Answer:
θ = 49.4584°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] cosθ = adjacent over hypotenuseInverse TrigStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = ?
Adjacent Leg = 13
Hypotenuse = 20
Step 2: Find Angle
Substitute in variables [cosine]: cosθ = 13/20Inverse Trig: θ = cos⁻¹(13/20)Evaluate: θ = 49.4584°A cylinder has a height of 11 feet and a radius of 7 feet. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
1682.46 cubic feet
Step-by-step explanation:
The formula for volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
---------------------------------------------------------------------------------------------------------------
3.14 × 49 × 11 = 1682.46
---------------------------------------------------------------------------------------------------------------
Have a good day :)
[tex]9.3x = 9 {^2} [/tex]
Answer:
If you are asking for what x is equal too, then x = 8.70968...
Hope that this helps!
Someone please help ASAP!
Help me please , x^4 - x^2 + 6 = 0
Answer:
x⁴-x²+6 = 0
= x²(x²-1)+6=0
Compare surfing in an incoming neap tide to surfing in an incoming spring tide.
Answer:
• Tides are the great rise and fall of sea water caused by the gravity of the moon and the sun.
Gió thổi trên mặt nước trong các đại dương chịu trách nhiệm cho dòng hải lưu. Tuy nhiên, dòng hải lưu trong đại dương không được hình thành bởi gió đơn thuần. Nước gần cực lạnh trong khi nước gần xích đạo ấm. Sự chênh lệch nhiệt độ giữa hai vùng nước này cũng chịu trách nhiệm cho sự hình thành dòng hải lưu. Địa hình đáy đại dương, mưa và thậm chí thủy triều cũng gây ra dòng chảy trong nước.
Step-by-step explanation:
Water freezes at 0 ° Celsius and 32° Fahrenheit. Water boils at 100° Celsius
and 212° Fahrenheit.
a. Write degrees Celsius as a linear function of degrees Fahrenheit (1 point).
b. What is the slope of your linear equation? What does it mean? (1 point)
c. What is the y-intercept and what does it mean? (1 point)
Answer:
See below.
Step-by-step explanation:
a.
We need degrees C as a function of degrees F.
Just like when we have y as a function of x, we have (x, y) ordered pairs, here we will have (F, C) ordered pairs.
We are given two ordered pairs: (32, 0) and (212, 100).
We can find the slope of the line.
m = (100 - 0)/(212 - 32) = 100/180 = 5/9
y = mx + b
C = mF + b
C = (5/9)F + b
Use point (32, 0) for F and C to solve for b.
0 = (5/9)(32) + b
b = -(5/9)(32)
C = (5/9)F - 5/9(32)
C = (5/9)F - 160/9
b.
The slope is 5/9. The slope is the rate of change of degrees F to degrees C. For each change of 9 degrees F, the corresponding change in degrees C is 5.
c.
The y-intercept is -160/9.
It means that a temperature of 0 degrees F equals -160/9 degrees C.
a coffee retailer has two grades of decaffeinated coffee beans, one wholesales at $4.00 a pound and the other for 6.50 a pound. she wishes to blend the beans to form a 150 pound mixture that sells wholesale for 4.75 a pound. how many pounds of each grade of bean should she use in the mixture?
Answer:
Step-by-step explanation:
To solve mixture problems like this the best way is to make a table. Here's the basic format of the table we will use, calling the first coffee C1 and the second coffee C2:
#lbs x $/lb = Total
C1
C2
Mix
This is the table we will fill in. First, we were given the cost per pound of each type of coffee, so we put that in first:
#lbs x $/lb = Total
C1 4
C2 6.50
Mix
Next, we are told that she wants to make a mix of these coffees so she has a total number of pounds as 150 and that she wants it to cost $4.75 per pound. That goes in next:
#lbs x $/lb = Total
C1 4
C2 6.50
Mix 150 * 4.75
That asterisk is the multiplication sign.
Here's where we are now responsible for filling out the rest of the chart. If she needs to mix these 2 coffees to get a mix that is `150 pounds, she can have x pounds of C1 which means that she has to have 150 - x of C2:
#lbs x $/lb = Total
C1 x * 4
C2 150 - x * 6.50
Mix 150 * 4.75
Now all we have left to do is what the table tells us to do, which is to multiply the first 2 columns and put that product under the Total column:
#lbs x $/lb = Total
C1 x * 4 = 4x
C2 150 - x * 6.50 = 975 - 6.50x
Mix 150 * 4.75 = 712.50
Since we have to add the 2 coffees together to get the pounds of mix in the first column, we also have to add the cost of those coffees together to get the total cost of the mix. The equation looks like this:
4x + 975 - 6.50x = 712.50 and combining like terms:
-2.5x = -262.5 so
x = 105
That means that there is 105 pounds of coffee 1 and 150 - 105 pounds of coffee 2.
C1 = 105 pounds, C2 = 45 pounds
Evaluate the function f(x)=x^2-5x+ 5 at the given values of the independent variable and simplify
a. f(9)
b. f(x+7)
c. f(-x)
a. f(9) =
(Simplify your answer.)
b. f(x + 7) =
(Simplify your answer.)
c. f(-x) =
(Simplify your answer.)
Step-by-step explanation:
The given function is :
[tex]f(x)=x^2-5x+ 5[/tex]
(a) To find f(9), put x = 9 in the above expression.
[tex]f(9)=9^2-5(9)+ 5=41[/tex]
(b) To find f(x+7), put x = x+7 in the above expression.
[tex]f(x+7)=(x+7)^2-5(x+7)+ 5\\\\=x^2+14x+49-5x-35+5\\\\=x^2+9x+19[/tex]
(c) To find f(-x), put x = -x in the above expression.
[tex]f(-x)=(-x)^2-5(-x)+ 5\\\\=x^2+5x+5[/tex]
Hence, this is the required solution.
Doug can download new songs for $1.19 each Write an equation to show how many songs he can download fir $12.00
Answer:
10.
Step-by-step explanation:
[tex]1.19X10=11.90.[/tex]
You will get 10 songs and have 10 cents left.
PLEASE HELP MEEEEEEEEEEEEE
Jeb and Lori went to a florist to buy flowers. Jeb bought 6 roses and 3 carnations for $20.25. Lori bought 8 roses and 3 carnations for $25.75. Find the price of one rose and the price of one carnation.
Answer:
first create an equation for Jeb flower then for Lori
then solve them by simultaneous linear equations
Answer:
One rose = $2.75
One carnations = $1.25
Step-by-step explanation:
Lets make the rose = x
and carnations = y
Jeb >> 6x + 3y = 20.25
Lori >> 8x + 3y = 25.75
Solve simultaneously using elimination method.
8x + 3y = 25.75
- 6x + 3y = 20.25
_______________
2x =5.5
2x/2 = 5.5/2
x = 2.75
plug 2.75(x) into any of the two equations to find y.
6(2.75) + 3y = 20.25
16.5 + 3y = 20.25
3y = 20.25 - 16.5
3y = 3.75
3y/3 = 3.75/3
y = 1.25
The cost of a phone is reduced by 20%. The new cost is $70.40. What was the original price?
Answer:
.8x = $70.40
x = 70.4/.8
x = $88
Step-by-step explanation:
Kind of confused on this question, please help
Answer:
4th option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{5}[/tex] x - 6 ← is in slope- intercept form
with slope m = [tex]\frac{3}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{5} }[/tex] = - [tex]\frac{5}{3}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - [tex]\frac{5}{3}[/tex] and (a, b ) = (- 2, 5 ) , then
y - 5 = - [tex]\frac{5}{3}[/tex] (x - (- 2) ) , that is
y - 5 = - [tex]\frac{5}{3}[/tex] (x + 2)
Sharma draws a floor plan of the local supermarket on a coordinate plane.
Part A Which is the location of the dairy?
A : 0, 1)
B : (1, 0)
C : (1, 1)
D : (1, 2)
Part B : What are the coordinators of the bakery in the boxes .
Part C : Bakery , Frozen foods , Dairy , produce ?
Answer:
The answer woupd be B, 1, 0
The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0) thus option (B) will be correct.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
As per the given floor plan,
Th coordinate of dairy is the horizontal and vertical distinctions from the reference axes(0,0).
Since it is 1 unit apart in the x and 0 apart in the y direction.
Thus (1,0) is the right coordinate.
Hence "The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0)".
For more about coordinates,
brainly.com/question/7869125
#SPJ2
The product of two consecutive even integers is 36 less than 18 times their sum. Find the two integers
Answers:
There are two possible outcomes
The integers are 0 and 2The integers are 34 and 36If your teacher wants only positive integers, then go for the second scenario.
=========================================================
Explanation:
x = smaller integer
x+2 = larger integer
We can see that x+2 follows directly after x, so they are consecutive. Also, there's a gap of 2 units between the values. This is due to the phrasing "consecutive even" instead of just "consecutive".
Their product is x(x+2) = x^2+2x
Their sum is x+(x+2) = 2x+2
The product is 36 less than 18 times their sum, which means,
product = 18*(sum) - 36
x^2+2x = 18(2x+2) - 36
x^2+2x = 36x+36-36
x^2+2x = 36x
x^2+2x-36x = 0
x^2-34x = 0
x(x-34) = 0
x = 0 or x-34 = 0
x = 0 or x = 34
-------------------------------------------
If x = 0, then x+2 = 0+2 = 2
The product is x*(x+2) = 0*2 = 0
The sum is x+(x+2) = 0+2 = 2
If we multiply the sum by 18, then we get 18*2 = 36. Subtracting off 36 leads to 36-36 = 0
Therefore the equation below
product = 18*(sum) - 36
has been satisfied
-----------------------------------------
If x = 34, then x+2 = 34+2 = 36
product = x*(x+2) = 34*36 = 1224
sum = x+(x+2) = 34+36 = 70
then we can see that...
product = 18*(sum) - 36
1224 = 18*(70) - 36
1224 = 1260 - 36
1224 = 1224
So that works as well.
----------------------------------------
There are two possible outcomes
Either the integers are 0 and 2
OR
the integers are 34 and 36
Samples of viewers were taken from two different movies to compare the ages of those
watching the movie. Fifty participants were asked their ages as they exited each movie. The
results are shown on the double box plot below. Which statistical measure was equal for the
two samples?
Movie
Answer:
The median are equal
Step-by-step explanation:
Given
I will answer this question with the attached plot (see attachment 2)
Required
The equal statistical measures
See attachment 1 on how to read a box plot
Using attachment 1 as a guide, we have the following observation
Movie 2 Movie 1
[tex]Minimum=7.5[/tex] [tex]Minimum=10[/tex]
[tex]Q_1 = 22.5[/tex] [tex]Q_1 = 15[/tex]
[tex]Median = 30[/tex]
[tex]Q_3 = 35[/tex] [tex]Q_3 = 40[/tex]
[tex]Maximum = 47.5[/tex] [tex]Maximum = 52.5[/tex]
By comparison, they have equal median (30)
Leon graphed y = 10 -0.05x to represent the number of gallons of gas left in
his car after driving x miles.
gallons
10
miles
200
What is a reasonable range for this situation?
O A. All real numbers
B. y20
O c. Osys 200
O D.Osys 10
Answer:
0≤y10
Step-by-step explanation:
Given the expresssion;
y = 10 - 0.05x
To get the range, we will first substitute for the value of y by substituting the value x =0
y = 10 - 0.05(0)
y = 10
Hence the required range of values falls between 0 and 10;
0≤y10
f(x) = |x| transforms into function g by a horizontal reflection, shifts left 3 times and 1 time down. What is
g(x)?
Answer:
[tex]g(x) = -|x+3|-1[/tex]
Step-by-step explanation:
1. horizontal reflection - reflection on x-axis: [tex]g(x) = - f(x)[/tex]
[tex]g(x) = -|x|[/tex]
2. shift left 3: [tex]g(x) = f(x+h)[/tex]
[tex]g(x) = -|x+3|[/tex]
3. shift down 1: [tex]g(x) = f(x) - k[/tex]
[tex]g(x) = -|x+3|-1[/tex]
Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,−2) and (7,2)
please help me
I WILL MARK BRAINLIEST!!!!
A, B C or D?
Box-and-whisker plot
Answer:
B.Q1, Q3, maximum
Step-by-step explanation:
The left side of the box is hovering over 65
The left side of the box represents quartile 1
The right side of the box is hovering over 85
The right side of the box represents quartile 3
The whisker at the end of the right side is hovering over 100
The whisker at the very end of the right represents the maximum
Hence, we can conclude that the answer is Q1 Q3 maximum
Graph the line with the equation y= -1/3x - 2
Answer:
I hoped this helped!
Step-by-step explanation:
Answer:
See attached image.
Step-by-step explanation:
You can either use a graphing calculator or make a table to find values for yourself.
X | 0 | 3
Y | -2 | -3
and so forth.
If a six-sided die(1-6) and a ten-sided die(1-10) are rolled simultaneously, then what is the probability of rolling both with a number greater than four
Answer:
[tex]Pr = 0.20[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 10[/tex] ---- 10 sided
[tex]n_2 = 6[/tex] --- 6 sided
Required
[tex]P(x_1,x_2 > 4)[/tex]
First, list out the sample space
[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]
[tex](7, 1) (7, 2) (7, 3) (7, 4) (7, 5) (7, 6) (8, 1) (8, 2) (8, 3) (8, 4) (8, 5) (8, 6)[/tex]
[tex](9, 1) (9, 2) (9, 3) (9, 4) (9, 5) (9, 6) (10, 1) (10, 2) (10, 3) (10, 4) (10, 5) (10, 6)\}[/tex]
[tex]n(S) = 60[/tex] --- total outcomes
The event that the outcome of both is greater than 4 is:
[tex]x_1,x_2> 4 = \{(5, 5) (5, 6)(6, 5) (6, 6)(7, 5) (7, 6) (8, 5) (8, 6)(9, 5) (9, 6) (10, 5) (10, 6)\}[/tex]
[tex]n(x_1,x_2>4) = 12[/tex]
So, the probability is:
[tex]Pr = \frac{n(x_1,x_2>4)}{n(S)}[/tex]
[tex]Pr = \frac{12}{60}[/tex]
[tex]Pr = 0.20[/tex]
what is the slope of the line i will make you brainlest!
Answer:
1x
Step-by-step explanation:
the slope goes up one a positive slope of 1
The isosceles triangle has a perimeter of 7.5 m.
Answer:
The isosceles triangle has a perimeter of 7.5 m. 2.1 + 2x = 7.5 can be used to find the value of x if the shortest side, y, measures 2.1 m. This answer has been confirmed as correct and helpful
Step-by-step explanation:
Answer:
So.... u forgot to put the question.
Step-by-step explanation:
im not sure what u want but heres this : The isosceles triangle has a perimeter of 7.5 m. if the shortest side, y measures 2.1 m
Hey all! Pls help
They are easy questions, pls show the working
Answer:
7. x = 6
8. x = 15/4
9. x = -7
Answer:
Hello there user, looks like your looking for help!
The correct answers should be:
7. x = 6
8. x = 3 3/4
9. x = -7
Step-by-step explanation:
3/2 = x/4
6/4 = x/4
x = 6
x/3 = 1 1/4
4x/12 = 15/12
x = 15/4
x = 3 3/4
(x + 1)/3 = (x-1)/4
(4x + 4)/12 = (3x-3)/12
x/12 = -7/12
x = -7
Solve for x.
Use the completing the square method.
x2 + 10x = 6
x2+10x=6
x2+10x-6=0
x=-10+-Square root of [10^2-4×(-6)]/2.1
x=-10+-Square root of 124/2
x=-5+square root of 31 and -5-square root of 31
A farmer has a rectangular garden plot surrounded by 200 ft of fence. Find the length and width of the garden if its area is 2475 ft2.
Answer:
[tex]l =45[/tex] --- length
[tex]w = 55[/tex] --- width
Step-by-step explanation:
Given
[tex]P = 200[/tex] --- perimeter
[tex]A = 2475[/tex] --- area
Required
The dimension of the farm
Let
[tex]l \to length; w \to width[/tex]
So:
[tex]p = 2(l+w)[/tex] --- perimeter
[tex]2(l+w)=200[/tex]
Divide by 2
[tex]l+w=100[/tex]
Make l the subject
[tex]l = 100 - w[/tex]
Also:
[tex]A= l*w[/tex] --- area
[tex]l * w = 2475[/tex]
Substitute: [tex]l = 100 - w[/tex]
[tex](100 - w) * w = 2475[/tex]
Open bracket
[tex]100w - w^2 = 2475[/tex]
Rewrite as:
[tex]w^2 - 100w +2475 = 0[/tex]
[tex]w^2 - 45w - 55w +2475 = 0[/tex]
Factorize
[tex]w(w - 45) - 55(w -45) = 0[/tex]
Factor out w - 45
[tex](w - 55)(w -45) = 0[/tex]
Take any one of the expression and solve for w
[tex]w -55 = 0[/tex]
[tex]w = 55[/tex]
Recall that: [tex]l = 100 - w[/tex]
[tex]l =100 - 55[/tex]
[tex]l =45[/tex]
Brian sent 9 more messages than salma and Chang sent 2 times more than Brian and they have 55 messages total how many messages do they have each
Answer:
Number of messages Salma sent = 7
Number of messages Brian sent = 16
Number of messages Chang sent = 32
Step-by-step explanation:
Let
Number of messages Salma sent = n
Number of messages Brian sent = n + 9
Number of messages Chang sent = 2(n + 9)
Total messages sent = 55
n + (n + 9) + 2(n + 9) = 55
n + n + 9 + 2n + 18 = 55
4n + 27 = 55
4n = 55 - 27
4n = 28
n = 28/4
n = 7
Number of messages Salma sent = n = 7 messages
Number of messages Brian sent = n + 9 = n + 9 = 16 messages
Number of messages Chang sent = 2(n + 9)
= 2(7 + 9)
= 2(16)
= 32 messages

HELP PLEASE I WILL MARK BRAINLIEST
Answer:
C
Step-by-step explanation:
hhhhhhhhheeeeeeeelllllllpppppp
Somebody please help meee!!!!
Answer:
[tex]area = 4\pi {r}^{2} \\ = 4 \times 3.14 \times {7.5}^{2} \\ = 706.86 \: {cm}^{2} [/tex]