be the length of one side of the cube. Then we have:

x² = 7(5)/8

Solving for x, we get:

x = √(7(5)/8) = sqrt(35/8)

The lateral surface area of the cube is the sum of the areas of the four non-base faces. Since the cube has six faces in total, the lateral surface area is:

Lateral surface area = 4 * (side length)²

Lateral surface area = 4 * x²

Lateral surface area = 4 * (√(35/8))²

Lateral surface area = 4 * 35/8

Lateral surface area = 35/2

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The NumPy matrix inverse is a function that calculates the inverse of a given square matrix.

The NumPy matrix inverse function is a strategy that works out the opposite of a square grid involving the NumPy library in Python. The inverse of a matrix is a matrix that, when duplicated by the first grid, creates the identity matrix.

In NumPy, the matrix inverse function is executed as the linalg.inv() technique, which takes a NumPy cluster as information and returns its converse as an exhibit. The matrix should be square and invertible, the importance of its determinant isn't equivalent to nothing. The matrix inverse is utilized in different fields of math, designing, and science to solve systems of linear equations, track down the eigenvalues and eigenvectors of a network, and perform different procedure on matrices.

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Answer:

The correct answers to this question would be 2. Tengo un hermano y dos hermanas and 4. Yo tengo tres hermanos.

The nth derivative of each function is n!.

Taking the nth derivative of a function is the process of calculating successive derivatives and observing the patterns that occur.

In your example, the function given is f(x) = xⁿ. To find the nth derivative, you need to calculate the first few derivatives and observe the pattern that occurs.

The first derivative of the function f(x) = xⁿ is f'(x) = [tex]nx^{n-1}[/tex]

The second derivative is f''(x) = [tex]n(n-1)x^{n-2}[/tex]

From here, you can see that the pattern is that the exponent of x decreases by 1 each time, and the coefficient of x increases by n-1 each time.

Therefore, the nth derivative of

f(x) = xⁿ => f^(n)(x) = [tex]n(n-1)(n-2)...(n-(n-1))x^{n-n}[/tex] = n!x⁰ = n!.

This result is true for any value of n, so the nth derivative of f(x) = xⁿ is always equal to n.

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The two planes that have created the parallel traits would be airplane 3 and airplane 5

To get the parallel lines, we would have to check the angles that are formed

for angle 3 angles on a line is 180

x + 110 = 180

x = 70 degrees

For angle 5

we can see that the position of x in 3 is the same position in 5

hence we can see that in plane 5, x = 70

hence these two would be parallel

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Any system of geometry that is not based on the principles of Euclidean geometry is known as non-Euclidean geometry.

Many geometrical systems that are not based on the parallel postulate or other Euclidean axioms are referred to as non-Euclidean geometry.

The parallel postulate asserts that given a line and a point off the line, there is only one line that can be drawn through the point parallel to the provided line.

Attempts to establish or refute this postulate gave rise to non-Euclidean geometries. Contrarily, non-Euclidean geometries are founded on diverse axioms that allow for various kinds of parallel lines, including multiple parallel lines in hyperbolic geometry and no parallel lines in elliptic geometry.

Non-Euclidean geometry is important to many fields of mathematics and science, including relativity theory and cosmology.

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Answer:

3x13=39

Step-by-step explanation:

ellie=13

kid 1=13

kid 2 =13

Answer:

1.5

Step-by-step explanation:

Answer: 1.5

Step-by-step explanation:

Divide 30 by 29.5735 to get the liquid ounce equivalent of 30 ml or around 1.0144 fluid ounces.

When measuring liquid components for cooking or baking, for example, it might be useful to convert milliliters (ml) to fluid ounces (fl oz).

It's vital to keep in mind that, depending on the amount of accuracy required by the recipe or activity at hand, it's typical when working with liquid measurement to round to the next tenth or hundredth of an ounce or milliliter.

To achieve precise and consistent findings, it's also crucial to utilize the proper measurement equipment and units.

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Answer:

its 320

Step-by-step explanation:

The total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

What is meant by percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. There is no dimension to percentages. As a result, it is known as a dimensionless number.

Given,

Number of students in sixth grade who has a pet dog = 112

The percentage of sixth grade students who has a pet dog = 35%

Let the number of total sixth grade students be x.

Percentage

= (Number of students with pet dog/Total number of sixth grade students *    100

35 = (112/x) * 100

35/100 = 112/x

x = (100/35) * 112 = 320

Therefore the total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

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The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.

Present Value A = Rs. 52,488

Depreciation rate r = 10 % per annum

Time t = 4 years

Let initial value be P

We know the formula, A =[tex]$\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$[/tex]

We obtain by substituting the supplied values.

52,488 =[tex]$\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\[/tex]

52,488 = [tex]$\mathrm{P}(0.9)^4 \\[/tex]

[tex]$\mathrm{P}=\frac{52488}{0.6561} \\[/tex]

P = 80,000

The complete question is:

The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was

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The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

The automotive dealer sells both cars and trucks and the ratio of cars to trucks on the lot is 1 to 3. This means that for every three trucks, there is one car. Therefore, if there are 51 trucks currently for sale, then the number of cars can be determined by dividing this number by 3. This equals 17 cars. Thus, the dealer has 17 cars for sale.

The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

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The value after converting the length 178 cm  to inches , is 178 cm is equivalent to 70 inches .

The Centimeters (cm) and inches are both the units of measurement that  are used to measure length .

They both belong to different systems of measurement. Centimeters are used in the International System of Units (SI), whereas  inches are used in the Imperial and US Customary systems.

We know that 1 centimeter is = 0.3937 inches .

that means that conversion factor is 0.3937 ,

So , we can write ; 178 cm = 178 × 0.3937 inches ;

⇒ 178 cm = 70.0786 inches ≈ 70 inches .

Therefore , 178 cm is approximately equal to 70 inches .

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The solution to the system is the area where shadings from both inequalities overlap one another

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Consider

x-2y ≤ -2

Find y

=> x +2  ≤  2y

=> x/2 + 1 ≤ y

=> (x+2)/2  ≤ y

Or

y ≥(x+2)/2  --------(1)

Consider 3x + y > -1

Find y

=> y > -3x -1---------(2)

By considering the equations with equal sign in place of inequality signs, find y values corresponding to the random x values

plot the points in (x,y) form, we get the 2 lines

For <, shade the region below the line

For >, shade the region above the line

If the inequality is "<" or ">" then connect the two points with a dotted line.  The dotted line is analogous to the open circle on the number line.  Otherwise, connect the two points with a solid line.

The solution to the system is the area where shadings from both inequalities overlap one another

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Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Step-by-step explanation: The Addition Rule states that for two disjoint events, the probability that one or the other occurs is the sum of the probabilities of the two events. (Book example on p. 280 about the probability that a randomly selected student is either a sophomore (A) or a junior (B) therefore P(A or B). The addition of probabilities for disjoint events is the third basic rule of probability: Rule 3: If two events A and B are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Step-by-step explanation: hope this helps0^0

A statistical package is likely to be used with quantitative research but not with qualitative research - True.

The collection and analysis of numerical data, such as survey responses or experimental measurements, is common in quantitative research, and statistical analysis is frequently used to summarise and interpret this data. In quantitative research, statistical software such as SPSS, R, or Stata are widely used to do data analysis and statistical tests.

In contrast, qualitative research often entails gathering and interpreting non-numerical data, such as interview transcripts or observational notes. Although statistical analysis may not be suited for this type of data, several software packages, such as NVivo, MAXQDA, or ATLAS.ti, can be used to manage and analyse qualitative data.

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