25 points !! Select the correct answer. Given: AD || BC Prove: DC = 6 units

Answer:

see attached

Step-by-step explanation:

The volume of the solid is 9 cubic units, which is determined by the base in the first quadrant bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. As the cross sections perpendicular to the x-axis are squares, the volume can be calculated.

The volume of the solid can be calculated by finding the area of the base and then multiplying it by the height of the solid. The base of the solid is in the first quadrant and is bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. This region forms a trapezoid, with an area of 6. As the cross sections perpendicular to the x-axis are squares, the height of the solid is 3 units. Thus, the volume of the solid is 6 multiplied by 3, which gives us a total volume of 9 cubic units. To calculate the volume, it is important to identify the base of the solid and the shape of the cross sections perpendicular to the x-axis. This will allow us to calculate the area of the base, and multiply it by the height of the solid to determine the total volume.

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The two values on the number line are of opposite values, and have a distance of three halves units to zero. Thus option B.

A number line is a system in which the position of a directed number is located. It extends from negative infinity to positive infinity, thus all numbers can be located on a number line.

A directed number is any type of number which has either a negative or positive sign i.e its direction.

Considering the values given in the question, it can be deduced that;

i. Both values are opposite of each other because of the negative and positive signs (i.e their directions)

ii. The two values are at a distance of one and a halve to the zero point. So that;

one and a halve = 1 1/2

                           = 3/2

Thus both values are at a distance of three halves to zero.

Therefore, the correct option is B. The values are opposites of each other, and their distance to zero is three halves units.

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On solving the provided question we can say that from the graph the value of the equation y = 4x^2 will 256.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here,

from the graph,

equation is = y = [tex]4x^2[/tex]

and x = 8

so, y = 256

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The absolute value function on the graph is the one in option D.

y = |x| + 1

On the graph we can see an absolute value function that has a vertex at (0, 1) and a slope of 1.

Remember that an absolute value function with a slope of 1 with a vertex at (h, k) can be written as.

y = |x -h| + k

So, knowing that the vertex is at (0, 1) we conclude that the absolute value function is:

y = |x| + 1

Thus the correct option is D.

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On solving the provided question we can say that three expression whose value = -3/4 are -1/4-3/4; -2/4-1/4; 1-1/4

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

by expression

three expression whose value = -3/4 are -1/4-3/4; -2/4-1/4; 1-1/4

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The rate of the motorboat in still water is 49 km/hr. The rate of the current is 6 km/hr.

We have, A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in the same amount of time. We have to calculate the rate of the boat in still water and the rate of the current. Let the speed of the boat in still water and rate of stream be "B" and "S" respectively.

Using the relative speed formula , the speed upstream is B - S and the speed downstream is B + S.

Use the distance , in speed/rate formula ,

Rate × Time = Distance

Upstream : (B-S)6 = 258

=> B - S = 43 --(1)

Downstream: (B+S)6 = 330

=> B + S = 55 --(2)

Solve the linear equations by elimination method. Add the two equations.

=> 2B = 98

=> B = 49 km/hr

Substitute this value of B in equation(2) and solve for S, B+S = 55

=> 49+S = 55

=> S = 6 km/hr

So, the rate of the current is 6 km/hr.

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Complete question:

A motorboat travels 258 km in 6 hours going upstream. It travels 330 km going downstream in same amount of time. What is the rate of the boat in still water and what is the rate of the current.

The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have the following;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Answer:

After a little bit of research I found that the right answer is a

reason

you divide the four $10 dollar Bill by 4

so 1 person gets one $10 dollar bill

then you exchange the 100 bill for eight 10 bill and twenty 1 dollar bill

so eight 10 bill divided by 4 so 1 person gets two 10 dollar Bill

twenty 1 dollar bill .Each person here gets five one dollar Bill

so finally

each person gets

1. one $10 dollar bill

2.two 10 dollar bill(from the 100 bill)

3.five 1 dollar bill(from.the 100 too)

Answer:

8

Step-by-step explanation:

This is a right triangle.

Since it's a right triangle with given side lengths,

we can use Pythagoras theorem, a² + b² = c² (a and b legs, c is hypotenuse)

to calculate the missing side.

Let x represent the missing side:

[tex]( {2 \sqrt{41} )}^{2} = {10}^{2} + {x}^{2} [/tex]

[tex]164 = 100 + {x}^{2} [/tex]

[tex]64 = {x}^{2} [/tex]

[tex]8 = x[/tex]

The velocity is always negetive for 0≤t≤5 so the particle does not change the direction.

The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity. The meter per second is the accepted unit of velocity magnitude (also known as speed).

A vector that depicts a point P on the line in reference to the origin O is used to represent the location of a particle travelling along a straight line. We write x(t) for the particle's position at time t since it is common to think of a particle's position as a function of time.

The rate of change of the particle's velocity with respect to time is known as its acceleration. A vector quantity is acceleration. When both the magnitude and the direction are altered, it changes.

The particle position is given as :

x(t) = 14 -6t³ + 812 + 41 - 6

The particle velocity is the time rate of change of position :

v(t) = d(x(t)/dt = -18t²

The velocity is always negetive for 0≤t≤5 so the particle does not change the direction.

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The p-value is less than a chosen significance level (alpha), such as 0.05, we reject the null hypothesis and conclude that there is evidence that the proportion of adults who would respond "yes" to the question changed from December 2007 to December 2008. Otherwise, we fail to reject the null hypothesis.

It is important to note that the sample size and the significance level used to calculate the p-value can affect the result of the test. Additionally, it's important to consider other factors that may have affected the results, such as economic conditions or media coverage.

To determine if the proportion of adults in the United States who would respond "yes" to the question changed from December 2007 to December 2008, we need to perform a hypothesis test. The null hypothesis is that the proportion of adults who would respond "yes" to the question did not change from December 2007 to December 2008, and the alternative hypothesis is that the proportion of adults who would respond "yes" to the question did change.

One way to perform the hypothesis test is by using a two-sample proportion test. The test statistic is calculated as:

(p1 - p2) = (676/1009 - 622/1020) = 0.0548

where p1 is the proportion of adults who responded "yes" in December 2008 and p2 is the proportion of adults who responded "yes" in December 2007.

Then, we need to find the p-value for the test statistic, which represents the probability of observing a test statistic as extreme or more extreme than the one calculated if the null hypothesis is true.

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Answer: 12, g with exponent 4, h with exponent 5 . (12

g

4

h

5

       Brainliest would be much apprechiated

Answer:

2+3+3=8

3×4=12

Step-by-step explanation:

The solutions to each equality are given as follows:

D) s = -1.

E) n = 10/7.

F) k = 3.

The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.

The solution for item d is given as follows:

3 - 2s + 2 = 13 + 6s -> Distributive property.

8s = 5 - 13 -> Combine the like terms.

8s = -8

s = -8/8

s = -1.

The solution for item e is given as follows:

2(n + 9) = -6(2n - 5) + 8

2n + 18 = -12n + 30 + 8 -> Distributive property.

14n = 20 -> Combine the like terms.

n = 20/14

n = 10/7.

The solution for item f is given as follows:

5(4k - 3) - 5k = 10 + 2(3k + 1)

20k - 15 - 5k = 10 + 6k + 2

15k - 15 = 12 + 6k

9k = 27

k = 27/9

k = 3.

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There are 6 four-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 that are greater than 3400.

To determine the number of four-digit numbers that can be formed using the digits 2, 5, and 3, we can use the formula nPr, where n is the number of digits we are working with (in this case, 3) and r is the number of digits we want in each combination (in this case, 4).

Therefore, the number of four-digit numbers that can be formed using the digits 2, 5, and 3 is 3P4 = 3! / (3 - 4)! = 3! / (3 - 4)! = 3! / -1! = 3! / 1 = 3 x 2 x 1 = 6.

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The red flags in the prescription are;

We know that the term prescription would have to do with the drugs that an individual has been asked to take in a  given situation. Usually, when a person is sick, the person would have to go to a doctor to get a prescription.

There may be certain red flags in a prescription and these would have to do with the state of health of the patient that is being given the prescription drugs to taken.

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The expected value of M is described as C: "it is the mean of the distribution of sample means.

In probability theory, the expected value of M is a generalization of the weighted average. In informal words, the expected value refers to the arithmetic mean of a large sample of independently chosen outcomes of a random variable.

Thus, the mean of the distribution of sample means is referred to as the 'expected value' of M. And it is always equal to the mean μ of the population. So the correct answer pertaining to this question is held in option 'C'.

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The percentage error in x/y to four significant figures is 1.5355%

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We are given that x=41.5 and y=13.2 correct to one decimal place.

Now we need to find the percentage error in x-y to four significant figures.

Max val of x 41.5 min 13.35

Max val of y 13.2 min 4.25

max value of x  41.5 = 3.1647

                   y   13.2

min value of x  13.35 = 3.069

                  y   4.35

The actual value of x  13.4 = 3.1163

                     y  =  4.3

Absolute error;

 3.1642  3.069 = 0.04785

Percentage Error;

0.04785 × 100 = 0.015355 × 100

=1.5355%

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The domain of a function is the set of all possible inputs for the function.

Let us consider y as our function.

         Therefore y = f(x)      ( since given )

let y = f(x) be a function with an independent variable x and a dependent variable y. Here x is being considered as an independent variable since we can give any input which is x and y is a dependent since it is the output dependent on the output value x.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

If x can be taken as any value as the function is not specified then the domain of f is (−∞,∞).

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Answer:

Exact answer: Square root of 80

Approximate answer: 8.94

Step-by-step explanation:

At this point, the scientist's elevation, in feet, is 255.3 feet.

The scientist's current elevation can be computed as the difference between the down and up distances covered.

Traveling down speed = 4.8 feet per second

The total time used = 74 seconds

The distance covered traveling down = 355.2 feet (74 x 4.8)

Traveling up speed = 3.7 feet per second

The total time taken = 27 seconds

Distance traveling up = 99.9 feet (3.7 x 27)

The difference in distances = 255.3 feet (355.2 - 99.9)

Thus, we can conclude that currently, the scientist is 255.3 feet below sea level.

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Answer:

108/11*sqrt*3

Step-by-step explanation:

CB=sqrt 108, DBC=90; DCB=35. CAB=60; ACD=65.

A. The result of the iterated integral by converting to polar coordinates is 0.

To evaluate this iterated integral, we will convert it to polar coordinates. First, we need to make the substitution x = rcos(θ) and y = rsin(θ). Then, we will need to find the limits of integration for r and θ. The region of integration is the area between the circles with radii a and 2 and between the x-axis and y-axis.

In polar coordinates, the integral becomes ∫∫r dr dθ from r = a to r = 2, and θ = 0 to θ = π/2.

We can now solve the integral by multiplying the integral of r by the integral of θ.

∫2^2 r dr dθ = ∫π/2^0 (-1/2)r^3 dθ = -1/2 * [(r^2)/2] from r = 2 to r = a = -1/2*(2^2 - a^2) = -1/2*(4-a^2) = -2+a^2/2

So the result of the integral is -2+a^2/2 = -2+4/2 = -2+2 = 0

Note that this is not a common way to solve iterated integrals, but rather a way to check the correctness of the solution. The common way is to find the limits of integration by solving the inequality and graphing the area of integration.

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The distance between coordinates is d = 7.1 units.

The intersection of two perpendicular lines results in the formation of the cartesian plane, a two-dimensional coordinate plane. The X-axis is the horizontal line, and the Y-axis is the vertical line. The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.

Given coordinates,

(3, 11) and (4, 3)

the distance between coordinates is

d=√((x₂ – x₁)² + (y₂ – y₁)²)

here x₁ = 3, x₂ = 4, y₁ = 11 and y₂ = 3

d=√((x₂ – x₁)² + (y₂ – y₁)²)

d=√((4 – 3)² + (4 – 11)²)

d = √(1 + 49)

d = √50

d = 7.0710 units

d = 7.1 units nearest tenth

Hence the distance is d = 7.1 units nearest tenth.

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The perimeter of the triangle is 21

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

The perimeter of the triangle is found by adding all the sides

The vertices of the triangle ABC are (-1,1), (-3, -4), and (5,-2). let A be (-1,1), B be (-3, -4) and C be (5,-2).

The distance between And B = √ (-3-(-1))²+( -4-1)²

Line AB = √ 2²+-5²

AB = √ 4+25

AB =√29 = 5.4

line AC = √5-(-1)² + (-2-1)²

AC = √ 6²+3²

AC = √ 36+9

AC = √ 45

AC = 6.7

The distance between B and C = √( -3-5)² + (-4-(-2)²

BC = √ 8²+4²

BC =✓64+16

BC = √80

BC = 8.9

Therefore the perimeter of the triangle is AB+ BC + AC = 5.4+6.7+8.9 = 21

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The number of solutions that the system of equations has is given as follows:

One solution at (2, −3).

The first step in obtaining the number of solutions of the system of equations is obtaining the linear function that represents each line.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The first line goes through these following points:

(-2,-5) and (0,-4).

The slope is given by change in y divided by change in x, hence:

(-4 - (-5))/(0 - (-2)) = 1/2 = 0.5.

When x = 0, y = -4, hence the intercept is of b = -4 and the function is given as follows:

y = 0.5x - 4.

The second line goes through these following points:

(0,1) and (1,-1).

Hence the slope is of:

m = (-1 - 1)/(1 - 0) = -2.

The intercept is of b = 1, and the equation is given as follows:

y = -2x + 1.

Hence the solution is obtained as follows:

-2x + 1 = 0.5x - 4.

-2.5x = -5.

x = 2.

Hence the y-coordinate of the solution is given as follows:

y = -2(2) + 1 = -3.

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The length of the walkway in feet is 15.

Any plane shape that has four equal length of sides is referred to as a square. Its area is the amount of space that it covers in a 2 dimensional plane. And the area of a square is given as;

area of a square = length x length

                           = length^2

It is measured in squared units.

Given that there are 5 square carpet tiles which covered an area of 45 square feet, then the area of one square carpet tile is;

area of one square carpet tile = total area covered/ number of tiles

                                     = 45/ 5

area of one square carpet tile = 9 square feet

But,

area of a square = length^2

9 = length^2

length = 3 feet

So that,

length of the walkway = 5 x 3

                                     = 15 feet

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If a rocking hi has a weight limit if 60lbs .The weight that is 95% of the limit is 33 pounds.

First step is to convert the 60lbs to kg

1 pounds to 1 kg = 0.453592

60 pounds = 27.2155kg or 27kg

OR

60 lbs×0.45359237 kg/1 lbs = 27.2155422 kg

Second step is to find the weight of the limit

Weight of the limit =  Weight limit - Kilogram

Weight of the limit = 60 -27

Weight of the limit = 33

Therefore we can conclude that the weight of the limit is 33 pounds.

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Answer:

[tex]21[/tex]

Step-by-step explanation:

[tex]\textrm{If y varies directly with x we can write this relationship as}[/tex]

[tex]y = k \cdot x[/tex]

[tex]\textrm{k is referred to as the constant of proportionality.}[/tex]

[tex]\textrm{Substituting these values into the above equation we get}[/tex]

[tex]3 = k \cdot 2[/tex]

[tex]So\; k = \dfrac{3}{2}[/tex]

[tex]\mathrm{When }[/tex] [tex]x = 14,[/tex]

[tex]y = \dfrac{3}{2} \cdot 14[/tex]

[tex]y = 21[/tex]

Answer:

Incorrect

Step-by-step explanation:

60 is the lowest common multiple of 12 and 15, not the greatest common factor.

The greatest common factor of 12 and 15 is 3, not 60.