Answers
Answer:
x-5=sqrt(2x+5)
then square both sides
x2-10x+25=2x+5
x2-8x+20=0
rest is trivial
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
Given
x - [tex]\sqrt{2x+5}[/tex] = 5 ( subtract x from both sides )
- [tex]\sqrt{2x+5}[/tex] = 5 - x ( divide all terms by - 1 )
[tex]\sqrt{2x+5}[/tex] = x - 5 ( square both sides )
2x + 5 = (x - 5)²
2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )
0 = x² - 12x + 20 ← in standard form
0 = (x - 2)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 2
2 - [tex]\sqrt{4+5}[/tex] = 2 - [tex]\sqrt{9}[/tex] = 2 - 3 = - 1 ≠ 5
Thus x = 2 is an extraneous solution
x = 10
10 - [tex]\sqrt{20+5}[/tex] = 10 - [tex]\sqrt{25}[/tex] = 10 - 5 = 5 = right side
Thus x = 10 is the solution
Related Questions
Holly's checking account has a dollar balance. Emily's checking account has a dollar balance. Which of the following is true about their account balances?
A.
Holly's account balance > Emily's account balance
B.
Holly's account balance < Emily's account balance
C.
Holly's account balance = Emily's account balance
Answers
Answer:
C
Step-by-step explanation:
Both Holly and Emily have the same account balance thus it is equal to
Answer:
Dont listen to the person its actually B
Step-by-step explanation:
On a number line, smaller numbers are to the left of larger numbers.
Negative values are always less than positive values.
So, the following is true.
Holly's account balance < Emily's account balance
Two gears are both connected to the same belt. The smaller of the two gears has a radius of 4ft & the larger of the two gears has a radius of 7 ft. The larger gear is turning at a rate of 50 revolutions per minute. What is the angular velocity of the larger gear in radians/second? What is the angular velocity of the smaller gear in radians/second?
Answers
Answer:
[tex]\omega_1 = \frac{5Rad}{3s}[/tex] and [tex] \omega_2 = \frac{35Rad}{12s}[/tex]
Step-by-step explanation:
Given that the larger gear is turning at the rate 50rpm. The angular velocity, [tex]\omega_1[/tex], of the larger gear can be calculated as follows:
[tex]\omega_1 = \frac{50rev}{m} [/tex] to convert that to secs, we know that 1 rev = 2πRad and 60secs make a min, so we have:
[tex]\omega_1 = \frac{50rev}{m} \times \frac{2\pi Rad}{1rev} \times \frac{1m}{60s} [/tex]
That gives
[tex]\omega_1 = \frac{100Rad}{60s}[/tex]
Which gives:
[tex]\omega_1 = \frac{5Rad}{3s}[/tex]
This is the angular velocity of the larger gear in rads/sec.
In order to get the angular velocity of the smaller gear, we know from the question that both gear are connected to the same belt. This implies that they have the same linear velocity. Thus let us find the linear velocity of the larger gear. This is given by
[tex]v = r_1 \times \omega_1[/tex] where v stands for linear velocity and [tex]r_1[/tex] for radius of larger velocity.
We are given the radius of the larger gear as 7ft so we have
[tex]v = 7ft \times \frac{5Rad}{3s} = \frac{35ft}{3s}[/tex]
To get the angular velocity of the smaller gear, we use
[tex]v = r_2 \times \omega_2[/tex] where [tex]r_2[/tex] is the radius of the smaller gear which is given as 4.
Since linear velocity is the same, we have
[tex] \omega_2 = \frac{35ft}{4 \times 3s}[/tex]
[tex] \omega_2 = \frac{35Rad}{12s}[/tex]
There are 50 cars on display at a car show. Of these,18 were manufactured before 1945. What percent of the cars were manufactured before 1945?
Answers
Answer:
36%
Step-by-step explanation:
The total number of cars is 50 and 18 were manufactured before 1945
Let's set up a fraction
18/50
A percent should be out of 100 so let's change the denominator to 100
18/50 (times 2 for 18 and 50 to get 50 to 100)= 36/100
36/100 is 36%
OR
divide 18 by 50 because the fraction line is like a division symbol
that equals 0.36, times 100 to get 36%
2,11,20 find the t15
Answers
Answer:
128
Step-by-step explanation:
There is a common difference between consecutive terms, that is
11 - 2 = 20 - 11 = 9
This indicates the sequence is arithmetic with n th term
[tex]t_{n}[/tex] = t₁ + (n - 1)d
where t₁ is the first term and d the common difference
Here t₁ = 2 and d = 9 , thus
t₁₅ = 2 + (14 × 9) = 2 + 126 = 128
In ABC, angle A = 30 degree , angle b=45 degree find the angle c
Answers
Answer:
95 degrees
Step-by-step explanation:
in a triangle angles add up to 180 degrees.
a + b + c = 180
30 + 45 + c = 180
85 + c = 180
c= 180 - 85
c= 95 degrees
Consider the system of inequalities and its graph.
y ≥
y ≤ x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 8, negative 2) and (0, 0). Everything above the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (3, 0). Everything to the right of the line is shaded. The section in quadrant 1 is labeled 3, the section in quadrant 2 is labeled 2, the section in quadrant 3 is labeled 1, and the section in quadrant 4 is labeled 4.
In which section of the graph does the actual solution to the system lie?
1
2
3
4
Answers
Answer:
3
Step-by-step explanation:
i don’t know how to find the equation for this problem
Answers
rise over run is 12/8 which simplifies to 3/2
and the y intercept is 1.5 or 3/2
i need help asap plz
Answers
Answer:The y-intercept is roughly D=25
Step-by-step explanation: The y-intercept is where the line passes through the y-axis. On this graph the y-axis passes through the y-intercept at 25.
I dont understand how to explain this.
Answers
Answer:
Angle F is 50° because their side lengths are different but the angle measurements did not change. All triangles add up to 180 degrees and a right angle is 90 and it gives you the other angle measurement. So you would do 40 plus 90 which would get you 130. To find the last angle you would do 180 minus 130 which is 50. Angle F is 50 degrees.
Step-by-step explanation:
this is what i would say
i need help
-3x-(2x+6)
Answers
Answer:
−5−6
Step-by-step explanation:
Hope this helps c:
Answer:
-5x - 6
Step-by-step explanation:
-3x - ( 2x + 6 )
Distribute the (-) sign
-3x - ( 2x + 6 )
-3x - 2x - 6
Simplify
-3x - 2x - 6
-5x - 6
What logarithm is equal to 4log3?
Answers
so we have log (x^x)= log(4^3)
log (x^x)=log(81)
The logarithm which is equivalent to the logarithm 4log3 as given in the task content is; Log 81.
What is an equivalent logarithm?According to the task content; we are required to determine the logarithm which is equivalent to the given logarithm; 4log3.
It follows from the laws of logarithm that the logarithm which is equivalent to the given expression is; log(3)⁴ = log 81.
Read more on logarithm;
https://brainly.com/question/25710806
#SPJ2
8) Shawna had $20 to spend on six pencils. After buying them she had
$2. How much did each pencil cost?
Answers
Answer: They were $6 each
Step-by-step explanation:
20-2=18
18/3=$6
Answer:
$3
Step-by-step explanation:
Since we know that there was $2 that she didn't use, we can subtract that from $20 to get $18 that was used (20 - 2 = 18)
We then divide 18 by 6 because she bought six pencils (18/6 = 3)
Each pencil costs $3
Hope this helps!
Edit: I saw your comment how you need to do the equation so here it is
(20 - 2)/6 = 3 (I could be wrong, but using my explanation and the information you gave, this would be correct)
Pete has a blueprint that shows the layout of his house. Every 4 inches on the blueprint represents 3 feet of the actual house. One of the walls on the blueprint is 30 inches long. What is the actual length of the wall?
Answers
7.5 * 3 = 22.5 feet long
Answer:
30÷4=7.5 ft ?I'm not sure if it's right
Brainliest for correct answer! There are several ways to collect data. Which of the following is crucial for statisticians to call a method an experiment?
A. Eliminating bias
B. Randomness
C. Researcher assigns subjects to groups
D. Placebos
Answers
Answer:
I think the answer would be A
Answer:
A
Step-by-step explanation:
Which of the inequalities matches the graph below?
Graph of an inequality with shading above the line passing through points (-6,4) and (0,2)
LaTeX: y\ge-3x+2
y
≥
−
3
x
+
2
y
≥
−
3
x
+
2
LaTeX: y\ge-\frac{1}{3}x+2
y
≥
−
1
3
x
+
2
y
≥
−
1
3
x
+
2
LaTeX: y\le-3x+2
y
≤
−
3
x
+
2
y
≤
−
3
x
+
2
LaTeX: y\le-\frac{1}{3}x+2
Answers
Answer:
y≤-1/3x+2 is the correct answer
Step-by-step explanation:
Fast question please gelp
Answers
Answer:
D
Step-by-step explanation:
3x+6=9
3x=3
x=1
I really need help!!!
if f(x)=x^2+4x-5, find f(-4)
Answers
Answer:
−5
Step-by-step explanation:
By substituting the value of x in f(x) with -4,
(-4)^2+4(-4)-5
=16+(−16)−5
=0−5
=-5
Your welcome :D
helpppppppppppp9oooooo
Answers
Answer:
55
Step-by-step explanation:
Given
m + (3n - 5)² ← substitute given values into the expression
= 6 + (3(4) - 5)²
= 6 + (12 - 5)²
= 6 + 7²
= 6 + 49
= 55
A family is on a road trip. The speed limit during the first 145 miles of the trip is 60 mph, and the speed
limit during the last 190 miles is 65 mph. How many miles per hour over the speed limits must they drive in
order to arrive at their destination in 5 hours?
Answers
Answer:
first 145 mile 7mph
next 190miles 2mph
Step-by-step explanation:
total distance to be covered = 145+190=335miles
time = distance/speed
first 145 miles
time = 145/60 =2.41hr
next 190 miles
time = 190/65 = 2.92hr
Total time = 2.41+2.92 = 5.33hr
but we need to cover the entire distance in 5hr
Speed = distance /time
= 335/5 = 67mph
That means in first 145 mile the speed over the speed limit will be 67-60= 7mph
similarly in the next 190miles speed over speed limit will be 65 - 67 = 2mph.
Graph the linear function that passes through the point (1. -9) and has a slope of -3. (just give me points :)
What is the zero of the function?
Answers
The slope intercept form is y=-3x-6.
And the zero of the function is x=-2.
To find the graph, use the slope intercept equation and the points.
The roots or “Zeros” are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for X.
I need to know what's 1131÷29 pronto
Answers
the answer is 39 because you need to divide.
I need help plzzzz answer quick
Answers
Answer:
what do you do, help
Step-by-step explanation:
A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. What is the solution to the system of equations?
Answers
Answer:
The solution to the system of equations is x = 4 and y = 2.
Step-by-step explanation:
From statement we know that the first line is [tex]y = 0.5\cdot x[/tex]. The second line is determined by knowing two distinct points and solving the resulting system of equations by definition of the equation of the line:
[tex](x_{1},y_{1}) = (3,1)[/tex] and [tex](x_{2}, y_{2}) =(-5,-7)[/tex]
[tex]3\cdot m + b = 1[/tex] (1)
[tex]-5\cdot m + b = -7[/tex] (2)
The solution of the system of equations is:
[tex]m = 1[/tex], [tex]b = -2[/tex]
The second line is represented by [tex]y = x-2[/tex]. And the resulting system of equations is:
[tex]0.5\cdot x -y = 0[/tex] (3)
[tex]x-y = 2[/tex] (4)
The soltuion to the system of equations is:
[tex]x = 4[/tex], [tex]y = 2[/tex]
The solution to the system of equations is x = 4 and y = 2.
-4х + 9y = 9
x - Зу = -6
Answers
Answer:
x= 9 y = 5, your welcome
Answer: x = 9 y = 5
Step-by-step explanation: I like to use elimination for problems like these. Start by multiplying everything in the second equation (x - 3y = -6) by 4. Your equation should then look like this: 4x - 12y = -24
Now add the two equations as if they were two numbers:
-4x + 9y = 9
4x - 12y = -24
Your x's will cancel out and 9y + -12y = -3y and 9 + -24 = -15. This will make your new equation look like:
-3y = -15
Divide both sides by -3 and you get that y = 5
Substitute 5 in for y for any of the original given equations and solve:
-4x + 9y = 9
-4x + 9(5) = 9
-4x + 45 = 9
-4x = -36
x = 9
Evaluate p2 - r2 for p = 10, r = -4 and t = 5.
Answers
Answer:
84
Step-by-step explanation:
p^2-r^2= 10^2-(-4)^2
100-16=84
Which method can be used to find the range of a set of data? Find the difference between the maximum and minimum values. Find the difference between the upper and lower quartiles. Find the median of the upper half of an ordered data set. Find the sum of the maximum and minimum values.
Answers
Using the range concept, it is found that the method used to find it is:
Find the difference between the maximum and minimum values.
What is the range of a data-set?The range of a data-set is given by the difference between the maximum value in the data-set and the minimum value in the data-set.
Hence, the correct option about the method used to find the range is:
Find the difference between the maximum and minimum values.
You can learn more about the range of a data-set at https://brainly.com/question/24732674
Answer:
(B) Find the difference between the upper and lower quartiles.
y-3= 5(x - 2)
NEED HELP
Answers
Answer:
Y = 5x -7
Step-by-step explanation:
That is written in slope intercept form, which I'm assuming is what you need. If not comment on my answer.
Answer:
y = 5x - 7
Step-by-step explanation:
y-3= 5(x-2)
y-3 = 5x - 10
y=5x -7
This is the answer if you have anymore questions please ask
Given h(x)=3x+4h(x)=3x+4, solve for xx when h(x)=1h(x)=1.
Answers
3x=-3
x=-1
Hope this helps!!!!
tell whether the given statement below illustrate quadratic inequality in one variable or not you may translate into mathematical symbols to justify your answers.
Answers
Answer:
Step-by-step explanation:
Let width of the parking space = x meters
Since, parking space is 6 meters longer than the width,
Length of the parking space = (x + 6) meters
Area of the parking space = Length × Width
= x(x + 6)
Area of the parking space is less than 40 square meters.
Therefore, inequality representing the area of the parking will be,
x(x + 6) < 40
x² + 6x < 40
x² + 6x - 40 < 0
x² + 10x - 4x - 40 < 0
x(x + 10) - 4(x + 10) < 0
(x - 4)(x + 10) < 0
-10 < x < 4
For -10 < x ≤ 0, width of the paring will be negative.
Therefore, possible values of x will be in the interval,
0 < x < 4
Or 0 < width < 4
Length of the parking space will be,
6 < Length < 10
if a cylinder has a volume of 99 cubic centimeters , what is the volume of a cone with the same dimensions
Answers
Answer:
900
Step-by-step explanation: