Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms.
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms
Tiles:
A).
(P^5) ^1/4
---------------
(P^-3 Q^-4)
B).
(P^2Q^7) ^1/2
----------
(Q^4)
C).
(P^6Q^3/2)^1/3
D).
(PQ^3)^1/2
--------------
(PQ)^-1/2
Pairs:
1.)
P^2Q^1/2
2.)
PQ^2
3.)
P^2Q
4.)
PQ^3/2
Find the possible value or values of n in the quadratic equation 2n2 – 7n + 6 = 0
Answer:
[tex]n=\frac{3}{2},\,\,n=2[/tex].
Step-by-step explanation:
The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is to factorize the polynomial on the left hand side. To factorize you can do the following:
(1) [tex]2n^2-7n+6[/tex]. The given polinomial
(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex]. Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]
(3) [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.
(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]
(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]
Then the given equation can be written as:
[tex]{(2n-3)(n-2)=0[/tex]
The product of two expression equals zero if and only if one of the expression is zero. From here we have that
[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]
From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].
Solve for x and y: 28x-49y=35 and 4x-7y=5
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answer:
Option C. is the correct option.
Step-by-step explanation:
Equation of line is represented as y = mx + c
where m = slope of the line
c = y - intercept
Since line is passing through origin (0, 0) and a point (6, 2)
Therefore y intercept of the line will be 0.
c = 0
Slope of the line [tex]m=\frac{y-y'}{x-x'}[/tex]
[tex]m=\frac{2-0}{6-0}[/tex]
[tex]m=\frac{2}{3}[/tex]
So the equation will be
[tex]y=\frac{1}{3}x[/tex]
Therefore, option C. is the answer.
Help please:((((((((((((((((
Answer:
B. The amount spent on grapes compared with the weight of the purchase.
Step-by-step explanation:
Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.
___
In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.
please help , show your steps , thanks
5 + 2*SQRT(x) = 15
subtract 5 from each side
2*SQRT(x) = 10
(2*SQRT(x))^2 =10^2
2^2 *x = 100
4x=100
x=400/4
x = 25
What is the graph of the function f(x) = the quantity of 3 x squared plus 2 x plus 10, all over x plus 3
A) a graph is shown with a vertical asymptote at x = -3 increasing from negative infinity to just under -35 and then decreasing back to negative infinity as well as decreasing to just under five and increasing to infinity
B) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals x minus 1
C) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals negative x minus 1
D) graph with vertical asymptote of x equals negative 3, and oblique asymptote of y equals negative x minus 1
What is the r value of the following geometric sequence?
64, 48, 36. 27
2/3
3/4
5/8
3/8
Which of the following is the sum of the polynomials 5x2 - 4x + 1 and -3x2 + x - 3 ?
2x2 + 3x + 2
8x2 - 5x - 2
2x2 - 3x - 2
-8x2 - 3x - 2
Find S8 for the geometric series 3 + -6 + 12 + -24 +…
the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]
The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:
- [tex]\( a \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the number of terms.
In our series:
- [tex]\( a = 3 \)[/tex] (the first term),
- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:
- [tex]\( \frac{-6}{3} = -2 \)[/tex]
- [tex]\( \frac{12}{-6} = -2 \)[/tex]
- [tex]\( \frac{-24}{12} = -2 \)[/tex]
So, [tex]\( r = -2 \)[/tex].
Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:
[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]
Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:
[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]
[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]
[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]
[tex]\[ S_8 = -255 \][/tex]
So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)
1. A grocer mixes two grades of coffee which sell for 70 cents and 80 cents per pound, respectively. How much of each must he take to make a mixture of 80 pounds which he can sell for 76 cents per pound?
2. How many quarts of pure alcohol must be added to 40 quarts of a mixture that is 35% alcohol to make a mixture that will be 48% alcohol?
3. If a container contains a mixture of 5 gallons of white paint and 11 gallons of brown paint, how much white paint must be added to the container so that the new mixture will be two-thirds white paint?
4. Can the sum of three consecutive odd integers be (a) 25? (b) 45?
5. A tank can be filled in 9 hours by one pipe alone, in 12 hours by a second pipe alone, and can be drained when full, by a third pipe, in 15 hours. How long would it take to fill the tank if it is empty, and if all pipes are in operations?
Arrange the functions in ascending order, starting with the function that eventually has the lowest value and ending with the function that eventually has the greatest value.
2x+5
2^x+3
2^x+10
2x
x²+2
x²
PLEASE HELP 20 POINTS PROVIDED
What is a variable?
a.
A variable is an unknown number or value represented by a letter
c.
A variable represents a change in value
b.
A variable always represents the total amount
d.
A variable is always represented by the letter x
Please select the best answer from the choices provided
what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??
What is the area of a rectangle with a length of 15 feet and a width of 9 feet?
Final answer:
The area of a rectangle with a length of 15 feet and a width of 9 feet is 135 square feet.
Explanation:
The area of a rectangle can be found by multiplying its length and width.
In this case, the length is 15 feet and the width is 9 feet.
To find the area, multiply 15 feet by 9 feet:
Area = 15 feet x 9 feet = 135 square feet
Therefore, the area of the rectangle is 135 square feet.
What is 78% written as a decimal
You will be charged 12.5% interest on a loan of $678. how much interest will you pay on the loan?
It is given in the question that
You will be charged 12.5% interest on a loan of $678.
So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125
So we have to find the value of 0.125 of 678.
[tex]0.125*678 = 84.75[/tex]
Therefore the interest that you will have to pay on loan is $84.75 .
Solve the inequality -2x is less than or equal to 3x + 1 is less than or equal to 10
A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?
[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]
Hello!
The number of pairs of shoes each man can repair is its speed times the time.
Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.
Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.
Thus, we can equate:
[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]
That is the speed of the assistant. Then, the speed of the repairman is:
[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]
That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)
3/4 of an hour is 45 minutes and this is the answer.To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.
Explanation:To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.
Let's denote the time it takes the repairman to repair one pair of shoes by x hours.
Since the assistant takes twice as long, their time would be 2x hours for one pair.
Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.
Now, we express their combined work rate as the sum of their individual work rates.
The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.
Together, this should equal their combined rate of 2 pairs per hour:
1/x + 1/(2x) = 2
Solving this equation for x, we first find a common denominator and get:
2/2x + 1/2x = 2
3/2x = 2
3 = 4x
x = 3/4
Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.
How many sides does a polygon have with an interior angle of 108?
If the lengths of two of the possible sides of a right triangle measure 4 root 15 and 7 root 6 what is the smallest possible length of the third side
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
f(0)=7
f(0)=-7
f(7)=0
f(-7)=0
Answer:
f(-7)=0 that is option 4th is correct.
Step-by-step explanation:
If we have given any polynomial then its factor means that value is giving zero of that polynomial
And opposite sign of factor is the zero of the polynomial
For example:
x+a is factor of any polynomial f(x) then f(-a)=0
Similarly, If x+7 is a factor of any polynomial then f(-7)=0
Hence, option 4th is correct.
find the magnitude of 6+2i
Final answer:
The magnitude of 6 + 2i is 2√10.
Explanation:
To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:
|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10
Therefore, the magnitude of 6 + 2i is 2√10.
The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the approximate area of wyoming? hint: the area of a rectangle is product of its length and width.
Assuming a regularly shaped rectangle, the formula for the area is given as:
A = L * W
where L and W are the length and width respectively
A = 3.6 x 10^2 miles * 2.8 x 10^2 miles
A = 100,800 square miles
or
A = 10.08 x 10^2 miles
Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Step-by-step explanation:
The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]
and height , [tex]H=2.8\times 10^{2}\, miles[/tex]
Area of rectangle , [tex]A=L\times W[/tex]
=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]
=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Help which is the correct function
Help me please!!!!!!
in the diagram which pair of angles are corresponding angles
Answer:
Option C is correct .i.e., ∠3 and ∠7
Step-by-step explanation:
Corresponding angles are the angles that are at the same corner at each Point of Intersection.i.e., if first angle is at the top left corner of one intersection then the angle at the other intersection is also at the top left.
From Given Figure,
Following are pairs of corresponding angles,
∠1 and ∠5
∠2 and ∠6
∠4 and ∠8
∠3 and ∠7
Therefore, Option C is correct .i.e., ∠3 and ∠7
Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.
Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations