Can an equation have more than one extraneous solution?

The correct answer is D. 3y + 5 − 7y = 4(-y + 1) + 5.

What is the solution of the equation?

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

The equation that has no solution is D. 3y + 5 − 7y = 4(-y + 1) + 5.

This is because the left-hand side is equal to -4y + 5, while the right-hand side is equal to y + 10. These two expressions are not equivalent, so there is no value of y that makes the equation true.

For equations A, B and C, we can simplify the left and right sides of the equation and see that they are equivalent and thus have solutions.

Hence, The correct answer is D. 3y + 5 − 7y = 4(-y + 1) + 5.

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Answer: 3.60$ it is very simple think about it

Answer:

3.60

Step-by-step explanation:

2 rulers = 1.20

2x3=6

so times 1.20 by 3 too

6 rulers = 3.60

The parametric equation of line is:

(x – x₁) / cosθ = r

and (y – y₁) / sinθ = r, where r is the parameter and θ is an angle made by straight line with x-axis.

We know that the parametric equation of a straight line passing through point (x₁, y₁) and which makes an angle θ with the positive X-axis is given by,

(x – x₁) / cosθ = (y – y₁) / sinθ = r,

where r is a parameter, which represents the distance between points (x, y) and  (x₁, y₁)

The parametric equations of the line are of the form:

x = x₀ + at,

y = y₀ + bt,

and z = z₀ + ct.

where the components a, b and c of are the direction numbers of the line.

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The equations are solved below.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here:

[tex]y=10^{3x-5} \\y=e^{-5x+3} \\y=e^{-4x+1}[/tex]

Thus taking log both sides of the equations we get

[tex]1) y=10^{3x-5}=logy=(3x-5).1\\\\(logy+5 )/3=x \\ \\2)y=e^{-5x+3}=lny=-5x+3.1\\ x=(lny-3.1)/-5\\\\3) y=e^{-4x+1} \\x=(lny-1)/-4[/tex]

Hence, The equations are solved for the above equations in terms of y

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The value of k should be less than 4 so that the given equation has distinct real roots.

This quadratic equation is of the form ax^2 + bx + c .

Now, the value b^2- 4ac is called the discriminant of the equation which decides the nature of the roots.

Here, three cases arise -

If b^2- 4ac > 0, the roots are real and distinct .

If b^2- 4ac=0, the roots are real and equal.

If b^2- 4ac < 0 , there are no real roots, all the rots are complex in nature.

Here, the equation is x^2 -4x + k =0.

Its discriminant is 16-4k. For this to have, distinct real roots,

16-4k>0

means 16 > 4k i.e. 4>k.

Thus, The value of k should be less than 4 so that the given equation has distinct real roots.

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Dina is 10 years younger than Mimi, thus she is 8 years older after 3 years. Mimi will be twice as old as Dina in 5 years.

The device tactic is a method of addressing dilemmas that entails first figuring out the price of a specific unit, then multiplication that value to figure out the needed value. Simply put, the unit method is used to derive a single unit value from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the price of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, numerical modeling, or mathematics of matrices or operators.

given

Dina should be x years old, and Mimi should be x + 10 years old.

After five years,

Mimi's age is x+10 + five years, = x+15 years for Dina.

x+ 15 = 2 ( x+ 5 )

Dina will be old in 3 years when

x + 3 = 5 + 3 = 8 years since

x + 15 = 2x + 10 x = 5.

Dina is 10 years younger than Mimi, thus she is 8 years older after 3 years. Mimi will be twice as old as Dina in 5 years.

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Answer:

4.5 cups of flour now.

Step-by-step explanation:

Trevor has 7.375 - 2.875 = 4.5 cups of flour now.

Answer:

Trevor has 4 ½ cups of flour now.

Step-by-step explanation:

To find the amount of flour Trevor has after using 2 ⅞ cups, we need to subtract 2 ⅞ cups from 7 ⅜ cups.

7 ⅜ cups - 2 ⅞ cups = 4 ½ cups

So, Trevor has 4 ½ cups of flour now.

The curve's gradient from point A to point 1 is 0.4. The slope of the curve is the same as the slope of the tangent.

The straight line in geometry that most closely resembles (or "clings to") the curve at a given location is called the tangent line to the curve. It is possible to think of the second point as the limiting position of straight lines that pass through the supplied point and a neighboring point of the curve as it approaches the first.

A tangent line is a line that only touches a curve once and does not cross it entirely. The point of tangency is the location where the curve and the tangent intersect.

A tangent line is a simple straight line that only touches a function once. The instantaneous rate of change of the function at that specific position is shown by the tangent line.

The coordinate of A be (8, 3).

The tangent passes through the point (1, 0.2).

The slope of the points (x₁, y₁) and (x₂, y₂) exists [(y₂ - y₁)/(x₂ - x₁)]

substitute the values in the above equation, we get

The slope of the tangent is (0.2-3)/(1-8) = 0.4.

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As the x-coordinate is negative and y-coordinate is zero ,Point (−4,0) lies on negative x-axis

Hey dear ,

I have just created graph for your

U can see that (4,0),(6,0),(8,0) lie on same line I. e X axis

Hence , they are collinear

they lie on a straight line which is the X axis as the y coordinate is zero

Here the x-coordinate of our point is −4 and the y-coordinate of our point is 0

As the x-coordinate is negative and y-coordinate is zero ,Point (−4,0) lies on negative x-axis

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The area of the shaded region is equal to 58 square units.

What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of the shaded region will be calculated as,

Area of entire object= 10 units x 7 units= 70 units.

Area of the gap= 2 units x 6 units= 12 units.

The area of the shaded figure= is 70 units - 12 units= 58 units.

Therefore, the area of the shaded region is equal to 58 square units.

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The sum of the first 140 natural numbers of the given arithmetic sequence is; 9870

The formula to find the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

The formula to find the sum of the n terms of an arithmetic sequence is;

Sₙ = ⁿ/₂(2a + (n - 1)d)

In this question, we see that;

a = 1

d = 1

n = 140

Thus;

S₁₄₀ = (140/2)(2(1) + (140 - 1)1))

S₁₄₀ = = 70(2 + 139)

S₁₄₀ = 9870

That is the sum of the first 140 terms in conclusion

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Answer:

88 cm

Step-by-step explanation:

the formula for circumference is π · d  

28 · 22/7 = 88

88 cm is the circumference of a circle with a diameter of 28 cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle with a diameter of 28 cm.

Radius = 28/2

Radius is 14 cm.

Circumference=2πr

=2×3.14×14

=87.92=88 cm

Hence, 88 cm is the circumference of a circle with a diameter of 28 cm.

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The number of such pairs will be 120, which is the same as the result obtained from the formula.

Let A = {0, 1, 5, 8}. The number of distinct pairs of disjoint non-empty subsets of A whose union is A can be calculated using the formula

C(2^n , 2) = C(2^4 , 2) = C(16 , 2) = 120

Therefore, there are 120 distinct pairs of disjoint non-empty subsets of A whose union is A. This can be verified by constructing all the possible pairs of disjoint non-empty subsets of A whose union is A. The number of such pairs will be 120, which is the same as the result obtained from the formula.

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Answer:

0.043

Step-by-step explanation:

the answer is 33.125

the correct substitutions of the values a,b, and c from the equation -2=-x+x squared into the quadratic formula is none.

ax2+bx+c=0, with "a" not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given that,  the equation -2=-x+x squared into the quadratic formula

Thus, the quadratic equation:

-2² = (-x + x)²

4 = x² + x² - 2x .x

=> 2x² -2x.x -4 = 0

Since the solution is zero

from the general formula of quadratic equation

ax2+bx+c=0

Therefore, the Value of a,b, and c will be zero for the given equation.

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The length of the side BC is 14.5 cm.

The triangle in the example has a right angle at angle C, and angle A equals 65.

The base and height of a right-angled triangle are the two sides that form the right angle or are perpendicular in a right-angled triangle. The hypotenuse of a right-angled triangle is the third and largest of the three sides.

It is clear from the figure that AB is the height, AC, BC is the base, and is the hypotenuse.

The trigonometric identities formula The angles between the hypotenuse and base are given below using sin, cos, and tan.

Substituting the value 65° for theta for hypotenuse and x for height in the formula for sine of the angle.

Thus, the length of the side BC is 14.5 cm.

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Tamera's punch recipe has a higher ratio of lemon-lime soda to pineapple juice.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The ratio for Tamera's recipe is 4 liters of lemon-lime soda to 8 liters of pineapple juice or a ratio of 4:8.

The ratio for Lien's recipe is 2 liters of lemon-lime soda to 6 liters of pineapple juice or a ratio of 2:6.

Since 4 is greater than 2, Tamera's recipe has a higher ratio of lemon-lime soda to pineapple juice.

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The slope - intercept form of the function is given as y = 6.5x - 5

Slope-intercept form is a way of expressing the equation of a straight line in the form of:

y = mx + b

Where:

The slope-intercept form is so named because it shows the slope (m) and y-intercept (b) of the line explicitly. It is considered one of the most useful forms for working with and graphing lines, as it allows you to easily see the steepness of the line and where it crosses the y-axis.

The slope of a line is a number that describes how steep the line is. It is calculated as the ratio of the change in y to the change in x. A positive slope means that the line is rising as it moves from left to right and a negative slope means that the line is falling as it moves from left to right. A slope of zero means that the line is horizontal, and a slope that is undefined means that the line is vertical.

In this problem, we take the points and find the slope.

f(2) = 8

y₁ = 8, x₁ = 2

y₂ = -5, x₂ = 0

slope (m) = y₂ - y₁ / x₂ - x₁

m = -5 - 8 / 0 - 2

m = 6.5

Using the slope, we can calculate the y - intercept.

y = mx + c

-5 = 6.5(0) + c

c = -5

The slope-intercept form is y = 6.5x - 5

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Your roommate can take 4 different collections of pets as he can't take both the dog and the cat.

The problem states that your roommate has six pets (fish, cat, turtle, dog, rock, and pony) and he wants to take three of them with him but he can't take both the dog and the cat because they will fight.

We can solve this problem using the combination formula which is (nCr) = n! / (r! * (n-r)!) where n is the total number of items and r is the number of items being chosen.

In this case, there are 6 pets and he wants to take 3 of them, but not the dog and the cat. So, we have 6-2=4 pets remaining.

So the number of different collections of pets he can take is (4C3) = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4.

So, your roommate can take 4 different collections of pets as he can't take both the dog and the cat.

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To graph f(x) = 3x, find two points on the line, then connect those two points with a straight line.

A linear equation is a line equation. The slope intercept from of an equations of line is:

y = mx + b

Where:

m = slope

b = y-intercept

To graph a line when its equation is given, it is sufficient to find two poins that lie on that line, then connect those points.

The given function is:

f(x) = 3x, or we can write:

y = 3x

To find two points on the line, take 2 x values, for example x = -4 and x = 3. Then, find the values of y which are equal to f(x).

x = -4  ---->  y = f(-4) = 3(-4) = -12

Hence, the coordinate is (-4, -12)

x = 3  ------> y = f(3) = 3(3) = 9

Hence, the coordinate is (3,9)

Connect (-4, -12) and  (3,9) with straight line and extent the line. The graph is shown in the attached picture.

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a) The rental rates for approximately 95% of rentals fall between $550 and $650.

b) The approximate probability that a rental rate is between $525 and $650 is 0.8413.

c) A rate of $630 is 0.12 standard deviations above the mean.

a) To find the rental rates for approximately 95% of rentals, we can use the empirical rule, also known as the 68-95-99.7 rule. This rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

Therefore, for this distribution with a mean of $600 and a standard deviation of $25, we can find the rental rates for approximately 95% of rentals as:

Lower Bound: $600 - (2 × $25) = $550

Upper Bound: $600 + (2 × $25) = $650

b) To find the approximate probability that a rental rate is between 525 and 650, we can use the standard normal distribution table to find the area under the curve between those two values. Since the standard deviation is known, we can standardize the values by subtracting the mean and dividing by the standard deviation.

P(525<x<650) = P( (525-$600)/$25 < (x-$600)/$25 < (650-$600)/$25) = P(-1.2<z<1.2)

The area under the standard normal curve between -1.2 and 1.2 is approximately 0.8413. Therefore, the approximate probability that a rental rate is between $525 and $650 is 0.8413.

c) To find how many standard deviations from the mean is a rate of $630, we can use the formula:

(x - mean) / standard deviation

In this case:

(630 - 600) / 25 = 3/25

So a rate of $630 is 0.12 standard deviations above the mean.

To summarize, the rental rates for approximately 95% of rentals fall between $550 and $650, the approximate probability that a rental rate is between $525 and $650 is 0.8413, and a rate of $630 is 0.12 standard deviations above the mean.

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The question is -

The monthly apartment rental rates near Enterprise College approximate a symmetrical, bell-shaped distribution. The sample means the rental rate is $600; the standard deviation is $25.

a) what are the rental rates for approximately 95% of rentals?

b) what is the approximate probability that a rental rate is between 525 and 650 days?

c) how many standard deviations from the mean is a rate of $630?

Answer:

20%

Step-by-step explanation:

To write a ratio as a percentage without a calculator, divide the part by the whole and multiply by 100. In this case, the ratio is the number of votes received by Debra (12) over the total number of club members (60).

So, 12/60 = 1/5

Multiplying by 100 gives: 1/5 * 100 = 20%.

Therefore, 20% of the club members voted for Debra.

Answer:

K = - 2J + 24

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept, where line crosses y- axis )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 24) and (x₂, y₂ ) = (6, 12) ← 2 points on the line

m = [tex]\frac{12-24}{6-0}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2

the line crosses the y- axis at (0, 24 ) ⇒ c = 24

y = - 2x + 24

convert y to K and x to J , in this case , then

K = - 2J + 24 ← equation of trend line

Answer: The answer to this question is 16.75.

Step-by-step explanation:

 16.40

+ 0.35            

 16.75

a) x > 11

b) j < 17

c) b => 9

d) h <= 104

e) k > -8/3

f) p < -24/5

g) q => -17/2

h) f <= 29.52

Answer: 20

Step-by-step explanation: 2 half triangles at the top can be made into 1 square of 4 units which added onto the other part to create 1, 4 by 5 shape which is 20

Answer:

dont

Step-by-step explanation:

The ordered pair for option C) (1,3) is not a solution of the equation 2x+y =7.

A solution of an equation is a set of values for the variables that make the equation true.

In the case of a linear equation in two variables, such as ax + by = c, where a, b, and c are constants, the solution can be found by using techniques such as substitution, elimination, and graphing.

To find the solution of equation 2x + y = 7, we need to find the values of x and y that make the equation true.

a. (1,5): when we substitute the x = 1, y = 5 in equation 2x + y = 7, 2(1) + (5) = 7, 2 + 5 = 7, which is true so this pair is a solution.

b. (3,1): when we substitute the x = 3, y = 1 in equation 2x + y = 7, 2(3) + (1) = 7, 6 + 1 = 7, which is true so this pair is a solution.

c. (1,3): when we substitute the x = 1, y = 3 in equation 2x + y = 7, 2(1) + (3) = 5, 2 + 3 = 7, which is not true so this pair is not a solution.

d. (0,7): when we substitute the x = 0, y = 7 in equation 2x + y = 7, 2(0) + (7) = 7, 0 + 7 = 7, which is true so this pair is a solution.

Therefore, The ordered pair for option C) (1,3) is not a solution of the equation 2x+y =7.

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