[tex]\sec \theta = \sqrt 2\\\\\implies \cos \theta = \dfrac 1{\sqrt 2}\\\\\implies \theta = 2n\pi \pm \dfrac{\pi}4\\\\\\\text{In the interval}~ 0 < \theta < 2\pi, \\\\\theta = \dfrac{\pi}4, \dfrac{7\pi}4~~ \text{or}~~ \theta = 45^{\circ}, 315^{\circ}[/tex]
Find the surface area of the figure. Be sure to show all of your work and steps in solving
for your answer.
Please show me the steps and solutions not just answers pls pls pls help me, tysm!!
The surface area of the figure which comprises two rectangular prisms is: 328 in.²
What is the Surface Area of a Rectangular Prism?Surface area = 2(wl+hl+hw)
Decompose the given figure into two.
Surface area of the figure = surface area of the top rectangular prism + surface area of the bottom rectangular prism - 2(area of base of the top rectangular prism)
Surface area of top rectangular prism:
l = 6 in.
w = 4 in.
h = 5 in.
Surface area = 2(wl+hl+hw) = 2(4×6 + 5×6 + 5×4) = 148 in.²
Surface area of bottom rectangular prism:
l = 6 in.
w = 9 in.
h = 4 in.
Surface area = 2(wl+hl+hw) = 2(9×6 + 4×6 + 4×9) = 228 in.²
Area of base of the top rectangular prism:
Area = (l)(w) = (6)(4) = 24 in.²
Surface area of the figure = 148 + 228 - 2(24)
Surface area of the figure = 328 in.²
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solve the inequality; x2-x-2>0
Answer:
x > 2/3
Step-by-step explanation:
2x -x - 2 > 0
add 2x and x (It becomes 3x)
3x -2 >0
subtract 0 from both sides
3x> 2
divide 3 on both sides
And the answer is
X> 2/3
I need help with this assignment, please help
Answer:
A
Step-by-step explanation:
We need to first find the number of dice rolls. The amount of dice rolls equals 8+9+5+15+2+11=50. And 8 out of thouse 50 were ones, so 8 out of 50 rolls is also 4 out of 25 rolls.
HELP! WILL GIVE BRAINLEST! On the unit circle, an arc of length 2 subtends an angle, β. What is the radian measure of β?
Answer:
2 rad
Step-by-step explanation:
Given :
arc length = 2 mradius of a unit circle = 1 mFormula
l = rβ⇒ β = l/rSolving for β
β = 2/1β = 2 radgift card for 25 dollars 4 dollars per pair 5 dollars off
Answer:
i dont know but i will try
Step-by-step explanation:
example
34 dolars look i have answer
Pls help quick
the
A garden store bought a fountain at a cost of $995. 66 and marked it up 100%. Later on,
store marked it down 25%. What was the discount price?
hope it really helps......!!!!!
Find the value of x. Round to the nearest tenth. 1.4ft 2.1 ft 2x x = [ ? ]ft
Perpendicular projected from center of a circle to its chord bisects it. The value of the x for this case is: x = 1.565 ft approximately.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or |AC| = |CB|
For this case, consider the diagram below.
The line OC divides AB in half.
Since it is given that:
Length of AB = |AB| = 2x ft,
therefore, we get:
|AC| + |CB| = 2x
|AC|+|AC| = 2x (as |AC|=|CB|)
therfore, we get: |AC| = x feet = |CB|
Now,as the triangle OBC contains a right angle, we can use Pythagoras theorem, and therefore, we get:
[tex]|OB|^2 = |OC|^2 + |CB|^2\\2.1^2 = 1.4^2 + x^2\\x^2 = 4.41 - 1.96\\x = \sqrt{2.45} \approx 1.565 \: \rm ft[/tex]
(took positive root as 'x' represents measurement of length, which is a non-negative quantity).
Thus, the value of the x for this case is: x = 1.565 ft approximately.
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raise r to the 7th power, then double the result
Answer:
[tex]\huge\boxed{\bf\:2r^{7}}[/tex]
Step-by-step explanation:
Let the variable be taken as 'r'.
Then, by raising it to the 7th power, we'll get the result as [tex]\downarrow[/tex]
[tex]\sf\:Raise \: r \: to \: the \: 7^{th} \: power = r \: with \: 7 \: as \: its \: exponent.\\\\\sf\:Then,\\\dashrightarrow \underline{\bf\:r \: ^{7}}[/tex]
Now, by doubling the result....
[tex]\sf\:To \: double \: the \: result = multiply \: the \: result \: by \: 2.\\\\\sf\:Then,\\\dashrightarrow \sf\:r \: ^{7} \\=\boxed{\bf\: 2r\:^{7}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Answer:
2r⁷
Step-by-step explanation:
Raise r to 7th power
= r⁷
Double it
= 2r⁷
_________
Hope it helps ⚜
The volume of a cone-shaped hole is 147 pi ft3 If the hole is 9 ft deep, what is the radius of the hole?
Please help!!
radius : 3.95 ft
[tex]\sf volume \ of \ cone: \dfrac{1}{3} \pi r^2h[/tex]
[tex]\hookrightarrow \sf \dfrac{1}{3} \pi r^2(9) = 147[/tex]
[tex]\hookrightarrow \sf r^2 = \dfrac{147*3}{\pi (9)}[/tex]
[tex]\hookrightarrow \sf r = \sqrt{\dfrac{147*3}{\pi (9)}}[/tex]
[tex]\hookrightarrow \sf r = 3.95 \ ft[/tex]
A bookshelf contains 9 mysteries and 7 biographies books. A book is randomly selected and not replaced.
What is the probability that the first book is mystery and the second is the biography?
Answer:
The answer is 7/30
Step-by-step explanation:
According to counting rules, we use permutation when we want to choose successively and without replacement, as given in this problem
Rule of permutation: nPr = n! /(n-r)!
where: n:objects and r:sample
n of mysteries=9 ; r of mysteries=1 ; ⇒ 9P1
n of biographies=7 ; r of biographies=1 ; ⇒ 7P1
n of total books=9+7=15 ; r of total books=2 ; ⇒15P2
Probability=( 9P1 x 7P1 ) / 15P2 = 49/210 = 7/30
Hope this helps :)
What value of x is the solution to the equation −3/2x−3/4=−1/5 ?
A
−19/30
B
33/40
C
−19/20
D
−11/30
Answer:
[tex]\Longrightarrow: \boxed{\sf{x=-\dfrac{11}{30} }}[/tex]
Step-by-step explanation:
Isolate the term of x from one side of the equation.
-3/2x-3/4=-1/5First, add by 3/4 from both sides.
[tex]\sf{-\dfrac{3}{2}x-\dfrac{3}{4}+\dfrac{3}{4}=-\dfrac{1}{5}+\dfrac{3}{4} }[/tex]
Solve.
⇒ = -3/2x=11/20
Then, you multiply by 2 from both sides.
2(-3/2x)=11*2/20
Solve.
11*2/20
11*2=22
22/20
Common factor of 2.
11/10
-3x=11/10
Divide by -3 from both sides.
[tex]\sf{\dfrac{-3x}{-3}=\dfrac{\dfrac{11}{10}}{-3}}[/tex]
Solve.
[tex]\Longrightarrow:\boxed{\sf{x=-\dfrac{11}{30} }}[/tex]
Therefore, the correct answer is D. x=-11/30.I hope this helps! Let me know if you have any questions.
The period of a function is 4
How many cycles of the function occur in a
horizontal length of 12pie?
DONE
Hence total cycles:-
12π/4π3cyclesAnswer is 3
The required there are 3π cycles of the function in a horizontal length of 12π.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
If the period of a function is 4, that means the function completes one cycle every 4 units of horizontal distance.
To find out how many cycles occur in a horizontal length of 12π, we need to divide 12π by the period of the function, which is 4:
Number of cycles = (12π) / 4
Simplifying the expression, we get:
Number of cycles = 3π
So, there are 3π cycles of the function in a horizontal length of 12π.
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Question 9 (1 point)
(03.01 LC)
What is the length of the unknown side of the right triangle? (1 point)
х
7
24
Оа
7
Ob
24
Ос
25
Od
31
Apply Pythagorean theorem
x²=24²+7²x²=576+49x²=625x=√625x=25Answer:
25 units
Step-by-step explanation:
Since this triangle is a right triangle, we can use pythogoras theorem to calculate the unknown side length (x). The pythogoras theorem states that the (longest side)² is equivalent to (Side)² + (Side)².
Let the longest side be "c" and the other side lengths be "a and b".
⇒ Pythogoras theorem formula: c² = b² + a²
If this statement is proven false, then the triangle shown is not a right triangle. Now, let's use the formula to determine the missing side length.
Let "c" be "x" and the other side lengths be "7 and 24 (as stated in image)"
⇒ c² = b² + a²⇒ x² = 7² + 24²SImplify both sides as needed.
⇒ x² = 49 + 576⇒ x² = 625Take square root both sides as needed.
⇒ √x² = √625⇒ x = 25 unitsThe measure of x is 25 units.
You know that the current exchange rate for us dollars (usd) to indian rupees (inr) is 1:45.85, that the exchange rate for indian rupees to bangladeshi taka (bdt) is 1:1.507, and that the exchange rate for bangladeshi taka to myanma kyat (mmk) at a rate of 1:0.0928. which of the following equations is set up properly to calculate the exchange rate from us dollars to myanma kyat? a. (1 u s d) times startfraction (1 u s d) over (45.85 i n r) endfraction times startfraction (1 i n r) over (1.507 b d t) endfraction times startfraction (1 b d t) over (0.0928 m m k) endfraction = (x m m k). b. (1 u s d) times startfraction (45.85 i n r) over (1 u s d) endfraction times startfraction (1.507 b d t) over (45.85 i n r) endfraction times startfraction (0.0928 m m k) over (1.507 b d t) endfraction = (x m m k). c. (1 u s d) times startfraction (45.85 i n r) over (1 u s d) endfraction times startfraction (1.507 b d t) over (1 i n r) endfraction times startfraction (0.0928 m m k) over (1 b d t) endfraction = (x m m k). d. (1 u s d) times startfraction (1 u s d) over (45.85 i n r) endfraction times startfraction (45.85 i n r) over (1.507 b d t) endfraction times startfraction (1.507 b d t) over (0.0928 m m k) endfraction = (x m m k).
The exchange rate from US dollars to Myanma Kyat is given as:
1 : (45.85 × 1.507) × (0.0928) (Option C).
What is an exchange rate?
The rate at which one currency is converted to another is what is referred to as Exchange Rate.
Recall that the following is given from the question:
Step One - Convert from USD to BDT
This gives us 1 : (45.85 × 1.507); Hence, the rate from BDT to MMK is 1 : 0.0928
Step Two: - Ascertain the current rate for USD to MMK
This gives us - 1 : (45.85 × 1.507) × (0.0928). To get a simplified version. One would have to open the brackets.
However, from the above, it is clear that the correct answer is Option C.
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Need some help please.
Applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.
What are the Rules of Exponents?Some of the rules of exponents to be applied are as follows:
[tex]x^0 = 1\\\\x^m \times x^n = x^{(m + n)}\\\\x^{-m} = \frac{1}{x^m} \\\\x^m \div x^n = x^{(m - n)}\\\\[/tex]
What are Equivalent Expressions?If two expressions have the same value, both are said to be equivalent expressions.
1. [tex]3^2 \times 3^{-5} = 3^{2 - 5}\\\\[/tex]
[tex]3^-3 = \frac{1}{3^3} = \frac{1}{27}[/tex]
Answer: H
2. 3³/6² = 27/36 = 3/4
Answer: R
3. [tex]\frac{3^2}{3^5} = 3^{2 - 5} = 3^{-3]} = \frac{1}{3^3} = \frac{1}{27}[/tex]
Answer: M
4. 7²/7² = 49/49 = 7° = 1
Answer: J
5. 8^-2 = 1/8² = 1/64
Answer: A
6. (4²)(4³) = 4^(2 + 3) = [tex]4^5[/tex]
Answer: L
7. (3²)³ = 3²*³ = [tex]3^6[/tex]
8. 4° × 4^-1 = 1 × 1/4 = 1/4
Answer: E
9. [tex]\frac{(2^4)^3}{(2^7)(2^5)} = \frac{2^{12}}{2^{12}}[/tex] = 1
Answer: U
10. [tex](3^2)^{-1} = 3^{-2}[/tex]
Answer: I
11. [tex]1^{98}[/tex] = 1
Answer: D
12. [tex]y^{10} \div y^5 = y^{10 - 5} = y^5[/tex]
Answer: F
13. [tex]8^{-2} \times 8^4 = 8^{(-2 + 4)}[/tex] = 8² = 64
Answer: S
14. [tex]2^{-3} \times 3^{-2} =[/tex] 1/2³ × 1/3² = 1/8 × 1/9 = 1/72
Answer: O
15. [tex]\frac{3^2}{3^2} = 3^{2-2} = 3^0 = 1[/tex]
Answer: N
16. [tex](\frac{1}{2} )^{-1} = (2^{-1})^{-1}[/tex] = 2
Answer: T
Thus, applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.
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Solve for the product of 2 4/5 x 4/6
Answer:
28x/15
Step-by-step explanation:
1. Find the value of X and Y:
2. Find the value of X:
Answer:
Step-by-step explanation:
What is the missing term?
Find the equation of the line shown
Answer:
that would be 1/1 or just 1 as your equation of the line.
Step-by-step explanation:
you find this by taking one part of the grid where a line perfectly intersects 2 parts, and you count to the next spot where this happens, in this case would be to the right 1 and up one, making the slope 1/1 which you can simplify into 1. and slope works like y/x, which y is the up and down movement while x is the side to side.
Answer:
y = x + 6
Step-by-step explanation:
two points are;
(0 , 6) & (4 , 10)
The slope: [tex]\frac{10-6}{4-0} =\frac{4}{4} =1[/tex]
The equation:
[tex]y-10=1(x-4)[/tex]
[tex]y-10=x-4[/tex]
[tex]y=x-4+10[/tex]
[tex]y=x+6[/tex]
Hope this helps
Science!
In the process of combustion, a fuel such as coal undergoes _________________.
Answer
Burning of coal undergoes combustion reaction. Combustion reaction is a type of reaction in which chemical species experiences oxidation by undergoing a reaction with the oxidizing agent which results in the emission of energy in the form of heat. It is an exothermic process.
Step-by-step explanation:
What are the zeros of the following function?
a) 2 and and -3
b) 2 and 3
c) 3 only
d) -3,2 and 3
Answer:
a
Step-by-step explanation:
"Zeroes" of the function are where the graph crosses the x- axis at -3 and 2
Goal: Gather and organize statistical data in frequency distribution table.
Role: Statistician, Data Analyst
Audience: Math Teacher, Adviser
Situation: Your Math Teacher asked your class to conduct a simple survey to
determine the number of learners who are using gadgets in your school.
Product/ Performance:
You were asked to look for at least 15 individuals among your friends within
your school and construct a frequency distribution table on each category:
A. gender
B. preferred distance learning modality (online, modular, blended)
C. available gadget used in distance learning (smartphone, laptop,
tablet, desktop, or none)
I'm looking for a serious answer. I need to pass this on monday. Thank you.
Frequency distribution tables are a tool for organizing data and obtaining additional information.
What is the frequency distribution?The frequency distribution is a term to refer to a type of tables that are used in the area of statistics to organize data.
In the frequency distribution tables, the different variables are arranged by rows. The columns show the number of occurrences for each value, percentages, among others. These types of tables are an ideal tool to analyze data and obtain specific information.
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You have $5,000 to invest for ten years. Crown of The Sun bank pays compound interest at an annual rate of 4.5%. Calculate your balance after 10 years. Round to the nearest hundreth
Answer: $7,764.85
Step-by-step explanation:
Use the formula for Compound Interest: CI = P(1 + r/n)^nt
CI = 5000(1 + 0.045/1)^10
CI = 5000(1.045)^10
CI ≅ $7,764.85
After 10 years, the balance should be $7,764.85
Answer:
$7764.85
Step-by-step explanation:
Assume the compounding is annual.
F = P(1 + r/n)^(nt)
F = 5000(1 + 0.045/1)^10
F = 7764.85
Answer: $7764.85
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A circle's diameter is 8 centimeters.
What is the circle's area (use 3.14 for pi and round to the nearest
tenth)?
Answer:
Formula for the area of a circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi(22/7 or 3.14), and 'r' stands for the radius being squared.
But, we are given a diameter instead of a radius.
So to find the radius of the diameter we must find 1/2(half) of the diameter:
Diameter/2 = Radius
Plug in what we know:
D/2 = R
8/2 = R
4 = R, 4 is our radius.
Now we use this radius in our formula;
A = π[tex]r^{2}[/tex]
A = 3.14(4^2) ← (The symbol ' ^ ' means to the power of.)
A = 3.14(16)
A = 50.24 centimetres is the area for this circle.
Benny went to his local zoo that featured 11 reptile exhibits. if these reptiles exhibits make up 55% of the zoo's exhibits, then how many exhibit does the zoo have in total?
Answer: 20 exhibits
Step-by-step explanation:
If 11 is 55%, we need to find 100%. We will set up a proportion and solve. Percents are on the bottom, exhibits are on the top.
[tex]\frac{11}{55}[/tex] = [tex]\frac{x}{100}[/tex]
Cross multiply:
1,100 = 55x
Divide:
20 = x
There are 20 exhibits in total.
1. Carol jogged 13 miles on 5 days last week.
She jogged 22 miles on 4 days this week.
Was her total distance greater last week or
this week? How much greater? Explain.
A store owner bought a grill for $180, then
marked it up 25% to sell in his store. If a
customer has a coupon for 25% off and
purchases the grill, which statement is true?
A. The customer paid the same
amount the store owner paid.
B. The customer paid $8.75 less
than the store owner paid.
C. The customer paid $11.25 less
than the store owner paid.
D. The customer paid $9.50 more
than the store owner paid.
Answer:
A. The customer paid the same
amount the store owner paid.
Step-by-step explanation:
its adding 25% of the original $180, then immediately decreasing 25% of the original $180, thus the customer paid the same amount the store owner paid.
James studied for his test. He started studying at 3:20 p.m. and studied for 2 hours
and 15 minutes. What time did he finished studying?
Answer:
5:35
Step-by-step explanation:
since he started at 3:20 , to find when he ended you add the 2 hours to that, which gives you 5:20. but, you still have the fifteen minutes which you just add to 5:20, giving you 5:35.
The diagram shows the curve with equation y = ( 1 + x ) cosx.
Complete the table below for points on the curve, giving the y values correct to 3 decimal places where appropriate.
Answer:
y = 1, 1.319, 1.024, 0
Step-by-step explanation:
Given equation:
[tex]y=(1+x)\cos x[/tex]
[tex]\textsf{when}\:x=0:[/tex]
[tex]\begin{aligned} \implies y & =(1+0)\cos 0\\\implies y & = 1\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{6}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{6}\right)\cos \left(\frac{\pi}{6}\right)\\\implies y & = 1.319\: \sf (3\:dp)\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{3}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{3}\right)\cos \left(\frac{\pi}{3}\right)\\\implies y & = 1.024\: \sf (3\:dp)\end{aligned}[/tex]
[tex]\textsf{when}\:x=\dfrac{\pi}{2}:[/tex]
[tex]\begin{aligned} \implies y & =\left(1+\frac{\pi}{2}\right)\cos \left(\frac{\pi}{2}\right)\\\implies y & = 0\end{aligned}[/tex]
Consider the following system of equations.
1. 75x + 1. 25y = 2. 75
7x + 5y = 9
What is the solution to the system?
Since 11 ≠ 9, there is no solution.
Since 0 = 0, there are infinitely many solutions.
There is one solution, x = 0 and y = 0.
There are two solutions (11, 0) and (0, 9)
Multiply the upper system by -4:
[tex] - 7x - 5y = - 11[/tex]
[tex]7x + 5y = 7[/tex]
[tex]0 = - 3[/tex]
[tex]this \: system \: admits \: no \: solutions[/tex]