a car traveled 120 miles at a certain average rate. by increasing its average rate by 10 mph, it traveled 160 miles in the same time it traveled 120 what is the average rate for the first trip

Answer:

See below.

Step-by-step explanation:

Let the smaller integer be n.

Then the larger integer is n + 2.

"When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer."

The correct equation is:

n + 3(n + 2) = 5n - 2

His mistake is not using parentheses on the left side. Since he left out the parentheses, the left side is not "the smaller integer added to three times the larger integer", but rather it is "the smaller integer added to 2 plus 3 times the smaller integer."

n + 3(n + 2) = 5n - 2

n + 3n + 6 = 5n - 2

4n + 6 = 5n - 2

8 = n

n = 8

n + 2 = 10

The integers are 8 and 10.

The differential equation is overdamped for values of "b" in the intervals (-∞, -2√k) ∪ (2√k, ∞), underdamped for values in the interval (-2√k, 2√k), and critically damped for values in the interval [-2√k, 2√k].

To determine the values of "b" that make the general solution of a second-order linear homogeneous differential equation overdamped, underdamped, or critically damped, we need to consider the characteristic equation associated with the equation.

Let's assume the differential equation is of the form:

m''(t) + b * m'(t) + k * m(t) = 0,

where m(t) represents the dependent variable, and m''(t) and m'(t) denote the second and first derivatives of m(t) with respect to time, respectively. The constants "b" and "k" correspond to the damping coefficient and the spring constant, respectively.

The characteristic equation associated with the differential equation is:

r^2 + b * r + k = 0,

where "r" is the characteristic root.

The discriminant of the characteristic equation is given by Δ = b^2 - 4 * k. The behavior of the system depends on the value of Δ:

1. Overdamped: The system is overdamped when Δ > 0 and b^2 > 4 * k. This occurs when the roots of the characteristic equation are real and distinct. In this case, the general solution contains exponential terms with negative exponents.

2. Underdamped: The system is underdamped when Δ < 0. This occurs when the roots of the characteristic equation are complex conjugates. The general solution contains oscillatory terms, represented by sine and cosine functions.

3. Critically damped: The system is critically damped when Δ = 0. This occurs when the roots of the characteristic equation are real and repeated. The general solution contains exponential terms with negative exponents, but without oscillatory behavior.

Now, let's find the intervals for "b" that correspond to each case:

1. Overdamped: The equation is overdamped for all values of "b" that satisfy b^2 > 4 * k. Thus, the interval for "b" is (-∞, -2√k) ∪ (2√k, ∞).

2. Underdamped: The equation is underdamped for all values of "b" that satisfy Δ < 0. Since Δ = b^2 - 4 * k, we have the interval for "b" as (-2√k, 2√k).

3. Critically damped: The equation is critically damped for all values of "b" that satisfy Δ = 0. Thus, the interval for "b" is [-2√k, 2√k].

In summary:

• The equation is overdamped for "b" in the interval (-∞, -2√k) ∪ (2√k, ∞).

• The equation is underdamped for "b" in the interval (-2√k, 2√k).

• The equation is critically damped for "b" in the interval [-2√k, 2√k].

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Answer:

Both have the same period which is 2π

Step-by-step explanation:

a. Range: (-∞, +∞) or (-∞, ∞) b. the largest possible range for G(x) is the set of all real numbers excluding the value of x = 1/2.

(a) To find the largest possible domain and largest possible range for the function F(x) = 2x² - 6x + 8:

Domain: The function F(x) is a polynomial, and polynomials are defined for all real numbers. Therefore, the largest possible domain for F(x) is the set of all real numbers.

Domain: (-∞, +∞) or (-∞, ∞)

Range: The range of a quadratic function depends on the shape of its graph, which in this case is a parabola. The coefficient of the x² term is positive (2 > 0), which means the parabola opens upward. Since there is no coefficient restricting the domain, the range of the function is also all real numbers.

Range: (-∞, +∞) or (-∞, ∞)

(b) To find the largest possible domain and largest possible range for the function G(x) = (4x + 3)/(2x - 1):

Domain: The function G(x) involves a rational expression. In rational expressions, the denominator cannot be equal to zero since division by zero is undefined. So, we set the denominator 2x - 1 equal to zero and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Therefore, the function is defined for all real numbers except x = 1/2. Hence, the largest possible domain for G(x) is the set of all real numbers excluding x = 1/2.

Domain: (-∞, 1/2) U (1/2, +∞)

Range: The range of the function G(x) depends on the behavior of the rational expression. Since the numerator is a linear function (4x + 3) and the denominator is also a linear function (2x - 1), the range of G(x) is all real numbers except for the value that would make the denominator zero (x = 1/2). Therefore, the largest possible range for G(x) is the set of all real numbers excluding the value of x = 1/2.

Range: (-∞, +∞) or (-∞, ∞) excluding 1/2

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Answer:

Water level and temperature

Step-by-step explanation:

Scatter plots are used to graph linear data containing to two variables, with the independent variable on the x - axis and the dependent variable on the y-axis. Linear data graphed on a scatter plot may be positive or negative depending on the type of relationship which exists between the two variables. Positive relationships are represented by positive slopes, with x increasing as y increases. Negative relationship on the other hand results in a reduction in Y as X increases and vice versa. Examples of negative correlation include the association between water level and temperature. ; water level will usually decrease as temperature rises. Therefore, any association between variables whereby a increase in one leads to a corresponding decrease on the other is tagged as a negative correlation.

Step-by-step explanation:

Geometry is in maths

Geology is in geography..

I hope you understand..

Answer:

y=2x-7

Step-by-step explanation:

y=mx+b

Slope (m)= \(\frac{9-3}{8-5} =\frac{6}{3} =2\)

Y-Intercept (b)= \(y=2x+b\\3=10+b\\b=-7\)

The hypotheses of Theorem 2.4.2 are satisfied when the points lie on the ty-plane. Specifically, the points should be in the region bounded by the inequality |ty| <=1.

Theorem 2.4.2 is also known as the Mean Value Theorem. It states that if a function f is continuous on a closed interval [a, b] and differentiable on an open interval (a, b), then there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

The hypotheses of the Mean Value Theorem are satisfied in the ty-plane at any point where the function is continuous and differentiable. This means that the function must have no breaks or sharp turns at that point. Additionally, the function must be defined at the endpoints of the interval [a, b] and must be differentiable on the open interval (a, b).

In the ty-plane, the hypotheses of the Mean Value Theorem are satisfied at any point that meets these conditions. For example, if the function f(t) = t^2 is graphed in the ty-plane, the hypotheses of the Mean Value Theorem are satisfied at any point on the curve because the function is continuous and differentiable at all points.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

\(speed = \frac{distance}{time} \\ = \frac{(1.2 \times 1000)m}{(10 \times 60)s} \\ = \frac{1200m}{600s} \\ = 2 \frac{m}{s} \)

The area of the surface generated by revolving the curve about the axis y = 9-x² is 12π

Surfaces of revolution are graphs of functions f(x,y) that rely exclusively on the distance from the origin of the point (x,y).

Polar coordinates (r,) are one approach to discuss such surfaces. A "surface of revolution" is formed by rotating a curve around an axis.

Consider a curve with coordinates x and z in the "x0" half of the Euclidean plane.

y = √(9-x²)

⇒ dy = (-2x)/2√9-x²)

= -x/√(9-x²)

Note that surface area (s) is given as:

\(\int\limits^b_a {2\pi y}\) √1 + (dy/dx)² dx

= 2\(\pi\) \(\int_{1}^{-1}\) √9-x² * √[1 + (-x)/√9-x²)]dx

= 2π \(\int_{1}^{-1}\)3dx
= 6π [x]₋¹₁

= 6π (1-(-1)

= 6π (2)

= 12π

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Answer:

bob

Step-by-step explanation:

ask your teacher

The coordinates of point b are  (1,3)

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

(x1,y1) = (-7, 1)

Let point b has coordinates (x2,y2)

M (-3, 2)

mid point formula:

M= [ (x1+x2)/2,   (y1+y2)/2 ]

(-3, 2) =  [ (-7+x2)/2,   (1+y2)/2 ]

=> -3= (-7+x2)/2                      ,  2 = (1+y2)/2

=> -6 = -7+x2                             => 1+y2 = 4

=> x2= -6+7 = 1                          => y2=4-1 =3

(x2,y2) = (1,3)

The coordinates of point b are  (1,3)

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Answer:

88 27 16 27 15 14 23 16

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

The given function is

We need to find the graph of the given function.

Substitute x=0 in the given function to find the y-intercept.

y-intercept of the function is (0,-4).

Substitute y=0 in the given function to find the x-intercept.

x-intercept of the function is (2,0).

Plot (0,-4) and (2,0) on a coordinate place and connect them by a straight line.

Only graph C intersect the x-axis at (2,0) and y-axis at (0,-4).

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here is the step-by-step explanation:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression by following the order of operations:
(4)(7)-(1)(7/6)+0

3. Simplify further:
28-7/6

4. Find a common denominator and combine the terms:
168/6-7/6

5. Simplify the expression to get the final numerical value:
161/6

Therefore, the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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The numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here are the steps to do this:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression inside the parentheses:
(2)²(7)-(1)²(7/6)+0

3. Simplify the exponents:
4(7)-1(7/6)+0

4. Multiply the numbers:
28-7/6+0

5. Simplify the expression by finding a common denominator and combining the terms:
28-7/6 = 168/6-7/6 = 161/6

So the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

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Answer:

3 in

Step-by-step explanation:

Answer:

5 ml

Step-by-step explanation:

1250 lb * ( 1 ml / 250 lb ) = 5 ml

The x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

The y-intercept is the point where the value of x is zero while the x-intercept is the point where the value of y is zero

Given the function below;

-4x + 7y = 3

For the x-intercept

-4x = 3

x = -3/4

The x-intercept is (-3/4, 0)

For the y-intercept

7y = 3

y = 3/7

The y-intercept is (0, 7/3)

Hence the x and y-intercepts are (-3/4, 0) and (0, 7/3) respectively

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Answer:

HOLA MATE HERE IS YOUR ANSWER....

{x}^{2} - 5x - 6x

2

−5x−6

WE WILL SOLVE IT BY MIDDLE TERM SPLITTING

product = {6x}^{2}product=6x

2

Sum = 5x

{6x}^{2} \times {1x}^{2} = {6x}^{2}6x

2

×1x

2

=6x

2

-6x + 1x = 5x

ANSWER :

{x}^{2} - 6x + 1x - 6x

2

−6x+1x−6

NOW WE CAN FURTHER CONTINUE IT BY TAKING COMMON

SO,

x(x - 6) + 1 (x - 6)

Answer :

(X+1)(X-6)

PLEASE MARK AS BRAINLIEST

Answer:

90 miles

$81

Step-by-step explanation:

Let m = number of miles driven.

Plan A:

cost = 0.40m + 45

Plan B:

cost = 0.90m

0.90m = 0.40m + 45

0.5m = 45

m = 90

The plans cost the same for 90 miles.

cost = 0.9m = 0.9(90) = 81

The cost is $81.

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

5x^2(2x-7)

Step-by-step explanation:

Hope this helps!

Answer:

7 Candy bars

Step-by-step explanation: She can buy 7 candy bars, just subtract 3 from 12 and you get 9, then keep subtracting 1.50 from each and you end up getting 7 candy bars.

The missing angle measures on the right triangle are given as follows:

First we obtain the measure of angle y. To obtain it, we consider that any angle is supplementary with it's exterior angle, that is, the sum of it's measures is of 180º.

As the exterior angle is of 135º, the measure of angle y is obtained as follows:

y + 135 = 180

y = 180 - 135

y = 45º.

Then we obtain the measure of angle x, considering that the sum of the measures of the three internal angles of a triangle is of 180º. Hence:

x + 45 + 90 = 180

x = 180 - 135

x = 45º.

The right triangle is given by the image shown at the end of the answer.

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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

224

Step-by-step explanation:

200*0.12=24

200+24=224

The amount to be paid for the loan is $248.

'Simple interest is the interest amount for a particular principal amount of money at some rate of interest.

According to the given problem,

Principal amount (P) = $200

Rate of interest (r) = 12%

Time period (t) = 2 years

We know,

Final amount to be paid with interest (A) = P( 1 + rt )  

                                                                   = 200{ 1 + ( 0.12 × 2 )

                                                                   = 200( 1 + 0.24 )

                                                                   = 200 × 1.24

                                                                   = $248

Hence, we can conclude, we have to pay $248 for the loan.

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Answer: The probability of getting two red marbles is P = 0.141

Step-by-step explanation:

We know that in the bag there are 3 blue marbles and 5 red marbles, then there is a total of 8 marbles in the bag.

The probability of taking at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles, this is:

p = 3/8

Suppose we got a red marble:

Now we replace the red marble we took, so in the bag there are again 3 red marbles and 8 total marbles, then the probability of getting another red marble is again:

q = 3/8

The joint probability (this is, the probability of both events happening) is equal to the product of the individual probabilities, with gives us:

P = p*q = (3/8)*(3/8) = 9/64 = 0.141

Therefore, the tree is 78.14 feet tall. Rounded to the nearest hundredth of a foot, the answer is 78.14 feet.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental part of geometry and is used in many areas of science, engineering, and technology.

by the question.

A represents the top of the tree, and the line segment AB represents the height of the tree, which we want to find. The angle of elevation, which is the angle between the ground and the line of sight to the top of the tree, is 54°. The distance from the point on the ground to the tree is 52 feet, which we'll call d. Finally, h represents the distance from the ground to the point where the line of sight intersects the tree.

Using trigonometry, we know that:

tan (54°) = h/d

We can rearrange this equation to solve for h:

\(h = d * tan (54)\)

Plugging in the values we know, we get:

\(h = 52 * tan (54) = 78.14\)

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