Tania is riding a train for $43.6$ miles to get to her destination. The train has $14.3$ more miles to travel before arriving at Tania's destination.

Which equation and solution correctly represent how many miles, $m$ , the train has already traveled?
Responses

Answer:

The two numbers are 4 and -6. Since -6 is less than 4, the lesser of these two numbers is -6.

The lesser number is -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Let's call the two numbers x and y. We know that:

We can solve this system of equations using substitution. Solving the first equation for x, we get:

x = -2 - y

We can substitute this expression for x in the second equation:

-2 - y + 2y = -8

Simplifying this equation, we get:

y = -6

Now we can use the first equation to find x:

x + y = -2

x + (-6) = -2

x = 4

So the two numbers are -6 and 4, and the lesser of the two numbers is -6.

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Any angle that shares a common vertex with <4 and whose measure adds up to 180 degrees is supplementary to <4.

To determine which angles are supplementary to <4, we first need to understand the concept of supplementary angles. Supplementary angles are pairs of angles whose sum is 180 degrees. In other words, if we have two angles, and their measures add up to 180 degrees, then they are supplementary to each other.

To find angles that are supplementary to <4, we need to look for other angles that add up to 180 degrees with <4. We can do this by examining the angles that intersect <4 or that share a common vertex with <4.

One way to identify such angles is to draw a diagram of the situation. Suppose we have a line with <4 marked on it. We can then draw another line that intersects the first line at <4, creating two angles on either side of <4. Let's call these angles A and B, where A is adjacent to <4 and B is adjacent to the other side of <4.

If we can find angle A or angle B, we can determine the other angle that is supplementary to <4. We know that A and B add up to 180 degrees, so if we find one of these angles, we can subtract it from 180 degrees to find the other angle.

To summarize, to find angles that are supplementary to <4, we can:

Draw a diagram of the situation, with <4 marked on a line and another line intersecting it at <4.

Identify the adjacent angles on either side of <4.

Label these angles A and B.

Determine the measure of either A or B.

Subtract the measure of the known angle from 180 degrees to find the measure of the other angle.

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Answer: 3/3 +4/2=3

Step-by-step explanation:

given: 3/3 + 4/2

 3/3+ 4/2 =1 +2

    =3

Answer:

3/3+4/2=3

Step-by-step explanation:

3/3+4/2

=1+2

=3

When x = 11, the value of y is approximately 8.276. We are given that the relationship between x and y is given by [tex]y = Ax^n[/tex]where A and n are constants.

We are also given the values of A and n:

[tex]A = e^0.5[/tex]

n = 3/8

We can substitute these values into the equation to get:

[tex]y = e^0.5 x^(3/8)[/tex]

Now, we are asked to find the value of y when x = 11. To do this, we substitute x = 11 into the equation:

[tex]y = e^0.5 x^(3/8)[/tex]

[tex]y = e^0.5 (11)^(3/8)[/tex]

We can use a calculator to evaluate this

First, we evaluate the exponent (3/8) using the exponent rules:

[tex](11)^(3/8) = (11^(1/8))^3 = 1.706[/tex]

Next, we substitute this value back into the equation:

[tex]y = e^0.5 x^(3/8)[/tex]

[tex]y = e^0.5 (11)^(3/8)[/tex]

[tex]y = e^0.5 (1.706)[/tex]

Using a calculator, we can evaluate this expression to get:

y ≈ 8.276

Therefore, when x = 11, the value of y is approximately 8.276.

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Answer: It basically just Pi

Step-by-step explanation:

Pi equals 27/3 right, so you say pi = 27/3

That's basically it!

8. The value of x is 3.5

9; The solution from the proportion is x = 3

Note that from the diagram given, we have that;

ΔRST ≅ ΔUVW

Also, we can see that a side of the larger triangle ΔRST measures 4 and the smaller triangle  ΔUVW measures 2.

We have a scale factor of 2

For the value of x, we have;

x = 7/2

Divide the values

x  = 3.5

For the proportion

Given the equation as;

12/x = 4/2x - 5

cross multiply

12(2x - 5) = 4x

expand the bracket

24x - 60 = 4x

collect like terms

24x - 4x = 60

subtract the values

20x = 60

x = 3

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The period of the function represented by the sinusoidal graph has a value of 0.7

Given that we have the graph of the sinusoidal function

By definition, the period of the function is the distance between cycles

i.e. the length of a cycle

From the given graph, we have

Initial = 0

Final = 0.7

So, we have

Period = 0.7 - 0

Period = 0.7

This can also be calculated from the equation as

Period = 2π/B

From the function, we have

B = 3π

This means that

Period = 2π/3π

Evaluate

Period = 0.67

When approximated, we have

Period = 0.7

So, the period is 0.7 (approximately)

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If Liam buys a laptop for Rs 840 (including 15% VAT) then the price of the laptop without VAT could be Rs 730.

Let the price of the laptop be 100 rupees.

After including 15% VAT, the price of the laptop would be 115 rupees.

The original price = (100 × 840)/115 = 730.

Hence the price of the laptop could be Rs 730.

This problem is the concept of discount and tax. In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax. In this lesson, we will study the tax computation when the selling price or price before tax is given. We calculate tax on a product by multiplying the tax rate with the product's net selling price.

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After answering the presented question, we can conclude that Hence, fat  expression accounts for around 28.2 pounds of the individual's weight.

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To establish how many pounds of an individual's weight are made up of fat, we must first determine the individual's body fat weight.

We may accomplish this by multiplying the individual's weight by the percentage of body fat (in decimal form):

Body fat weight = 163 pounds x 0.173 = 28.199 pounds

Hence, fat accounts for around 28.2 pounds of the individual's weight.

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Answer: -1

Step-by-step explanation

Applying the property of the diagonals of a kite, the measure of angle F is calculated as: 71°.

The property of the diagonals of a kite is that they intersect at a right angle, while the shorter diagonal divides it into two isosceles triangles.

Thus, FH is a diagonal that divides the kite into two isosceles triangles, therefore:

m<EFH = 1/2(180 - 142)

m<EFH = 19°

m<GFH = 1/2(180 - 76)

m<GFH = 52°

m<F = m<EFH + m<GFH

m<F = 19 + 52

m<F = 71°

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Answer:

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

Property of kites:

In the given kite we can see a pair of different angles, ∠G and ∠E.

It means the other two angles are congruent:

We know the sum of interior angles of a quadrilateral is 360°.

Find the missing angle measure:

Thus, the total number of clients that got haircuts have blond hair is 9.

A prospective outcome of an experimentation or trial is described to as an outcome in probability theory. Only one result will materialise on each trial of an experiment since each possible outcome is distinct and numerous results are mutually exclusive.

Given number of hair colours:

Total colours = 12

Probability = favourable event / total outcome

Probability(blond hair) = 3/12 = 1/4

Total customers = 36

Number of clients have blond hair = 1/4 *36 = 9

Thus, the total number of clients that got haircuts have blond hair is 9.

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Answer:

12.25pi

Step-by-step explanation:

area of ciricle: pi* r^2

the radius can be found by divding the diameter in half so, 3.5

now square 3.5 and multiply with pi

so, 12.25pi

~lmk if you got Qs

Step-by-step explanation:

given -

2

x

−

3

y

=

18

The slope of the equation of the form

a

x

+

b

y

=

c

is -

m

=

−

a

b

=

−

2

−

3

=

2

3

To find the y-intercept put

x

=

0

2(0)−

3

y=

18

−

3

y

=

18

y

=

18

−

3

=

−

6

Slope

m

=

2

3

Y intercept

(

0

,

−

6

)

graph{2x-3y=18 [-6.58, 13.42, -7.28, 2.72]}

2x+3y = -18

First, I'm going to find the x-intercept.

2x+3(0)= -18

2x+0= -18

2x=-18

x=-9

Next, the y-intercept.

2(0)+3y= -18

3y= -18

y= -6

Hope this helps!

The triangle formed by a complex number and its complex conjugate with the origin is an isosceles right triangle.

When a complex number and its complex conjugate are plotted in the complex plane, the two points are reflected about the real axis. Thus, the triangle formed by these points and the origin is an isosceles triangle with the real axis as its axis of symmetry.

Since the complex conjugate has the same magnitude as the original complex number, the two sides of the isosceles triangle have equal length. Therefore, the angle opposite the base (i.e., the origin) is a right angle, since it is the angle between the real axis and the imaginary axis.

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Given that sin B = -5/13 and angle B is in quadrant III, we can use the Pythagorean identity to find the value of cos B:cos² B + sin² B = 1

cos² B + (-5/13)² = 1

cos² B = 1 - 25/169

cos² B = 144/169

cos B = -12/13 (since cos B is negative in quadrant III)a) To find csc B, we can use the reciprocal identity:

csc B = 1/sin B

csc B = 1/(-5/13)

csc B = -13/5b) To find cot B, we can use the quotient identity:

cot B = cos B/sin B

cot B = (-12/13)/(-5/13)

cot B = 12/5c) To find cos B, we have already calculated it above:

cos B = -12/13d) To find sec B, we can use the reciprocal identity:

sec B = 1/cos B

sec B = 1/(-12/13)

sec B = -13/12e) To find tan B, we can use the ratio identity:

tan B = sin B/cos B

tan B = (-5/13)/(-12/13)

tan B = 5/12Therefore, the values of the trigonometric functions for angle B in standard position with terminal side in quadrant III and sin B = -5/13 are:

a) csc B = -13/5

b) cot B = 12/5

c) cos B = -12/13

d) sec B = -13/12

e) tan B = 5/12

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

Sue's average for 9 games of bowling is 108. Therefore, the total scores for the 9 games is:

[tex]= 108 \times 9[/tex]

[tex]= 972[/tex]

To have an average of 110 in 10 games, her total score will be:

[tex]= 110 \times 10[/tex]

[tex]= 1100[/tex]

Therefore, the lowest score that she can get will be the difference between the values calculated above and this will be:

[tex]= 1100 - 972[/tex]

[tex]\bold{= 128}[/tex]

Thus, the value of the quadratic function obtained using the zeros is found as: f(x) = [tex]x^{2}[/tex] + 5x - 14.

f(x) = a[tex]x^{2}[/tex] + bx + c, for which a, b, and c are numbers and an is not equal to zero, is a quadratic function.

A parabola is the shape of a quadratic function's graph. Even though "width" or "steepness" of a parabola can vary as well as its path of opening, they all share the same fundamental "U" structure.

Given zeroes of the quadratic function is:

x1 = -7 and x2 = 2

Zeros in terms of factors are written as:

(x + 7) and (x - 2)

Let f(x) be the quadratic function:

f(x) = (x + 7)(x - 2)

On simplifying:

f(x) = [tex]x^{2}[/tex] + (7 -2)x - 7*2

f(x) = [tex]x^{2}[/tex] + 5x - 14

Thus, the value of the quadratic function obtained using the zeros is found as: f(x) = [tex]x^{2}[/tex] + 5x - 14.

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The expression for the total amount of money collected in Keiko's class is 0.25 x 27 + 0.10 x 92 + 0.05 x 140 + 0.01 x 255

To find out how much money Keiko’s class collected, the teacher needs to add up the value of each coin.

The value of a quarter is 25 cents, a dime is 10 cents, a nickel is 5 cents, and a penny is 1 cent.

In dollars, the expression to find the total amount of money collected  can be written as follows:

0.25 x 27 + 0.10 x 92 + 0.05 x 140 + 0.01 x 255 = $25.50

Therefore, the total amount of money collected by Keiko’s class was $25.50

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[tex]A= \pi r^{2}[/tex]

Answer:

it’s A=pi R squared

lolll it’s fine

2021 Riverside Red Dragon Football Season Points

0 0 3

1 1 7 7 7 7

2 0 0 0 2 4 8 8

3 1 3

Key 1|1 = 11

This stem-and-leaf plot correctly graphs the data set.

We have that, The size of a given insect population is given by [tex]P(t) = 100e^{.03t}[/tex]. Where t is measured in days, we obtain the following:

a. To find the initial size of the insect population, we need to evaluate P(t) at t=0:

[tex]P(0) = 100e^(.03 * 0)P(0) = 100e^0\\P(0) = 100(1)\\P(0) = 100\\[/tex]

Therefore, initially there were 100 insects.

b. To find the differential equation satisfied by P(t), we need to find the derivative of P(t) with respect to time (t):

[tex]dP(t)/dt = d(100e^{(.03t))}/dt\\dP(t)/dt = 100(.03)e^{(.03t)}[/tex]

Then, the differential equation satisfied by P(t) is:

[tex]dP(t)/dt = 3e^{(.03t)}[/tex]

c. To find the time when the population doubles, we need to find t when P(t) = 200:

[tex]200 = 100e^{(.03t)}\\2 = e^{(.03t)}\\[/tex]

Now, take the natural logarithm (ln) of both sides:

[tex]ln(2) = ln(e^{(.03t)})\\ln(2) = .03t[/tex]

Solve for t:

[tex]t = ln(2)/.03 \approx 23.10.[/tex]

Therefore, the population will approximately double in t = 23.10 days.

d. To find the time when the population equals 300, we must solve for t at P(t) = 300:

[tex]300 = 100e^{(.03t)}\\3 = e^{(.03t)}[/tex]

Take the natural logarithm (ln) of both sides:

[tex]ln(3) = ln(e^{(.03t)})\\ln(3) = .03t[/tex]

Solve for t:

[tex]t = ln(3)/.03 \approx 36.32.[/tex]

Therefore, the population will equal approximately 300 at t = 36.32 days.

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The expression that will make the given equation true when simplified is: B. (4 x 3) ÷ 2

To determine the expression that makes the equation true, simplify both sides of the equation and then compare them to the given options to identify the one that equals the simplified equation.

Let's simplify the left-hand side of the equation first:

1/2 * (3 * 5 + 1) - 2 = 1/2 * (15 + 1) - 2 = 1/2 * 16 - 2 = 8 - 2 = 6

Now we can check which expression equals 6:

4 * (2+3) = 4x5 = 20

(4x3) ÷ 2 = 12÷2 = 6

6 ÷ 3 + 2 = 2+2 = 4

6+8 ÷ 4 = 6 + 2 = 8

Therefore, the expression that makes the equation true is (4x3)÷2, which equals 6.

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Using Order of operations, the expression that makes the equation true is: (4 × 3) ÷ 2

The order of operations has an acronym which is PEMDAS. This acronym stands for: parentheses, exponents, multiplication, division, addition, then subtraction.

We are given the equation as:

¹/₂ × (3 × 5 + 1) - 2

Using order of operations, we use multiplication inside the bracket first to get:

¹/₂ × (15 + 1) - 2

We solve the bracket to get:

¹/₂ × 16 - 2

We use multiplication to get:

8 - 2 = 6

Looking at the given options, the only that gives same answer as the above is option B as seen below:

(4 × 3) ÷ 2

= 12 ÷ 2

= 6

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The dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 cantered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

A scale factοr is defined as the ratiο between the scale οf a given οriginal οbject and a new οbject, which is its representatiοn but οf a different size (bigger οr smaller).

5).Tο find the cοοrdinates οf the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K, we need tο perfοrm the fοllοwing steps:

Find the cοοrdinates οf pοint K after dilatiοn.

Since the center οf dilatiοn is K, the image οf K will be itself.

Therefοre, the cοοrdinates οf the image οf pοint K will be (8, 12).

Find the cοοrdinates οf the images οf pοints J, L, and M after dilatiοn.

Tο find the image οf pοint J, we can use the fοrmula fοr dilatiοn:

(image οf J) = (center οf dilatiοn) + (scale factοr) x (vectοr frοm center tο J)

(image οf J) = (8, 12) + (1/4)(vectοr JO)(image οf J) = (8, 12) + (1/4)(-4, 0)

(image οf J) = (7, 12)Similarly, we can find the images οf pοints L and M:

(image οf L) = (8, 12) + (1/4)(vectοr ZK)(image οf L) = (8, 12) + (1/4)(-4, -12)

(image οf L) = (7, 9)(image οf M) = (8, 12) + (1/4)(vectοr KM)(image οf M) =

(8, 12) + (1/4)(-16, -8)(image οf M) = (4, 10)

Therefοre, the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).

6). Tο find the image οf triangle XYZ after a dilatiοn centered at the οrigin with a scale factοr οf k = -3/2, we need tο apply the dilatiοn fοrmula tο each vertex.

Fοr vertex X(0, 2):

x-cοοrdinate οf image = k * x-cοοrdinate οf X = -3/2 * 0 = 0y-cοοrdinate οf image = k * y-cοοrdinate οf X = -3/2 * 2 = -3

Sο the image οf vertex X is X'(0, -3).

Fοr vertex Y(4, 6):x-cοοrdinate οf image = k * x-cοοrdinate οf Y = -3/2 * 4 = -6y-cοοrdinate οf image = k * y-cοοrdinate οf Y = -3/2 * 6 = -9

Sο the image οf vertex Y is Y'(-6, -9).

Fοr vertex Z(8, 0):x-cοοrdinate οf image = k * x-cοοrdinate οf Z = -3/2 * 8 = -12y-cοοrdinate οf image = k * y-cοοrdinate οf Z = -3/2 * 0 = 0

Sο the image οf vertex Z is Z'(-12, 0).

Therefοre, the image οf triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

Hence, the dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

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The minimum perimeter of a rectangle with an area of 80 ft2 is 56 ft. The dimensions of this rectangle would be 8 ft x 10 ft.

explanation: Let length be L and breadth be B of the rectangular room. A = L × B, given A = 80 ft² (Area of the room)The perimeter of the rectangle, P = 2(L + B) = 2L + 2BTo minimize P, we need to express one variable in terms of the other.

Let's consider L as the variable, and write B in terms of L from the given equation.=> B = (A/L)Therefore, P = 2L + 2B= 2L + 2(A/L) => P = 2(L² + 40/L)Differentiate P w.r.t L to find the critical point.= 2[(d/dL)(L²) + (d/dL)(40/L)]= 2(2L – 40/L²)For the critical point, dP/dL = 0=> 2L – 40/L² = 0=> L = ±2√10

Therefore, L = 2√10 (since L cannot be negative)Thus, B = (A/L) = 80/(2√10) = 4√10The dimensions of the room are 2√10 × 4√10 = 8.94ft × 35.76ft (rounded to the nearest hundredth).

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Rate of change is not a method that can be used to solve a system of equations.

When solving a system of equations, it is important to use a valid method to find the solution. A system of equations is a set of two or more equations with multiple variables that must be solved simultaneously. There are different methods to solve a system of equations, but some methods are more effective than others.

Elimination (Linear Equations) is a method of solving a system of equations by adding or subtracting the equations to eliminate one of the variables. This allows the remaining variable to be solved easily. Substitution is another method where one variable is solved for in one equation and then substituted into another equation to solve for the other variable. Graphing involves plotting the equations on a graph and finding the intersection point(s) of the two lines. This is the solution(s) to the system of equations.

Rate of change, on the other hand, is not a method of solving a system of equations. It refers to the ratio of the change in one variable to the change in another variable. It is a concept used in calculus and differential equations, but it is not a valid method to find solutions to systems of equations. Therefore, when solving a system of equations, it is important to use a valid method to ensure accurate results.

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