Using the equation
[tex] \sqrt{x + 7} + 5 = x[/tex]
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.​

Answers

Answer 1

Given:

The equation is:

[tex]\sqrt{x+7}+5=x[/tex]

To find:

Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.

Solution:

We have,

[tex]\sqrt{x+7}+5=x[/tex]

Subtract 5 from both sides.

[tex]\sqrt{x+7}=x-5[/tex]

Taking square on both sides, we get

[tex]x+7=(x-5)^2[/tex]

[tex]x+7=x^2-10x+25[/tex]

[tex]0=x^2-10x+25-x-7[/tex]

[tex]0=x^2-11x+18[/tex]

Splitting the middle term, we get

[tex]x^2-2x-9x+18=0[/tex]

[tex]x(x-2)-9(x-2)=0[/tex]

[tex](x-2)(x-9)=0[/tex]

[tex]x=2,9[/tex]

Now, substitute [tex]x=2[/tex] in the given equation.

[tex]\sqrt{2+7}+5=2[/tex]

[tex]\sqrt{9}+5=2[/tex]

[tex]3+5=2[/tex]

[tex]8=2[/tex]

This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.

Substitute [tex]x=9[/tex] in the given equation.

[tex]\sqrt{9+7}+5=9[/tex]

[tex]\sqrt{16}+5=9[/tex]

[tex]4+5=9[/tex]

[tex]9=9[/tex]

This statement is true. So, 9 is a solution of given equation.

Therefore, 2 is an extraneous solution and 9 is a solution of given equation.


Related Questions

Dada a função fx=0,15.X+900 , determine a) f(80) b) f(120) c) f(200) d) f(56)

Answers

Answer:

See answers below

Step-by-step explanation:

Given the function:

f(x) = 0.15x + 900

a) f(80) = 0.15(80) + 900

f(80) = 12 +  900

f(80) = 912

b)  f(120) = 0.15(120) + 900

f(120) = 18 +  900

f(120) = 918

c) f(200) = 0.15(200) + 900

f(200) = 30 +  900

f(200) = 930

d)  f(56) = 0.15(56) + 900

f(56) = 8.4 +  900

f(56) = 908.4

in a group of 120 students,90 students study mathematics and 72 study science. if 10 of the student does not study any subject
1)find the no.of students who study atleast 1 subject
2)number of students studying both subjects
3)how many students will study mathematics only?
4)how many students will study science only?

Answers

Answer:

Step-by-step explanation:

Total students = 120

Number of students studying Mathematics P(A) = 90

Number of students studying Science P(B) = 72

Number of students who doesn't study both subjects P(AUB)'= 10

1) Number of students studying atleast on subject = 120 -10 = 110

2) Number of students studying both math and science = (90 +72) -110

                     = 162 -110 = 52

3) Number of students studying only mathematics = 90 -52 = 38

4) Number of students studying only science = 72 -52 = 20

Diego has a standard 52 card playing deck, which includes
13 heart cards, 13 spade cards, 13 diamond cards, and 13
club cards. If he draws one card at random, what is the
probability that the card will be a heart?

Answers

Answer:

13/52

Step-by-step explanation:

A gum ball machine has 6 red gum balls, 3 green gum balls, and 5 blue gum balls. What is the probability that the next gum ball that comes out will be red?

Answers

Answer:

Step-by-step explanation:

P(red gum ball)= 6/14=3/7

6/14 can be simplified to 3/7 by dividing by 2. 6/2=3. 14/2=7.

P(red gum ball)=3/7

Which input value produces the same output value for the two functions on the graph

Answers

X = 1

Because where the two lines intersect, they have the same x value, one

Answer:

x = 1

Step-by-step explanation:

Look at the graph to see where the lines intersect.

f(1) = 1

g(1) = 1

When x = 1, the output value of both functions is 1.

Answer: x = 1

Consider the equation and its solution.
— 15(x-O) = 25
— 15х+ 30 = 25
— 15х = -5
What number should be in the empty box?
-30
-2
Оооо
30

Answers

The correct answer to your question is -2

NEED HELP ASAPPP PLZ JUST NEED THE ANSWER NOT THE WORK THANK YOU.

Answers

Answer:

C. 2^8 • 2^(2/10) • 2^(4/100)

•Sequences and functions
( 10 points )
Please help me loves with the answer and understanding

•Please actually help me out I want to better understand this

•trolls will be reported

Answers

the answer is D

when it comes to geometric progression the common ratio (r) must be the same.

to find r, use this formula :

r = T2/T1

= 12/72 = 1/6

= 2/12 = 1/6

Tell whether the triangle with the given side lengths is a right triangle. 36, 77, 85, true or false

Answers

Answer:

True the triangle is a right triangle.

Step-by-step explanation:

the Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex]

so,

[tex]85^{2} =7225\\77^{2} =5929\\36^{2} =1296\\5929+1296=7225[/tex]

please help. its for an assignment that is due today.

Answers

Area of isosceles triangle is 7.8235

Height = base/2 x tan 41 = 2.61

Base length = 2 x ( side length of triangle) x cos 41

6= 2 x ( side length of triangle, assume it b ) x 0.754

6= 1.509 x b

b = 6/ 1.509

b= 3.975

Area = 1/2 b x h

= 1/2 x b^2 Sin square theta

= 7.8235


The length of a box is 6 inches, the width is 4 inches and the height is 2/8 inches. What is the volume of the box?

Answers

Answer:

6 cubic inches

Step-by-step explanation:

To find the volume of a box you do Length * Width * Height

So we can do:

6*4*2/8

=24*2/8

=6

The volume of the box is 6 cubic inches

Which of the following is equivalent to 5(4-m)-2(m+3)? *

don’t give me that link .

Answers

[tex]\longrightarrow{\green{Option\:1.\:(14\:-\:7m)}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]5 \: (4 - m) - 2 \: (m + 3) \\ \\ = 20 - 5m - 2m - 6[/tex]

Combining like terms, we have

[tex] = 20 - 6 - 5m - 2m \\ \\ = 14 - 7m[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]

Jacqui likes to travel to the beach on weekends. She starts at her house, drives d miles, and then spends t hours walking the remaining w miles to get to the beach. Jacqui drives three times as long as she walks during the trip. The equation below represents Jacqui's average speed, a, in miles per hour, when traveling to the beach. a=d+w/3t+t What is the meaning of 3t + t3t+t in the equation above? -The total time that Jacqui spends traveling to the beach -The time that Jacqui spends driving to the beach -The total distance that Jacqui travels to the beach -Jacqui's maximum speed during her trip Jacqui's average speed during one trip to the beach was 3636 miles per hour. If Jacqui drove 70 miles and the entire trip to the beach took her 22 hours, how many miles did she walk to get to the beach?

Answers

Answer:

The answer is below

Step-by-step explanation:

1) Average speed is the ratio of the total distance travelled to the total time taken. Hence it is given by:

Average speed = total distance / total time

Total distance = d miles + w miles

Jacqui drives three times as long as she walks during the trip, hence:

time spent driving = 3t

Total time = 3t + t

Average speed = total distance / total time

a = (d + w) / (3t + t)

2) (3t + t) represents the total time that Jacqui spends traveling to the beach.

3) Given that a = 36 miles per hour, total time = 2 hours

a = total distance / total time

36 miles per hour = total distance / 2 hours

total distance = 72 miles

Total distance = distance walk + distance drove

72 = distance walk + 70

Distance walk = 2 miles

What is the volume of the prism?

Answers

Answer:

[tex]volume \: of \: the \: prism = 4 \frac{1}{2} \times 2 \ \frac{1}{2} \times 6 \\ = \frac{9}{2} \times \frac{5}{2} \times 6 \\ = 67.5 {cm}^{3} [/tex]

Please help me please I will really appreciate

Answers

Answer:

Step-by-step explanation:

If we draw this triangle with Q as the vertex angle (the one at the top of the triangle) then the 2 sides are congruent and this is an iosceles triangle. Because this is an isosceles triangle, then the 2 base angles, angle R and angle S are congruent. If Q measures 114 degrees, then angles R and S together have to add up to the difference between 180 and 114:

180 - 114 = 66

Divide that in half so R = S = 33 degrees each

hi, i know this is basic math and stuff but I still need some help​

Answers

Answer:

the answer is :

20 for the first figure

12 for the second figure

30 for the last figure

Answers:

Perimeter = 22 cmPerimeter = 22 cmPerimeter = 30 cm

==============================================

Explanation:

The perimeter is the total distance around the outer edge of the figure. It's the total amount of fence you need to enclose the region.

So we simply add up all the side lengths. Refer to the diagram to see any missing sides that aren't labeled (shown in blue).

For instance, the perimeter for problem 1 is 5+2+2.5+4+2.5+6 = 22 cm. Problems 2 and 3 are handled the same way.

It's not a typo that the perimeters of problems 1 and 2 are the same value. This is because both figures can be surrounded by a rectangle that is 6 cm across and 5 cm tall. The perimeter of the surrounding rectangle is exactly the same as the perimeter of the inner fenced region. We're effectively just moving fence around but not changing the perimeter.

What is the slope of the line passing through the points (-5, -4) and (-1, 6)?

Answers

Step-by-step explanation:

using the formula (y2-y1)/(x2-x1)we plug the numbers In the slop formula (6--4)/(-1--5)= 10/4

Answer:

Step-by-step explanation:

(x1,y1)= (-5,-4)

(x2,y2)=(-1,6)

Distance=√(x2-x1)²+(y2-y1)²

=(-1-5)²+(6-4)²

=(-6)²+(10)²

=36+100

=136 answer,,

therefore, the slope of the line is 136unit


HELP PLEASE I WILL MARK BRAINLIEST

Answers

Answer:

i beleive its option number 1

Answer:

first graph

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Then g(x) = | x | - 4 is the graph of f(x) shifted down by 4 units

This is represented by the first graph on the left

State if triangles HAG and CAB are similar and why.

Answers

i think the answer is they are similar by SSS, but they are definitely similar

yes need help again im on my math exam review thing i.dk wut it tis also here are some extra points im feelin nice today btw dont jus answer for the points or put a site or ill report.


ᴍɪʟʟʏ~

Answers

Answer:

(-5) + 8 + (-5) = -2

Step-by-step explanation:

The first point is 5 points to the left of 0, or -5

Next, it goes right 8 units (+8) and lands on 3

THen it goes back 5 units (-5) and lands on -2

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

¿¿ Cuanto es "6 + -7 - (-8) + 4 – 2" ??

Answers

Answer:

9

Step-by-step explanation:

Do it left from right.

[6+-7]-(-8)+4-2

[-1-(-8)]+4-2=[-1+8]+4-2

[7+4]-2

11-2

9

I don't know Spanish/what laugnange you speak sorry.

if the sub total is 5.00 and tax is 5% how much is tax

Answers

Answer:

$0.25

Step-by-step explanation:

So total of 5.25 after tax Sorry if i am wrong am pretty sure this is correct.

Which inequality represents “six times a number is less than negative
6x >-39
4
6 + x>-39
6x < -39
4
6x5-393
4

Answers

Answer:

6x < - 39 3/4

Step-by-step explanation:

help guys pls i beg u cannot do the math this so hard someone help ☺️☺️☺️☺️☺️☺️☺️☺️

Answers

200= 13.5xV+65
200 because that’s what she needs to equal. Then multiple 13.5 by V because you are accounting for how many times she visits and how many points she will get per visit. Then you add 65 because she already has that amount from signing up.
V >= (200 - 65) / 13.5
V >= 10

a submarine starts out at 120 feet below sea level it dives another 175 feet and then rises 228 feet. what is the current depth of the submarine

Answers

67 feet below sea level
120+175=295
295-228=67

570
1. Volume of a pyramid: 192 ftº: Volume of a rectangular prism:
2. Volume of a pyramid:
Volume of a rectangular prism: 729m
3. Volume of a cylinder: 285 cm: Volume of a cone:
4. Volume of a sphere:
Volume of a cylinder: 600cm
5. Volume of a cone: 50 m: Volume of a cylinder:

Answers

Answer:

576 FT^3

243 m^3

95 cm^3

400 cm^3

150 m^3

Step-by-step explanation:

Volume of a pyramid = 1/3 x ( length base x height)

Volume of a prism= ( length base x height)

1. prism = 192 x 3 = 576 FT^3

2. prism = 729 / 3 = 243 ft^3

volume of a cylinder = nr^2h

Volume of a cone =  1/3(nr^2h)

3. cone = 285/3 = 95

5. cylinder = 50 x 3 = 150

4. sphere = 600 / 1.5 = 400

5. The property depicted in the expression 2/( 3) ×(1/3+ 4/5)=(2/3 × 1/3)+(2/3 × 4/5) is *
associative property of addition
associative property of multiplication
distributive property of multiplication
closure property of multiplication

Answers

Answer:

distributive property of multiplication over addition

Step-by-step explanation:

a(b + c) = ab + ac

The a to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.

This is the distributive property of multiplication over addition.

2/3 × (1/3 + 4/5) = (2/3 × 1/3) + (2/3 × 4/5)

The 2/3 to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.

This is the distributive property of multiplication over addition.

which expressions have value between 1 and 2? choose all that apply.

Answers

Think 1 or the other one

Answer:

its the first, 3rd, and 5th option

Step-by-step explanation:

Work out the base of a square with area,
A
= 64cm2.

Answers

Answer:

32

Step-by-step explanation:

because 64 divided by 2 is 32

On a coordinate plane, 4 lines are shown. Line L M goes through (negative 5, negative 3) and (0, 3). Line N O goes through (negative 6, negative 5) and (0, 0). Line J K goes through (negative 6, 1) and (0, negative 4). Line P Q goes through (negative 5, 4) and (0, negative 2).
Which line is perpendicular to a line that has a slope of Negative five-sixths?

Answers

Answer:

The slope of line LM is perpendicular to the given line.

Step-by-step explanation:

L (- 5, - 3), M (0, 3)

N (- 6, - 5) , O (0, 0)

J (- 6, 1) , K (0, - 4)

Slope of given line = -5/6

Slope of perpendicular line = 6/5

Slope of line LM

[tex]\frac{3 + 3}{0 + 5}=\frac{6}{5}[/tex]

Slope of line NO

[tex]\frac{0+5}{0+6}=\frac{5}{6}[/tex]

Slope of line JK

[tex]\frac{-4-1}{0+6}=\frac{-5}{6}[/tex]

Answer: LM is the correct answer

Step-by-step explanation: Just took the test

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