Answer:
23ºC to 25ºC (74° F - 77° F)
Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile?
Answer:
about 0.81 miles
Step-by-step explanation:
Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...
x^2 = 19^2 +28^2
x^2 = 1145
x = √1145 ≈ 34 . . . . hundredths of a mile
Then Alyssa's total route is ...
0.19 + 0.28 + 0.34 = 0.81 . . . . miles
Answer:
about 0.81 miles
Step-by-step explanation:
Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...
x^2 = 19^2 +28^2
x^2 = 1145
x = √1145 ≈ 34 . . . . hundredths of a mile
Then Alyssa's total route is ...
0.19 + 0.28 + 0.34 = 0.81 . . . . miles
There are 7 new books and 8 used books on a shelf.
(a) What is the ratio of all books to used books?
(b) What is the ratio of new books to all books?
Answer:
(a) 15:8
(b) 7:15
Step-by-step explanation:
a: All the books together is 15. The ratio of all books(15) to used books(8) is therefore 15:8
b: As I said above, all the books together is 15. So the ratio of the new books(7) to all books(15) is 7:15
The ratio of all books to used books 15:8
The ratio of new books to all books 7:15
What is ratio?A ratio indicates how many times one number contains another.
Given:
New books =7
used books= 8
total books =8+7=15 books
a) ratio of all books to used books,
= total books: used books
= 15:8
b) ratio of new books to all books,
= new books: all books
=7:15
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Find the slope-intercept equation of the tangent line to the graph of f(x)=x^2 at (-3,9).
Answer:
y = -6x -9
Step-by-step explanation:
The derivative is ...
f'(x) = 2x
so the slope at x=-3 is ...
f'(-3) = 2(-3) = -6
Then the point-slope form of the tangent line can be written ...
y = m(x -h) +k . . . . . . for line with slope m through point (h, k)
y = -6(x -(-3))+9 = -6x -18 +9 . . . . . filling in your values, eliminating parens
So, the slope-intercept equation of the tangent line is ...
y = -6x -9
The set (3,5,___________
could not be the sides of a triangle
3,2,5,7
Answer:
(3, 5, 2)
Step-by-step explanation:
Many authors interpret the triangle inequality to mean the sum of the two short sides must exceed the length of the long side. For side measures 2, 3, 5, the sum of the two short sides is exactly equal to the long side, in violation of the triangle inequality. Hence (3, 5, 2) is not a triangle.
___
Comment on the triangle inequality
Other authors allow the "or equal to" case, meaning sides of lengths 2, 3, 5 will be considered to be a triangle because 2+3=5. This interpretation of the triangle inequality will result in no solution to your question.
A (3, 5, 2) "triangle" will look like a line segment of length 5. It will have an area of zero.
Answer:
The answer to your question would be
3, 5, 2.
Phil had made $1200 deposits in an annuity due at the beginning of each quarter in an account earning 6% interest compounded quarterly. What is the future value of the account in 2years? pay attention this is Annuity due not ordinary annuity
ractice Tests
10271.20
$5,835.12
$5,991.53
$5,902.99
Formula and set up:
A = P(1 + r/n)^(nt)
You want A.
A = 1200(1 + (0.06)/2)^(0.06)(2)
Plug right side into calculator to find A.
Which linear equation passes through the points (0, - 2) and (4, 10)?
y = 3x - 2
y = - 1/3x - 2
y = 1/3x - 2
y = - 3x - 2
Answer:
y = 3x - 2
Step-by-step explanation:
You can easily find the equation of a line through two points by using the point-slope form, [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is one of the points.
First, let's find the slope of the line through (0, -2) and (4, 10).
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1} = \frac{10-(-2)}{4-0}=\frac{12}{4}=3[/tex]
Next, we plug this into point-slope form. Remember that we let (0, -2) be our first point, [tex](x_1,y_1)[/tex].
[tex]y-(-2)=3(x-0)[/tex]
Finally, we rearrange this equation to get the slope-intercept form [tex]y=mx+b[/tex], where b is the y-intercept.
[tex]y+2=3x \\ y=3x-2[/tex]
We can verify using the attached graph that both points lie on this line.
(x – 3)³
Given: (x – y)³ = x³ – 3x²y + 3xy² – y³
ANSWER
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
EXPLANATION
We want to expand:
[tex] {(x - 3)}^3[/tex]
Using the identity;
[tex] {(x - y)}^{3} = {x}^{3} - 3 {x}^{2}y + 3x {y}^{2} - {y}^{3} [/tex]
We substitute y=3 into the above identity to obtain:
[tex] {(x - 3)}^{3} = {x}^{3} - 3 {x}^{2}(3) + 3x( {3}^{2} ) - {(3)}^{3} [/tex]
Let us simplify to get:
[tex]{(x - 3)}^{3} = {x}^{3} - 9 {x}^{2} + 27x - 27[/tex]
The absolute value function, f(x) = –|x| – 3, is shown. What is the range of the function? all real numbers all real numbers less than or equal to 0 all real numbers greater than or equal to –3 all real numbers less than or equal to –3
Answer:
all real numbers less than or equal to –3
Step-by-step explanation:
Look at the y-values that the graph shows. There are none greater than -3. Any value of -3 or less is possible.
Answer: D. all real numbers less than or equal to –3
Not sure how to even start this problem please help
Explanation:
DeMoivre's theorem tells you the 7th roots of unity are the 7 points evenly spaced around (on) the unit circle, including 1∠0°. They will be located at angles ...
{0, 2π/7, 4π/7, 6π/7, 8π/7, 10π/7, 12π/7} . . . in radians
Given that the circle shown is graduated in increments of π/6, you will need to do some estimating as to the actual location of the root.
___
The attached graph shows lines at increments of π/7 radians, so your graph will match every other one.
Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer, as a fraction in simplified form, in the box.
Answer:
1/3
Step-by-step explanation:
if you multiply 24 by 1/3, you recieve 8 which is the reduced dilation
Which equation of a line passes through the points (3, −1) and (6, 1)?
Y = 2/3x - 3
Y = - 2/3x + 5
Y = - 2/3x + 10
Y = 3/2x - 8
Answer:
Y = 2/3x - 3
Step-by-step explanation:
Recall the general equation for a straight line is
y = mx + b
where m is the gradient and b is the y-intercept
given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:
m = [tex]\frac{y1-y2}{x1-x2}[/tex]
in this case, x1 = 3, y1 = -1, x2 = 6, y2=1
applying these values to the formula for m will give
m = (-1 -1) / (3-6) = 2/3
We can see immediately that only the first (top-most) answer has this value for m and we can guess that this is probably the answer.
But we can still check to confirm:
If we substitute this back into the general equation, we get:
y = (2/3)x + b
In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (6,1)
1 = (2/3)(6) + b
1 = 4 + b
b = -3
Confirm Y = 2/3x - 3 is the answer.
What is the volume of the cone with diameter 7 in. and height 9 in.? Round to the nearest cubic inch.
Answer: [tex]115in^3[/tex]
Step-by-step explanation:
The volume of a cone can be calculated with the following formula:
[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
The radius is half the diameter, then "r" is:
[tex]r=\frac{7in}{2}\\\\r=3.5in[/tex]
Since we know that radius and the height, we can substitute them into the formula.
The volume of the cone to the nearest cubic inch is:
[tex]V_{(cone)}=\frac{1}{3}\pi (3.5in)^2(9in)[/tex]
[tex]V_{(cone)}=115in^3[/tex]
Answer:
The volume of cone = 115 cubic inches
Step-by-step explanation:
Points to remember
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the volume of cone
Here diameter = 7 in then r = 7/2 = 3.5 in and h = 9 in
Volume = (πr²h)/3
= (π * 3.5² * 9)/3
= (3.14 * 12.25 * 9)/3
= 115.395 ≈ 115 cubic inches
Therefore volume of cone = 115 cubic inches
How many zeroes do we write when we write all the integers 1 to 243 in base 3?
Answer:
289 numbers
Step-by-step explanation:
Above you will find the list of integers from 1 to 243 in base 3:
(1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1201, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2000, 2001, 2002, 2010, 2011, 2012, 2020, 2021, 2022, 2100, 2101, 2102, 2110, 2111, 2112, 2120, 2121, 2122, 2200, 2201, 2202, 2210, 2211, 2212, 2220, 2221, 2222, 10000, 10001, 10002, 10010, 10011, 10012, 10020, 10021, 10022, 10100, 10101, 10102, 10110, 10111, 10112, 10120, 10121, 10122, 10200, 10201, 10202, 10210, 10211, 10212, 10220, 10221, 10222, 11000, 11001, 11002, 11010, 11011, 11012, 11020, 11021, 11022, 11100, 11101, 11102, 11110, 11111, 11112, 11120, 11121, 11122, 11200, 11201, 11202, 11210, 11211, 11212, 11220, 11221, 11222, 12000, 12001, 12002, 12010, 12011, 12012, 12020, 12021, 12022, 12100, 12101, 12102, 12110, 12111, 12112, 12120, 12121, 12122, 12200, 12201, 12202, 12210, 12211, 12212, 12220, 12221, 12222, 20000, 20001, 20002, 20010, 20011, 20012, 20020, 20021, 20022, 20100, 20101, 20102, 20110, 20111, 20112, 20120, 20121, 20122, 20200, 20201, 20202, 20210, 20211, 20212, 20220, 20221, 20222, 21000, 21001, 21002, 21010, 21011, 21012, 21020, 21021, 21022, 21100, 21101, 21102, 21110, 21111, 21112, 21120, 21121, 21122, 21200, 21201, 21202, 21210, 21211, 21212, 21220, 21221, 21222, 22000, 22001, 22002, 22010, 22011, 22012, 22020, 22021, 22022, 22100, 22101, 22102, 22110, 22111, 22112, 22120, 22121, 22122, 22200, 22201, 22202, 22210, 22211, 22212, 22220, 22221, 22222, 100000)
If you count them, you will find that there are 289 numbers in total!
Final answer:
When writing the integers from 1 to 243 in base 3, there are exactly five zeros written. These are associated with the numbers that are powers of 3 (3, 9, 27, 81, 243) each represented in base 3 by a 1 followed by zeros (10, 100, 1000, etc.). Zeroes are not used as trailing digits in any other non-zero numbers in base 3.
Explanation:
Calculating Zeroes in Base 3 from Integers 1 to 243
To determine how many zeroes are written when we write all the integers from 1 to 243 in base 3, we need to understand the representation of numbers in base 3. Every integer can be expanded in powers of 3, where, similar to the decimal system, we have different 'places' representing powers of 3 instead of 10. In base 3, we do not have the digit '0' at the end of any non-zero integer, as that would imply a multiple of 3, which is not represented in the standard form of base 3 notation. Therefore, the only time we write a zero is within the numbers themselves.
Let's look at how numbers are built in base 3:
1 in base 3 is 13 in base 3 is 10 (3¹ + 0)9 in base 3 is 100 (3² + 0)27 in base 3 is 1000 (3³ + 0)And so on, with powers of 3Thus, for every power of 3, we write a single '0' at the end of the number in base 3 notation (excluding the number 3⁰, which is 1). To find out how often this occurs up to 243, we list the powers of 3:
3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, hence there are 5 powers of 3 within our range.
Therefore, we have the number 3¹ written as 10, the number 3² written as 100, and so on, up to 3⁵, which is written as 100000 in base 3. Each of these numbers includes exactly one zero, leading to a total of five zeroes when writing out all the integers from 1 to 243 in base 3.
A new one-year membership at recplex costs $160. A registration fee of $28 is paid up front ,and the rest is paid monthly. How much do new members pay each month? Define the variable
Let n = how much each new member must pay each month.
$160 - $28 = $132
n = $132 ÷ 12 months in a year
n = $11
You can also look at it this way:
n = (160 - 28)/12
After paying a $28 registration fee, the remaining cost of the membership is divided into 12 monthly payments of $11. The variable 'M' can be defined to represent the monthly payments.
Explanation:
The subject of the question is Mathematics, particularly in the area of basic algebraic operations and real life applications of mathematics. The problem involves calculating the cost of a membership at recplex. This is a real-world problem that uses mathematical concepts of subtraction and division. First, we isolate the cost that will be paid on a monthly basis. The total cost of the membership is $160, but $28 is paid up front; hence, the total amount to be divided into monthly payments is $160 - $28, which equals $132. The question doesn't specify the number of months, but since this is a yearly membership, we can assume it is 12. Therefore, $132 divided by 12 is $11 per month.
In this scenario, the variable could be defined as 'M', where 'M' represents the monthly payment.
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1/2x + 1/3y = 7
1/4x + 2/3y = 6
What is the solution of the system shown?
A. (1/6, 14)
B. (6, 12)
C. (10 2/3, 5)
let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.
[tex]\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill[/tex]
In ΔABC, what is the value of cos B?
A) 5/13
B)12/13
C)5/12
D)13/12
Answer:
Value of cos B is B)12/13
The value of cos B in triangle ΔABC cannot be definitively determined without additional information such as side lengths. However, assuming a right triangle configuration with an adjacent side of length 12 and a hypotenuse of length 13, the cos B could be calculated as 12/13.
Explanation:In the triangle ΔABC, the value of cos B can be calculated if we know the measures of the sides of the triangle. Without the values of the sides, we can't give an exact value for cos B. However, from the given options, we would assume that the triangle is a right-triangle, and B is the angle formed by the adjacent side of length 12 and the hypotenuse of length 13. Thus, the value of cos B would be equal to the adjacent side (b) divided by the hypotenuse (c), which matches option B) 12/13.
Remember that in a right triangle:
The cosine of an angle (cos B) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This formula, cos B = b/c is a direct application of the Pythagorean theorem.
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Mustafa is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by (y+2)^2=9(x-2), where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?
(4.25, –2)
(4.25, 0)
(4.25, 2)
(4.25, 4)
Answer: (4.25,-2)
Step-by-step explanation:
Answer:
(4.25, -2) is the focus point
Step-by-step explanation:
Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.
answers:
a) y2 = 4x
b)8y = x2
c)x = 1 divided by 8y2
d) y = 1 divided by 8x2
Answer:
[tex]y^2=\frac{1}{8}x[/tex]
Step-by-step explanation:
The focus lies on the x axis and the directrix is a vertical line through x = 2. The parabola, by nature, wraps around the focus, or "forms" its shape about the focus. That means that this is a "sideways" parabola, a "y^2" type instead of an "x^2" type. The standard form for this type is
[tex](x-h)=4p(y-k)^2[/tex]
where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one). That means that the vertex has to be equidistant from the focus and the directrix. If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0). So h = 0 and k = 0. p is the number of units from the vertex to the focus (or directrix). That means that p=2. We fill in our equation now with the info we have:
[tex](x-0)=4(2)(y-0)^2[/tex]
Simplify that a bit:
[tex]x=8y^2[/tex]
Solving for y^2:
[tex]y^2=\frac{1}{8}x[/tex]
Answer: x = -1/8y^2
Step-by-step explanation
Focus: (-2,0)
Directrix: x=2
It meets the criteria.
Perform the following operations s and prove closure. Show your work.
Answer:
1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex] = [tex]\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]
2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex] = [tex]\frac{1}{(x+2)(x-4)}[/tex]
3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex] = [tex]\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]
4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex] = [tex]\frac{1}{(x-2)(x-4)}[/tex]
Step-by-step explanation:
1. [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)
[tex]=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\[/tex]
Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.
2. [tex]\frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}[/tex]
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors
[tex]=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}[/tex]
Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.
3. [tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex]
Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)
Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors
[tex]\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}[/tex]
Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)
[tex]\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}[/tex]
[tex]=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}[/tex]
Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4. [tex]\frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}[/tex]
Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
[tex]\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}[/tex]
Converting ÷ sign into multiplication we will take reciprocal of the second term
[tex]=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}[/tex]
Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.
The given equations are the algebric equations for obtaining solution the equation can be simplified by algebric operations.
1).
[tex]\dfrac{x}{x+3} + \dfrac{x+2}{x+5}[/tex]
Taking LCM of denomenator (x+3) and (x+5).
[tex]=\dfrac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex]
Further simplification has been done by multtiplication in the numerator.
[tex]=\dfrac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)}=\dfrac{2x^2+10x+6}{(x+3)(x+5)}[/tex]
2).
[tex]\dfrac{x+4}{x^2+5x+6}\times \dfrac{x+3}{x^2-16}[/tex]
For further simplification of above equation factorization of [tex]x^2+5x+6[/tex] and [tex]x^2-16[/tex] has been performed.
[tex]= \dfrac{x+4}{(x+3)(x+2)}\times \dfrac{x+3}{(x-4)(x+4)}[/tex]
[tex]= \dfrac{1}{(x+2)(x-4)}[/tex]
3).
[tex]\dfrac{2}{x^2-9}-\dfrac{3x}{x^2-5x+6}[/tex]
For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-9[/tex] has been performed.
[tex]=\dfrac{2}{(x-3)(x+3)}-\dfrac{3x}{(x-3)(x-2)}[/tex]
Taking LCM of denomenator (x+3)(x-3) and (x-3)(x-2).
[tex]=\dfrac{(2\times(x-2))-(3x\times(x+3))}{(x-3)(x+3)(x-2)}=\dfrac{2x-4-3x^2-9x}{(x-3)(x+3)(x-2)}[/tex]
[tex]= -\dfrac{3x^2+7x+4}{(x-3)(x+3)(x-2)}[/tex]
4).
[tex]\dfrac{\dfrac{x+4}{x^2-5x+6}}{\dfrac{x^2-16}{x+3}}[/tex]
For further simplification of above equation factorization of [tex]x^2-5x+6[/tex] and [tex]x^2-16[/tex] has been performed.
[tex]=\dfrac{\dfrac{x+4}{(x-3)(x-2)}}{\dfrac{(x-4)(x+4)}{x+3}}=\dfrac{x+3}{(x-3)(x-2)(x-4)}[/tex]
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If A=29 and a=4.6, find c
Answer:
Step-by-step explanation:
Following your description I got
sin 29° = opp/hyp = 4.6/c
csin29 = 4.6
c = 4.6/sin29
= 9.48826.. or appr 9.5
Answer:
Option (D)
Step-by-step explanation:
8. Combine the like terms in this expression: –3x + 2xy + 4y – xy + 2x – 11y
A. 23X + y
B. 2xy + 15
C. –7xy
D. –X+XY–7y
Answer:
D. –X+XY–7y
Step-by-step explanation:
We just have to combine (add) the similar terms... so all terms that have an x in them for example.
–3x + 2xy + 4y – xy + 2x – 11y
Let's first re-write it placing similar terms next to each other
(-3x + 2x) + (2xy - xy) + (4y - 11y)
Then we sum them up, for each similar terms
1x + 1xy -7y
so, x + xy -7y
Answer D.
Plz, answer! 34 + 2 ⋅ 5 =
[tex]3^{4}[/tex] + 2 × 5
To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
Parentheses
There are none for this steps so go on to the next step
Exponent:
[tex]3^{4}[/tex]
81
so...
81 + 2 × 5
Multiplication:
81 + 2 × 5
2 × 5
10
so...
81 + 10
No division in this equation so skip this step and go to the next one
Addition:
81 + 10
91
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
44
Step-by-step explanation:
Order of operations
PEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
Do multiply from left to right.
2*5=10
Add the numbers from left to right to find the answer.
34+10=44
44 is the correct answer.
I hope this helps you, and have a wonderful day!
12. Find m?1 if m?2 = 35° in parallelogram ABCD. A. 55° B. 35° C. 75° D. 40°
Answer: A
Step-by-step explanation: Complementary angles must add up to 90 degrees.
In a first -aid kit the ratio of large bandages is 3 to 2. Based on this ratio, how many large bandages are in the kit if there are a total of 80 bandages?
Answer:
48
Step-by-step explanation:
The total number of ratio units is 3+2 = 5, and the 3 ratio units representing large bandages make up 3/5 of that total. Thus, large bandages will make up 3/5 of the total number of bandages:
3/5×80 = 48 . . . . number of large bandages in the kit
11. 10ac × 6ab × (–2bc) = ?
A. 14a2b2c2
B. 2a + 2b + 2c + 14
C. –120a2b2c2
D. 2a + 2b +2c – 120
Answer:
C. –120a2b2c2
Step-by-step explanation:
We'll just the multiplications one at a time...
10ac × 6ab × (–2bc) = 60a²bc * (-2bc) (multiplying 10ac × 6ab)
60a²bc * (-2bc) = -120a²b²c²
We just have to multiply the numbers together (like 10 and 6),
then all similar letters together (like ac * ab = a²bc). If a letter is already present (like a in this example), then we add up its powers a * a = a², a² * a would be a³ and so on). If the letter is not present (like 'b' in 'ac', we suppose it's there as b^0 which is equal to 1)... so we still add up its exponent (power)... so it makes b^0 * b = b
can someone help me with this, please
Answer:
(0,4) vertex and (1,3) another pt
Step-by-step explanation:
The parabola has been shifted up 4 units from parent function (there is also a reflection)...but we only really care about the shift 4 units up from (0,0) for our vertex... Our vertex is (0,4)
Now just plug in another number to find another point...let's do x=1
Plug in you get -1^2+4=-1+4=3 so another point is (1,3)
Emily, Carl and Antony altogether has 121 stamps. How many stamps does each of them have, if it is known, that Emily has 40% more than Carl, and Carl has 60% more than Antony?
simplify the radical expression square root of 20x^13y^5/5xy^7. The answer choices are: a( sqrt 4x^12/y^2 b( 2x^6/y^2 c( 2 sqrt x^12/y^2 d( 2x^6y
Answer:
Option C is correct
Step-by-step explanation:
We need to simplify the radical
[tex]\sqrt{\frac{20x^{13}y^5}{5xy^7}}[/tex]
We know that a^m/a^n = a^m-n and 20/5 = 4
Solving
[tex]\sqrt{4x^{13-1}y^{5-7}}\\\sqrt{4x^{12}y^{-2}}\\[/tex]
Now, √4 = 2 and a^-m = 1/a^m
Applying,
[tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex]
So, Option C [tex]2\sqrt{\frac{x^{12}}{y^2}}\\[/tex] is correct.
In mathematics, the Nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/N. So, the first harmonic number is 1, the second is 1.5, the third is 1.83333... and so on. Assume that n is an integer variable whose value is some positive integer N. Assume also that cl is a variable whose value is the Nth harmonic number. Write an expression whose value is the (N+1)th harmonic number.
Answer:
cl + 1/(N+1)
Step-by-step explanation:
If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl
And we know that the (N+1)th harmonic number can be found by doing
1+1/2+1/3+1/4+...+1/N+1/(N+1)
=cl + 1/(N+1)
The (N+1)th harmonic number is cl + 1/(N+1) given that the Nth term is cl
Other way to see the answers:
Maybe you want to write it as a single fraction so you have
[cl(N+1)+1]/(N+1)=[cl*N+cl+1]/(N+1)
The expression value is [tex]hn+(\frac{1}{n+1} )[/tex].
Assume that [tex]n[/tex] is an integer variable whose value is some positive integer [tex]N[/tex].
Assume also that [tex]hn[/tex] is a variable whose value is the [tex]N_{th} [/tex] harmonic number.
An expression whose value is the [tex](N+1)th[/tex] harmonic number is [tex]hn+(\frac{1}{n+1} )[/tex].
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The cost of a movie theater ticket is given by the expression 10a, where a is the number of people in the theater. The cost of a drink at the theater is given by the expression 5a. Which is the expression if every person buys a drink?
a-5a+10
b-25a
c-15a
d-10a+5
Answer: c. 15a
explanation: if a movie ticket is 10 per person and a drink is 5 per person and everyone buys a drink that would mean each person would be spending 15 and the # of people is unknown so it would be 15a.
Answer: should be c. 15a because 10+5=15 and the # of people in unknown so the answer should be 15a