Answer:
x= п/2+пn; nE Z
x= п/6+пn; nEZ
Step-by-step explanation:
(cosx)^2- √3sinxcosx=0
Factorise it
cosx(cosx-√3sinx)=0
cosx=0 or cosx=√3sinx
x= п/2+пn; nE Z cosx/cosx= √3sinx/cosx
1/√3= tgx
x= arctg 1/√3+пn; nE Z
x= п/6+пn; nEZ
The answer is x= п/2+пn; nE Z
x= п/6+пn; nEZ
Arturo's goal is to find a job that provides an income of at least $60,000 a year. Kristen's Furniture offers him a job paying a base salary of $14,000 a year, plus a commission of 7% of his sales. Determine what Arturo's total sales will need to be for him to have a yearly income greater than or equal to $60,000.
If Arturo takes the job with Kristen's Furniture, he will need to have at least
$
in total sales to have a yearly income greater than or equal to $60,000 per year.
Answer:
He will need at least 657,142.86
Step-by-step explanation:
Determine how much commission he needs
60000-14000
46000
Commission is 7%
Let x be the sales
x*7% = 46000
x*.07 = 46000
Divide each side by .07
x = 46000/.07
x =657142.85714
Rounding to the nearest cent
x = 657,142.86
If 1 ounce of silver costs $5.50, how much money is needed to buy 2 1/2 pounds of silver?
16 oz = 1 pound
Answer:
0.858
Step-by-step explanation:
2 1/2 from oz to pound is 0.156 and then mutiply that by 5.50 is 0.858
PLease help
Belinda is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 186,160 193,606.40 201,350.66
House 2 (value in dollars) 190,000 201,000 212,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a house that would have the greatest value in 30 years. Will there be any significant difference in the value of either house after 30 years? Explain your answer, and show the value of each house after 30 years. (4 points)
There are several types of functions, but this question is limited to just 2 types, which are the exponential function and the linear function.
House 1 has an exponential function of [tex]f(x) = 179000 * 1.04^x[/tex] while house 2 has a linear function of [tex]f(x) =11000x+179000[/tex]. House 1 will have a greater value in 30 years and the difference between the values of the two houses is significant.The given parameters can be represented as:
[tex]\begin{array}{cccc}{Years} & {1} & {2} & {3} & {House\ 1} & {186,160 } & {193,606.40 } & {201,350.66} & {House\ 2} & {190,000 } & {201,000 } & {212,000} \ \end{array}[/tex]
(a): The type of function
First, we check if the function is linear by calculating the difference between each year
House 1
[tex]d = 193606.40 - 186160 = 7446.4[/tex]
[tex]d = 201350.66 - 193606.40 = 7744.26[/tex]
The difference are not equal; hence, the function is not linear. So, we can assume that it is exponential
House 2
[tex]d = 201000 - 190000 =11000[/tex]
[tex]d = 212000 - 201000 =11000[/tex]
The difference are equal; hence, the function is linear.
(b): The function of each
House 1
An exponential function is represented as:
[tex]y = ab^x[/tex]
When [tex]x = 1;\ y =186,160[/tex]
We have:
[tex]186,160 =ab^1[/tex]
[tex]186,160 =ab[/tex] ---- (1)
When [tex]x = 2;\ y =193606.40[/tex]
We have:
[tex]193606.40 =ab^2[/tex] --- (2)
Divide (2) by 1
[tex]\frac{193606.40}{186160} =\frac{ab^2}{ab}[/tex]
[tex]1.04 = b[/tex]
[tex]b = 1.04[/tex]
Make a the subject in (1)
[tex]186,160 =ab[/tex]
[tex]a = \frac{186160}{b}[/tex]
[tex]a = \frac{186160}{1.04}[/tex]
[tex]a = 179000[/tex]
So, the function for house 1 is:
[tex]f(x) = 179000 * 1.04^x[/tex]
House 2
A linear function is represented as:
[tex]y = mx + b[/tex]
First, we calculate the slope (m)
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{201000 - 190000}{2 - 1}[/tex]
[tex]m = \frac{11000}{1}[/tex]
[tex]m = 11000[/tex]
So, the equation is:
[tex]y =m(x-x_1) + y_1[/tex]
Substitute known values
[tex]y =11000(x-1) + 190000[/tex]
[tex]y =11000x-11000 + 190000[/tex]
[tex]y =11000x+179000[/tex]
So, the function for house 2 is:
[tex]f(x) =11000x+179000[/tex]
(c): House with the greatest value in 30 years
This means that:
[tex]x = 30[/tex]
For house 1, we have:
[tex]f(x) = 179000 * 1.04^x[/tex]
[tex]f(30) = 179000 * 1.04^{30}[/tex]
[tex]f(30) = 580568.15[/tex]
For house 2, we have:
[tex]f(x) =11000x+179000[/tex]
[tex]f(30) = 11000 * 30+ 179000[/tex]
[tex]f(30) = 509000[/tex]
By comparison;
[tex]580568.15> 509000[/tex]
House 1 will have a greater value in 30 years
And the difference between the values is significant
The difference is:
[tex]d =580568.15-509000[/tex]
[tex]d =71568.15[/tex]
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A runner covers the last straight stretch of a race in 3 s. During that time, he speeds up from 5 m/s to 11 m/s.What is the runner's acceleration in this part of the race?
Answer:
From first Newton's equation of motion:
[tex]{ \bf{v = u + at}}[/tex]
Substitute the variables:
[tex]{ \tt{11 = 5 + (a \times 3)}} \\ { \tt{3a = 6}} \\ { \tt{a = 2 \: {ms}^{ - 2} }}[/tex]
Acceleration is 2 ms-²
Using trig to solve for missing angles
Answer:
0.9⁰
Step-by-step explanation:
let unknown angle be x
sin x=47/60
sin x=0.783333
x=sin(inverse) 0.7833333
x=0.9⁰
SOMEONE HELP ME PLEASE
Answer:
what are the answer choicesss
Step-by-step explanation:
Find the measure of 2
Answer:
92
Step-by-step explanation:
Angle 2 and 92 are corresponding angles and corresponding angles are equal when the lines are parallel
Answer:
[tex]\angle 2=92^{\circ}[/tex]
Step-by-step explanation:
When two parallel lines are cut by a traversal, their corresponding angles are always equal. Corresponding angles can be found if you took each point of intersection and aligned them up with each other.
In this case, we see that [tex]\angle 2[/tex] and the angle marked as 92 degrees correspond with each other. Since all corresponding angles are equal, we have:
[tex]\angle 2=\boxed{92^{\circ}}[/tex]
Which expression is equivalent to (x^-6/x-2)^3
Answer:
= (6/x - 2)^3
What is the standard deviation of the following data set rounded to the nearest tenth? 300,785,670,187,760,724
Answer:
S.D = 236.5
~~~~~~~~~~~~~~~~~~
300,
785,
670,
187,
760,
724
Answer:
300, 790, 670, 190, 760, 720
write an example of a monomial of degrees 5
Answer:
find the value of:Cos = 0.54
If I take a 7 question multiple choice test, with 4 choices per question, what is the probability that I get 1 wrong
Answer:
The probability is [tex]\frac{3}{4^7}[/tex].
Step-by-step explanation:
Total questions = 7
Number of choices of each question = 4
Probability to give the correct answer = 1/4
Probability to give the wrong answer = 3/4
Probability to give 1 answer wrong
[tex]\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}\\\\= \frac{3}{4^7}[/tex]
Help again this is my last retake
The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal.
What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?
$60
$80
$90
$100
Answer:
80
Step-by-step explanation:
I = Prt
I = 40 R = .10 T = 5
40 = P (.10)(5)
40 = P(.5)
Divide each side by .5
40/.5 = .5P/.5
80 = P
The interest over 5 years is $80.
The correct option is B.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The Formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.
We can use the formula I = Prt to solve for P. We know that I = 40, r = 0.10, and t = 5. Substituting these values, we get:
40 = P(0.10)(5)
Simplifying:
40 = 0.5P
Dividing both sides by 0.5:
P = 80
Therefore, the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years is $80.
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the numbers written in rectangles are the products of the numbers in connecting circle. Please solve it fast its urgent
Answer:
It is the third one
Step-by-step explanation:
c
The radius of the large sphere is times longer than the radius of the small sphere.
How many times the volume of the large sphere is the volume of the small sphere?
Help! Help! Help! Please!
Answer:
A. ¹/27
Step-by-step explanation:
✔️Volume of large sphere = ⁴/3πr³
r = 18.6 in.
Volume of large square = ⁴/3*π*18.6³ = 26954.26 in.³
✔️Volume of small sphere = ⁴/3πr³
r = 6.2 in.
Volume of small sphere = ⁴/3*π*6.2³ = 998.31 in.³
✔️Ratio of the volume of the smaller sphere to the larger sphere = 998.31 : 26954.26
= 1 : 27
Therefore, the volume of the large sphere is ¹/27 of the volume of the small sphere.
If one angle of a triangle is 60°and the ratio of other two is 1:3,find all the angles and the ratio of the sides.
Answer:
30, 90
1 : √3 : 2
Step-by-step explanation:
let the smaller angle be x
hence, the other angle = 3x
180-60=4x
4x = 120
x = 120/4 = 30
other angle = 3(30) = 90
the triangle is a 30-60-90 triangle,
hence the ratio of the sides are 1:√3:2
( short leg : long leg : hypotenuse )
25. A pizza shop offers 30% off the price of a large pizza every Tuesday
night. If the regular price is $25, what is the discounted price?
Answer:
25 -(.3*25)
25-7.50 = $17.50
Step-by-step explanation:
Answer:
17.50
Step-by-step explanation:
First find the amount of the discount
25 * 30%
25 * .3
7.5
Subtract this from the original amount
25 - 7.5
17.50
In the diagram below, what is the approximate length of the minor arc AB?
Answer:
The answer is "Option C"
Step-by-step explanation:
Given:
[tex]r= 30 \ cm\\\\\theta =60^{\circ}[/tex]
Using formula:
[tex]\frac{A}{\theta}=\frac{\pi r^2}{2\pi}\\\\\frac{A}{\theta}=\frac{\pi r^2}{2}\\\\A=\frac{r^2\times \theta}{2}[/tex]
Use the given conditions to write an equations for the line in slope- intercept form. passing through (1,-8) and (-7,8)
Answer:
y = -2x - 6
Step-by-step explanation:
Going from the first point to the second, we see x decreasing by 8 from 1 to -7 (this is the 'run') and y increasing by 16 from -8 to +8 (this is the 'rise'). Thus, the slope of the line through these two points is m = rise/run = 16/(-8) = -2.
Using the point-slope formula y - k = m(x - h) and the point (1, -8), we get:
y + 8 = -2(x - 1), or
y = -8 - 2x + 2, or
y = -2x - 6 (in slope-intercept form)
Let R={0, 1, 2, 3} be the range of h(x) = x - 7. The domain of h inverse is_____.
{-7, -6, -5, -4}
{7, 8, 9, 10}
{0, 1, 2, 3}
Answer:
{-7,-6,-5,-4}
Step-by-step explanation:
Answer:
thats not correct answer thats an odyssey question and i just tried the answer and its not right just wanted everybody to know
Step-by-step explanation:
The total cost of a flower bouquet depends on the types of flowers in the arrangement. A bouquet containing 6 roses, 3 lilies, and 2 carnations costs $26.75. A bouquet containing 3 roses, 4 lilies, and 5 carnations costs $25.50. A bouquet containing 1 of each flower costs $6.75. Which system of equations represents this situation, where r represents the number of roses, l represents the number of lilies, and c represents the number of carnations?
Answer:
Roses 2.70, Lillies 2.45, Carnations 1.60
Find the value of x given in the right triangle
Answer: 7.1 units
Step-by-step explanation:
Using Pythagorean theory, c^2 - a^2 = b^2
We know c= 10
We know a=7
We are looking for b
10^2 - 7^2 = b^2
51= b^2
Take square root of both sides
7.1=b
simplify -8/2 ÷ 6/-3
Answer: the answer is 2 or C
-8/2 x -3/6
*Always do the recipical*
(-8 x -3) / (2 x 6)
-8 x -3= +24
2 x 6= 12
24/12= 2
The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
Given that the expression is,
-8/2 x -3/6
The expression will be solved as below,
E = (-8 x -3) / (2 x 6)
The numerator will get reciprocal and multiplied to the denominator,
E = 24 / 12
Divide the number 24 by 12 and get the solution,
E = 2
Therefore, the solution of the expression will be 2. The correct option is B.
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5^3x +2 = 25^x – 8
step by step please
Answer:
-8
Step-by-step explanation:
It wont let me upload anything so i will come back with steps later
Independent Practice
Find the number of solutions of the equation.
0 = x2 + 2x + 9
A.
3
B.
2
C.
1
D.
0
Answer:
Option D
Step-by-step explanation:
There are no real solution for the given equation
Answered by GAUTHMATH
SOMEONE HELP ME PLEASE
Answer:
1/36
Step-by-step explanation:
There are 6 possible outcomes 1,2,3,4,5,6
P(1) = number of outcomes that equal1 / total
=1/6
Roll again
P(1) = 1/6
These are independent events so we can multiply the probabilities
P(1 roll again 1) = 1/6 * 1/6 = 1/ 36
what is the solution to this?
Answer:
x = -3,y = 2
Step-by-step explanation:
3x-2y = -13
4x-3y = -18
~~~~~~~~~~~~~~~~
9x -6y = -39
-8x+6y = 36
x = -3
-12 -3y = -18
-3y = -6
y = 2
Given that x= –1/2 and y = 4 , evaluate 3x²y + xy²
Answer:
-5
Step-by-step explanation:
3x²y + xy²
Let x = -1/2 and y = 4
3(-1/2)^2 (4) + (-1/2) (4)^2
Exponents first
3(1/4) (4) + (-1/2) 16
Multiply
3 - 8
Subtract
-5
Answer: [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\huge \boldsymbol {-5}[/tex]
Step-by-step explanation: simplify it [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} 3x^2y+xy^2=xy(3x+y)[/tex] evalute [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd \displaystyle\ \Large \boldsymbol{} -\frac{1}{2} \cdot 4 (-3\cdot \frac{1}{2}+4)=-2\!\!\!\!\diagup\cdot\frac{5}{2\!\!\!\!\diagup} =\boxed{-5}[/tex]
find the original price if the price was 420 after a 10% discount
Answer:
466.67
Step-by-step explanation:
Let p be the original price
p - 10 % p = 420
p - .10p = 420
.9p = 420
Divide each side by .9
.9p/.9 = 420/.9
p =466.666666
Rounding to the nearest cent
p = 466.67
Please help me answer this question
Answer:
a, 14.13. b, 39.25
Step-by-step explanation:
so for a the diameter is 6 so the radius is 3. The equation for the area of the circle is πr2. So 3x3=9. then 9x3.14=28.26. But then we have to divide by two cause we are finding only the shaded area. 28.26/2=14.13.
A is 14.13
for b, its the same thing, so the radiu is 5 and 5x5=25. 25x3.14=78.5, and divide two, so 78.5/2=39.25.
B is 39.25
WARNING: I am not sure this is correct, so if this is wrong i'm sorry, i'm learning too :)
