Mathematics High School

help me create an extraneous radical equation please using this model!! :) thank you.
[tex]a \sqrt{x}+b + c = d[/tex]

I don't need you to solve it, just help me pick numbers for variable a, b, c, and d to create an extraneous solutuion

Answers

Answer 1
If you are sure that's exactly what the equation is:

b,c,d are all numbers, so indeed, focus on a single number, say 'e'. Also a can't be zero, or there is no equation at all! So, again all numbers can be grouped:

a*sqrt(x) + b+c=d ---> sqrt(x) = f, f some number.

x = f^2 is the solution.

To be extraneous, means that it does not solve the equation.

Why here? Because by definition in mathematics sqrt( f^2) is not f! but abs(f), that is:

sqrt(9)=3,

So you just need to set the numbers to -3: (thinking x=9)

2*sqrt(x) + 7 -4 = -3

this gives: sqrt(x) = -3, from which x= 9, but sqrt(9) = 3.

It's kind of tricky, because many forget the definition that sqrt(a^2) = abs(a).

The same does not happen when looking for roots.

You should ask your teacher to make sure this is what they want.

Let me say that usually extraneous solutions are those which come out after solving an equation but make no sense when substituted in the original equation. But with sqrt(x) and your so particular equation, there is nothing else to say.

Related Questions

Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.

Answers

check the picture.

π radians is the angle 180 degrees, so π/4 radians is 180°/4=45°.

to construct the angle [tex]5 \frac{ \pi}{4} [/tex] we can proceed as shown in the figure, that is, we open an angle equal to 5 half right angles.

We see that the line making the angle 5pi/4 is the same line making the angle pi/4 radians, that is 45 degrees.

A line making the angle 45 degrees with the x axis, has slope equal to 1. 

Remark, we have considered a line passing through the origin, as it represents all other lines making 5pi/4 radians.

Answer: slopi=1

a telephone pole casts a shadow that is 34 m long. find the height of the telephone pole if a statue that is 36cm tall casts a shadow 77cm long

Answers

This is the concept of proportionality, the length of the pole will be given by:
[length of the post]/[length of the shadow]=[length of the statue]/[length of the shadow of statue]
thus;
suppose the length of the pole is x m
thus;
x/34=36/77
x=36/77*34
x=15.8 m
the answer is 15.9 m

The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282

Answers

The growth function is
V (t)=V0 (1+r)^t
V (t) ?
V0 225000
R 0.035
T 8 years

V (8)=225,000×(1+0.035)^(8)
V (8)=296,282

The value of the house in 8 years. (D) ≈ $296,282

How to predict the value?

The given parameters are:

Initial value, a = $225,000

Rate, r = 3.5%

The scenario is an illustration of an exponential growth function.

So, we have:

V(x) = a * (1 + r)^x

Substitute known values

V(x) = 225000 * (1 + 3.5%)^x

This gives

V(x) = 225000 * (1.035)^x

Next, we plot the graph of V(x)

See attachment

From the attached graph

V(x) = $296,282

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A perfect circle figure has four lines of symmetry. True or false?

Answers

True, because the lines can be drawn from all directions of the circle, therefore that must be at least 4 lines of symmetry 

What is the length of the side opposite the 30° angle? HELP

Answers

the answer is B
√3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long.

determine the valie of x for which v || w if m2 =100 and. m7 =4x+10

Answers

I believe that x=22.5

A person died leaving behind inheritance of Rs. 300000. Distribute the amount among 4 sons and 3 daughters so that each son gets double of what a daughter gets. Find the share of each when a debt of Rs. 80,000 was also to be paid.

Answers

s=2d

4s+3d=300000-80000

4s+3d=220000, now using s=2d in this equation you get:

4(2d)+3d=220000

8d+3d=220000

11d=220000

d=20000

So each daughter gets 20000 and each son gets 40000.

The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.

The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.

First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:

Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000

Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:

3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000

Simplifying:

3x + 8x = Rs. 220,000

11x = Rs. 220,000

x = Rs. 20,000 (share of each daughter)

Consequently, the share of each son will be double that of a daughter, which is:

2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)

George plays basketball in a week-long camp. On Day 2, he scored 8 points. On day 4, he scored 12 points. Explain how to measure his average rate of change

Answers

you got the avg of two days((8+12)\2=10)so you can guess that its around 70 in a week.
avg rate of change is x+2=y


Solve each system of equations by using elimination.

7)2t-u=17
3t+u=8

8)2j-k=3
3j+k==2

9)3c-2d=2
3c+4d=50

Answers

7. 5t= 25. 3(5)+u=8
t= 5. 15+u=8
u=-7

8. 5j= 5. 3(1)+ k= 2
j=1. k= -1

9. 6c - 4d= 4. 3(6)+4d= 50
3c +4d= 50. 18 + 4d= 50

9c = 54. 4d= 32
d= 8
c = 6

PLEASE HELP!!!! If a function, f(x) is shifted to the left four units, what will the transformed function look like?

Answers

If you shift f(x) to the left four units, then the coordinate axis effectively moves four units to the right. This "four units to the right" movement for the axis means that every x is replaced with x+4.

So that means f(x) turns into f(x+4)

For example, say we had the function f(x) = 5x^2 + 10x
Shifting f(x) four units to the left leads to
f(x) = 5x^2 + 10x
f(x+4) = 5(x+4)^2 + 10(x+4) ... notice the replacements in bold
f(x+4) = 5(x^2+8x+16) + 10(x+4)
f(x+4) = 5x^2 + 40x + 80 + 10x + 40
f(x+4) = 5x^2 + 50x + 120

Find the greatest common factor for the group of numbers. 12 ​, 28 ​, 24

Answers

Final answer:

The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.

Explanation:

To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:

28 = 2 x 2 x 7

The smallest power of 3 that is common is just 3.

Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.

A scale model of a human heart is 198 inches long. The scale is 34 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.

Answers

 would be 198 / 34 =  5.82  = 6 inches to nearest whole number.

The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.

Answers

By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W

A = LW = 33
L = 2W-5

Substituting the second equation to the first,

A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3

Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,

L = 2(5.5)-5
L = 6 m

Therefore, the dimensions of the rectangle is 6 m by 5.5 m.

Erica purchased adult and youth tickets for a movie. She bought x adult tickets for $7 each and y youth tickets for $5. Write an expression that can be used to show the total cost, C, of all tickets.

Answers

7x plus 5y equals C(cost)

Answer:

7x + 5y = C

Step-by-step explanation:

X is the number of people buying an adult ticket

Y is the number of people buying a youth ticket

Using this we can find C, cost

How many three-letter "words" can be made from 5 letters "fghij" if repetition of letters (a) is allowed?

Answers

From the given, there are 5 letters to choose from. For the first letter of the three-letter word, we can choose from all 5 of them. 

Also, for the second letter of the word, we can also have 5 choices because it is stated that repetition is allowed. Similarly, there are also 5 choices for the last letter of the word. By fundamental principle of counting, we multiply the numbers identified in the sentences above,
   
                                n = 5 x 5 x 5 = 125

Thus, 125 words can be formed from the given letters. 

Write the sum using summation notation, assuming the suggested pattern continues.

-1 + 2 + 5 + 8 + ... + 44

A) summation of negative three times n from n equals zero to fifteen
B) summation of the quantity negative one plus three n from n equals zero to fifteen
C)summation of negative three times n from n equals zero to infinity
D) summation of the quantity negative one plus three n from n equals zero to infinity

Answers

The answer is C. Summation of negative three times n from n equals zero to infinity

HELP ASAP 30 POINTS


Evaluate f(3) for the piecewise function: f(x) = Which value represents f(3)?
–11
8
12.5
16

Answers

Answer:

-11

Step-by-step explanation:

what is the sum of 27 and 5 times a number is 187

Answers

27+5x=187
5x=160
x=32
.

Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1450 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour

Answers

the first mechanic = a
the second mechanic = b

the first mechanic works for 4 hours = 4 * a
the second mechanic works for 15 hours = 15 * b
total charged = t

t = 4a + 15b

sum of their rates:
a + b = 160
b = 160 - a

t = 4a + 15b
1450 = 4a + 15 * (160 - a)
1450 = 4a + 2400 - 15a

now let's make the formula easier.

15a - 4a = 2400 - 1450
11a = 950

a = 86.36
b = 160 - 86.36 = 73.64

I NEED THIS QUICK

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36
6x + 2.5y = 24

Answers

After multiplying by the given coefficients and adding, the new equation obtained is:
8y - 7.5y = 0

 after doing the calculations the answer is:
y = 0
x = 4

Because the two equations formed were independent, they had one solution

Answer:

its C

Step-by-step explanation:

Find the value of x if B is between A and C, AB = 4x – 9, BC = 3x + 5 and AC = 17.

Answers

If A,B and C lie on the same line:

4x- 9 + 3x+5 = 17

7x = 21

x = 3
AB + BC = AC
4x - 9 + 3x + 5 = 17
7x - 4 = 17
add 4 to both sides
7x = 21
divide both sides by 7
x = 3

A triangle has one leg measuring 10 inches and the hypotenuse measuring 20 inches. the other leg measures 10\sqrt[]{3} 10 3 inches. what type of triangle is represented here?

Answers

From the description given for the triangle above, I think the type of triangle that is represented would be a right triangle. This type of triangle contains a right angle and two acute angles. In order to say or prove that it is a right triangle, it should be able to satisfy the Pythagorean Theorem which relates the sides of the triangle. It is expressed as follows:

c^2 = a^2 + b^2

 where c is the hypotenuse or the longest side and a, b are the two shorter sides.

To prove that the triangle is indeed a right triangle, we use the equation above.

c^2 = a^2 + b^2
c^2 = 20^2 = 10^2 + (10sqrt(3))^2
400 = 100 + (100(3))
400 = 400

What is the simplified expression for ?

Answers

The simplified expression is 16

Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.

Answers

By the Pythagorean theorem:

#1
[tex]t= \sqrt{13^2-12^2}= \sqrt{169-144}= \sqrt{25}=5 [/tex]

#2
[tex]a= \sqrt{12^2-9^2}= \sqrt{144-81}= \sqrt{63}= \sqrt{9*7}=3 \sqrt{7} [/tex]

#3
[tex]x= \sqrt{6^2+9^2}= \sqrt{36+81}= \sqrt{117}= \sqrt{9*13}=3 \sqrt{13} [/tex]

Answer:

i) t = 5

ii) a = 3√7

iii)  x =3√13

Step-by-step explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

i)

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13

A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. if two candies are selected simultaneously, what is the probability that they are both the same flavor?

Answers

the answer is shown below

How many hours is from 9:00am to 6:00 pm?

Answers

9 am to 6 pm is a 9 hour difference. hope this helps

The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.4 radians
1.2 radians
2.8 radians
0.4 radians

Answers

The length of the arc is a fraction of the circumference of the circle depending on the length of the radius and the intercepted angle. This can be calculated through the equation,

                    L = (2πr) x (θ /360)

where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees. 

Substituting the known values to the equation,

                   36 = (2π)(15)  x (θ / 360)

We translate the equation to find the value of θ,

                               θ = (36)(360) / 2π(15)

The value of θ is equal to 137.51°. 

This can be coverted to radians through the equation below,

                              θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad

What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2

Answers

Answer:

Your answer is in the picture below

The graph approaches x=−2 asymptotically, has no x-intercepts, and the y-intercept of the graph is the point (0, 5).

Attached graph.

The graph of the function f(x) = (x² + 3x + 5 )/(x+ 2) is a parabola that is shifted to the left by 2 units.

The parabola is similar to the graph of the function y = x², but it is narrower because the denominator of the fraction is x + 2.

The graph also has a hole at the point (-2, 5), which is the point where the denominator of the fraction is 0.

Attached graph.

Here are the steps on how to sketch the graph of the function:

Sketch the graph of the function y = x².

Shift the graph to the left by 2 units.

Add a hole at the point (-2, 5).

The attached figure shows the graph of the function f(x) = (x² + 3x + 5 )/(x+ 2):

The graph of the function has the following features,

The domain of the function is all real numbers except for -2.

The range of the function is all real numbers except for 5.

The function has a minimum point at (-4, 1).

The function has a hole at the point (-2, 5).

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Triangle END is translated using the rule (x, y) → (x − 4, y − 1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? (1 point

Answers

Here are the choices for this problem:
They are parallel and congruent.
They are perpendicular to each other.
They share the same midpoints.
They create diameters of concentric circles.

The transformation that is done is a translation. Which means that the coordinates will be translated or moved in the coordinate plane without changing the size and the orientation of the image. If is a line was drawn from E to E' and another line was drawn from N to N', the two lines would be parallel and congruent since the translation done to E is the same to that of N.

The answer is
They are parallel and congruent. 

This answer is right!!!!! They are parallel and congruent.

Find the equation of the quadratic function with zeros -1 and 1 and vertex at (0, -4).

Answers

since the vertex is at 0,-4 and the zeros are above it, we'll use a vertical parabola equation, namely with the dependent variable to be the "y".

bear in mind that, a zeor or solution of say -1 and 1, simply means x-intercepts at -1, 0 and 1,0.

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex\ (0,-4)\ \begin{cases} h=0\\ k=-4 \end{cases}\implies y=a(x-0)^2-4\implies y=ax^2-4 \\\\\\ \textit{we also know that } \begin{cases} y=0\\ x=-1 \end{cases}\implies 0=a(-1-0)^2-4 \\\\\\ 0=a(-1)^2-4\implies \boxed{4=a}\qquad thus\implies \boxed{y=4x^2-4}[/tex]
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