Answer:
Step-by-step explanation:
LHS = tanθ/secθ - 1 + tanθ/secθ + 1
Cross multiplication,
tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ
= tanθ(1 - secθ - 1 - secθ)/-tan^2θ
= -2secθ/-tanθ
= 2 x 1/cosθ / sinθ/cosθ
= 2cosecθ = RHS
Hence proved.
A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water. Let s equal the families paddling speed and c represent the current
a.
s + c = 2.75
s - c = 1.5
2.125 mi/h
c.
s + c = 2.75
c - s = 1.5
.60 mi/h
b.
2.75s = c
1.5s = c
1.725 mi/h
d.
2.75c = s
1.5c = s
30 mi/h
On solving the provided question, we can say that In still water, a family must paddle at a speed of 2.125 miles per hour.
What is speed?Speed is the amount of distance traveled by an object in one unit of time when it is in motion.
Given that, a family is paddling a boat (with the current). Their average speed in relation to the riverbanks is 2.75 miles per hour. On the way back, they paddle upstream (against the current), moving toward the riverbank at an average speed of 1.5 miles per hour.
Here, Let the family's speed on still water be x and the current's speed be y. Upstream speed is calculated using the formula 1.5 = x - y - - - - (1)
2.75 downstream speed = x + y - - - - (1)
Equations 1 and 2 are solved as follows: 2x = 4.25 and x = 2.125 miles per hour In still water, a family must paddle at a speed of 2.125 miles per hour.
To know more about speed visit:
https://brainly.com/question/7359669
#SPJ1
tinkerbell is gathering data on the number of girls and boys that go on a particular ride at disneyland one morning she observes that 300 girls go on the ride and 500 boys go on the ride this represents the ratio of girls and boys that go on the ride complete the table below to show this relationship explain or show how you completed the table
Girls Boys Total
blank blank 8
6 blank blank
blank 20 blank
30 blank blank
300 500 800
blank 800 blank
The complete table is given in the solution.
What is ratio?A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.
Given that, at Disneyland there are 300 girls go on the ride and 500 boys go on the ride this represents the ratio of girls and boys that go on the ride
The ratio of girls to boys = 3:5
Therefore, The complete table is as follows:-
Girls Boys Total
3 5 8
6 10 16
12 20 32
30 50 80
300 500 800
480 800 1280
Hence, the complete table is above
For more references on ratios, click;
https://brainly.com/question/13419413
#SPJ1
Which of the following shows the prime factorization of using exponential notation?
Which of the following shows the prime factorization of using exponential notation?
Which of the following shows the prime factorization of using exponential notation?
Which of the following shows the prime factorization of using exponential notation?
Which of the following shows the prime factorization of using exponential notation?
how do i simplify 12 /16 to the lowest terms and find equivalent fraction that has a denominator of 32
The prime factorization of 72 using exponential notation is 2³ x 3².
What is Prime Factorization?Prime factorization is a process of writing all numbers as a product of primes.
Given:
Prime factorization is representing a number in form of products of its primes.
Consider the given number 72
72 = 2 x 2 x 2 x 3 x 3
So, 72 can be written as 2 × 2 x 2 × 3 × 3.
Thus, exponential notation it can be written as 2³ x 3².
Also, Simplifying 12 /16 as
= 12/16
= 3/4
and, the equivalent fraction whose denominator is 32.
Then, 3/4 = x/32
4x = 96
x = 24
Learn more about Prime Factorization here:
https://brainly.com/question/29775157
#SPJ1
Answer the problem in the photo below! Please answer simply:)
Answer:
32
Step-by-step explanation:
Let's start with x to the third power. x=4 So that would be 4 to the third power. that would be 4x4=16. 16x4=64. So that would be 1/2*64. That equals 32
Find the area of the shapes
Answer:
45.5km
Step-by-step explanation:
AREA= base x height
So with this equation, we know that 5km is the height, and 9.1km is the base.
So to find out the area all we have to do is 9.1x5 which equals 45.5
A community theater performed a play each Saturday evening for 10 consecutive
weeks. The graph shows the attendance for the performances in weeks 1, 4, 6, and 10.
Describe the rates of change in attendance with respect to time.
Weeks 1-4:
Weeks 4-6:
Weeks 6-10:
300
250
200
150
100
50
y
Attendance
Play Attendance
(4, 230)-
(1,131)
(6,208)
(10,60)
Week of performance
0
0 1 2 3 4 5 6 7 8 9101112
The rates of change in attendance in week 1-4 is 33, week 4-6 is -11, week 6-10 is -37 people per week
What is rate of change of attendance?The rate of change in attendance with respect to time is calculated by taking the difference in attendance between two weeks and dividing by the number of weeks between those weeks. This is done to find the average rate of change in attendance per week. The formula used is:
[tex]Rate =\frac{Attendance at week 2 - Attendance at week 1}{week 2 - week 1}[/tex]
Weeks 1-4:
The rate of change in attendance with respect to time is 33 people per week. This can be calculated by taking the difference in attendance between weeks 1 and 4 (230-131) and dividing by the number of weeks between those weeks (4-1 = 3).
[tex]rate =\frac{230-131}{4-1}\\[/tex]
hence rate is 33 people per week
Weeks 4-6:
The difference in attendance between weeks 4 and 6 (230 - 208)
The number of weeks between those weeks (6-4 = 2).
[tex]rate =\frac{208-230}{6-4}[/tex]
Hence rate is -11 people per week
Weeks 6-10:
The difference in attendance between weeks 6 and 10 (60-208)
The number of weeks between those weeks (10-6 = 4).
[tex]rate=\frac{60-208}{10-6}[/tex]
Hence rate is -37 people per week
To know more about rate of change, check out:
https://brainly.com/question/12752108
#SPJ1
Factor the expression using the GCF.
50+65h=
Greatest common factor (GCF) of 50 and 65 is 5.
How to find the GCF of 50 and 65?We will first find the prime factorization of 50 and 65. After we will calculate the factors of 50 and 65 and find the biggest common factor number .
Step-1: Prime Factorization of 50
Prime factors of 50 are 2, 5. Prime factorization of 50 in exponential form is:
50 = 21 × 52
Step-2: Prime Factorization of 65
Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:
65 = 51 × 131
Step-3: Factors of 50
1, 2, 5, 10, 25
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 50 and 65. The biggest common factor number is the GCF number.
So the greatest common factor 50 and 65 is 5.
To learn more about GCF refers to;
brainly.com/question/18937608
#SPJ1
The perimeter of a rectangle is 64 feet. The length is two more than double the
width. Find the dimensions of the rectangle.
(Remember Perimeter of rectangle = 2L+ 2w)
Answer:
To solve this problem, we can set up the following equation:
2L + 2W = 64
We are told that the length of the rectangle is two more than double the width, so we can write the following equation:
L = 2W + 2
Substituting this equation into the first equation, we get:
2(2W + 2) + 2W = 64
Simplifying this equation, we get:
6W + 4 = 64
Subtracting 4 from both sides, we get:
6W = 60
Dividing both sides by 6, we get:
W = 10
The width of the rectangle is 10 feet.
To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:
L = 2(10) + 2
= 20 + 2
= 22
The length of the rectangle is 22 feet.
Therefore, the dimensions of the rectangle are 10 feet by 22 feet.
Step-by-step explanation:
if the parent function is y=3×,which is the dunction of the graph?
On solving the provided question, we can say that - the linear equations, is [tex]x =10 / 5 = 2 = > x=2[/tex]
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
Here,
to solve the system of equations given. .
[tex]2x + y = 4 \\+\\3x - y = 6\\= > 5x =10[/tex]
system of equations 2x + y = 4 ,
6=3x-y is 5x =10
The value of x :
[tex]x =10 / 5 = 2\\ x=2[/tex]
To know more about linear equation visit:
https://brainly.com/question/11897796
#SPJ1
Show 24÷1/4 step by step
Answer:
96
Step-by-step explanation:
24 divided by 1/4 is 96
you turn 24 into a fraction by putting a one under is and then you keep it change it flip it
24/1 Divided by 1/4
24/1 times 4/1
24 times 4= 96
1 times 1= 1
96/1=96
evaluate 7 to the 3rd power x 7 to the 3rd power
Answer:117649
Step-by-step explanation:
Person A baked 4 1/2 Dozens of cookies for a bake sale.
Person B Baked 1 1/2 as many as Person A
Person C Baked 2 1/3 as many as Person B
How many cookies did each person bake? How many did they bake altogether?
Please also tell me how you got the answer, thanks.
This question is related to Fractions.
The cookies that each person bake will be:
A = 4 1/2 dozen cookies
B = 6 3/4 dozen cookies
C = 15 3/4 dozen cookies.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
Person A baked 4 1/2 Dozens of cookies for a bake sale. Person B Baked 1 1/2 as many as Person A. This will be:
= 1 1/2 × 4 1/2
= 6 3/4
Person C Baked 2 1/3 as many as Person B. This will be:
= 2 1/3 × 6 3/4
= 7/3 × 27/4
= 15 3/4
Learn more about fractions on
brainly.com/question/78672
#SPJ1
3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10
-1 on the left x-axis and 4 on the right y-axis.
Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.
Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.
Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.
step 1: ascend the y-axis six times.
Step 2: Use 4/1 to increase from the y-4 axis's by 1 to the right
To learn more about graphs from given link
https://brainly.com/question/17144308
#SPJ1
To make an apron, Jaylen’s mother bought 3.9 yards of cloth. If a yard of cloth costs $9.50, how much did Jaylen’s mother spend?
Answer:
She spent 37.05
Step-by-step explanation:
multiply both values
The cost c in pounds of hiring a van for d days is given by the formula c=10+45d work out the cost for 5 day
The cost c in pounds of hiring a van is 235
The cost c in pounds for 1 day =45
Then cost c in pounds for five days is c=10+45d
Which is multiple 5 days to the 45
5 x 45 = 225
Add the 10 to the answer
225 + 10 = 235
The cost of a van hiring for number of days is 5
Then the final answer for cost c in pounds of hiring a van for five days are 235
To know more about cost on
https://brainly.com/question/15718779
the inaugural attendance of an annual film festival is 20,000. The attendance y increases by 5% each year
A. write a function that represents the attendance after t years.
B. about how many people will attend the festival in the fifth year?
A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).
B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.
y = 20,000(1 + 0.05 * 5)
y = 20,000(1 + 0.25)
y = 20,000(1.25)
y = 25,000
So, approximately 25,000 people will attend the festival in the fifth year.
Learn more about function
https://brainly.com/question/25638609
#SPJ1
The sum of the age of a girl and her brother is 34. The girl is 8 years older than her heather, how old is her brother
Answer:
26
Step-by-step explanation:
if she is 8 years older, then is just 34-8 which is 26
Find the product.
(6a² + 4b) (a²- b)
On solving the provide question, we can say that - the quadratic equation [tex](6a^2 + 4b)(a^2 - b)[/tex] = -4
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
here, we have
[tex](6a^2 + 4b)(a^2 - b)[/tex]
a = 0 and b = 1
-4
To know more about quadratic equation visit:
https://brainly.com/question/30098550
#SPJ1
A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line.
The line passes through the point (-10,1) and has a slope of 3/20 has the equation as: y - 1 = 3/2 (x + 10)
How to write the equation of the lineThe general form of a linear equation is y - y₁ = m (x - x₁).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept)
The point slope formula is given by y - y₁ = m (x - x₁), where:
y = output value
y₁= the given y coordinate point
m = slope
x = input value
x₁ = the given x coordinate
substituting the point (-10,1) and slope 3/2
y - y₁ = m (x - x₁)
y - 1 = 3/2 (x + 10)
Learn more on linear equation at:
https://brainly.com/question/14323743
#SPJ1
-50 POINTS- don’t explain
Answer:
3
Step-by-step explanation:
like you said don't explain
I need help, and I forgot how to do this
Answer: 5. 2x+8 6. 5(x-9) 7. -3x+-21
Step-by-step explanation: Multiply the number outside the parenthesis by everything inside it
there are no good answers on brainily can someone pls answer this
Answer:
D
Step-by-step explanation:
first simplify everything
2/9v + 1/3v - 5/9
A and B is wrong because it is - 5/9 not + 5/9
C is wrong because it is -1/3v not 1/3, it is supposed to be - 5/9
You can solve this problem without much solving
hope this helps :)
Find the sum and express it in simplest form.
(7t³ + 3t - 1) + (-9t³ + 2t)
DO
Enter the correct answer.
Answer:
-2[tex]t^{3}[/tex] + 5t - 1
Step-by-step explanation:
(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)
7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1 Combine like terms
-2[tex]t^{3}[/tex] + 5t - 1
Like terms have to have the same variable and the same exponents to be like terms.
which is the highest 4,16,77 and lowest
Answer:
highest 77 and lowest is 4
name all the terms realted to subtraction
Answer:
Other words for subtraction:
taking away
withdrawal
abstraction
removal
discounting
Step-by-step explanation:
Pls, solve this equation with the steps u took. 30 POINTS! posted this for the 2nd time
Answer:
x=2/3
Step-by-step explanation:
when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.
Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle
Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued to read it at the same
rate, how long did it take Tyler to finish reading the guidebook before his family's trip?
Solve the following equation for aa. Be sure to take into account whether a letter is capitalized or not.
2n= a(d+g)
The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]
How to solve for a in the equationThe equation is given as 2n= a(d+g), we are to make a the subject of the equation
in order to have a stand on its own we would have to divide the two sides of the equation by d + g
hence we would have:
[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]
this would cancel out on the right hand side such that we would have:
[tex]\frac{2n}{(d + g)} =a[/tex]
Read more on equations here: https://brainly.com/question/2972832
#SPJ1
PLEASE ANSWER
Write an equation in point-slope form passing through the given point and parallel to the given line:
(- 4, 4)
y = - 7/4x + 2
Answer:
y-4=-7/4(x+4)
Step-by-step explanation:
Point Slope Form: y-y*sub*1=m(x-x*sub*1)
Parallel lines have the same slope as the line to which they are parallel.
y-4=-7/4(x+4)
Hope this helps :)
Please help. Assignment is due today. I am terrible with math, I don't understand this. Thanks in advance.
Answer:
a. A' (-3, -1) B' (3, 2) C' (6, 0); b. A' (-1, -3) B' (1, 6) C' (2, 0); c. A' (-2, -3) B' (2, 6) C' (2, 0)
Step-by-step explanation:
Solutions for graph a, b and c are attached.
a. (x, y) to (3x, y)
A' (-3, -1) B' (3, 2) C' (6, 0)
b. (x, y) to (x, 3y)
A' (-1, -3) B' (1, 6) C' (2, 0)
c. (x, y) to (2x, 3y)
A' (-2, -3) B' (2, 6) C' (2, 0)
REMEMBER: Connect the lines to make the triangles for each graph BEFORE submitting.