Which values of x make this equation true?

x^2+8x=-15

There doesn't exist any extraneous solution for the given problem.

To assess whether or not your solutions are unnecessary, you must re-enter each one into the original equation.

When you square the two sides of a square root problem, there are two solutions, which leads to the appearance of extraneous solutions (the positive and negative number).

A solution that is added but does not fulfill the starting equation will therefore be represented by one of those figures.

Given, the equation is -

√2x+3-√x+2=0

⇒ √2x+3 = √x+2

Squaring on both sides

⇒ 2x + 3 = x + 2

⇒ 2x - x = 2 - 3

⇒ x = -1

Now, putting x = -1 back in the question,

⇒ √1 = √1

Hence, LHS = RHS, therefore, there doesn't exist any extraneous solution.

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Answer:

The statement "when 7 is added to 3 times a certain number, the result is 22" can be written as an equation:

3x + 7 = 22

To solve for the unknown number (which we'll call "x"), we need to get x by itself on one side of the equation. We can do this by subtracting 7 from both sides of the equation:

3x + 7 - 7 = 22 - 7

Simplifying the left side gives us:

3x = 15

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 15 / 3

= 5

So, the number that we were looking for is 5.

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

"When 7 is added to 3 times a certain number, the result 22"

Write this sentence algebraically.

7 + 3x = 22

We need to try and get 3x by itself to find its value, so subtract 7 from both sides.

3x = 22-7 = 15

3x = 15

3x simply means 3 multiplied by x.

So:

x = 15/3 = 5

x=5

the "certain number" is 5.

To check:

7 + 3x5 should equal 22.

7 + 15 = 22.

Hope this helps.

The value of f(5 + h) - f(5)h when h =0 is 60.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 12x

Now,

f(5 + h) = 12 (5 + h) = 60 + 12h

f(5) = 12 x 5 = 60

Now,

f(5 + h) - f(5)h

= 60 + 12h - 60h

h = 0

= 60 + 0 - 0

= 60

Thus,

The value of the limit is 60.

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Answer:

9/12 or simplified as 3/4

Step-by-step explanation:

We are given 3 fractions that we have to add because the question says "What fraction of the can did she use in all?​"

First: Write down [tex]\frac{1}{3} + \frac{1}{4} +\frac{1}{6}[/tex]

Then: We can't just add up all these fractions, we need a LCM. The LCM (Least Common Multiple) We need all the denominators (3, 4, and 6) to be the same. To do that we need to find a number that they can multiply to get. Let's find out all the multiples of each number: (just write the first 5 down because most of the time we can find it easily from this list)

3: 3, 6, 9, 12, 15

4: 4, 8, 12, 16, 20

6: 6, 12, 18, 24, 30

After: just change all the fractions one at a time by whatever you multiply the bottom number to get 12, do it to the top:

[tex]\frac{1}{3} -- > \frac{4}{12}[/tex]

[tex]\frac{1}{4} -- > \frac{3}{12}[/tex]

[tex]\frac{1}{6} -- > \frac{2}{12}[/tex]

Finally we get to add everything up to get:

[tex]\frac{4}{12} +\frac{3}{12} +\frac{2}{12} =\frac{9}{12}[/tex]

(simplified as 3/4)

Answer: help is on the way

Step-by-step explanation:

The number of solutions which the equation y = -2x² -7x + 5 has as required in the task content is; 2.

As evident in the task content; the number of solutions which the given equation has is to be determined.

Since the given equation; y = -2x² -7x + 5 is a quadratic equation.

It follows that the number of solutions which the equation has is two.

PS; Quadratic equations are polynomials with degree 2 and hence, have two solutions.

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(3 × 4) + (3 × 7) = 12 + 21 = 33

7(60 + 6) = 7(66) = 462

4(100 − 3) = 4(97) = 388

(5 × 9) − (5 × 6) = 45 − 30 = 15

So, the correct input-output pairs are:

(3 × 4) + (3 × 7) = 33

7(60 + 6) = 462

4(100 − 3) = 388

(5 × 9) − (5 × 6) = 15

Answer: 33,462,48,388, and 15

Step-by-step explanation:

The scale factor of the smaller figure to the larger figure is 5:2

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Given that two triangles are similar.

The side lengths of the triangle must be proportional.

Let us consider first triangle as ABC, where AB is 35, BC is 40 and AC is 25.

and triangle DEF as DE is 14 and EF is 16.

Now AB/DE=BC/EF

35/14=40/16

5/2=5/2

Hence, the scale factor of the smaller figure to the larger figure is 5:2

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The equation that passes through the point  (-4,1)  y=-3/2x-5

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here, the line that passes through the point (-4,1) and has a slope of -3/2 then let the equation of the line be y=mx+c then we get

⇒1= -3/2×-4+c

⇒c= -5

Hence, The equation that passes through the point  (-4,1)  y=-3/2x-5

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The range of the relation plotted in the graph is {-2, 0, 1, 3}.

Range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest.

Given, A relation plotted on the graph in that there are four points whose coordinates are (0, -2), (3, 0), (-1, 1), and (1, 3)

Since The y-axis on a graph represents the possible output values, or range. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

Therefore, The graphed relation's range is between -2, 0, 1, and 3.

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Answer:

9.5ft

Step-by-step explanation:

a²+b²=c²

equation

24²=c²

22²=a²

put in the variables

24²-22²=b²

Rearrange the equation

576-484=92

square

√92

Square root answer

9.5ft

Answer

Edward drives 160.9 kilometres per month

Edward drives 12,000 miles per year

There are 12 months in a year, this means that Edward travels 12,000 miles in 12 month

The number of kilometres travelled per month can be calculated as follows

12,000= 12

x= 1

cross multiply both sides

x= 12,000/12

x= 100

The next step is to convert 100 miles to kilometres

100 × 1.609

= 160.9 kilometres

Hence Edward travelled 160.9 kilometres per month

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Answer:

Step-by-step explanation:

It sounds like you have a right triangle with one angle of 90 degrees and the lengths of the sides are 24 cm, 60 cm, and 80 cm. If this is the case, then you can use the Pythagorean theorem to find the length of the hypotenuse, which is the side opposite the right angle.

The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we have:

c^2 = a^2 + b^2

c^2 = 24^2 + 60^2

c^2 = 576 + 3600

c^2 = 4176

c = 64.47214

So the length of the hypotenuse, or the length of the pond, is approximately 64.47214 cm.

The fraction module in Python can be used to create fractions such as 3/4. This module can be imported and then the Fraction class can be used to create the fraction object. The fraction object can then be printed to display the fraction.

1. Import the fraction module: from fractions import Fraction

2. Create the fraction object: f = Fraction(3, 4)

3. Print the fraction: print(f)

4. The output will be: 3/4

The fraction module in Python is used to create and manipulate fractions. This module can be imported using the following command: from fractions import Fraction. Once imported, the Fraction class can be used to create the fraction object. The Fraction class takes two parameters which represent the numerator and denominator of the fraction. The fraction object can then be printed to display the fraction. For example, to create a fraction of 3/4, the following code can be used: f = Fraction(3, 4). This will create a fraction object which can then be printed with the print() function to display 3/4. The fraction module in Python is a great way to work with fractions in a programmatic way.

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The equation given in B which is  "5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )" has no solution.

In order to determine which equation has no solution we need to solve the equation to check to see if after solving they give the left-hand side (LHS) and right-hand side (RHS) equal.

If both LHS and RHS are equal, it means the equation has a solution; but if LHS and RHS are not equal, it means that the equation has no solution.

So first solve the equation given in A:

4 ( x + 3 ) + 2x = 6 ( x +  2 )

4 x + 12 + 2 x = 6x + 12

6 x  + 12 =  6 x + 12

LHS is equal to RHS so this equation has the solution.

So now solve the equation given in B:

5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )

5  + 6 + 4 x = x + 3 x + 3

11  + 4 x =  4 x + 3

or

(4 x + 11) = (4 x + 3)

LHS is not 'equal' to RHS so this equation has no solution.

"

Complete question is

Which equation has no solution

A: 4 ( x + 3 ) + 2x = 6 ( x +  2 )

B:  5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )

"

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When the rate of change of AB is -1/5, and line CD is 5 then line AD will be -1

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the change of the output values to the input values, otherwise known as the rate of change.

In the figure, the rate of change is given to be -1/5 and by definition rate of change which is the slope has the formula

m = change of the output values / change in the input values

m = AC / CD

-1/5 = AC / 5

hence AC = -1

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The point on the number line which represents the approximate volume of the cone is 38.

A cone is a figure in three dimensional geometry for which it has a circular base and the plane formed by set of all the points on the base connected to a point called vertex which is not located on the base.

Volume of a cone = [tex]\frac{1}{3}[/tex] π r² h, where r is the radius, h is the height of the cone and π is the pi constant with value 3.14.

Here, r = 3 units and h = 4 units.

Volume =  [tex]\frac{1}{3}[/tex] π r² h

             =  [tex]\frac{1}{3}[/tex] × 3.14 × 3² × 4

             = 37.68 unit³

             ≈ 38 units³

Hence the point 38 on the number line represents the approximate volume of the cone.

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Answer:

38-- the dot close to 40

Step-by-step explanation:

Answer:2

Step-by-step explanation:

She has 2

9 - 5 = 4

no more to give so only 2

Among the given statements, the following statement "Compared with location A, the miles were driven for location B display more variability and the median is greater" provides the best comparison of the two locations.

Hence, option (C) is the correct choice.

For finding the interquartile range for location, first, find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.

The interquartile range for location B is Q3 - Q1 = almost 140 - 40 = 100, while it is Q3 - Q1 = nearly 60 - 40 = 20 for location A.

Therefore, the miles travelled for position B are more variable than they are for place A.

Greater than Location A's almost 50 medians is Location B's nearly 80 median.

Therefore, location B's median miles driven is higher than it is for location A.

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Bill invested $2000 at 5% annual interest

To solve for the word problem, you need to set up two equations.

Let B and J represent how much Bill and Janette invested respectively

The interest of 5%  = 5/100 = 0.05 and 7%  = 7/100 = 0.07

Based on the given info, we can write that:

J + B = 5000 --- (1)

0.05B + 0.07J= 310 --- (2)

From (1):

J = 5000 - B --- (3)

Put (3) in (2):

0.05B + 0.07(5000 - B) = 310

0.05B + 350 - 0.07B = 310

-0.02B = 310-350

-0.02B = -40

0.02B = 40

B = 40/0.02

B = $2000

Thus, Bill invested $2000

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The completed table is given as follows:

The greater rate is that of:

Michaela.

The difference for 40 hours of work is given as follows:

$100.

Marcus' graph is given by the image at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

From the table, Marcus' hourly rate is given as follows:

k = 19/2 = 9.50.

Hence the proportional relationship is:

y = 9.5x.

Which is graphed at the end of the answer.

The table is completed as follows:

From the graph, Michaela's hourly rate is given as follows:

120/10 = $12.

Which is greater than Marcus'.

The hourly difference is given as follows:

12 - 9.5 = 2.5.

Hence the difference for 40 hours is given as follows:

40 x 2.5 = $100.

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Answer:4.9

Step-by-step explanation:

if a=2√5/2 it means it is equal to 2.23

So (2.23×2)/2+1/(2.23×2)

it means a2+1/a2=(2.23×2)/2+1/(2.23×2)= 2.23+0.22=4.9

Answer:

6 roses

Step-by-step explanation:

divide 21 and 3.50 hope this helps:)

Answer:6

Step-by-step explanation:

21 Divided by 3.5 = 6

Answer:

29 2/3 ft

Step-by-step explanation:

The perimeter is found using the formula

P = 2 ( l+w)

 where l is the length and w is the width

P = 2(8 1/6 + 6 2/3)

Getting a common denominator

P = 2 ( 8 1/6 + 6 4/6)

  = 2 ( 14 5/6)

  = 28 10/6

Changing the improper fraction to a mixed number

  = 28 + 1 4/6

Simplifying

  = 29 2/3 ft

The incorrect statement is that a large sample drawn from the population will guarantee accurate results. So, correct answer is option (I).

Population: It Contains all elements of a dataset, and measurable properties of the population such as mean and standard deviation are called parameters. For example, "Everyone in India" refers to India's population.

Sample: It Contains one or more observations drawn from a population, the measurable property of the sample is a statistic. Sampling is the process of selecting samples from a population. For example, some people living in India are a sample of the population. A sample statistic (or just a statistic) is defined as any number calculated from sample data. Examples include sample mean, median, sample standard deviation, and percentile. From the above discussion it is clear that sample is subset of population set and statistic and poplution are related terms of sample and poplution respectively. So, all the statements are correct except statement (I).

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Complete question:

Which of the following statement is INCORRECT? I) A large sample drawn from the population will guarantee accurate results.

II) A sample is a subset drawn from a population of interest.

III) A statistic is a number calculated based on a sample.

IV) A parameter is an unknown quantity about a population.

it cost 5 pound then = 1912.5*5= 9562.5 when  the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65

a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer.

the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn.

if each box costs $1.65, how much will it cost to fertilize the lawn?

We would solve this question by cross multiplication.

If a sound of fertilizer covers 45 square feet of lawn and the lawn is 8666.7 square feet

To get fertilizer quantity we have

1 pound = 45 square

Unknown = 8666.7 square feet

8666.7/45

= 192.59 when approximated we get 193.

Therefore she has to buy 193 pounds of fertilizer

total become 25.5*75=1912.5

it cost 5 pound then = 1912.5*5= 9562.5

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The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

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The graph consists of the relationship between the height of the object and time.

The graph is a demonstration of curves that gives the relationship between the coordinate axes x and y-axis.

here,
In the figure,
The graph shows the relationship between the height of the object dependent on time. Where the vertical axis represents the height of the object, and the horizontal axis represents the time.

Thus, the graph shows the relationship between the height of the object and time.

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The total amount that is earned by Alex in five years is $41528.

We have to note that we need to look at the equation that shows the raise in the salary of Alex and we can be able to write from the equation that;

A =Pe^rt

A = amount that is earned after t years

r = rate of the increase of the salary

t = time taken to increase the salary

We now know from the question that

A = ?

P = $34,000

r = 0.04

t = 5

Thus;

A = 34000e^(0.04 * 5)

A = $41528

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