[tex]\sqrt{x^{2}-16 }-3\sqrt{x-4}=0[/tex]

Answers

Answer 1

Answer:

[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 \\ [/tex]

Step-by-step explanation:

[tex]\tt{} \sqrt{ {x}^{2} - 16 } - 3 \sqrt{x - 4} = 0[/tex]

[tex]\tt{} \sqrt{ {x}^{2} - 16 } = 3 \sqrt{x - 4} [/tex]

[tex]\tt{}{x}^{2} - 16 = 9(x - 4)[/tex]

[tex]\tt{}(x - 4).(x + 4) = 9(x - 4)[/tex]

[tex]\tt{}(x - 4) \times (x + 4 - 9) = 0[/tex]

[tex]\tt{}( x - 4) \times (x - 5) = 0[/tex]

[tex]\tt{}x - 4 = 0 \\ \tt{}x - 5 = 0[/tex]

[tex]\tt{}x = 4 \\ \tt{}x = 5 \\ \\ [/tex]

[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 [/tex]

Answer 2

Answer:

x = 4, 5.

Step-by-step explanation:

√(x^2 - 16) - 3√(x - 4) = 0

√(x^2 - 16) = 3√(x - 4)

Square both sides of the equation:

x^2 - 16 = 9(x - 4)

x^2 - 9x - 16 + 36 = 0

x^2 - 9x + 20 = 0

(x - 4)(x - 5) = 0

x = 4, 5.

As the original equation contained square roots:

We test for extraneous solutions:

x = 4:

√(4^2 - 16) - 3√(4 - 4) = 0 - 3*0 = 0  so x = 4 is OK.

x = 5:

√(5^2 - 16) - 3√(5 - 4) = √9 - 3√1 = 0  so x = 5 is also OK.


Related Questions

determine if the graph represents a function​

Answers

Answer:

the asnwer is YES

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think it 3256

If (1 + 2x)^5+ (1 - 2x)^5 = a + bx + cx?
find the values of the constants a, b and c.

Answers

Answer:

steps below

Step-by-step explanation:

5th level of Pascal triangle: 1,5,10,10,5,1

(1+2x)⁵ = 1*1⁵*(2x)⁰+5*1⁴*2x+10*1³*(2x)²+10*1²*(2x)³+5*1¹(2x)⁴+1*1⁰*(2x)⁵

           = 1 + 10x + 40x² + 80x³ + 80x⁴ + 32x⁵   .. (1)

(1-2x)⁵ =  1  - 10x + 40x² - 80x³  + 80x⁴ - 32x⁵  .. (2)

(1)+(2): (1+2x)⁵ + (1-2x)⁵ = 160x⁴ + 80x² +2

a + bx + cx ?? suppose it's ax⁴ + bx² + cx, if you have other set up.. adjust by yourself

a = 160,    b = 80,    c = 2

a) 7x^2-7=0
b)x^2-x=0
c)5x-15=0
d)x^2-4x+4=9.(x-2)
e)3(x+3)-x^2-3x=0

Answers

Answer:

[tex]a)x = 1 \\ x = - 1 \\ b)x = 1 \\ x = 0 \\ c)x = 3 \\ d)x = 11 \\ x = 2 \\ e)x = 3 \\ x = - 3[/tex]

Bridgette measured an Italian restaurant and made a scale drawing. The scale of the drawing was 8 millimeters: 5 meters. The restaurant's kitchen is 30 meters long in real life. How long is the kitchen in the drawing?

Answers

Answer:

The kitchen drawing is 48 millimeters long.

Sachin used synthetic division to divide a polynomial, p(x), by x + 5 and found that there was no remainder. What does this tell Sachin about how p(x) and x + 5 are related?
A. x + 5 is a factor of p(x)
B. p(x) divided by x + 5 is 0
C. x + 5 is not a factor of p(x)
D. x + 5 cannot be divided evenly into p(x)

Answers

Answer:

A

Step-by-step explanation:

The x + 5 is a factor of p(x) this represents that p(x) and x + 5 are related.

Given that,

Let us assume polynomial be p(x), and it is divided by x + 5.There is no remainder.

Based on the above information, we can say that

x + 5 represent the factor of p(x).

Therefore we can conclude that the first option is correct.

Learn more: brainly.com/question/24169758

-54/87 simplified to a fraction

Answers

Answer:

-18/29

Step-by-step explanation:

54 ÷ 3 = 18 - numerator

84 ÷ 3 = 29 - denominator

-54/84 = -18/29

The sum of two numbers is 179.
Their difference is 133. Find both numbers.

Answers

Answer:

156,23

Step-by-step explanation:

let the numbers be x and y and x>y

x+y=179

x-y=133

add

2x=312

x=156

156+y=179

y=179-156=23

Answer:

156 and 23

Step-by-step explanation:

We can use system of equations to solve this problem.

Step 1: Set up the system of equations.

[tex]\left \{ {{x+y=179} \atop {x-y=133}} \right.[/tex]

Step 2: Solve x + y = 179 for x.

[tex]x + y = 179[/tex] [tex]x + y - y = 179 - y[/tex] (Subtract y from both sides)[tex]x = -y + 179[/tex]

Step 3: Substitute -y + 179 for x in x - y = 133.

[tex]x-y=133[/tex] [tex]-y+179-y=133[/tex] [tex](-y-y)+(179)=133[/tex] (Combine like terms)[tex]-2y + 179 = 133[/tex] [tex]-2y + 179 - 179 = 133 - 179[/tex] (Subtract 179 from both sides)[tex]-2y = -46[/tex] [tex]\frac{-2y}{-2} = \frac{-46}{-2}[/tex] (Divide both sides by -2)[tex]y = 23[/tex]

Step 4: Substitute 23 for y in x = -y + 179

[tex]x = -23 + 179[/tex] [tex]x = 156[/tex]

Therefore, the numbers are 156 and 23.

Find the interval(s) on which the function is negative.

y = x^2 - 6x - 16

I. (-∞, -2)
II. (-∞, 3)
III. (-2, 8)
IV. (8,∞)

A. III only
B. I only
C. II only
D. I,II

Answers

Answer:

I am going to say that it is option A.

Step-by-step explanation:

I hope this helped out a lot!

True or False?

VERY STUCK!!! PLEASE HELP!!!!

Answers

Answer:

I'm pretty sure it's True

Step-by-step explanation:

Congruent triangles are triangles that are the same shape and size. Each triangle has the numbers 71, 47, 62 so I'm assuming the answer is True

Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!

What is the factored form of this expression?

4t2 − 27t + 18

A.
(4t − 18)(t − 1)
B.
(4t − 3)(t − 6)
C.
(2t − 9)(2t − 2)
D.
(2t − 6)(2t − 3)

Answers

Answer:

B

Step-by-step explanation:

Answer:

Have a great rest of your day :)

Step-by-step explanation:

please help on number 8!! it would be much appreciated

Answers

Answer:

a.) 135 degrees

b.) 45 degrees

c.) 45 degrees

Step-by-step explanation:

Use this link to see a visual representation on how to solve for these types of angles, it lets you click on any type of angle and see how it corresponds to other angles within the parallel line and traversal, give it a try!

https://www.mathsisfun.com/geometry/alternate-exterior-angles.html

William says that 15 years from now, his age will be 3 times his age 5 years ago. if x represents William's present age, what equation represents his claim? What is Willaim's current age?

Answers

Answer:

x + 15 = 3 (x - 5)

William’s current age: 15. Years old

Step-by-step explanation:

x + 15 = 3(x-5)

x + 15 = 3x - 15

15 + 15 = 3x - x

30 = 2x

x = 15

Solve the equation. Prove that it makes the equation true.
3b-8=d-6

Answers

Answer:

um just one question are you sure it's supposed to be d-6 instead of b-6

Step-by-step explanation:

if it's b-6 instead of d then the answer is 1

b= 1/3d + 2/3 , der

PLEASE HELP WILL MARK BRAINLIEST
What is -100 represented in exponents

Answers

Step-by-step explanation:

[tex] { - 100}^{1} [/tex]

From the story the Black cat why did the man take out the cats eye

Answers

Answer:

Removing the cat's eye is the beginning of the end, so to speak, for the narrator. Until that moment, the cat had thus far escaped his drunken cruelty, so this act signifies that the narrator had reached a certain mental point: there were no longer any limits to his violent behavior.

Step-by-step explanation:

Compare the graph of a linear inequality in two variables with the graph of a linear equation in two variables

Answers

Answer:

k but where is the graph

Step-by-step explanation:

[3 - | -5/6 - 2(-3)|) ÷ (-17) What is the value of the expression? Enter your answer as a simplified fraction in the box.
HELP ME PLEASE!!​

Answers

Answer:

-1/6

Step-by-step explanation:

i took the quiz

Can someone help me with this please?​

Answers

Answer: OO! i remember this but i forgot

Step-by-step explanation: ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.

amogusඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.

A box of cereal states that there are 87 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are in 2 cups of cereal?

Answers

Answer: for 2 cups, There are 232 Calories.

Step-by-step explanation:

Step 1

Let the calories in one cup be represented as C

Therefore

3/4 x C = 87 calories

C = 87 X 4 / 3 = 116

unit rate is 116 calories per cup.

Step 2- Solving the number of calories in 2 cups

1 cup serving = 116 calories

2 cups servings = 116 x 2= 232 calories

Find the slope of the line that passes through each pair of points A. (-3,4) and (2,-3)

Answers

Answer:

slope = (4-(-3))/(-3-2)=7/-5=-[tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Answer: m=-7/5

Step-by-step explanation:

[tex](-3,4) (2-^-3) \\\\\frac{-3-4}{2-^-3} \\m=-\frac{7}{5}[/tex]


What does m represent in the equation y = mx + b?
A. the y-intercept of the
graph of y = mx + b

B. the slope of the graph of
y = mx + b

C. the run in the ratio rise
/ run

D. None of these

Answers

Answer:

B. the slope of the graph of y = mx + b

Step-by-step explanation:

m is the slope.

y is the y value

x is the x value

b is the y intercept

the answer is

d. none of these

8 to the second power.(2+6) divided by 4=

Answers

i'm a little confused on the format but if you mean 8^2(2+6)/4 then the answer is 128

8x8 is 64, 64x8 is 512. 512/4 is 128

The value of given numerical expression is 128.

The given numerical expression is [8²×(2+6)]/4.

What is the exponent?

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Now, the given expression can be solved as follows:

[8²×(2+6)]/4

= (64×8)/4

= 64×2

= 128

Therefore, the value of given numerical expression is 128.

To learn more about the exponents visit:

https://brainly.com/question/15993626.

#SPJ2

chu vi của một hình chữ nhật là 240 cm. Tính diện tích hình chữ nhật đó, biết tỉ số độ dài hai cạnh là 5 và 7

Answers

(-) Tỉ số độ dài 2 cạnh là 5 và 7
=> Chiều rộng = 5:12, chiều dài = 7:12
(-) Chu vi = 240 suy ra tổng chiều dài + chiều rộng = 240 : 2 = 120
(-) Chiều rộng = 120 x 5 : 12 = 50
Chiều dài = 120 x 7 : 12 = 70
(-) Diện tích = 50 x 70 = 3500

Help me show my work on 13.

Answers

Answer:

Just show basic multiplication skills that we learned in 3th grade i suppose since your teacher dosen't have a brain to figure this out

Please solve the math problem... I will mark you brainliest

Answers

I need a better picture of the shape

The 4th term in an arithmetic sequence is 18 and 9th term is 43. Find the first 5 terms of the sequence

Answers

Answer:

3, 8, 13, 18, 23

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₄ = 18 and a₉ = 43 , then

a₁ + 3d = 18 → (1)

a₁ + 8d = 43 → (2)

Subtract (1) from (2) term by term, eliminating a₁

5d = 25 ( divide both sides by 5 )

d = 5

Substitute d = 5 into (1) for value of a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3 , then

a₂ = a₁ + 5 = 3 + 5 = 8

a₃ = a₂ + 5 = 8 + 5 = 13

a₄ = a₃ + 5 = 13 + 5 = 18

a₅ = a₄ + 5 = 18 + 5 = 23

The first 5 terms are 3, 8, 13, 18, 23

HEY I RLLLLLLY NEED HELP! 50 POINTS AND BRAINLIEST IS YOU'RE RIGHT!!!!

If
f(x) = 2x + 1
and
g(x) = x - 3

g(f(x)) = 2x + ????

I will report if you answer just for points. I'd love help please :P

Answers

Answer:

g(f(x)) = 2x - 2

Step-by-step explanation:

Given:

f(x) = 2x + 1

and

g(x) = x - 3

Find g(f(x)), substitute the value of f(x) into equation:

g(f(x)) = g(2x + 1) = (2x + 1) - 3 = 2x - 2

GIVING BRAINLIEST THOSE WHO PROVIDE PICTURES
graph the solution to this system of inequalities in the coordinate plane.
3y>2x+12
2x+y<-5

Answers

Here is the answer, you just simplify the equation to get y alone then graph :)

a girl that is 5ft tall casts a shadow 4ft long. at the same time, a tree casts a shadow 24 ft long. how long is the tree?

Answers

Answer:

25 Feet

Step-by-step explanation:

Im sorry if i am wrong, but it is 25 because the girl is 5 feet, and one feet less of a shadow. So it is obvious to me that the tree is 1 foot larger.


A car is traveling at a rate of 72 miles per hour. What is the car's rate in feet per second? How many feet will the car travel in 2 seconds? In your computations,
use the fact that I mile is equal to 5280 feet. Do not round your answers,

Answers

Answer:

The rate of travel is 105.6 feet per second, so 211.2 feet could be travelled in 2 seconds.

Step-by-step explanation:

If you take 5280 times 72 it equals 380160 which is the total amount of feet travelled in an hour so you divide it by 60 giving you 6336 which is the total feet travelled in 1 minute and you divide it 1 more time to get 105.6 which is the total feet travelled in 1 second. Hope this helps!

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