Antonio and Candice had a race. Their distances past a particular landmark as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Which statement is true regarding Antonio and Candice’s race?

When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles

Distance is a measure of how far away two objects or points are from one another. In physics or daily life, the term "distance" can refer to a physical distance or an estimate based on other criteria (for example, "two counties over").

|AB| can be used to denote the distance between two points. In most situations, the distance from point B to point A can easily be used in place of the distance from point A to point B.

A distance metric or function is a way to explain what it means for elements of a space to be "far apart from" or "close to" each other. It is a generalisation of the idea of physical distance in mathematics.

If the train stops at Tucson in return trip, distance he travelled is,

d = 1893 + (1893 - 1408)

d = 2378 miles

And, miles the train have left to travel is

⇒ 1893 + 1893 - 2378

= 3786 - 2378

= 1408 miles

Thus, When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles.

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Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0.Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.Real or complicated solutions are both possible.

Option A , x = 7/5 and x= -1

Formula: Let ax² + bx + c = 0 be the quadratic equation,

x = [-b±√(b²-4ac)]/2a

The given quadratic equation be

5x² -2x = 7

⇒ 5x² -2x - 7 = 0  

a = 5, b = -2 and c = -7

Therefore x = [-b±√(b²-4ac)]/2a

x=[-(-2) ±

√((-2)²-4*5*(-7))]/2*5

x =[2 ± √144)]/10

x =[2 ± 12)]/10

x = (2+12)/10 and x = (2-12)/10

x = 14/10 = 7/5 and x= -12/10 = -1

Therefore,the correct answer is Option A , x = 7/5 and x= -1.

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Tthe probability that the difference in the diameters of the two ball bearings is less than 0.06 mm is 0.0478

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

Mean = 11.5

Standard deviation = 0.05

Let the diameters be X and Y

So, we have

P(|X - Y| < 0.06)

Using this information, we have

P(|X - Y| < 0.06) = P( -0.06 < X - Y < 0.06)

= P(X - Y < 0.06) - P(X - Y < -0.06)

= 0.0478

Hence, the probability is 0.0478

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Answer:

Step-by-step explanation:

so you have 1/2 times 3 = 1.5

Given that tan alpha = -24/10 and pi < alpha < 2pi, we can use the trigonometric identities to find the value of sin alpha.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

Since tan alpha = -24/10, we know that sin alpha / cos alpha = -24/10

We can find the value of cos alpha by using the fact that pi < alpha < 2pi, so 0 < alpha - pi < pi.

Therefore, cos alpha = cos (alpha - pi) = -cos (alpha - pi)

We can substitute this into the equation above:

sin alpha / (-cos (alpha - pi)) = -24/10

We can then solve for sin alpha:

sin alpha = (-24/10) * (-cos (alpha - pi))

We can simplify the expression, but we cannot determine the exact value of sin alpha without knowing the value of alpha.

Note that tangent is negative in the second and third quadrant, so the angle is in the third quadrant.

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Answer: x belongs to (0, 0.4444)

Step-by-step explanation:

By analyzing the graph, we can see that the transformed function, F(x), is the one in option D.

F(x) = 2*x^2 + 3

On the graph, we can see the graphs of both equations, F(x) and G(x), where G(x) = x^2

First, we can see that the vertex of the quadratic of F(x) is at the point (0, 3).

So first we have a translation of 3 units upwards, we also can see that the parabola of F(x) is narrower (horizontally) than the one of G(x), then we must have a scale factor larger than 1 multiplying the function.

Then we have something like:

F(x) = k*G(x) + 3 = k*x^2 + 3

Where k > 1.

The only option that has this form is option D.

F(x) = 2*x^2 + 3

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Answer:

27540

Step-by-step explanation:

yes

The mean of y-values is referred to as [tex]\bar{y}[/tex]. So, option b is the correct choice.

A variable in a set of sample data in statistics is symbolized by the little Latin letter x. If a letter has a horizontal bar above it, it means the variable it is placed over is considered the average or mean.

We would add all of the sample data points, divide by the sample size, and then compute the x-bar, or sample mean. This is given by [tex]\bar{x}=\frac{x_1+x_2+x_3+\cdots\cdots+x_n}{n}[/tex] where n is referred to as the sample size and [tex]\bar{x}[/tex] is the sample mean.

Therefore, the central tendency of the data is represented by this [tex]\bar{x}[/tex] or the x bar. Therefore, the mean of y-values is represented by y bar or [tex]\bar{y}[/tex].

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Answer:[tex]\sqrt{61}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]\sqrt{5^{2} +6^{2} } =\sqrt{25+36}=\sqrt{61}[/tex]

The distance between A and B = [tex]\sqrt{61}[/tex]

Answer:

The completed table is given below and the equation for the given situation is 15=4a+0.50s.

Given that, it costs $0.50 to download an individual song and $4 to download an album.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Jada has $15 to spend downloading music.

Let s be number of songs and a be number of albums

So an equation for the given situation is 15=4a+0.50s

From table, in row 1

Given number of songs is 6

15=4a+0.50(6)

⇒ 15=4a+3

⇒ 4a=12

⇒ a=3

From table, in row 2

Given number of albums is 1

15=4(1)+0.50s

⇒ 0.50s=11

⇒ s=11/0.50

⇒ s=22

From table, in row 3

Given number of albums is 30

15=4a+0.50(30)

⇒ 15-15=4a

⇒ a=0

Hence, the completed table is given below and the equation for the given situation is 15=4a+0.50s.

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Step-by-step explanation:

On using the exterior angle theorem the value of ∠G  is obtained as option D: 88 degrees.

What is exterior angle theorem?

The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem.

The measure of ∠F = (6x - 10)°

The measure of ∠E = 38°

The measure of ∠G = (7x + 18)°

But, in the given image it can be seen that the ∠G lies outside the triangle.

Apply the exterior angle theorem to solve the value for x.

According to the exterior angle theorem, the equation will be -

∠F + ∠E = ∠G

Substitute the values into the equation -

(6x - 10)° + 38° = (7x + 18)°

Simplify the equation -

6x - 10 + 38 = 7x + 18

Collect the like terms -

6x - 7x = 18 + 10 - 38

-x = -10

x = 10

So, the value of x is obtained to be 10°.

Substitute the value of x in ∠F and ∠G -

∠F = (6x - 10)°

∠F = (6(10) - 10)°

∠F = (60 - 10)°

∠F = 50°

∠G= (7x + 18)°

∠G= (7(10) + 18)°

∠G= (70 + 18)°

∠G= 88°

Therefore, the values of angles are ∠F = 50° and ∠G= 88°.

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The solution for the given system of equations is (-2, -2).

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.

Given:

The system of equations,

3x + 7y = -20          ..(1)

-3x + 6y = -6            ..(2)

We have to solve this system of equations using addition method.

Adding equation (1) and (2)

      3x + 7y = -20

 +  -3x + 6y = -6

__________________

       0 + 13y = -26

13y = -26

  y = -2

Plug y = 2 in equation (1), we get

3x + 7(-2) = -20

3x - 14 = -20

3x = -20 + 14

3x = -6

x = -2

Hence, the solution for the given system of equations is (-2, -2).

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If we assume that each student's heart creates the same amount of energy as a single person, the energy created would be enough to drive the truck for 192000 meters.

If we assume that each student's heart creates the same amount of energy as a single person, we can estimate the total amount of energy created by the class.

If one person's heart creates enough energy to drive a truck for 32 kilometers,

Then six people's hearts would create enough energy to drive the truck for 32 x 6 = 192 kilometers.

In meters, it would be 192 x 1000 = 192000 meters.

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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy that is created by all the students in your math class for a week, how many meters could the truck drive?

Number of students is 6

The drawbacks of early forms of money include their propensity to be easily divided and to crumble.

The unit technique is a method of problem-solving where you first calculate the value of a specific unit, then expand that value to get the answer. Simply expressed, a minimum unit value is extracted from a specified multiple using the unit method.  The method used to accomplish this might be standardized. a solitary nation. anything has a distinguishing component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Logical Analysis, Mathematics of Matrix or Operators)

given

then you multiply and cross.

so,18x6= 4x

4x/4=108/4

x=27

The drawbacks of early forms of money include their propensity to be easily divided and to crumble.

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We can compute the integral of the velocity function's absolute value. In other words, the area under the velocity function's curve's absolute value equals the distance a particle travels.

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Answer:

Step-by-step explanation:

Mp, Lp, and NQ are indeed the central lines of a large briangle MNL, according the problem. Particles entersect at point P.This is referred to as a baryc enter of a friangle.And has the quality Np= 2PQ, therefore we can obtain it.   When you are aware, the point p is indeed the barycenter of a large triangle, and this is an important trait. 

The perimeter of trapezoid JKLM is

9 + √(2) + √(5) units.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

First, we find the lengths of each side of the trapezoid.

JK = distance between points J and K

JK = √((4 - 4)² + (-4 - (-7))²) = √(9) = 3

LM = distance between points L and M

LM = √((3 - 3)² + (-8 - (-2))²) = √(36) = 6

KL = distance between points K and L

KL = √((3 - 4)² + (-2 - (-4))²) = √(5)

JM = distance between points J and M

JM = √((3 - 4)² + (-8 - (-7))²) = √(2)

Now,

We can add up the lengths of each side to find the perimeter.

Perimeter = JK + KL + LM + JM

Perimeter = 3 + √(5) + 6 + √(2)

Perimeter = 9 + √(2) + √(5)

Therefore,

The perimeter of trapezoid JKLM is

9 + √(2) + √(5) units.

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The value of x is 1 and the value of y is 3, this can be obtained using the substitution method.

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another.

The given equations are:

x + 2y = 7 and 3x -2y = -3

In the given equation x + 2y = 7 isolate the value of x:

x = 7 - 2y

Substitute the value of x in 3x -2y = -3:

3( 7 - 2y) - 2y = -3

21 - 6y - 2y = -3

21 + 3 = 8y

24 = 8y

y = 3

Substitute the value of y in equation to find the value of x:

x + 2(3) = 7

x + 6 = 7

x = 1

Hence, the value of x is 1 and the value of y is 3.

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The function f(x, y) = sqrt(4 - 4x^2 - y^2) is defined over a disk of radius 2 centered at the origin in the xy-plane. The z-value of the function is always non-negative and reaches its maximum value of 2 at the origin (0,0).

This can be confirmed by noting that the partial derivatives of the function at the origin are both negative, indicating that it is a maximum. The traces of the function in the xy, yz, and xz planes are circles with radius 2 centered at the origin, with the range of the function being limited to the upper semi-circle in each of these planes.

When these traces are combined with the domain of the function, we get the graph of a paraboloid of revolution that opens downward, with a saddle point at the origin (0,0) and a maximum value of 2.

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No, His answer is not reasonable.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Tarren estimates that the product of 10 and 4 is about 120.

Now, We know that;

The product of 10 and 4 is,

⇒ 10 × 4 = 40

Thus, His answer is not reasonable.

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The rotation of figure R about its center will produce the image of R as given in option C.

Rotation is a type of rigid transformation which involves turning a given figure or object at a an angle about a reference point to produce an image. This process can be used to explain the question given.

Some other types of rigid transformation are; dilation, translation, reflection.

All these have their distinct procedures and would be applied as expected or stated in the question.

When figure R is rotated about the center at 180 degrees, it would produce an image of R as shown in option C.

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Answer: x ∈ {-0.0107639, 10.3225694}

Answer:

120

Step-by-step explanation:

To fill up the water tower, the liters of water needed, based on the volume of the water tower, is 982, 000 liters

To find the amount of water it would take to fill up the water tower, you need to convert the water tower volume from cubic meters to liters.

As per the conversion table, the cubic meters can be converted as such:

1 cubic meter = 1, 000 liters.

This means that a volume of 982 m ³ will be:

= 982 x 1, 000

= 982, 000 liters

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Answer:

The correct answer is 8 miles

Step-by-step explanation:

. If Yasmin runs at a pace of 7 miles per hour ... to run will always reduce down to the same fraction on a straight line

Answer:

84,480 pennies!

Step-by-step explanation:

Answer:

Right

Step-by-step explanation:

because the biggest angle of the triangle is equal 90

Answer:

C. Right angled triangle