Answer:
[tex]\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================[/tex]
[tex]=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta[/tex]
Part 3 out of 3 How much will Alice pay for carpet that costs $2.50 per square foot? Alice will pay $ for the carpet.
Answer:
How big is the carpet though.
Step-by-step explanation:
You will just times the square foot by $2.50 to get an answer.
If it is 4 square feet then just go 4 times $2.50 = $10
Write the equation -3x+2y=7 in slope intercept form.
Answer:
[tex]y=\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
Slope-intercept form is given by y = mx + b
We need to re-arrange the equation given to have y to the left side of the equal sign (in other words, solve for y). Steps are shown below:
[tex]-3x+2y=7\\2y=3x+7\\y=\frac{3x+7}{2}\\y=\frac{3x}{2}+\frac{7}{2}\\y=\frac{3}{2}x+\frac{7}{2}[/tex]
the last answer is correct.
For this case we have that the line equation of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
We have the equation:
[tex]-3x + 2y = 7[/tex]
By adding 3x to both sides of the equation we have:
[tex]-3x + 3x + 2y = 7 + 3x\\2y = 3x + 7[/tex]
Dividing between 2 on both sides of the equation:
[tex]\frac {2y} {2} = \frac {3x} {2} + \frac {7} {2}\\y = \frac {3x} {2} + \frac {7} {2}[/tex]
ANswer:
Option D
A manatee surfaced for air 3 times in 120 seconds. How many seconds went by before the manatee surfaced the first time if it held its breath for the same rate?
Answer:40
Divide 120 by 3
so lets simplify this equation to do it mentally
turn 120=12
now 12÷ 3=4
the zero from 120 will be added to 4
because of the tens place it becomes 40
hope this helps! if so please leave a brainliest.
The humpback whales traveled 2240 miles in 28 days. The gray whales traveled 2368 miles in 32 days. If the humpback whales had traveled at the same rate for 32 days how many more miles would they have to travel
Answer:
192
Step-by-step explanation:
32 days would be 80×32=2560
and 2560-2368= 192
So if the humpback were to travel for 32 days it would travel 192 miles more than the gray whale.
A company policy requires that, for every 40 employees, there must be 3 supervisors. If the are 285 supervisors at the company how many employees does the company have?
Answer:
11,400.0
Step-by-step explanation:
There needs to be 40 employees per every 3 supervisors, so this means multiplication, or division, but I went with the multiplication route.
285 x 40 = 11,400.
11,400 / 40 = 285.
The reason I multiplied 285 by 40 is because the supervisors was the main piece to the puzzle, and was much easier than if it gave you employees first, and that's when you'd divide by 3.
If there's 285 supervisors, you have the full amount of supervisors, now you need employees, so you are free to multiply by 40, since thats how many supervisors are available every 40 employees. I hope this helps.
To solve this problem, we'll first establish the ratio of employees to supervisors as given by the company policy. The policy states that for every 40 employees, there must be 3 supervisors.
To find the number of employees that can be supervised by a single supervisor, we'll divide the number of employees by the number of supervisors in that ratio.
So, for every 3 supervisors, there are 40 employees. We want to know how many employees would be there per 1 supervisor. Thus, we divide 40 (the number of employees) by 3 (the number of supervisors):
Number of employees per supervisor = \( \frac{40 \text{ employees}}{3 \text{ supervisors}} \)
Now, if there are 285 supervisors at the company, we can find out the total number of employees by multiplying the number of supervisors by the number of employees per supervisor.
Therefore, the total number of employees \( E \) is:
\( E = 285 \text{ supervisors} \times \frac{40 \text{ employees}}{3 \text{ supervisors}} \)
The "supervisors" unit cancels out, and we are left with only the "employees" unit.
Now let's do the multiplication. We divide 40 by 3 and then multiply the result by 285:
\( E = 285 \times \frac{40}{3} \)
Calculating that results in:
\( E = 95 \times 40 \)
\( E = 3800 \)
Thus, the company has 3,800 employees.
what is the answer to this??
Answer:
∠1 = 23°
Step-by-step explanation:
∠WXZ = ∠WXY + ∠YXZ
Note that ∠2 = 4∠1 ( angle 2 is 4 times angle 1 )
Hence
4∠1 + ∠1 = 115
5∠1 = 115 ( divide both sides by 5 )
∠1 = 23°
Which equation has solutions of 6 and -6?
A. x^2-12x+36=0
B. x^2 + 12x – 36 = 0
C. x^2 + 36 = 0
D. x^2 – 36 = 0
Answer is D
use the factor method to get the answer
x^2-36=0
x^2-6^2=0
(x-6)(x+6)=0
x=6 or -6
I need help on this
Answer:
12 + 12 + 60 + 216 = 300 ft squared
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
First find the area of the rectangle which would be 18 times 12. This will give you 216 for the rectangle. To find the area of the trapezoid you would add the base of the trapezoid for top and bottom. 10+18. This will give you 28. Next divide it by 2. This will give you 14. Now multiply 14 by the height of the trapezoid which is 6. This will give you 84 for the trapezoid. Now add the rectangle and the trapezoid 84+216=300. The area of the figure is 300.
doris tiene en su cartera billetes de $10 y de $20.si en total tienen 25 billetes y $330 ¿cuantos billetes tiene cada uno?
Answer:
8 billetes de 20
17 billetes de 10
Step-by-step explanation:
Answer:
17 $10s y 8 $20s
Step-by-step explanation:
The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form? 3x3 + 2x2 – x + 3 3x3 + 2x2 – x – 3 3x3 + x2 – 6x + 9 3x3 + x2 + 6x – 9
Answer:
AB - C² = 3x³ + x² + 6x - 9 ⇒ last answer
Step-by-step explanation:
* Lets study the problem to solve it
- The variables are:
# A = x²
# B = 3x + 2
# C = x - 3
* At first lets find AB
∵ A = x² and B = 3x + 2
∴ AB = x²(3x + 2)
∵ x² × 3x = 3x³ ⇒ same base so we added the power
∵ x² × 2 = 2x² ⇒ coefficient of x² is 1 multiplied by 2
∴ AB = 3x³ + 2x²
* At second find C²
∵ C = x - 3
∴ C² = (x - 3)²
- To solve bracket to the power of 2 use this rule:
# square the first term + 1st term × 2nd term × 2 + square the 2nd term
∴ (x - 3)² = (x²) + (x) (-3) (2) + (-3)² = x² - 6x + 9
∴ C² = x² - 6x + 9
* Now lets find AB - C²
∵ AB - C² = 3x³ + 2x² - (x² - 6x + 9) ⇒ multiply the bracket by -ve sign
∵ -ve × -ve = +ve
∵ -ve × +ve = -ve
∴ AB - C² = 3x³ + 2x² - x² + 6x - 9 ⇒ Add the like terms
∴ AB - C² = 3x³ + x² + 6x - 9
* AB - C² = 3x³ + x² + 6x - 9
Answer:
d for edge2020
Step-by-step explanation:
asap!!
85=2x(x^2+3)(2x+5) use quadratic equation
Answer:
Step-by-step explanation:
85=2x(x^2+3)(2x+5)
85=2x(2x^3+5x^2+6x+15)
85=4x^4+10x^3+12x^2+30x
4x^4+10x^3+12x^2+30x-85=0
2x^2(2x^2+5x+6)+30x-85=0
shoot, this isn't possible with quadratic, maybe you can get somewhere from here
Given the functions: f(x) = 7x + 10 and g(x) = 1.75x + 10. Make a table of values for each function to determine which value of x is closest to where g(x) begins to exceed f(x). A) x = 5 B) x = 6 C) x = 7 D) x = 8
Your answer Would be c
Your answer will be C
if the mean of a set of 12 number is 13 then the sum of the number is?
The sum of the numbers is 156.
Explanation:The sum of a set of numbers can be calculated by multiplying the mean by the total number of elements in the set. In this case, the mean is 13 and the total number of elements is 12. Therefore, the sum of the numbers is 13 multiplied by 12, which is 156.
Learn more about Mean and sum here:https://brainly.com/question/37982106
#SPJ3
To find the sum of 12 numbers with a mean of 13, we multiply the mean by the number of numbers, resulting in a sum of 156.
If the mean of a set of 12 numbers is 13, we can find the sum of the numbers using the formula for the mean.
The formula for the mean is : Mean = Sum of Numbers / Number of Numbers
Given:
Mean = 13
Number of Numbers = 12
We need to find the sum of the numbers:
Sum = Mean x Number of Numbers
Substitute the given values:
Sum = 13 x 12
Sum = 156
This means the sum of the 12 numbers is 156.
The volume of a box with height x, length x-1, and width 2x+2 is given by the binomial 2x^3-2x. What is the volume of the box if it’s height is 4 feet?
Height = x
Length = x - 1
Width = 2x + 2
And it's said that height = 4 feet
So, x = 4
Then:
H = 4
L = 4 - 1 = 3
W = 2.4 + 2 = 10
The volume is:
V = 4 . 3 . 10
V = 120 ft³
solve the inequality 5x+3 ≥48
Answer:
x≥9
Step-by-step explanation:
First you need to take 3 from both sides.
5x + 3 -3 ≥ 48 -3 which is 5x ≥ 45
Then you need to divide both sides by 5.
5x÷5 ≥ 45÷5 with gives the answer x ≥ 9
The solution to the given inequality (5x+3 ≥48) is x ≥ 9
To solve an equation or an inequality, we will determine the value of the variable in the equation or inequality.
From the question,
To solve the given inequality 5x+3 ≥48
We will determine the value of the variable x, that satisfies the inequality.
Now, to do this
First, subtract 3 from both sides, that is
[tex]5x+3-3 \geq 48-3[/tex]
We get
[tex]5x \geq 45[/tex]
Now, divide both sides by 5
[tex]\frac{5x}{5} \geq \frac{45}{5}[/tex]
[tex]x\geq 9[/tex]
Hence, the solution to the given inequality is x ≥ 9
Learn more here: https://brainly.com/question/17448505
Please help me with this question and my next one!
Answer:
Step-by-step explanation:
If the price is linear, then the slope between each pair of points must be the same.
m = Δy/Δx
m = (150 - 70) / (5 - 1) = 20
m = (450 - 150) / (20 - 5) = 20
m = (1050 - 450) / (50 - 20) = 20
So the equation is indeed linear. It has a slope of 20 and y-intercept of 50.
p = 20n + 50
What similarity statement can you write relating the three triangles in the diagram?
Answer:
Option A
Step-by-step explanation:
Suppose ∠I = 30° in ΔHIF,
∴ ∠F = 60°
Now consider the ΔGFH,
∠G = 90° and ∠F = 60°
∴ ∠GHF = 30°
Also in ΔGHI,
∠G = 90° and ∠I = 30°
∴∠GHI = 60°
∴ ΔGFH ≈ ΔGIH ≈ ΔHIF
Answer:
a
Step-by-step explanation:
3.
(07.04A)
If y = 5x − 4, which of the following sets represents possible inputs and outputs of the function represented as ordered pairs? (4 points)
{(0, −4), (2, 6), (4, 20)}
{(0, −4), (2, 6), (4, 16)}
{(0, 4), (2, 6), (4, 16)}
{(0, 4), (2, −6), (4, 20)}
Answer:
the answer is B {(0,-4),(2,6)(,4,16)
happy to help
Answer:
B {(0,-4),(2,6)(,4,16)
Step-by-step explanation:
What is the first step in evaluating the expression shown below?
12÷(7.4−3.6)+8−2
A. Subtract 7.4−3.6.
B. Divide 12÷7.4.
C. Add 3.6+8.
D. Subtract 8−2.
Answer:
the answer is A
Step-by-step explanation: because the way you work out problems with parenthesis is Parenthesis Exponents Multiplication Division Adding Subtraction and what ever id in the parenthesis comes first
A is the correct answer as you should always do the expression that’s in parentheses first
The sum of the measures of angle M and angle R is 90 °
•the measure of angle M is (5x+10)°
•the measure of angle R is 55°
What is the value of x?
The value of x is 5.
Given:
angle M + angle R = 90°angle M = (5x+10)°angle R = 55°Recall:
Two angles that add up to give you 90°, is a complementary angle.Thus,
Since angle M and angle R sum up to give 90°, they are complementary angles.The following equation can be created to solve for the value of x:
[tex]m\angle R + m\angle M = 90[/tex]
Substitute[tex]55 + 5x+10 = 90\\[/tex]
Add like terms[tex]5x + 65 = 90[/tex]
Subtract 65 from both sides[tex]5x = 90 - 65\\\\5x = 25[/tex]
Divide both sides by 5[tex]x = 5[/tex]
Therefore, the value of x is 5
Learn more here:
https://brainly.com/question/15592900
Write a quadratic equation in factored form whose solutions are 7 and -5
[tex]\bf \stackrel{~~ solutions~\hfill }{ \begin{cases} x=7\implies &x-7=0\\ \cline{1-2} x=-5\implies &x+5=0 \end{cases}}\qquad \implies \stackrel{\textit{factored form}}{y=(x-7)(x+5)}[/tex]
Answer:
y = (x - 7)(x + 5)
Step-by-step explanation:
Given the solutions are x = 7 and x = - 5 then the factors are
(x - 7) and (x + 5)
The quadratic equation is the product of the factors
(x - 7)(x + 5) = 0 ← in factored form
What is x for the following:
|x-1/x-1|=1
and...
x-1/x-1
Answer:
2, or any negative number
Step-by-step explanation:
For the first one x=2
Susan walks 10 feet in 4 steps at this rate how many steps will it take her to walk 1 mile
Answer:
2112 Steps
Step-by-step explanation:
It would take her 2112 step to walk for 1 mile
Earth has a diameter of about 2292 leagues long. What is the total surface area of earth? Rounded to the nearest whole number.
Answer: 16,503,616 leagues²
Step-by-step explanation:
Assume that the Earth is a sphere. Then, you need to use the formula for calculate the surface area of a sphere:
[tex]SA=4\pi r^2[/tex]
Where r is the radius.
Divide the diameter by 2 to calculate the radius of the Earth:
[tex]r=\frac{2,292\ leagues}{2}\\r=1,146\ leagues[/tex]
Substituting values into the formula [tex]SA=4\pi r^2[/tex], you get that the total surface of the Earth to the nearest whole number is:
[tex]SA=4\pi (1,146\ leagues)^2=16,503,616\ leagues^2[/tex]
The correct answer is that the total surface area of Earth is approximately 510 million square kilometers.
To calculate the total surface area of Earth, we can use the formula for the surface area of a sphere, which is [tex]\( A = 4\pi r^2 \)[/tex], where r is the radius of the sphere. Since the diameter of Earth is given as 2292 leagues, we first need to convert leagues to kilometers. Historically, one league was approximately 5.556 kilometers.
Using this conversion, the radius of Earth in kilometers is:
[tex]\[ r = \frac{2292 \text{ leagues} \times 5.556 \text{ km/league}}{2} \] \[ r = \frac{2292 \times 5.556}{2} \] \[ r = 1146 \times 5.556 \] \[ r \approx 6337.536 \text{ km} \][/tex]
Now, we can calculate the surface area using the radius:
[tex]\[ A = 4\pi r^2 \] \[ A = 4\pi (6337.536 \text{ km})^2 \] \[ A = 4\pi (404,089,630.24 \text{ km}^2) \] \[ A \approx 4\pi (4.04 \times 10^9 \text{ km}^2) \] \[ A \approx 4 \times 3.14159 \times 4.04 \times 10^9 \text{ km}^2 \] \[ A \approx 50.26548 \times 10^9 \text{ km}^2 \] \[ A \approx 5.026548 \times 10^{10} \text{ km}^2 \][/tex]
Rounding to the nearest whole number, the total surface area of Earth is approximately 510 million square kilometers.
What is the length of BC round to the nearest 10th of a unit
Answer:
8.6 units
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(1, 6) and (x₂, y₂ ) = C(8,1)
d = [tex]\sqrt{(8-1)^2+(1-6)^2}[/tex]
= [tex]\sqrt{7^2+(-5)^2}[/tex]
= [tex]\sqrt{49+25}[/tex]
= [tex]\sqrt{74}[/tex] ≈ 8.6
Celia uses the steps below to solve the equation -3:8(-8-16d)+2d+24
Answer: i think it’s the last one
Step-by-step explanation:
Find the surface area of a melon with circumference of 18 in. Round your answer to the nearest square inch.
that is, the length down the middle of the melon is 18.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=18 \end{cases}\implies 18=2\pi r\implies \cfrac{18}{2\pi }=r\implies \cfrac{9}{\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{surface area of an sphere}\\\\ A=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} \boxed{r}=\frac{9}{\pi } \end{cases}\implies A=4\pi \left( \cfrac{9}{\pi } \right)^2\implies A=4\pi \cdot \cfrac{81}{\pi ^2} \\\\\\ A=4\cdot \cfrac{81}{\pi }\implies A=\cfrac{324}{\pi }\implies A\approx 103.13\implies \stackrel{\textit{rounded up}}{A=103}[/tex]
PLEASE HELP!!!!!!!!! The scale on a map shows that 5 centimeters = 2 kilometers. What number of centimeters on the map represents an actual distance of 5 kilometers?
Answer:
12.5 cm
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
5 cm = 2 km
? cm = 5 km
5 cm = 2 km
( ÷ 2 )
2.5 cm = 1 km
( × 5 )
12.5 cm = 5 km
5(2y - 1) = 3(y - 4)
How would I do this question/what is the answer?
Answer:
Step-by-step explanation:
=10y - 5 = 3y - 12
=7y - 5 = -12
=7y = -7
y = 1
Answer:
y = -1
Step-by-step explanation:
to solve this equation, you would solve for y by isolating y on one side of the equation
5(2y - 1) = 3(y - 4) < distribute 5 into 2y - 1 and 3 into y - 4
5(2y - 1)
5 x 2y = 10y
5 x - 1 = -5
= 10y - 5
3(y - 4)
3 x y = 3y
3 x -4 = -12
= 3y - 12
we get the new equation:
10y - 5 = 3y - 12 < add 12 to both sides to eliminate -12 from the right side
+ 12 + 12
10y + 7 = 3y < subtract 10y from both sides
-10y -10y
7 = -7y < divide both sides by -7 to isolate y
7/-7 = -1
-7y/-7 = y
-1 = y
our solution to the equation is y = -1. we can see if this is an answer by plugging it in and seeing if both sides are equal, but its not necessary. i will show the check anyway:
CHECK
5(2y - 1) = 3(y - 4) when y = -1
5(2(-1) - 1) = 3((-1)- 4)
5(-2 - 1) = 3( -1 - 4)
5(-3) = 3(-5)
-15 = -15
both sides check out so y = -1 is a solution to the equation
Solve for x in the equation x^2-14x+31=63.
Answer:
-2; 16
Step-by-step explanation:
Rewrite the equation [tex]x^2-14x+31=63[/tex] as:
[tex]x^2-14x+31-63=0\\ \\x^2-14x-32=0[/tex]
Now use the quadratic formula:
[tex]D=b^2-4ac\\ \\D=(-14)^2-4\cdot 1\cdot (-32)\ \ [a=1,\ b=-14,\ c=-32]\\ \\D=196+128=324=18^2[/tex]
Now
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}\\ \\x_{1,2}=\dfrac{-(-14)\pm\sqrt{18^2}}{2\cdot 1}=\dfrac{14\pm18}{2}=\dfrac{-4}{2},\ \dfrac{32}{2}=-2,\ 16[/tex]
Answer:
x = 16 or x = -2
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + = 0 is given by
x = [-b ± √(b² - 4ac) ]/2a
To find the solution of equation
We have x² - 14x + 31 = 63
x² - 14x + 31 - 63 = 0
x² - 14x - 32 = 0
a = 1, b = -14 and c = 32
x = [-b ± √(b² - 4ac) ]/2a
= x = [- -14 ± √((-14)² - 4*1 * (-32)) ]/2*1
= [14 ± √324]/2
x = -2 or x = 16