Which trigonometric function(s) have a value of sqrt 3 / 2 ?
a sin pi/3
b sin 5pi / 6
c cos 5pi / 3
d cons pi / 6
Answer:
sin (π/3)= √3/2
cos (π/6) =√3/2
Chloe is putting up a wallpaper border in her room. She has drawn a sketch on a coordinate grid. The diagram is
shown below.
How many feet of border should Chloe buy?
A) 38 feet
B) 42 feet
C) 80 feet
D) 88 feet
Given:
The figure of a wallpaper border.
To find:
The total required border.
Solution:
The given figure has 8 vertices and 8 edges (sides).
From the given figure it is clear that the length ( in feet) of 8 edges of the figure are 12, 2, 2, 2, 2, 3, 12, 7.
We need to find the total required border. So, we have to find the perimeter of the figure.
Add the lengths of all edges to get the perimeter of the given figure.
[tex]Perimeter=12+2+2+2+2+3+12+7[/tex]
[tex]Perimeter=42[/tex]
So, Chloe should buy 42 feet of border.
Therefore, the correct option is B.
Children and adults purchased tickets for a local amusement park.all tickets were sold at the park entrance-season passes,discount,atc.we’re not allowed.A child’s tickets cost $8 while an adult ticket cost $15.A total of 5,500 was collected.600 tickets were sold.how many of each type of ticket were sold?
Answer:
x = number of children tickets sold = 500
y = number of adult tickets sold = 100
Step-by-step explanation:
Let
x = number of children tickets sold
y = number of adult tickets sold
x + y = 600 (1)
8x + 15y = 5,500 (2)
From (2)
x = 600 - y
Substitute x = 600 - y into (2)
8x + 15y = 5,500 (2)
8(600 - y) + 15y = 5,500
4,800 - 8y + 15y = 5,500
- 8y + 15y = 5,500 - 4,800
7y = 700
y = 700/7
y = 100
Substitute y = 100 into (1)
x + y = 600 (1)
x + 100 = 600
x = 600 - 100
x = 500
x = number of children tickets sold = 500
y = number of adult tickets sold = 100
Svp aidez moi )
Un père a 42 Ans et sa fille 12 Ans
On veut trouver la réponse à cette question : dans combien d’années l’âge du père sera t-il le triple de celui de sa fille ?
Answer:
Dans 3 ans l’âge du père sera le triple de celui de sa fille
Step-by-step explanation:
X= années qui doivent passer
3(12+X ) = 42 +X
36+ 3X = 42 +X
2X = 6
X = 3
La fille 15 ans
Le père 45 ans (15x3=45)
What is the area of the hexagon?
Answer:
[tex]Split \ the \ hexagon \ into \ 2 \ trapezoid .\\\\Area \ of \ trapezoid = \frac{a + b}{2} \times h \\\\a = 5 \ , \ b = 9.28, h = 4\\\\Area \ of \ 1\ trapezoid = \frac{5 + 9.28}{2} \times4 = 28.56cm^2\\\\Total \ area = 2 \times 28.56 = 57.12cm^2[/tex]
Answer:
[tex]Area:-[/tex]
[tex](1/x\times~5\times~4)x2[/tex]
[tex]+4x(1/2\times4.64\times4^2)[/tex]
[tex]=20+37.12[/tex]
[tex]=57.12~cm^2[/tex]
------------------------
hope it helps..
have a great day!!
Find the volume of the frustrum of the right circular cone generated by rotating the line y = 3x+1 about the x-axis between x = 0 and x = 2.
Answer:
38π cubic units
Step-by-step explanation:
The volume V = ∫₀²πy²dx
Since y = 3x + 1, dy = 3dx ⇒ dx = dy/3
So, when x = 0, y = 3(0) + 1 = 0 + 1 = 1
when x = 2, y = 3(2) + 1 = 6 + 1 = 7
So, changing the variable to y and the limits of integration from y = 1 to y = 7, we have
V = ∫₀²πy²dx
V = π∫₁⁷y²dy/3
V = π[y³/3]₁⁷/3
V = π[y³]₁⁷/9
V = [7³ - 1³]π/9
V = [343 - 1]π/9
V = 342π/9
V = 38π cubic units
NEED ASAP
The arithmetic mean of the monthly salaries of two people is $4444. One person earns $3191 per month. What is the monthly salary of the other person?
Step-by-step explanation:
Write what you know
mean is: Sum of all data points / Number of data points
any unknown number we'll call x
so youd write
(x + $3191) / 2 = $4444
Solve for x
let me know if you need further help
The school is adding one light to its baseball stadium. The light will cover the baseball field and 25° on both sides of the field as shown in the drawing.
Please help I need to finish it due 3:30
=======================================================
Explanation:
Let x be the angle measure of that dark area. That angle x must add to the other angles 25, 90, and 25 to get a full 360 degree rotation.
So,
x+25+90+25 = 360
x+140 = 360
x = 360-140
x = 220
The dark area angle is 220 degrees
This is known as a reflex angle due to it being larger than 180 degrees, but it's less than 360 degrees. In symbolic terms, any reflex angle is one such that 180 < x < 360.
Please Help ASAP!!! Last question!
Initially, the ratio of Alex's toy cars to Pete's toy cars was 7:3. After Alex gave 20 toy cars to Pete, they each had an equal number of cars. how many toy cars did they have altogether?
Answer:
100 cars
Step-by-step explanation:
Alex: Pete
7: 3
Multiply by x to get the number of cars
Alex has 7x cars
Pete has 3x cars
Now Alex gives pete 20
Alex has 7x-20
Pete has 3x+20
They have the same number of cars so set the expressions equal
7x-20 = 3x+20
Subtract 3x from each side
7x-20-3x = 3x+20-3x
4x-20 = 20
Add 20 to each side
4x-20+20 = 20+20
4x= 40
Divide by 4
4x/4 = 40/4
x = 10
Alex had 7x = 7*10 = 70 to start
Pete had 3x = 3*10 = 30 to start
Together 70+30 = 100 cars
Answer:
100 cars
Step-by-step explanation:
Alex: Pete
7: 3
Multiply by x to get the number of cars
Alex has 7x cars
Pete has 3x cars
Now Alex gives pete 20
Alex has 7x-20
Pete has 3x+20
They have the same number of cars so set the expressions equal
7x-20 = 3x+20
Subtract 3x from each side
7x-20-3x = 3x+20-3x
4x-20 = 20
Add 20 to each side
4x-20+20 = 20+20
4x= 40
Divide by 4
4x/4 = 40/4
x = 10
Alex had 7x = 7*10 = 70 to start
Pete had 3x = 3*10 = 30 to start
Together 70+30 = 100 cars
I am in need of help :) please and thank you :):
Answer:
2nd Option:[tex] 6 {x}^{2} + 43x + 55[/tex]Step-by-step explanation:
Given,
Dimensions of the rectangular garden = 2x+11, 3x + 5
Therefore ,
Area of the rectangular garden
= (2x+11) × (3x + 5)
= 3x(2x + 11) + 5(2x + 11)
[tex] = {6x}^{2} + 33x + 10x + 55[/tex]
[tex] = 6 {x}^{2} + 43x + 55(ans)[/tex]
Nina operate the dog walking service she charges a flat fee for $15 plus $5 per hour. which equation represents this liner relationship.
y= 15x - 5
y= 15x + 5
y= 5x - 15
y= 5x + 15
Answer: I think it’s the first one
Step-by-step explanation:
It says per hour and 15 bucks plus 5 bucks PERhour so you would have to be multiplying I did a question like this long ago hope you get it right
The equation represents this linear relationship for total cost is y= 5x + 15 thus option (D) is correct.
What is a linear function?A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
She charges a flat fee of $15 plus $5 per hour.
For x number of hours, the total cost will be as,
y = 15 + 5x
Hence "y= 5x + 15 is the equation that depicts this linear relationship for total cost".
For more about the linear function,
brainly.com/question/21107621
#SPJ2
write answer in equation y=mx+b
Answer:
y = 50x + 150
Step-by-step explanation:
The y-intercept is 150. b = 150
The slope is found using two points such as (2014, 450) and (2010, 250)
m = (450 - 250)/(2014 - 2010) = 200/4 = 50
y = mx + b
y = 50x + 150
(trigonometry) solve for x
Step-by-step explanation:
since given triangle is right angle,
Taking angle X as reference angle.
Tan x =p/b
Tan x=37/8
Tan x=4.625
X=tan^-1(4.625)
X=77.79
X=78°
A box contains 60 identical marbles where x of them are red while the rest are yellow. If a marble is drawn and the probability that it is white is 1/12, find the value of x.
b: How many white marbles must be added to the box so that the probability of choosing a white marble is 5/16?
Please answer I will make brianliest!!
Answer:
a. x is 55
b. 20 white marbles
Step-by-step explanation:
Question: A box contains 60 identical marbles where 'x' of them are red while the rest are white; (given that in the original question, the box only contains red and yellow marbles, the yellow can be replaced by white to explain the question idea)
a. The number of identical marbles in the box, n = 60
The number of red marbles = x
The number of white marbles = The rest of the marbles which are not red
The probability that a marble drawn is white, P(y) = 1/12
Let 'y' represent the number of white marbles
From probability theory, we have;
The number of white marbles, y = n × P(y) = 60 × 1/12 = 5
The number of red marbles, x = n - y = 60 - 5 = 55
x = 55
b. The number of white marbles that must be added to make the probability of choosing a white marble = 5/16 is given as follows;
Let Δy represent the number of white marbles added, therefore;
P(y) = (y + Δy)/(y + Δy + x)
∴ P(y) = (5 + Δy)/(5 + Δy + 55) = 5/16
5 × (60 + Δy) = 16 × (5 + Δy)
300 + 5·Δy = 80 + 16·Δy
16·Δy - 5·Δy = 300 - 80
11·Δy = 220
Δy = 220/11 = 20
The number of white marbles that must be added, Δy = 20 white marbles
4. Janet wants to spend no more than $45 her friend's birthday gift. She already bought her a
$15 bracelet. Write an inequality to show how much can she still spend on her friend?
Answer:
Step-by-step explanation:
45=15+x
45-15=x
30=x
its me arg i need help
Answer:
x=8
Step-by-step explanation:
so since the whole thing should equal 180, and the right triangle is 90,
(3x+11)+(5x+15)=90 then solve for that
8x+26=90
8x=64
divide both sides by 8
so x=8
then plug in 8 for the xs so c is 3(8)+11 --> 24+11 so m<C=35*
m<D=90*
5(8)+15 40+15 so m<E=55
AJ needs $800. So far, he has saved $290. If his job pays him $12 per hour, write and solve an inequality that can be used to determine the minimum number of hours that he needs to work in order to have enough money for the computer.
Answer:
The minimum number of hours is 43.
Step-by-step explanation:
Total money required = $ 800
Saved money = $ 290
Per hour income = $ 12
Let the number of hours be n.
According to the question
[tex]290 + 12n \geqslant 800\\\\12 n \geqslant 510\\\\n\geqslant 42.5[/tex]
So, the minimum number of hours is 43.
Answer:
800 - 290 = 510. 510 = 12h
Step-by-step explanation:
$800 is the amount he is trying to save.
$290 is the amount he has so far.
$800 - $290 = $510.
$510 is the amount more he needs to earn.
12h.
12 represents the amount he is paid every 1 hour
H represents the hours he works.
Mrs. Rios put a wallpaper border around the room shown below. She used 70 feet of wallpaper border. What is the unknown side length?
Answer: 16 feet
Step-by-step explanation:
Looking at the shape, one can notice that the unknown side can be found by adding the sides that are circled because they will give the same distance.
The length of the unknown side is therefore:
= 8 + 8
= 16 feet
HELP ASAP
Find x to the nearest hundredth.
Answer:
x = 10.28
Step-by-step explanation:
sin = opp/hyp
sin 40 = x / 16
multiply both sides by 16
16 * sin40 = x
x = 10.284601754984629
Rounded
x = 10.28
Which ordered pair is a solution of the equation?
-x- 4y = -10
Answer:
There are many ordered pairs that are solutions to the equation but here are the few; (0,2.5), (2,2), (4,1.5), (-2,3), (-4,3.5), (-6,4), (6,1), (8,0.5), etc...
Step-by-step explanation:
I used a graphing calculator
hope this is helpful
If the truck has a mass of 3,000 kilograms, and a velocity of 45 m/s, what is its momentum? show working
Answer: p = 70,000 kg m/s
Step-by-step explanation:
14. Jerry charges a fee of $45 plus $15 per hour to rent a motorbike. Write an equation to
calculate rental cost and tell what x and y mean. If you have $120 to spend, how long can you rent
for?
Answer:
5 hours, y= how much money it will cost, and x represents how many hours
Step-by-step explanation:
y= 15x+45
120= 15x+45
-45 -45
75= 15x
75/15×= 5 hours
i have 1 hour to do this. please help me :). 20pts!!!
is 4.083 rational number
Plz I really need help with this
Answer:
25
Step-by-step explanation:
HELP ASAP, really really need help for these
Answer:
9 plus 11 plus 12 =
Step-by-step explanation:
x is 22
On the Unit Circle:
If cos x < 0 which Quadrant(s) is the angle?
1. I &IV
2. II & III
3. I &II
4. III & IV
Answer:
Quadrant I and quadrant IV
Step-by-step explanation:
Given that cos x< 0
x < arccos 0
x < 90degres
Since cos s positive in the first and 4th quadrant, hence the angle lies in the Quadrant I and quadrant IV
Chloe and Ainsley start an art club. The first week they are the only 2 people in the club. They invite more friends to join. Each week the
number of people in the club doubles.
How many people are in the club on the third week?
Answer:
8.
Step-by-step explanation:
first week: 2
second week: 2×2=4
third week: 4×2=8
hence, 8 members joined the club on the third week.
whats the answer to 876 + 17.2638
893.2638
is this what you mean?
Which choice is equivalent to the expression below when y2 0?
√y^2 + √16y^3 – 4y√y
Answer:
Option C.
Step-by-step explanation:
We start with the expression:
[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}[/tex]
where y > 0. (this allow us to have y inside a square root, so we don't mess with complex numbers)
We want to find the equivalent expression to this one.
Here, we can do the next two simplifications:
[tex]\sqrt{16*y^3} = \sqrt{16} \sqrt{y^3} = 4*\sqrt{y^3}[/tex]
And:
[tex]y*\sqrt{y} = \sqrt{y^2} *\sqrt{y} = \sqrt{y^2*y} = \sqrt{y^3}[/tex]
If we apply these two to our initial expression, we can rewrite it as:
[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y}[/tex]
[tex]\sqrt{y^3} + 4*\sqrt{y^3} - 4\sqrt{y^3} = \sqrt{y^3}[/tex]
Here we can use the second simplification again, to rewrite:
[tex]\sqrt{y^3} = y*\sqrt{y}[/tex]
So, concluding, we have:
[tex]\sqrt{y^3} + \sqrt{16*y^3} - 4*y\sqrt{y} = y*\sqrt{y}[/tex]
Then the correct option is C.
Answer:
C:YsqrtY
Step-by-step explanation:
A P E X:L E A R N I N G