How much greater is 16x² + 7x + 5 than-18x² - 13x + 8?
Answer:
34x² + 20x - 3Step-by-step explanation:
Given
1st Polynomial : 16x² + 7x + 52nd Polynomial : -18x² - 13x + 8We need to subtract the 2nd polynomial from the 1st.
16x² + 7x + 5 - [-18x² - 13x + 8]16x² + 7x + 5 + 18x² + 13x - 834x² + 20x - 3Which of the following numbers must be added to complete the square in the equation below? x^2 +16x=5 27
O A. 64
O B. 25
O C. 16
O D. 8
Answer:
A) 64
Step-by-step explanation:
16/2=8
8^2= 64
x^2 +16x +64= 69
(x +8)^2= 69
Solving Trig. Equations
In each solution, n is an arbitrary integer.
1. Nothing fancy, just take the inverse tangent.
tan(x) = -5
x = arctan(-5) + nπ
x = -arctan(5) + nπ
2. Recall the identity cos(2x) = 2 cos²(x) - 1, then factorize:
cos(2x) - 3 cos(x) + 2 = 0
(2 cos²(x) - 1) - 3 cos(x) + 2 = 0
2 cos²(x) - 3 cos(x) + 1 = 0
(2 cos(x) - 1) (cos(x) - 1) = 0
2 cos(x) - 1 = 0 or cos(x) - 1 = 0
cos(x) = 1/2 or cos(x) = 1
[x = arccos(1/2) + 2nπ or x = -arccos(1/2) + 2nπ]
… or x = arccos(1) + 2nπ
x = π/3 + 2nπ or x = -π/3 + 2nπ or x = 2nπ
3. By definition, csc(x) = 1/sin(x) :
csc(2x) + √2 = 0
csc(2x) = -√2
1/sin(2x) = -√2
sin(2x) = -1/√2
2x = arcsin(-1/√2) + 2nπ or 2x = π - arcsin(-1/√2) + 2nπ
2x = -π/4 + 2nπ or 2x = 5π/4 + 2nπ
x = -π/8 + nπ or x = 5π/8 + nπ
4. More factorization:
2 sin²(x) - sin(x) = 0
sin(x) (2 sin(x) - 1) = 0
sin(x) = 0 or 2 sin(x) - 1 = 0
sin(x) = 0 or sin(x) = 1/2
x = arcsin(0) + 2nπ
… or [x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ]
x = 2nπ or x = π/6 + 2nπ or x = 5π/6 + 2nπ
5. Yet more factorization. Also recall that |cos(x)| ≤ 1 for all x.
4 cos²(x) - 8 cos(x) + 3 = 0
(2 cos(x) - 3) (2 cos(x) - 1) = 0
2 cos(x) - 3 = 0 or 2 cos(x) - 1 = 0
cos(x) = 3/2 or cos(x) = 1/2
The first case gives no solution since 3/2 > 1.
x = arccos(1/2) + 2nπ or x = -arccos(1/2) + 2nπ
x = π/3 + 2nπ or x = -π/3 + 2nπ
6. Recall the identity sin(a - b) = sin(a) cos(b) - cos(a) sin(b).
sin(2x) cos(x) - cos(2x) sin(x) = -√3/2
sin(2x - x) = -√3/2
sin(x) = -√3/2
x = arcsin(-√3/2) + 2nπ or x = π - arcsin(-√3/2) + 2nπ
x = -π/3 + 2nπ or x = 4π/3 + 2nπ
PLEASE HURRY DUE TODAY
3. Leo designs a stand for the new statue on display at the local library. The stand is in the shape of a right trapezoidal prism. The base of the prism has an area of 4 ft^2 and the prism stands 2.4 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 32 ft^2. (a) Leo is asked to purchase roping that will be used to close off the area around the statue. He purchases a length that is five times the perimeter of the stand in roping. How much roping does he purchase? (b) Leo plans to add gold leaf to the sides of the stand but not to the two bases. What percent of the area of the stand will have gold leaf? Round your answer to the nearest whole number
Answer A: 45 5/16
B: The present of the area as 83%
Step-by-step explanation:
(a)
35= 3+3+3.2x+3.2x+3.2x+3.2x
35= 6 + 12.8
29/12.8 +12.8x/12.8
X=2.265625 = 2/12/64
1x = 2 17/64 * 4 + 9 1/16
P = 45 5/16
(b)
The present of the area as 83%
35 – the bases or 6 = 29
29/35 + 0.82857142857
0.82857142857 * 100 = 82.8571428571
Rounded to the nearest whole number is 83%
Graph the function. f(x)=3/5x-5
Please help me with this math problem
Answer:
P1:40% P2:47500 P3:10%
Step-by-step explanation:
2/5 = 0.4 =40%
5/8= .625
.625 x 76000 =
47500
Find the circumcenter of the triangle with vertices at A(2,4),
B(8, 4), and C(6, 10).
Help please I have a d in this class
Answer:
2. Elana's Family. Elana's Family.
3. 8 minutes 4 seconds
4. Elena's family will have driven 2.76 miles while Andre's family will have driven which is farther.
Step-by-step explanation:
A grocery store sells a bag of 6 oranges for $3.24. How much does one orange cost
y=x^2-6x+7 write equation in vertex form
Answer:
y=(x−3)2−2
Step-by-step explanation:
The vertex form of a quadratic function isy=x^2-6x+7 , where x, y, are constants. of the parabola is at (x, y).
Determine the shaded area.
9 ft
(
The shaded area is
(Round to two decimal places as needed.)
Shaded area = area of square - area of a circle.
[tex] \\ \\ [/tex]
For this we have to find area of both square and circle which is visible in the picture.
[tex] \\ [/tex]
Part one :
In this part we'll find area of circle.
Given :
radius = 9ftTo find :
Area of circleSolution:
We know :
[tex] \boxed{ \rm Area \: of \: circle =\pi {r}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2} [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\ [/tex]
[tex] \\ [/tex]
Part 2
As it's visible diameter of circle = side of square.
So we have to find diameter of circle.
We know :-
[tex] \boxed{ \rm Diameter \: of \: circle =2 \: radius}[/tex]
[tex] \\ [/tex]
Steps:-
[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Diameter \: of \: circle =18 \: ft[/tex]
We have :
side of square = 18 ftTo find:
Area of squareSolution:
We know :
[tex] \boxed{ \rm Area \: of \: square= {side}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: square= {side}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: square= {18}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: square= {18} \times 18[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2} [/tex]
Part three:
Remember the first line of answer ? :)
So let's insert here:-
[tex] \boxed{ \text{Shaded area = area of square - area of a circle}}[/tex]
Steps :-
[tex] \dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\textsf{Shaded area = 324 - 254.57} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\ [/tex]
Emily recently started a part time job. She is saving for a car, which she will need when she attends college next year. She plans to deposit $400 at the end of each month into an account that 3.6% per year, compounded monthly . How much will Emily have saved at the end of six months? pays
Answer:
$2418.07
Step-by-step explanation:
Problems involving the time-value of money are conveniently solved using a TVM app on a suitable calculator or spreadsheet. The result of doing that is shown in the attachment.
__
If you would like to compute the value of Emily's account by hand, the annuity formula is the one you want.
A = Pn((1 +r/n)^(nt) -1)/r . . . . where r is the annual interest rate, n is the number of times per year it is compounded (12), t is the number of years (1/2), and P is the periodic payment into the acccount (400).
Using the given values in the formula, we have ...
A = 400(12)((1 +0.036/12)^(12/2) -1)/0.036 = 4800×(1.003^6 -1)/0.036
A ≈ 2418.07
At the end of 6 months, Emily will have saved $2418.07.
PLEASE HELP ME ON THIS
Answer:
About 154 Square
Explanation:
To find an area of a circle you multiply pi by the radius squared so 7² = 49 and 49 x 3.14 = 153.86 which is the closest to 154.
A b c d or e what one will give brainlest
20. Which value of x makes the inequality
3x 27 true?
A. x=8
B. x =10
C. X=12
D. x 14
Hey there!
3x = 27
DIVIDE 3 to BOTH SIDES
3x/3 = 27/3
CANCEL: 3/3 because it give you 1
KEEP: 27/3 because it help solve for the x-value
NEW EQUATION: x = 27/3
SIMPLIFY IT!
x = 9
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
Help please!!!!! Asap!!!
Answer:
Step-by-step explanation:
[tex]\sqrt{3}[/tex] =1.73205 In between 1 and 2 closer to 2
[tex]\sqrt{8}[/tex]=2.82842 In between 2 and 3 closer to 3
[tex]\sqrt{23}[/tex]=4.7958 In between 4 and 5 closer to 5
A sample of students is taken from the school's A honor roll. The school estimates that there are 360 students on the A honor roll. Using this sample how many students on the A honor roll are 8th graders. There are 14 8th graders on the A honor roll.
Answer:
Number of 7th grade = 360 - X
Step-by-step explanation:
As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from &th grade. As we know: Total number of students on the A honor roll = 360 We are asked to calculate, number of students from 7th grade on the A honor roll. So, let's assume that "X" represents the all the students who are on the A honor roll except 7th grade. Mathematical Expression: Number of 7th Graders = Total number of students on the A honor roll - X Number of 7th Graders = 360 - X So, if you know the value of X, you can easily calculate the number of students which are from 7th grade on the A honor roll.
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
Since there are 14 8th grade A honor roll students out of 40 A honor roll students. That means that the fraction is 14/40. After that we do 14/40x360 which results in 126.
Solve: (x + 4)2 – 4 = 16
O x= - 4+2V5
O
O x= – 4 + 20
O x= 4 + V20
O x= +4
Answer:
[tex] {x} = - 4 \pm \: 2\sqrt{5} [/tex]
Step-by-step explanation:
[tex] {(x + 4)}^{2} - 4 = 16 \\ \\ \implies \: {(x + 4)}^{2} = 16 + 4 \\ \\ \implies \: {(x + 4)}^{2} = 20 \\ \\ \implies \: {(x + 4)} = \pm \: \sqrt{20} \\ \\ \implies \: {x + 4} = \pm \: 2\sqrt{5} \\ \\ \implies \: {x} = - 4 \pm \: 2\sqrt{5} [/tex]
What is the image point of (3,8)(3,8) after a translation right 4 units and up 1 unit?
Answer:
The point [tex](3,8)[/tex] will transform into [tex](7,9)[/tex]
Step-by-step explanation:
When you move the unit right, you make the number larger. right and left deal with the X value. you add 4 to 3, and you get 7. Now you move 1 point up, which is just 8+1, which is 9. You get your answer, [tex](7,9)[/tex].
Hope This Helps! :)
Jason opened the triangular pyramid-shaped box to cover it with wrapping paper. How much wrapping paper will he need?
Answer:
How might the situation lead to bullying?
Step-by-step explanation:
How might the situation lead to bullying?
the answer B
Determine the longest distance inside a rectangular prism with dimensions of 8 ft x 3 ft by 9 ft
Answer:
8*3*9 = 216 sq. ft³.Step-by-step explanation:
This is like volume!
Equation:
8 * 3 * 9Solve:
8 * 3 * 9= 24 * 9= 216Simplify:
8 * 3 * 9= (8 * 3) * 9= 24 * 9= 216.Answer is 216 sq. ft³.
When you multiply a whole number by 10 to the 5th power , will there always be the same number of
zeros before the decimal point as in your answer to Part A? Explain your reasoning.
Answer:
Answer:
Step-by-step explanation:
a whole number can be ANY counting number
10 to the 5th power = × 10 × 10 × 10 × 10 × 10
when you multiply by any positive power of ten, you are making it really big
23 × 10 × 10 × 10 × 10 × 10 = 2,300,000
30 × 10 × 10 × 10 × 10 × 10 = 3,000,000
100 × 10 × 10 × 10 × 10 × 10 = 10,000,000
the pattern is the whole number followed by 5 zeros that show 5 place values
What is the inverse of f(x)=3-x/7
Answer:
I got f^-1 (x) = -7x + 21
Step-by-step explanation:
Dr. Weinstein took 50 ounces of a 20% silver
alloy and mixed it with a 40% silver alloy to get
a 30% silver alloy. How many ounces of the 40%
silver alloy did he use?
Answer:
I think it is 100
Answer:
Step-by-step explanation:
The answer is 50 ounces
Because 30% silver is right in between 20% silver and 40% silver, it would have to be the same amount to be 30%
If y=x+4 then what is (x-y)^3
Answer:
64
Step-by-step explanation:
y = x + 4
y - x = 4
4^3 = 64
Question 3
1 pts
Use the diagram to answer the question. Find the measure of the
arc in degrees, type in a number only.
180° hope it's correct and really helps....!!!!
solve for x ~
[tex]x {}^{2} - 36 = 0[/tex]
thankyou ~
Answer:
[tex]x {}^{2} - 36 = 0 \\ \\ x {}^{2} = 36 \\ \\ x = \sqrt{36} \\ \\ x = + 36 \: \: or \: \: - 36[/tex]
hope helpful -,-
A men's department store sells 14 different suit jackets, 6 different shirts, 10 different ties, and
8 different pairs of pants. How many different suits consisting of a jacket, shirt, tie, and pants are
possible? *
Answer:
The total number of different suits consisting of a jacket, shirt, tie, and pants are possible is 576 ways and this can be determined by using the given data.
Given :
A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants.
The following steps can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible:
Step 1 - The arithmetic operations can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible.
Step 2 - According to the given data, the total number of shirts is 6, ties is 8, suit jackets is 3, and pants is 4.
Step 3 - So, the total number of different suits consisting of a jacket, shirt, tie, and pants are possible is:
= 576 ways
Step-by-step explanation:
M log_5(8) rewrite to log _?(?)
Answer:
[tex]\log_5 8^{M}[/tex]
Step-by-step explanation:
[tex]\text{We know that,}~ b\log_a c = \log_a c^b[/tex]
Five members of a mystery-book club each read a 1,296-page book. Nine members of a fantasy-book club each read a 398-page book. How many more pages did the mystery-book club read than the fantasy-book club? Select all the correct equations or set of equations that could be used to solve the problem.
Answer:
2898
Step-by-step explanation:
number of people * number of pages in each book they read =total
mystery bookclub:
5 * 1,296 = 6480
fantasy bookclub:
9 * 398 = 3582
mystery - fantasy = difference in books between the two groups
6480 - 3582 = 2898
possible equation:
(1296 x 5) - (398 x 9) = x
x = answer
Answer:
Step-by-step explanation:
hey i got a couple (10) calculus questions in my profile and im pretty desperate right now
can u pls help