Answer:
We know that:
Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
Then if we use this property in our expression:
sin(a-30)-sin(a+30)
We get:
sin(a)*cos(-30°) + sin(-30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
Now remember that:
sin(-x) = -sin(x)
and
cos(-x) = cos(x)
Then we can rewrite our expression as:
sin(a)*cos(30°) - sin(30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
= -2*sin(30°)*cos(a)
and sin(30°) = 0.5
Then:
-2*sin(30°)*cos(a) = -2*0.5*cos(a) = -cos(a)
So we get:
sin(a-30)-sin(a+30)= - cos(a)
2mn – 5z + 7
PLEASE HELP!!
Answer:
it's already simplified
what do you want me to do? tell me what kind of equation it is?
it's a linear trinomial
Step-by-step explanation:
rewarding 20 points pls help.
Which ordered pair is a solution of y = x+4
A.(0,0)
B.(5,54)
C.(7,28)
D.(9,13)
A carnival attraction tests your strength by how far in the air you can drive a weight with a hammer. If the weight reaches 15 feet, you win a prize. The equation h = -16t 2+ 31t + 2 gives the height, in feet, and time, in seconds of the weight after it is hit.
a. How long is the weight in the air?
b. What was the weight’s maximum height?
c. Did you win a prize? Why or why not?
Answer:
a. 2 secondsb. ~17 feetc. yesStep-by-step explanation:
Given function:
h(t) = -16t² + 31t + 2a.h(t) = 0 will give us the y-intercept of the graph. The greater value of t is the time the weight in the air
-16t² + 31t + 2 = 016t² - 31t - 2 = 0t = [31 + √(31²+4*16*2)]/32t = (31 + 33)/32t = 2 secondsb.Maximum height is reached at vertex.
The x coordinate of the vertex is determined as x = -b/(2a), considering the standard form of a quadratic function f(x) = ax² + bx + c
t = -31/(-16*2) = 31/32 = 0.96875h(0.96875) = -16(0.96875)² + 31*0.96875 + 2 = 17.015625 ftc.You win the prize as the maximum height is greater than 15 feet9 = 3 (1/2 + k)
explanation
witch function defines (g . f)(x)
f(x)=log(5x)
g(x)=5x+4
a.) (g . f) (x)=5x log(5x) + 4log(5x)
b.) (g . f) (x)=5x log(5x)+ 4
c.) (g . f) (x)=5x + 4 +log(5x)
d.) (g . f) (x)=5x - 4 - log(5x)
Answer:its A
Step-by-step explanation:
I ask my teacher so its A
Solve the expression using absolute value.
|−16|+|−12|
Answer:
16 + 12 = 28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
Hello!
Remember that any negative number inside of the absolute value brackets turns positive, and any positive number stays positive.
Simplify|-16| + |-12|16 + 1228
The simplified expression is 28.
which expression is equivalent to 7/12 - 2/12
Answer:
5/12
Step-by-step explanation:
7/12-2/12=5/12=0.416
y = x + 45
What is the y-intercept of the relationship?
A. 45
B. x + 45
C. x
D. y - 45
Answer:
A. 45
Step-by-step explanation:
Answer: A. 45
Step-by-step explanation:
In the y=mX+b formula the number by itself with no variable or b is the y-intercept.
Evaluate the expression when d= 75
2d + –45d = 0
Answer:
- 3225
Step-by-step explanation:
d = 75
2d + ( - 45 d )
= 2 ( 75 ) - 45 ( 75 )
= 150 - 3375
= - 3225
2t + t =68
a. find t
b. fint 2t
Answer:
t = 22[tex]\frac{2}{3}[/tex]
2t = 45[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
3t = 68
t = 68/3
Anyone know the answer to this question?
Find ? (inscribed angle)
9514 1404 393
Answer:
107°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
X = 180° -Q
X = 180° -73° = 107°
Use the graph to write a linear function that relates y to x
y=
Olivia will deposit $1,530 in an account that earns 6% simple interest every year. Her sister
Melinda will deposit $1,500 in an account that earns 8% interest compounded annually. The
deposits will be made on the same day, and no additional money will be deposited or
withdrawn from the accounts. Which statement about the balances of Olivia's account and
Melinda's account at the end of 3 years is true?
A Olivia's account will have about $5.40 more than Melinda's account.
B Olivia's account will have about $84.17 more than Melinda's account.
C Melinda's account will have about $5.40 more than Olivia's account.
D Melinda's account will have about $84.17 more than Olivia's account.
D. Melinda's account will have about $84.17 more than Olivia's account.
Answer:
Olivia 275.4 and Melinda 360
Step-by-step explanation:
Olivia 1,530 x .06 = 91.8
91.8 x 3 = 275.4
Melinda 1,500 x .08 = 120
120 x 3 = 360
plz mark brainleist
What is the value of the function f(x)= 1/4 x-3 when x=12
Answer:
0
Step-by-step explanation:
f(x)=1/4x-3
f(12)=(1/4 times 12) -3
f(12)=(3)-3
0
Abeer sat a French test and a German test.
In the French test she scored 34 out of 50.
In the German test she scored 14 out of 20.
In which test did she do better?
You must show your working.
Answer:
German Test
Step-by-step explanation:
Find common denominator:
34/50=68/100
14/20=70/100
Therefore, Abeer did better on the German test as 14/20>34/50
f(x) = 5x^2 + 9x – 4
g(x) = – 8x^2 – 3x – 4
Find (f + g)(x).
Answer:
(f + g)(x) = – 3x^2 + 5x - 8
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 5x^2 + 9x – 4 + (– 8x^2 – 3x – 4)
= 5x^2 + 9x – 4 – 8x^2 – 3x – 4
Combine
= – 3x^2 + 5x - 8
The sum of the given functions is defined as the expression (f + g)(x) which is equal to -3x² + 6x – 8.
Use the concept of quadratic function defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
The given functions are:
f(x) = 5x² + 9x – 4
g(x) = – 8x² – 3x – 4
Since (f + g)(x) = f(x) + g(x)
Then put the functions,
(f + g)(x) = (5x² + 9x – 4) + ( – 8x² – 3x – 4)
Rearranging like terms,
(f + g)(x) = 5x²– 8x² + 9x – 3x – 4 – 4
Simplifying it,
(f + g)(x) = -3x² + 6x – 8
Hence,
The expression for (f + g)(x) is -3x² + 6x – 8.
To learn more about quadratic equations visit:
https://brainly.com/question/30098550
#SPJ6
A game show is offering a prize of 1 cent on the first day , 3 cents on the second day 9 cents on the third day , etc. What is the total amount of money earned from this prize in two weeks ?
Answer:
$15943.23
Step-by-step explanation:
each day the total of the day before is multiplied by 3 so if you do that for 14 days you will get the answer
Answer:
2,391,4.84 dollars
Step-by-step explanation:
1, 3 , 9...
on the 1st day, 3^0
on the 2nd day, 3^1
on the 3rd day, 3²
:
one the 14th day, 3^(14-1)
=> 3^13
=> 1,594,323
"Total about of money" => have to add up the money from the 1st day to the 14th day:
1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561 + 19683 + 59049 + 177147 + 531441 + 1594323 = 2,391,484
The range of the numbers 34 32 12 65 and 45 is
Answer:
53
Step-by-step explanation:
Range is found by subtracting the largest number in a set by the smallest number.
Set: {12, 32, 34, 45, 65}
Largest number: 65
Smallest number: 12
65 - 12 = 53
hope this helps and is right :)
If u want to know what students think is the best season of the school year from school 76, what is the best way sample the students?
Answer:
B
Step-by-step explanation:
this will include all people and not just a specific group like all in a certain grade/s or all in the same class
Answer: break them up into parts
Step-by-step explanation:
URGENT!! I NEED HELP ASAP NOT ROCKY
Ryan wishes to purchase a new boat and can afford monthly payments of up to $300 per month. Finance is available and the terms are that the loan lasts for 3 years, and the annual interest rate is 12%. What is the maximum price for a boat that Ryan's budget can afford? Round your answer to the nearest hundred dollars.
Answer:
$9000Step-by-step explanation:
Given
Monthly payment P = $300Time t = 3 years = 36 monthsNumber of payments n = 36Interest rate r = 12% PA = 1% per month = 0.01 timesUse loan payment formula:
P = r(PV) / (1 - (1 + r)⁻ⁿ), where P- monthly payment, PV - present value (amount of the loan), r -rate of interest, n- number of paymentsSubstitute values and solve for PV:
300 = (0.01*PV) / (1 - (1 + 0.01)⁻³⁶)PV = 300*(1 - 1.01⁻³⁶ )/ 0.01 PV = 9032.25 ≈ $9000 (rounded to the nearest hundred dollars)
A baker has small and large bags of sugar for making cakes. The large bag contains 30 cups cups of sugar and is 2.5 times larger than the small bag. The small bag contains enough sugar to make 9 cakes and have 0.75 cups of sugar remaining. How many cakes can be made with a large bag of sugar?
Answer:
Step-by-step explanation:
The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.
What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.
9x + 0.75 = 12
First, subtract 0.75 from both sides. With that, we can solve for x directly.
9x = 12 - 0.75
9x = 11.25
Now, divide both sides by 9.
x = 11.25/9
x = 1.25
With that, we now know that each cake needs 1.25 cups of sugar.
With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.
With that done, we have our answer. 24 cakes can be made with a large bag of sugar.
I hope this helps! (⌒ω⌒)
In Springfield, a specific town in the US, 6 women and 25 men earned bachelor degrees in 2000. In 2010, however, 391 women and 410 men in that town earned bachelor degrees. Assume that the rate of change was constant between 2000 and 2010.
a. Without using regression, write a system of equations that model the number of bachelor degrees earned by men and women in Springfield as a function of x, the number of years since 2000. Show your work.
Equation for Springfield’s men:
Equation for Springfield’s women:
Answer:
See belowStep-by-step explanation:
For women, the initial number is 6, constant rate of change is w, number of years is x.
Find the rate of change and work out the required formula:
10w + 6 = 391 ⇒ 10w = 385 ⇒ w = 38.5Formula:
W(x) = 38.5x + 6Similarly for men, we get:
10m + 25 = 410 ⇒ 10m = 385 ⇒ m = 38.5Formula:
M(x) = 38.5x + 25Answer:
Women = 44.5
Men = 63.5
Step-by-step explanation:
Help me PLEASEEE NO LINKS AND PLEASE DO NOT ANSWER FOR POINTS YOU WILL BE REPORTED IF YOU DO AND THANK YOU TO THOSE WHO ARE GOING TO HELP ME
Answer:
160 the total area
Step-by-step explanation:
10×10=100=area of square
5×12=60=area of triangle
Tamara invested $15,000 in an account that pays 4% annual simple interest. Tamara will not
make any additional deposits or withdrawals. How much Interest will Tamara earn on her
Investment at the end of 3 years?
F $1,800
G $600
H $450
J $1.873
Answer:
F $1800
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
I = 15000 × 0.04 × 3 = 1800
I = $ 1,800.00
The simple interest accumulated
on a principal of $ 15,000.00
at a rate of 4% per year
for 3 years is $ 1,800.00.
Answer:
F. $1800
Step-by-step explanation:
Simple interest means that a percent of the initial amount will be paid back each year, this amount will not change from year to year. To calculate the simple interest over a given unit of time, multiply the amount by the interest rate in decimal form, then multiply that value by the time span that this was taken over. The result will be the amount earned.
The following formula can be used to describe this scenario,
[tex]simple\ interest=(time)((amount)(interest\ rate))[/tex]
Substitute,
[tex]=(3)((15000)(4))[/tex]
To convert a percent to decimal form, divide the percent by (100)
[tex]=(3)((15000)(0.04))[/tex]
[tex]=(3)(600)\\\\=1800[/tex]
Hurry and answer i need a real answer
Answer:
C
Step-by-step explanation:
Spinner B has 4/12ths of yellow and spinner a has 2/6ths. 2/6 is equivalent to 4/12ths
Answer:
C :>
Step-by-step explanation:
help please
........
9514 1404 393
Answer:
noyesStep-by-step explanation:
Put the values of x and y in the equation and see if it is true.
1. 2 = 2×0 . . . . False (not a solution)
2. 12 = 6×2 . . . True (is a solution)
1 plus 1 please help!!1!!!1
Answer:
1 plus 1 equals window........
Answer:
I think the answer is orange
Step-by-step explanation:
#Eleventeen
The sum of ten and the quotient of a number x and 6 please help !
Answer:
10 + x/6
Step-by-step explanation:
10 + x/6 represents this phrase
Find the center and the radius of the circle with the equation:
x^2 - 2x + y^2 + 4y + 1 = 0
Answer:
center: (1, -2)
radius: 2