For this case we have:
By properties of the radicals [tex]\sqrt {a} = a ^{\frac {1} {2}}[/tex]
So:
[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2[/tex].
Now, for power properties we have:
[tex](b ^ {\frac {c} {d}}) ^ e = b ^ {\frac {c * e} {d}}[/tex]
Thus, [tex](7 ^ {\frac {1} {2}}) ^ 2 = 7 ^ {\frac {2} {2}} = 7[/tex]
So:
[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form
Answer:
[tex](\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2= 7 ^ {\frac {2} {2}} = 7[/tex] in its simplest form.
[tex]7 ^ {\frac {1} {2}} = \sqrt {7}[/tex]in its radical form
Answer:
in its radical form
explanation:
The local high school hosted a hockey tournament. Tickets were sold before the tournament and at the door. When reviewing the ticket sales, the director of the tournament realized that there were 80 more tickets purchased before the tournament than at the door. A total of 820 tickets were sold. Which statements about ticket sales are true? Check all that apply.
The first thing we must do for this case is to define variables: x: number of tickets sold before the tournament. y: number of tickets sold at the door. The system of equations that adapts to this situation is given by: x + y = 820 x-y = 80 Answer: The correct options are: option 2 option 3 option 5
Answer:
The correct options are:
option 2
option 3
option 5
Step-by-step explanation:
You invest $400 in an account that pay3% interest compounded by annaully what will your balance be after 1year
After investing $400 in an account with 3% interest compounded annually, the balance after one year will be $412.
The question is asking how much the balance will be after investing $400 in an account that pays 3% interest compounded annually after one year. The formula to calculate compound interest is [tex]A = P(1 +\frac{ r}{n})^{nt[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. As the interest is compounded annually, n is 1.
For this question, we substitute P with $400, r with 0.03 (3% as a decimal), n with 1 (since it's compounded annually), and t with 1 (since it's compounded for one year).
Now, our formula looks like this: [tex]A = 400(1 + \frac{0.03}{1})^{1*1[/tex] = 400(1 + 0.03) = 400 * 1.03 = $412.
Therefore, after one year, the balance in the account will be $412.
The sides of a right triangle ...
Answer: Choice A)
x^2 + (x+2)^2 = (x+4)^2
========================================
Consecutive even integers are whole numbers that are as close as possible and they are also even as well. One example of having 3 of them is {2, 4, 6}. Another example is {4,6,8} and another example is {6,8,10}. You start with any even integer you want, then count up by 2 each time to get the next values.
In general, if x is your first even number, then x+2 is the next number up. Eg: x = 10 so x+2 = 10+2 = 12. Then after that, x+4 is the third number (if x = 10, x+4 = 10+4 = 14)
a = x is the side length of the shorter leg
b = x+2 is the side length of the longer leg
c = x+4 is the side length of the hypotenuse
Use the pythagorean theorem to get
a^2 + b^2 = c^2
x^2 + (x+2)^2 = (x+4)^2
1. Find the sum of the series (IMAGE) . Show your work.
2. A supermarket display consists of boxes of cereal. The bottom row has 23 boxes. Each row has three fewer boxes than the row below it. The display has six rows.
(a) Write and use a function to determine how many boxes are in the top row. Show your work.
(b) Use the appropriate formula to determine the number of boxes in the entire display. Show your work.
3. The number of visitors to a website in the first week is 50. The number of visitors each week is double the number of visitors the previous week. What is the total number of visitors to the website in the first 8 wk? Show your work.
Answer:
QUESTION 1 ANSWER
The series is
[tex]\sum_{n=1}^{15}{ (2n-1)}[/tex]
So the nth term of this sequence is
[tex]U_n=2n-1[/tex]
We generate some few terms of the sequence as follows:
When [tex]n=1[/tex],
The first term of the sequence becomes,
[tex]U_1=2(1)-1[/tex]
[tex]U_1=1[/tex]
When [tex]n=2[/tex],
[tex]U_2=2(2)-1[/tex]
[tex]U_2=3[/tex]
When [tex]n=3[/tex],
[tex]U_2=2(3)-1[/tex]
[tex]U_2=5[/tex]
The constant difference is [tex]d=2[/tex].
The sum of the series is given by,
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
There are 15 terms in the series, therefore [tex]n=15[/tex]
[tex]S_{15}=\frac{15}{2}(2(1)+(15-1)2)[/tex]
[tex]S_{15}=\frac{15}{2}(2+14(2))[/tex]
[tex]S_{15}=\frac{15}{2}(30)[/tex]
[tex]S_{15}=15\times 15[/tex]
[tex]S_{15}=225[/tex]
ANSWER TO QUESTION 2
The bottom row has [tex]23[/tex] boxes. This means [tex]a=U_1=23[/tex]
a) Since each row has 3 fewer boxes [tex]d=-3[/tex].
The nth row is given by,
[tex]U_n=23+(n-1)\times(-3)[/tex]
[tex]U_n=23+-3n+3[/tex]
[tex]U_n=23-3n[/tex]
The top row is the 6th row, meaning [tex]n=6[/tex].
[tex]U_6=23-3(6)[/tex]
[tex]U_6=23-18[/tex]
[tex]U_6=5[/tex]
b) The number of boxes in the entire display is given by
[tex]S_n=\frac{n}{2} (a+l)[/tex]
Where [tex]a=23[/tex], the first term(row) and [tex]l=5[/tex], the last term(row).
Since there are 6 rows,
[tex]S_6=\frac{6}{2} (23+5)[/tex]
[tex]S_6=3 (28)[/tex]
[tex]S_6=84[/tex]
ANSWER TO QUESTION 3
The number of visitors in the first week is [tex]a=5[/tex].
Since the number of visitors each week is doubled the number of visitors in the subsequent weeks, the sequence is a geometric progression with a common ratio of [tex]r=2[/tex].
The general term of a geometric sequence is
[tex]U_n=ar^{n-1}[/tex]
So in the 8th week, we have
[tex]U_8=5\times 2^{8-1}[/tex]
[tex]U_8=5\times 2^{7}[/tex]
[tex]U_8=5\times 128[/tex]
[tex]U_8=640[/tex]
Hence 640 people visited the website in the 8th week
What does I mean when it’s asking for P’ and Q’?
To round 74.58 to the nearest tenth, which digit do you look at first
To round 74.58 to the nearest tenth, look at the digit in the hundredth place (8) and round up the digit in the tenths place (5) by adding 1 to get 74.6.
To round 74.58 to the nearest tenth,
We have to look at the digit in the hundredth place, which is 8.
The rule for rounding to the nearest tenth is to look at the digit in the hundredth place.
If it is 5 or greater, you round up the digit in the tenths place by adding 1. If it is less than 5,
Simply drop the digit in the hundredths place and leave the digit in the tenths place as it is.
In this case,
The digit in the hundredths place is 8, which is greater than 5.
Therefore, we must round up the digit in the tenths place, which is 5, by adding 1 to get 6.
Thus, 74.58 rounded to the nearest tenth is 74.6.
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Find the interval(s) over which the function is decreasing
Answer : (0,3) U (3, ∞)
We need to find the interval(s) over which the function is decreasing
We look at the intervals of x where the graph is decreasing
Decreasing interval of the graph is the part where the graph goes down
We look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph changes direction and start decreasing at x=0
the graph is decreasing till x=3
so first decreasing interval is x=0 to 3. we write it as (0,3)
After x=3 the graph starts decreasing and it goes to infinity
So the second decreasing interval is 3 to infinity . We write it as (3, ∞)
Now combine both intervals by a 'U' union
(0,3) U (3, ∞)
Graph Behavior u3l10
1. (-∞,-1) U (-1,0)
2. (0,3) U (3,∞)
3. x-intercept: none | y-intercept: (0,-4)
4. x=-1, x=3, y=0
5. even
6. (-∞,-4)
7. x-intercepts: (0,0),(3,0) | y-intercepts: (0,0)
8. f(3)=6
9. There is a jump discontinuity at x=-3
10. neither
11. f(x)=x/x^8+8x^4-7 | f(x)=x^3+4x
12. f(x) --> -∞ as x --> ∞ and f(x) --> 0 as x --> -∞
13. 2nd and 3rd graph (2nd graph has left arm facing down and right arm facing up and 3rd graph looks like a W)
14. 1st and 4th graph (1st graph has 2 lines, the one on the left side is point upwards and the line on the right side is pointing downwards, 4th graph is 1 line with the left arm facing up and right arm facing down)
15. reciprocal; y=1/x
16. f(x)=x^3
17. power; y=x^n | root; y=n√x
18. power; y=x^n ; n is even and greater than 0 | absolute value; y=|x|
19. reflection over the x-axis | horizonal compression by a factor of 3
20. reflection over the y-axis | horizontal shift to the left 2 units
21. reflection
22. 1st graph (starts from the left side (-2,0) and points towards the right side a bit more downwards)
23. 1st graph (ill describe it as a right angle with the curve facing left on the negatives side or a point where the curve is on is (-2,0))
happy "studying"!
The equation of a line is -6x-2y=-18
What is the x-intercept of the line?
-6x - 2y = -18
-6x - 2(0) = -18
-6x - 0 = -18
-6x = -18
-6 -6
x = 3
hope this helps :)
Answer: 3
Step-by-step explanation:
Simplify the following expression in your notebook. Select the correct answer.
7 - 3[(n 3 + 8n) ÷ (-n) + 9n 2]
-24n2 + 31
n3 - 24n2 + 31
9n2 - 24n + 7
21n + 31
-24n2+31 if im correct!
Answer:
[tex]-24n^2 + 31[/tex]
Step-by-step explanation:
[tex]7 - 3[(n^3 + 8n) divide (-n) + 9n^2][/tex]
To simplify it we use order of operation PEMDAS
Parenthesis , exponents , multiply, divide, add and subtract
[tex]7 - 3[(n^3+ 8n) divide (-n) + 9n^2][/tex]
LEts start with parenthesis (divide by -n)
[tex]7 - 3[-n^2-8+ 9n^2][/tex]
Now we simplify the parenthesis by combining like terms
[tex]7 - 3[-8+8n^2][/tex]
multiply by -3
[tex]7+24 -24n^2[/tex]
[tex]-24n^2 + 31[/tex]
Match the expression with its name 9x^4-3x+4
Which of the following is not a polynomial?
For this case we have the following:
[tex]\frac{3}{x^{-1} }+ \frac{3}{2}[/tex] which can be rewritten as [tex]3x + \frac{3}{2}[/tex], is a polynomial. [tex]x ^ 2 + x^{\frac{1}{2} }+ x + 6[/tex] is not a polynomial because it has a coefficient that is not integer. [tex]x ^ 3-9[/tex] is a polynomial [tex]\sqrt{16x^{4} }[/tex] that can be rewritten as [tex]4x ^ 2[/tex], is a polynomialSo:
[tex]x ^ 2 + x^{\frac{1}{2} }+ x + 6[/tex] is not a polynomial
Answer:
Option B
The expression which is not a polynomial is:
B) [tex]x^2+x^{\dfrac{1}{2}}+x+6[/tex]
Step-by-step explanation:We know that the general form of a polynomial expression is given by:
[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+......+a_2x^2+a_1x+a_0[/tex]
i.e. P(x) is a polynomial of degree n , where n belongs to natural numbers and [tex]a_i's[/tex] belong to the real numbers.
and [tex]a_n\neq 0[/tex]
A)
[tex]\dfrac{3}{x^{-1}}+\dfrac{3}{2}[/tex]
which could also be written by:
[tex]3x+\dfrac{3}{2}[/tex]
Hence, this expression is a polynomial expression.
Option: a is incorrect.
B)
[tex]x^2+x^{\dfrac{1}{2}}+x+6[/tex]
Since in the second term the power of x does not belong to the set of natural numbers.
Hence, option: b is not a polynomial expression.
Hence, the correct answer is option: b
C)
[tex]x^3-9[/tex]
Since, the expression matches the definition of the polynomial expression.
Hence, option: c is incorrect.
D)
[tex]\sqrt{16x^4}[/tex]
This could also be written as:
[tex]=4x^2[/tex]
Hence, it is a polynomial expression.
Hence, option: d is incorrect.
x/-4=-1.11 what is x
Answer:
4.44 is your answer
Step-by-step explanation:
Isolate the x. Multiply -4 to both sides
(x/-4)(-4) = (-1.11)(-4)
x = (-1.11)(-4)
Multiply
x = 4.44
4.44 is your answer
~
Answer:
The value of x is 4.44.
Step-by-step explanation:
Given : Expression [tex]\frac{x}{-4}=-1.11[/tex]
To find : What is the value of x?
Solution :
Expression [tex]\frac{x}{-4}=-1.11[/tex]
Multiply both side by 4,
[tex]\frac{x}{-4}\times 4=-1.11\times 4[/tex]
[tex]-x=-4.44[/tex]
Cancel negative sign both side,
[tex]x=4.44[/tex]
Therefore, The value of x is 4.44.
HELP!! 20 PONTS!!!
Solve for x: −4|x + 5| = −16
Select one:
a. x = 21 over 4 , x = − 11 over 4
b. x = −1, x = 9
c. x = −1, x = −9
d. No solution
5x10^2
please help me solve it and how.
5 x 10^2
= 5 x 100
= 500
Alright, so to solve this we have to use P.E.M.D.A.S. There are no parenthesis, so we move on to exponents. 10^2. Well, we know that 10 multiplied by 10 is 100. So the new equation is 5 multiplied by 100. The answer is 500.
Graph y=4/7x−2
I just need someone to explain where this would go on a graph.
Adriana bought 20 dogs and each dog price was $8:89 each how much she spent?
Wich is better to buy 3 pounds for $8.31 or 5 pounds for $12.95 explain.
Compute the special products. (-3+5i)2
we are given
[tex](-3+5i)^2[/tex]
we can expand it
[tex](-3+5i)^2=(-3+5i)(-3+5i)[/tex]
now, we can FOIL it
[tex](-3+5i)^2=-3\times -3-3\times 5i+5i\times -3+5i\times 5i[/tex]
now, we can simplify it
[tex](-3+5i)^2=9-15i-15i+25i^2[/tex]
we know that
[tex]i^2=-1[/tex]
so, we can plug it
[tex](-3+5i)^2=9-30i+25(-1)[/tex]
[tex](-3+5i)^2=9-30i-25[/tex]
[tex](-3+5i)^2=-16-30i[/tex]..............Answer
Brinns rectangular kitchen has an area of 81 square feet.The kitchen is 9 times as many square feet as brinns pantry.If the rectangular pantry is 3 feet wide, what is the length of the pantry?
Please Help!
The product of a number minus ten and nine equals fifty when decreased by seven. Which equation represents the sentence?
A) 7(x - 10) - 9 = 50
B) 7(10 - x) - 9 = 50
C) 9(x - 10) - 7 = 50
D) 9(10 - x) - 7 = 50
This question i know. It is C
For this one, the best way to answer is to use the question and it will guide us to the answer.
First, you can eliminate two choices:
the problem states that a number minus ten and nine
so you can eliminate B and D because it is 10 minus a number. In math, you can be picky and take the question exactly.
Then, look at the last part, "when decreased by seven." So now look between A and C and see which one is decreasing by 7. Based on that C would be your answer
C) 9(x-10) -7 = 50
Hope this helps!
What is the unknown number in 2.48>2.4 1>2.463
Please help and thank you
Answers: Angle A is 36 degrees, angle C is 54 degrees
=================================================================
Work Shown:
The angles A and C are complementary, meaning they add to 90 degrees.
(Angle A) + (Angle C) = 90
(2x-4) + (2x+14) = 90
(2x+2x)+(-4+14) = 90
4x+10 = 90
4x+10-10 = 90-10 .... subtract 10 from both sides
4x = 80
4x/4 = 80/4 ..... divide both sides by 4
x = 20
If x = 20, then,
angle A = 2x-4 = 2*20-4 = 40-4 = 36 degrees
angle C = 2x+14 = 2*20+14 = 40+14 = 54 degrees
Note how A+C = 36+54 = 90 which helps confirm our answers.
Mr. Venn knows that 60% of his students will score no more than 5 points above or below the class average, 75%, on the test. Write an inequality that represents the test scores of 60% of his students.
Answer:
[tex]80\leq x\leq 70[/tex]
Step-by-step explanation:
Mr. Venn knows that 60% of his students will score no more than 5 points above or below the class average, 75%, on the test.
Means the greater marks can be up to 80 and lowest marks can be up to 70.
So, the inequality that represents the test scores of 60% of his students is :
[tex]80\leq x\leq 70[/tex]
Select ALL statements that are true about the linear equation.
y=1/2x-2
The graph of the equation is a single point representing one solution to the equation.
The graph of the equation is the set of all points that are solutions of the equation.
The point (-2, -1) is on the graph of the equation.
The point (10, 3) is on the graph of the equation.
If you're the one answering the easiest way to save time would be to call out the answer in #'s.
1-4
The answers are 2 and 4
The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation thus, options (A) and (D) are correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
A graph is the locus of all points that are the solution of the function.
Substitute x = 10 into y = (1/2)x - 2
y = (1/2)10 - 2
y = 5 - 2 = 3 thus, (10,3) will be on the graph.
Hence "The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation".
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Which shows the line 3x-2y=-18 in slope intercept form?
A) y=3/2x+9
B) y=2/3x+9
C) y=-3/2x+9
D) y=2/3x-9
Hello,
The answer is A or y= 3/2x+9
How to solve;
The formula: Y=mx+b
Now solve the problem: 3x-2y=-18
Subtract -3x from both sides.
Now we have -2y=-3x-18
So divide both sides by y to get y by it self.
-2/-2=-3x-18/-2
Simplify and the answer is y=3/2x+9
Thus answer A
Hope that helps have a great day.
Hank's pickup can travel 72 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 54 miles?
Answer:
Hank's pickup need 3 gallons of gas to travel 54 miles.
Explanation:
Hank's pickup can travel 72 miles on 4 gallons of gas
Miles travel by Hank's pickup with 1 gallon of gas = 72/4 = 18 miles.
We need to find gallons of gas required for Hank's pickup to travel 54 miles.
Gallons of gas required = Miles need to travel/ Miles travel with 1 gallon of gas
= 54/18 = 3 gallons of gas.
So Hank's pickup need 3 gallons of gas to travel 54 miles.
Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.
Answer: [tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex]
Explanation:
Please follow the diagram in attachment.
As we know median from vertex C to hypotenuse is CM
[tex]\therefore CM=\frac{1}{2}AB[/tex]
We are given length of CG=4
Median divide by centroid 2:1
CG:GM=2:1
Where, CG=4
[tex]\therefore GM=2[/tex] ft
Length of CM=4+2= 6 ft
[tex]\therefore CM=\frac{1}{2}AB\Rightarrow AB=12[/tex]
In [tex]\triangle ABC, \angle C=90^0[/tex]
Using trigonometry ratio identities
[tex] AC=AB\sin 30^0\Rightarrow AC=6[/tex] ft
[tex] BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3}[/tex] ft
[tex] CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3}[/tex] ft
In [tex] \triangle CAN, \angle C=90^0[/tex]
Using pythagoreous theorem
[tex]AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}[/tex]
Length of AG=2/3 AN
[tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex] ft
Find the percent increase of $3.49 to $3.89 then round to the nearest percent
11.46% is the percent increase
A cinema has three screens last Saturday there were 500 visitors 40% went to screen 1 ,25% went to screen 2 the rest went to screen 3 work out how many visitors attended each screen
Answer:
200 visitors went to screen 1.
125 visitors went to screen 2.
175 visitors went to screen 3.
Step-by-step explanation:
We will find number of visitors who went to screen 1 by finding 40% of 500 as we are told that 40% of 500 visitors went to screen 1.
[tex]500*\frac{40}{100} =5*40=200[/tex]
Therefore, 200 visitors went to screen 1.
Now we will find number of visitors who went to screen 2. We are told that 25% of 500 visitors went to screen 2.
[tex]500*\frac{25}{100} =5*25=125[/tex]
Therefore, 125 visitors went to screen 2.
Now we will find the number of visitors who went to screen 3 by subtracting combined number of visitors who went to screen 1 and screen 2 from total number of visitors.
[tex]500-(200+125)[/tex]
[tex]500-325=175[/tex]
Therefore, 175 visitors went to screen 3.
Please help me 16% of what is 41?
The answer is 256.25
EXPLANATION
Let [tex]x[/tex] represent the number.
Then, [tex]\frac{16}{100}x=41[/tex]
We cross multiply yo obtain,
[tex]16x=41\times 100[/tex]
We now divide both sides by 16.
[tex]x=\frac{4100}{16}[/tex]
This will give us,
[tex]x=256.25[/tex]
Therefore the number is 256.26