Answers
_______________________________________________
Explanation:
_______________________________________________
Given:
_______________________________________________
(x − 2) = √(2x + 1) ;
→ "Square" each side of the equation; that is, raised EACH SIDE of the equation to the power of "2" ; to get rid of the "radical" ; as follows:
_______________________________________________
[(x - 2)]² = [ √(2x + 1) ] ² ;
to get:
→ (x - 2)² = (2x - 1) ;
Expand the " (x - 2)² " ;
→ (x - 2)(x -2) = ?
NOTE: (a + b)(c + d) = ac + ad + bd .
→ = (x * x) + (x * -2) + (-2 * x) + (-2 * -2) ;
= (x²) + (-2x) + (-2x) + (4) ;
= x² − 2x − 2x + 4 ;
= x² − 4x + 4 ;
______________________________________________
Now, rewrite the entire question:
→ (x − 2)² = (2x − 1) ;
→ as follows:
______________________________________________
→ " x² − 4x + 4 = 2x − 1 " ;
Now, subtract "2x" from each side of the equation;
& add "1" to each side of the equation:
→ " x² − 4x + 4 − 2x + 1 = 2x − 1 − 2x + 1 " ;
to get:
→ " x² − 6x + 5 = 0 " ; Solve for "x" ;
Let us if : " x² − 6x + 5 " can be factors:
_____________________________________
What factors of "positive 5" ; add up to "-6" ;
-5 ,-1 ; → -5 + (-1) = - 6; YES.
5, 1 ; → 5 + 1 = 6 ; NO.
_____________________________________
So, we have: " (x − 5) (x − 1) = 0 " .
x = 5, and -1 .
_________________________________________
Related Questions
Jesse made a model of a mountain range for class. to do this, he bought a cylinder of cardboard and cut it into three cones. each cone is 5 inches tall and has a diameter of 4 inches. what was the volume of the original cylinder jesse bought in terms of \piπ?
Answers
V = (1/3) (π) (r ^ 2) (h)
Substituting values we have:
V = (1/3) (π) ((4/2) ^ 2) (5)
V = (20/3) (π)
Then, the volume of the cylinder is:
Vc = 3 * V
Vc = 3 * (20/3) (π)
Vc = 20π
Answer:
the volume of the original cylinder jesse bought is:
Vc = 20π
The volume of the original cylinder that Jesse bought is 20π cubic inches.
To find the volume of the original cylinder Jesse bought, we need to use the volume formula for a cylinder:
V = πr²h
First, we need to find the volume of each cone using the formula:
Volume of a cone = (1/3)πr²h
Given:
Height(h) of each cone = 5 inchesDiameter of each cone = 4 inches, so the radius(r) = 4/2 = 2 inchesVolume of one cone:
V_cone = (1/3)π(2)²(5) = (1/3)π(4)(5) = (20/3)π cubic inches
Total volume of three cones:
V_total_cones = 3 × (20/3)π = 20π cubic inches
Since the volume of the cylinder equals the total volume of the cones:
V_cylinder = 20π cubic inches
PLEASE HELP!
The center of a circle is at (2, −5) and its radius is 12.
What is the equation of the circle?
(x−2)2+(y+5)2=144
(x+2)2+(y−5)2=144
(x+2)2+(y−5)2=24
(x−2)2+(y+5)2=24
Answers
Of the following options, what could be a possible first step in solving the equation −7x − 5 = x + 3?
Adding 7x to both sides of the equation
Subtracting 5 from both sides of the equation
Adding x to both sides of the equation
Combining like terms, −7x + x = − 6x
Answers
Subtracting 5 from both sides wouldn't cancel anything out, adding x to both sides wouldn't cancel anything out, and you can't combine like terms on either side of the equation.
add 7x to both of the sides
a vertical pole 10 meters high, casts a shadow 8 meters long. at the same time, a nearby tree casts a shadow 40 meters long. find the height of the tree in meters
Answers
1. You have the following information given in the problem above:
- The vertical pole is10 meters high and casts a shadow 8 meters long.
- The tree casts a shadow 40 meters long.
2. Then, by similarity, you have:
x/10=40/8
8x=(10)(40)
8x=400
x=400/8
x=50 meters
3. Therefore, as you can see, the answer is: The height of the tree is 50 meters.
Use Euler’s Formula to find the number of edges in a polyhedron with seven faces: two pentagons and five rectangles.
Answers
To determine the number of edges in a polyhedron with seven faces, two being pentagons and five being rectangles, you apply Euler's formula, resulting in a total of 15 edges.
To find the number of edges in a polyhedron with seven faces using Euler's formula, which is V - E + F = 2, we first need to determine the number of vertices (V) and faces (F) of the polyhedron.
Given that the polyhedron has two pentagons and five rectangles, we can calculate the total number of vertices. Each pentagon has 5 vertices and each rectangle has 4, but since rectangles share sides, some vertices will be counted twice.
Therefore, for the rectangles, we should calculate the vertices as if there were four distinct ones and then subtract the overlaps. Assuming all rectangles share exactly one side with its adjacent, we would have 4 vertices for each rectangle minus 2 for each shared side, resulting in 2 vertices per rectangle.
With five rectangles, that's 10 vertices, plus the 10 from the two pentagons, we get 20 vertices in total. Now, we apply Euler's formula: V - E + F = 2, substituting the values:
E = V - F + 2
E = 20 - 7 + 2
E = 15
Therefore, the polyhedron has 15 edges. .
The number N is the produce of the first 1000 positive integers and can be written as 1000!.We say "1000 factorial."This is, N=1000!=1000x999x998x997x...x3x2x1.N is divisible by 5, 25, 125, 625,...Each of these factors is a power of 5.That is 5=5^1, 25=5^2, 125=5^3,625=5^4, and so on. Determine the largest power of 5 that divides N.
Answers
Therefore, the total sum is 5^(200+40+8+1) = 5^249. Therefore, the largest N = 249.
hELPP
A total of 300 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adults tickets sold. How many adult tickets were sold?
Answers
225 Students
You can get this information using this system of equations:
x + y = 300
x - 3y = 0
By setting up and solving an equation, it was determined that 75 adult tickets were sold for the school play.
To solve the problem of determining how many adult tickets were sold for the school play, we can set up an equation. Let's represent the number of adult tickets sold as A, and since the number of student tickets sold was three times that of adult tickets, we can express the student tickets sold as 3A. We know the total tickets sold were 300, so the equation to represent this scenario is:
A + 3A = 300
Combining like terms, we get:
4A = 300
Dividing both sides of the equation by 4 to solve for A gives us:
A = 300 / 4
A = 75
Therefore, 75 adult tickets were sold.
Given f(x)=x2+14x+40 .
Enter the quadratic function in vertex form in the box.
Answers
f(x)=x2+14x+40 => f(x)=x^2+14x+40
Next, complete the square:
f(x)=x^2+14x+ 49 - 49 +40 = (x+7)^2 - 9
Write this in the form y = (x+7)^2 - 9 or y + 9 = (x+7)^2
Comparing this result to y = a(x-h)^2 + k, we see that h = -7 and k=-9
In vertex form, the equation is y + 9 = (x+7)^2 and the vertex is at (-7, -9).
What percent of data set is represented in Q1
Answers
Maggie only wore sandals tracker on two of the days that she trained so from her fitness trackers she verified that on the third day she biked 20 miles and on the eighth day she biked 35 miles use these two data points to determine the equation of the line best of fit set for Maggie’s data
Answers
To relate our two point we are going to use the slope formula: [tex]m= \frac{x_{2}-x_{1}}{y_{2}-y_{1}} [/tex]
We can infer form our points that [tex]x_{1}=3[/tex], [tex]y_{1}=20[/tex],[tex]x_{2}=8[/tex], and [tex]y_{2}=35[/tex]. so lets replace those values in our slope formula:
[tex]m= \frac{35-20}{8-3} [/tex]
[tex]m= \frac{15}{5} [/tex]
[tex]m=3[/tex]
Now that we have the slope, we can use the point-slope formula determine the equation of the line that best fit the set for Maggie’s data.
Point-slope formula: [tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-20=3(x-3)[/tex]
[tex]y-20=3x-9[/tex]
[tex]y=3x+11[/tex]
We can conclude that the equation of the line that best fit the set for Maggie’s data is [tex]y=3x+11[/tex].
Christine runs 7 miles in 60 minutes. at the same rate, how many miles would she run in 24 minutes?
Answers
[tex] \frac{7 miles}{60 min} = \frac{x miles}{24 min} [/tex]
Now we are going to cross-multiply and solve for x.
60x = 7(24)
60x = 168
x = 168 / 60
x = 2.8
Christine runs 2.8 miles in 24 minutes.
Christine would run approximately 2.8 miles in 24 minutes at the same rate she runs 7 miles in 60 minutes.
Explanation:To find out how many miles Christine would run in 24 minutes, we can set up a proportion. We know that Christine runs 7 miles in 60 minutes, so we can write the proportion as:
7 miles / 60 minutes = x miles / 24 minutes
Now, we can cross-multiply and solve for x:
7 * 24 = 60 * x
168 = 60x
x = 168 / 60
x ≈ 2.8 miles
So, her speed would be 7/60 = 0.1167 miles per minute. Now, to find out the distance she would cover in 24 minutes at this speed, we multiply her speed per minute by 24 minutes. So, 0.1167 * 24 = approximately 2.8 miles. Therefore, at the same rate, Christine would run about 2.8 miles in 24 minutes.
Learn more about proportion here:
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An organization will give a prize to a local artist. The artist will be randomly chosen from among 10 painters, 3 sculptors, and 5 photographers. What is the probability that the artist chosen will be a sculptor or a photographer?
Answers
The probability is 8/18 or 44%.
Since there are 3 sculptors and 5 photographers, and the question is asking for either a sculptor or photographer, you add them together. There are a total of 18 artists, and the probability is the chance of a certain thing happening over the total amount of things that can happen (i.e. a coin landing on heads is 50%).
The answer would be 8/18.
3+5=8
18 is the total number of artists.
What happens to correlation if you multiply every x in the data set by .5?
Answers
In which quadrant of the coordinate plane is (-2a - 3, -3b - 5), if a = -3 and b = 3?
Answers
- 2a - 3 = -2(-3) - 3 = 6 - 3 = 3
-3b - 5 = -3(3) - 5 = -9 - 5 = -14
(3, -14)
answer:
quadrant IV
After substituting a = -3 and b = 3 into the point (-2a - 3, -3b - 5), we get the point (3, -14), which lies in the fourth quadrant of the coordinate plane.
To determine in which quadrant of the coordinate plane the point (-2a - 3, -3b - 5) is located, we substitute the values a = -3 and b = 3 into the coordinates. First, for the x-coordinate we have:
-2(-3) - 3 = 6 - 3 = 3
And for the y-coordinate:
-3(3) - 5 = -9 - 5 = -14
The resulting point is (3, -14), which is located in the fourth quadrant because the x-value is positive and the y-value is negative.
Amanda owns a clothing store that sells graphic t-shirts. n is the number of shirts she sells each month. the revenue function of her store is r = 25n. the cost function of her store is c = 10n + 900. using your calculator, what is the break-even point of amanda's store?
Answers
[tex]25n=10n+900[/tex]
[tex]25n-10n=900[/tex]
[tex]15n=900[/tex]
[tex]n=60[/tex]
The break-even point is attained when n equals 60.
Answer:
n = 60 shirts
Step-by-step explanation:
The break-even point is the point where revenue is equal to cost. This means we take the equation for revenue, r = 25n, and set it equal to the equation for cost, c = 10n + 900:
25n = 10n + 900
Subtract 10n from each side:
25n - 10n = 10n + 900 - 10n
15n = 900
Divide both sides by 15:
15n/15 = 900/15
n = 60
A pizza shop offers 12 different topping choices. if you order a large pizza with two toppings, how many possibilities would you have?
Answers
The number of combinations of 12 things take 2 at a time is
12C2
=(12!)/[(12-2)!2!]
=(12!)/(10!*2!)
=12*11/2
=66
Answer: 66
100 points! Evaluate the equation. Look at the picture. Do #7.
Answers
There are 210 ways to choose 6 from a group of 10.
What is compound interest?
A - the interest earned on the principal of an investment
B - the interest earned on both the principal and interest of an investment or savings account
C - the interest earned on a mutual fund
D - the interest earned on a loan
Answers
The correct answer is
The interest is earned on the principal and interest earned previously
:)
PLS HELP ME ASAP WITH THESE! THANKS!!
(Brainliest will be given hopefully)
(Random answers gets moderated.)
Answers
2. Whenever you're counting things, the appropriate set of numbers to use is "whole numbers." Both people (domain) and devices (range) are objects being counted, so the appropriate choices are ...
2) whole numbers
Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the relationship between the values of m and n? Explain.
Answers
Sample Response: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.
(on the assignment)
1. What is the value of x in the equation –6 + x = –2?
A. 4
B. –8
C. 8
D. –4
2.
How many solutions does the equation –3a + 3a + 6 = 7 have?
A. Infinitely many
B. Two
C. One
D. None
3.
What is the solution to the equation 1.2m – 0.8 = –2.0m?
A. m = 0.25
B. m = 4
C. m = 1
D. m = 0.4
4.
How many solutions does the equation 4p + 7 = 3 + 4 + 4p have?
A. Two
B. Infinitely many
C. None
D. One
5.
What is the value of y in the equation 2(2y – 12) = 0?
A. 4
B. 8
C. 7
D. 6
6.
What is the value of z in the equation 2(4z – 9 – 7) = 166 – 46?
A. 19
B. 34
C. 26
D. 21
7.
Which of these is a simplified form of the equation 7y + 7 = 9 + 2y + 2y?
Answers
2. D. If you simplify the a terms you will get 6 = 7 which is never true.
3. A. Subtract 1.2m from both sides and then divide to solve.
4. B. If you simplify you get 7 = 7 which is always true.
5. D. Distribute the 2 and then add the 24 to both sides. Then divide to solve.
6. A. Simplify the right side and then divide all by two. Then add 16 to both sides and divide by 4.
7. 3y - 2
The ratio of men to women working for a company is 4 to 5. if there are 52 men working for the company, what is the total number of employees?
Answers
so 117 employees
Write the first 6 terms of an arithmetc sequence if the first number is 9 and the common diffrence is 5
Answers
A fair number cube with sides labeled from 1 to 6 is rolled 20 times. the results of the simulation are shown in a dot plot. which dot plot models an unfair data-generating process?
Answers
The dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
What is dot plot?A dot plot, also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
Since the width of each "bar" of dots is equal to the number of items in a certain class, a dot plot is similarly to a bar diagram.
We have:
A fair number cube with sides labeled from 1 to 6 is rolled 20 times.
Total number on, a fair number of cubes = 6
So the dot plot can be shown as:
1:4, 2:4, 3:0, 4:4, 5:4,6:4
There is a face with 3 has not rolled.
Thus, the dot plot will be 1:4, 2:4, 3:0, 4:4, 5:4,6:4 and there is a face with 3 has not rolled option second is correct.
Learn more about the dot plot here:
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What is y+7/7y÷3y^2+21y/14y−5 simplified?
Answers
[(y+7)/7y] x [(14y-5)/(3y^2+21y)]= [(y+7)/7y] x [(14y-5)/3y(y+7)]= [1/7y] x [(14y-5)/3y]= [(14y-5)/21y]
Prove that x²+6x+18 is always greater than
[tex]2 - \frac{1}{x} [/tex]
For any value of x.
Answers
You could also do this algebraically: write the inequality
x^2+6x+18 > 2 -1/x. This can be rewritten as x^2+6x+18-2+1/x > 0, or
x^2+6x+16+1/x > 0
Try x=-3. Then 9-18+16-1/3 = 6 2/3, which is greater than 0.
Or you could graph x^2+6x+16+1/x by hand or on a calculator. Is the graph always above the x-axis? If so, x²+6x+18 is always greater than 2-1/x.
Which solid has a volume that is 3 times the volume of a cone with the same base and height?
a.cylinder
b.prism
c.pyramid eliminate
d.sphere?
Answers
The formula for volume of a cone = 1/3 π r² h
The formula for volume of a cylinder = π r² h
write an inequality for the following situation
No more than 8 books are in your bag
A. x ≤ 8 B. x < 8 C. x ≥ 8 D. x > 8
Answers
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman. Another flower is then chosen at random and given to a different woman. What is the probability that both flowers are pink roses?
Answers
On Monday, there was no snow on the ground in Buffalo, New York. On Tuesday, three inches of snow fell.On Wensday a half an inch of snow melted. On Thursday two and a half more inches fell. On Friday another inch and a half melted. How much snow was left on the ground Friday night.
Answers
Monday- 0 in.
Tuesday- 3 in.
Wedsnday- 2 1/2 in.
Thursday- 5 in.
Friday- 3 1/2 in.
Therefore, the answer is - 3 1/2 inches of snow was left on Friday.
Hope this helps you!
~DL