The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.
How to find a coterminal angle?
For any angle A, all the coterminal angles are of the form:
B = A + n*(2ㅠ).
Where n is an integer different than zero.
In this case, the angle is A = -ㅠ/2
So the coterminal angles are of the form:
B = -ㅠ/2 + n*(2ㅠ)
We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:
B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2
Then we can conclude that the correct option is b.
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A hen lays 3 eggs every 5 minutes. How many eggs will the hen lay in 2 hours?
Answer:
72
Step-by-step explanation:
2 hrs = 120 min
120 min / 5 min = 24 times in 2 hrs
24 x 3 = 72 eggs in 2 hrs
Answer:
Step-by-step explanation:
3 eggs/5 minutes = x/120 minutes
5x = 360
x = 72 eggs in 2 hours
A principal of $3900 is invested at 7.5% interest compounded annually how much will the investment be worth after 9 years
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]
How do I answer this question
Answer:
9³
Step-by-step explanation:
We know that,
[tex]a^b[/tex] ÷ [tex]a^c[/tex] = [tex]a^b^-^c[/tex]
By following the above, let us solve the given question.
Let us solve now.
⇒ 9⁵ ÷ 9²
⇒ 9⁵⁻²
⇒ 9³
You decide to buy a car that costs $10,000. The normal depreciation for such a car is 5% per year. How much will the car be worth in 2 years?
Answer:
11,000
Step-by-step explanation:
10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.
What is the difference of a surface area and a volume
Surface area is all the area of all sides while volume is the amount of space (a substance) occupies in a solid.
For example:
A cube has a length,breadth and height of 5cm,find:
a) surface area of the cube;
b) and the volume of the cube.
a) area of one side of the cube = 5 x 5
= 25cm²
Total surface area = 25cm x 6 (a cube has 6 sides)
= 150cm²
b) volume of cube = length x breadth x height
= 5 x 5 x 5
= 125cm³
Hope this helps you :]
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Element X is a radioactive isotope such that every 26 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 680 grams, how much of the element would remain after 19 years, to the nearest whole number?
Answer:
410 g
Step-by-step explanation:
Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).
y = a(1/2)^(t/h)
__
We can use this equation with the given values to find the amount remaining.
y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)
y ≈ 410 g
About 410 grams of element X will remain after 19 years.
2. At the sale, Jessica bought 4 pairs
sunglasses. How much did she
of
spend?
8.78176.60
A $51.58
B $51.80
C$55.80
D$54.80
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide. saif is building a second pen that is 75% the length of the original and 125% the width of the original. write an equation to determine the length of the second pen. what is the length of the second pen? . .
The length of the second pen is 11.25 units.
What is a Rectangle ?A rectangle is a polygon with four sides , the opposite sides are parallel and equal .
it is given in the question that
Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide
length new = 75% length initial
Length new = (75/100) * 15
Length new = 0.75 * 15
Length new = 11.25 units
The length of the second pen is 11.25 units.
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27 Solve for x to the nearest tenth: x² + x - 5 = 0.
Answer:
Step-by-step explanation:
We can use the quadratic formula to get the answer to this
Quadratic Formula: -b +- √b² - 4ac/2a
Once we input A, B, and C into this, and solve any multiplication, we get
x = -1 +- √1 + 20/2
We divide by 2a, which 2a = 2.
-0.5 +- 10.5.
these are the following values of x:
x = 10
x = 11
Pretty sure this is it, hope it helps!
There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?
Answer:
12.5% is the answer.
Step-by-step explanation:
what is an equation of the line that passes through the point (-4, -6) and is perpendicular to the line 4x+5y=25 ?
Answer:
5x -4y = 4
Step-by-step explanation:
An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.
__
new lineSwapping the coefficients gives us ...
5x +4y = c . . . . . for some constant c
Negating the y-coefficient (so the x-coefficient remains positive) gives ...
5x -4y = c
constantPutting (x, y) = (-4, -6) into the equation gives us the value of c:
5(-4) -4(-6) = c
-20 +24 = c = 4
equationThe line perpendicular to the given line and through the point (-4, -6) will have equation ...
5x -4y = 4
Jeff is going snowboarding this weekend and wants to determine the exact slope of this hill.
Answer:
-2/5
Step-by-step explanation:
the distance between -1 and -3 on the y-axis is 2. 2 is the rise of your slope. two find the run, find the distance between -5 and 0. The distance is negative 2. Rise over run equals the slope so -2/5 is the answer
how many whole numbers are less than n?
10
Select the correct answer.
Which equation is equivalent to the given equation?
- 4(x - 5) + 8x = 91 - 3
OA -5x = 2
OB. 5 = 17
OC. -5x = -23
OD. 5x = -12
Recet
Next
The equation that is equivalent to the given equation is 4x = 68. No answer is correct
Equations and expressionsEquations are two expressions equated to each other. Given the equation below;
- 4(x - 5) + 8x = 91 - 3
Expand
-4x + 20. + 8x = 88
Collect the like terms
4x + 20 = 88
4x = 88 - 20
4x = 68
Hence the equation that is equivalent to the given equation is 4x = 68
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A rectangle is divided into exactly 20 congruent squares. Then these squares are lined up in a single row extending 36 inches (3 feet). What was the area of the rectangle?
The area of the rectangle is 64.8 square .inch
What is a Rectangle ?A rectangle is a polygon with four sides , opposite sides are parallel and equal.
It is given that
A rectangle is divided into exactly 20 congruent squares
If they are lined up the Length is 36 inches
Therefore the length of each square or the side of the square = 36/20
= 1.8 inch
The area of the rectangle will be
20* Side of square * Side of square
=20*1.8*1.8
= 64.8 square inch
The area of the rectangle is 64.8 square .inch
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Find f(5)+j(-2) if f(x)=12-3x ind j(x)=x² + 4x − 1
The value of the expression f(5) + j(-2) is -8 where f(x)=12-3x and j(x)=x² + 4x - 1
How to solve the equation?The expression is given as:
f(5) + j(-2)
Where f(x)=12-3x and j(x)=x² + 4x - 1
Calculate f(5) and j(-2)
f(5)= 12 - 3(5) = -3
j(-2) = (-2)² + 4(-2) - 1 = -5
So, we have:
f(5) + j(-2) = -3 - 5
Evaluate
f(5) + j(-2) = -8
Hence, the value of the expression f(5) + j(-2) is -8
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what’s the surface area Due by tomorrow!!!
Answer: The surface area = 2040.
Step-by-step explanation: Have a great day!
Kaminsky’s bronze sculpture is 5 feet in diameter, which is approximately 1.524 meters. If the sculpture was made of solid bronze, its weight could be approximated using the density of bronze , the volume, , in cubic meters, the mass, , in kilograms and applying the formula . Approximately, how many pounds would the sculpture weigh if it was made of solid bronze?
The weight of the spherical sculpture in pounds is approximately 251607 pounds
How to find the weight of the sculpture in pounds?
The sculpture is spherical and its made of solid bronze.
Therefore,
density = mass / volume
where
density = 7700 kg / m³
volume = 4 / 3πr³
volume = 4/ 3 × 3.14 × 1.524³
volume = 44.4574491494 / 3
volume = 14.8191497165 m³
Therefore,
mass = 7700 × 14.8191497165
mass = 114107.452817 kg
1 kg = 2.205 pounds
114107.452817 = ?
cross multiply
mass in pounds = 114107.452817 × 2.205
mass in pounds = 251606.933461
mass in pounds = 251607 pounds
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One week, Genesis earned $367.40 at her job when she worked for 22 hours. If she is paid the same hourly wage, how many hours would she have to work the next week to earn $584.50?
Answer:
35 hrs
Step-by-step explanation:
Hope this helps! Have a great day!!
I kinda need help with this
Applying the leg rule, the value of x in the given right triangle is: A. 6.
What is the Leg Rule?The leg rule for solving a right triangle having an altitude is expressed as:
hypotenuse/leg = leg/part.
In the image given we have the following:
Hypotenuse = 4 + 5 = 9 units
Leg = x
Part = 4
Plug in the values into the leg rule formula:
9/x = x/4
(x)(x) = (9)(4)
x² = 36
x = √36
x = 6 units.
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find the measure of the indicated angle
?
82°
58⁰
__ degrees
A rental car company charges $63.41 per day to rent a car and $0.05 for every mile driven. Ella wants to rent a car, knowing that: She plans to drive 275 miles. She has at most $200 to spend. What is the maximum number of days that Ella can rent the car while staying within her budget?
Answer:
2 days
Step-by-step explanation:
275 miles times 0.05 = $13.75 for mileage
200-13.75=186.25 left
186.25/63.41(daily fee)= 2.93
She can rent it for 2 days
Factorise 2x^2 + x - 6
[tex] \rm \: {2x}^{2} + x - 6[/tex]
[tex] \rm \: {2x}^{2} + 4x - 3x - 6[/tex]
[tex] \rm \: {2x} \times (x + 2)- 3x \times (x + 2)[/tex]
[tex] \rm \: (x + 2) \times (2x - 3)[/tex]
if x=0 and y<0, where is the plot (x,y) located
Mark me the Brainliest!
Answer:
The point will be plotted on Y axis
A pennant in the shape of a right triangle has a base of 48 inches and a height of 14 inches what is the hypotenuse of the pennant?
Answer:
50 inches
Step-by-step explanation:
48^2 + 14^2 = h^2
Answer is 50 inches if you solve...
Lexi had 3/4 of an apple pie. She gave 1/4 of what she had to her friend Julie. What fraction of the whole pie did Julie get?
Answer:
3/16 of the whole pie
Step-by-step explanation:
Lexi had 3/4 of an apple pie. She gave 1/4 of it to Julie. That means what Julie receives is the product of the whole and the portion.
==========================================================
Solving :
Therefore, the equation is :
⇒ 3/4 × 1/4
⇒ 3/16 of the whole pie
PROVE :
sin^2(-300°).cos^2 (120)+ cos^2(-240 ).sin^2(390)=1/4
Step-by-step explanation:
[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]
[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]
[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]
[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]
PLEASE HELP I’LL MAKE YOU THE BRAINIEST!! What is the value of x in simplest radical form
What is 3.14 x 16
Can i have a step by step solution???
Answer:
3.14 × 16 is 18,84
Method in picture
[tex]{\color{aqua}{\boxed{\mathfrak{LordKeyarga23}}\:}}[/tex]
The value of the multiplication of the numbers 3.14 and 16 will be 50.24.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
3.14 and 16
Then the multiplication of the numbers 3.14 and 16 will be given by putting a cross sign between them. Then we have
⇒ 3.14 x 16
⇒ 50.24
The value of the multiplication of the numbers 3.14 and 16 will be 50.24.
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Find the quotient of 1 4/5 and 1 1/5
Give your answer as a fraction in its simplest form
Answer: 1 1/2
Step-by-step explanation:
1 4/5 = 9/5
1 1/5 = 6/5
[tex]\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}[/tex]