Worth 30 points.
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
the square root of x minus 3 plus five equals x.
Picture of question and equation attached.
Answers
Answer:
x=7 valid solution
x=4 extraneous solution
Step-by-step explanation:
sqrt( x-3) +5 = x
Subtract 5 from each side
sqrt( x-3) +5 -5= x-5
sqrt( x-3) = x-5
Square each side
(sqrt( x-3))^2 = (x-5)^2
Foil the right side ( x-5)(x-5) =x^2 -5x-5x+25 = x^2 -10x+25
x-3 = x^2 -10x+25
Subtract x from each side
-3 = x^2 -10x -x+25
Add 3 to each side
0 = x^2 -11x +25 +3
0 = x^2 -11x+28
Factor
0 = (x-7)(x-4)
Using the zero product property
x-7 =0 x-4=0
x=7 x=4
Check the solutions
sqrt( x-3) +5 = x
x=7
sqrt( 7-3) +5 = 7
sqrt(4) +5 = 7
2 +5 = 7 valid solution
x=4
sqrt( 4-3) +5 = 4
sqrt(1) +5 = 4
1 +5 = 4 not true extraneous solution
Related Questions
A diver started at 4 feet above ground. After diving he ended at 58 feet below the surface
of the water. What was the change in elevation of the diver? Solve and write an equation,
then model with a number line.
Answers
Answer:
62
Step-by-step explanation:
If the diver started 4 four feet above the ground and ended 58 feet below the surface, the diver went down, so we can solve this by taking the total distance traveled like so:
[tex]|4+58|[/tex] = 62
Help plz and thanks
Answers
Answer:
8
Step-by-step explanation:
4x4=16x8=128
−9x+5<17 and 13x+25<−1 solve for x
Answers
-9x + 5 < 17
Subtract 5 from both sides:
-9x < 12
Divide both sides by -9, and because you are dividing by a negative value the inequality sign gets reversed:
X > -12/9
Simplify:
X > -4/3
13x + 25 < -1
Subtract 25 from both sides:
13x < -26
Divide both sides by 13:
X < -26/13
X < -2
Answer:
There are no solution. if you using khan answer is B
Step-by-step explanation:
I did it and got it correct
To all math experts here. Please answer it.
Answers
Answer:
where are the functions below? or should they be equated? like f(x) with the g(x)??
PLZ ANSWER THIS QUICK! THANK U!!
Answers
What does this mean exactly?
Answers
Answer: Choice B [tex]y \le 0[/tex]
========================================================
Explanation:
They want to know what are all the possible y values here. The range is the set of all possible outputs of a function.
The largest y value is y = 0 which occurs at the vertex, in this case the highest point. There is no smallest y value as those arrows point downward forever.
So y is between negative infinity and 0, which means we write [tex]-\infty < y \le 0[/tex]
Converting that to interval notation leads to [tex](-\infty, 0][/tex]. Note the square bracket to include the endpoint.
The compound inequality [tex]-\infty < y \le 0[/tex] simplifies to [tex]y \le 0[/tex]
One way to describe this particular relation's range is to say "The set of negative real numbers with 0 included".
Side note: The domain is the set of all possible x inputs. In this case, the domain is the set of all real numbers.
If DEF ~= PQR, which congruences are true by CPCTC? Select all that apply.
a. DF = PR
b. DE = PR
C. EF = QR
D. Q = D
E. E = Q
F. F= R
Answers
Answer:
A, C, E, F
Step-by-step explanation:
I need help with Regis question.
Answers
Answer:
It is 3/13
Step-by-step explanation:
it is because there are 13 total marbles and 3 yellow ones
A car travels about 74 feet in one second. At this speed, about how many feet will the car travel in 6 seconds?
Answers
444 ft traveled in 6 seconds.
If the car travels 74 ft in 1 second, all you have to do is multiply 74 by 6 to find the answer, which is 444 ft.
Select the table that represents a linear function. (Graph them if necessary.)
Answers
Y 5 10 15 20
Answer C
Because the X’s increase in a constant rate By 1
And the Y’s increase in a constant rate by 5
Erica and 4 friends are going out for pizza for dinner. They split one pizza and 5 small drinks. The pizza costs $13.00. They spend a total of $20.50. Find the cost of one small drink. Define the variable, write and solve an equation, and answer the question.
Answers
to find the cost of a small drink, you might want to:
subtract the decimalstotal cost : $20.50
cost of pizza :$13.00.
cost of one small drink : total cost - cost of pizza
: $20.50 - $13.00.
: 20.50
- 13.00
: 07. 50
: $ 7.50
An equo equila Teral Traingle has
nearest mm workout The Lower
bound of its Perimeter mcm
sides of Lenght 6.2 cm correct to
Answers
Answer:
Step-by-step explanation:
Given parameters:
Dimensions of the equilateral triangle = 6.2cm
Unknown:
Perimeter = ?
Solution:
The perimeter of the triangle is the sum of all its sides;
Perimeter = 3(L) for an equilateral triangle;
Perimeter = 3(6.2) = 18.6cm
to the nearest mm = 19.0cm
Write 12 2/3% as a fraction in simplest form
Answers
Answer:
1/4
What is 3/12 Simplified? - 1/4 is the simplified fraction for 3/12.
Step-by-step explanation:
The total budget for a landscaping project was $349.02, and the project called for 42 plants. What is the average cost per plant? Explain the method used for solving the problem.
Answers
Answer:
349.02 / 42 = answer
Step-by-step explanation:
method used is dividing total cost by number of goods used gives the exact cost of each plant
Neuma has a container that held 9/54 of a kilogram of rainbow sprinkles she divided the sprinkles Evenly to put on top of the 9 servings of ice cream that she was making for her friends at the sleepover.To determine the weight of each serving neuma performed the calculations below she concluded that each serving weighs 1/6 of a kilogram. What is Neumas error?
Answers
Answer:
c. neuma should have only divided 9 by 9, not 54 by 9.
Step-by-step explanation:
Neuma had a container that held 9/54 of a kilogram of rainbow sprinkles. she divided the sprinkles evenly to put on top of the 9 servings of ice cream that she was making for her friends at the sleepover. to determine the weight of each serving, neuma performed the calculations below. she concluded that each serving weighs 1/6 of a kilogram. what is neuma’s error?
a. neuma should have multiplied by 54, not divided.
b. neuma should have multiplied by 9, not divided.
c. neuma should have only divided 9 by 9, not 54 by 9.
d. neuma should have only divided 54 by 9, not 9 by 9
Neuma's calculation
9/54
= 1/6
Kilogram of rainbow sprinkles = 9/54
Ice cream servings = 9
Correct calculation
Weight of each servings = total weight / number of servings
= 9 / 54 ÷ 9
= 9 / 54 × 1 / 9
= 1 / 54
Each servings = 1/54 kilogram
c. neuma should have only divided 9 by 9, not 54 by 9.
Answer:
c
Neuma should have only divided 9 by 9, not 54 by 9.
im failing pls help !!!!!
Answers
Answer:
ill suck ya wang
Step-by-step explanation:5$ and ill suck yo wang to do your homework
Answer:
It is C.
Step-by-step explanation:
If you multiply 2 times 2 you get 4. Then multiply 4 by 5 and you get 20.
Therefore, it is C.
I need help with this is anyone
Answers
Answer:
-w+41
Step-by-step explanation:
5(w+4)-3(2w-7)
5w+20-6w+21
-w+41
3. 100x2-36y2 ??
ito pa guys pleasedddd!!
Answers
Answer:
4(5x - 3y)(5x + 3y)
Step-by-step explanation:
Assuming you require the expression factored.
Given
100x² - 36y² ← factor out 4 from each term
= 4(25x² - 9y²) ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
25x² - 9y²
= (5x)² - (3y)² ← with a = 5x and b = 3y
= (5x - 3y)(5x + 3y)
Thus
100x² - 36y² = 4(5x - 3y)(5x + 3y) ← in factored form
FOR THOSE WHO WANT A CHALLENGE owen has a collection of quarters nad nickels worth 8.10. if the nickels were quarters and the quarters were nickels, the value would be 17.70. find the number of each coin.
Answers
Answer:
Nickels: 67
quarters: 19
Step-by-step explanation:
It's fairly simple if you know how to use algebra
Carl drives to the beach at 50 mph. When he returns home he is able to travel at 55
mph. Assuming the trip home takes him a half hour less, find the distance to the beach.
Answers
Answer:
the distance to the beach is 27.5 miles (multiple choice is under rated)
What is the slope of the line that passes through the points (5, -11) and (-2, 10)?
Answers
10. Separate the number 38 into two parts so
that one number is 6 less than the other
number
Answers
Answer:
16, 22
Step-by-step explanation:
x+x+6=38
2x+6=38
2x=32
x=16
One number is 16, Another number is 22
16+22=38
22-16=6
If 25% of the students in Pre-Algebra courses receive a grade of A, and there are 300 students enrolled in Pre-Algebra this year, how many students will receive an A? *
125
67
57
75
Answers
Answer:
75 students
Step-by-step explanation:
300/4
Answer:
75
Step-by-step explanation:
At the end of a snow storm, Amelia saw there was a lot of snow on her front lawn. The temperature increased and the snow began to melt at a steady rate. After the storm, the snow started melting at a rate of 1.5 inches per hour and it is known that 4 hours after the storm ended, the depth of snow was down to 12 inches. Write an equation for S,S, in terms of t,t, representing the depth of snow on Amelia's lawn, in inches, tt hours after the snow stopped falling.
Answers
Answer:
s= -1.5t + 18
Step-by-step explanation:
The Equation to represent the depth of snow is s= -1.5t + 18.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
We learn from the question that the snow's depth is s and that it takes hours to melt the snow.
The amount of snow is 12 inches deep after 4 hours of melting.
Now, keep in mind that the melting rate is 1.5 inches per hour.
and, 1.5 x 4 = 6 inches of snow will have melted in the four hours.
Thus, the initial snow depth will be 6 + 12 = 18 inches.
Hence, the Equation to represent the depth of snow is s= -1.5t + 18.
Learn more about equation here:
https://brainly.com/question/18510627
#SPJ5
Simply the question in the picture
Answers
Answer:
1
Step-by-step explanation:
8800000 in scientific notation
Answers
Answer:
8.8 x 10 to the power of 6
Step-by-step explanation:
The folding chair has different settings that change the angles formed by its parts. Suppose m∠2 is 31 and m∠3 is 65. Find m∠1. The diagram is not to scale.
Answers
Answer:
m∠2=31
m∠3=65
m∠1=?
Notice that measure of angle 2,3 and the angle that's next to angle 1 will form a triangle. Let's name the angle next to 1 to be x.
31+65+x = 180
96+x = 180
x = 180-96
x = 84
Now, you can easily find the m∠1.
84+m∠1 = 180 (REASON: Linear pair)
m∠1 = 180-84
m∠1 = 96
I need help what is -0.5 _ -0.2
Answers
because I need more characters
how do you add two areas together
Answers
Answer:
You would just add them like normal
Step-by-step explanation:
How does a circle help create a trianglular shape
Answers
Answer:
Make a dot where the circles intersect at the top. Using the ruler, draw a straight line from the top dot to each center point. Then connect each center dot with a horizontal line. This is the birth of the triangle!