Answers
Answer:
Step-by-step explanation:
I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )
We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:
[tex]9sin^2(x)+3cos^2(x)=3[/tex]
From here we will factor out a 3 to get:
[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:
[tex]3sin^2x+cos^2x=1[/tex]
Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:
[tex]sin^2x+cos^2x=1[/tex], then
[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:
[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:
[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:
[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:
[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:
[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.
Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:
3sin(0) + √3cos(0) = -√3. We need to see if this is true.
The sin of 0 is 0; the cos of 0 is 1, so
0 + (√3)(1) = -√3?
The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?
3sin(180) + √3cos(180) = -√3. We need to see if this is true.
The sin of 180 is 0; the cos of 180 is -1, so
0 + (√3)(-1) = -√3?
The left side is -√3 and so is the right side, so
x = 180°
Related Questions
1. An average orange has a mass of 270 grams. What is the mass of 8 oranges in kg?
.
.
2. 1 milliliter of ink can print 50 pages of text. If you had 100 gallons of ink then how many pages could you print? 1 gallon = 3.79L
.
.
3. If you are driving 55 miles per hour, how many feet per second are you traveling?
Convert hours to minutes:
Convert minutes to seconds: Convert miles to feet:
.
.
4. Ivan’s car has 40 L gas tank. If gas costs $3.67 per gallon how much does it cost to fill her tank?
1 L = .264 gallons
Convert liters to gallons: Calculate the cost of gasoline:
.
.
5. A child requires a 5 mL dose of medicine each day. How many days would a liter of this medicine last?
Answers
Answer:2.the answer is 189,250pages
Step-by-step explanation:
1L=1000ml
3.785=?3785
1ml=50pages
3785ml=?
The answer is 189,250
HE SODA MACHINE
The soda machine at your school offers several types of soda. There are two buttons for your favorite drink, Blast,
while the other drinks (Slurp, Lemon Twister, and Diet Slurp) each have one button.
Describe the input and output of this soda machine.
While buying a soda, Ms. Whitney pushed the button for Lemon Twister and got a can of Lemon Twister.
Later she went back to the same machine, again pushing the Lemon Twister button, but this time she got a can
of Blast. Is the machine functioning consistently? Why or why not?
BLAST
BLAST
BLUSO
ooo
Students, write your resnonsel
Answers
Answer:
yes and no
Step-by-step explanation:
if a machine is work a lot lot LOT, then it might be jamed
or the teacher might have accidentally pressed blast and you might have not seen the buttons correctly
( also i am not a student of yours )
If AC = 40, find the length of JK.
Answers
Answer:
JK = 24
Step-by-step explanation:
Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is
[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values
[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )
5JK = 120 ( divide both sides by 5 )
JK = 24
the triangles are all similar, because they have proportional sides and equal angles.
if you assume the smallest, equal part of side to be x
the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .
since they're similar, ratio of their corresponding sides is constant or equal.
[tex] {BK\over BC}={JK \over AC}[/tex]
BK/BC=3/5
and AC=40
so JK = 40*3/5=24
The population of fruit flies tripled every day and the population today is 200 fruit flies.
a) Write an equation modeling the growth in the population of fruit flies.
b) What was the population of fruit flies 3 days ago?
Answers
Answer:
Equation = 600nNumber of fruit flies after 3 days = 1800 fruit fliesStep-by-step explanation:
Given:
Number of fruit flies = 200
Rate of growth = 3 times per day
Find:
A . Equation
B . Number of fruit flies after 3 days
Computation:
A . Equation = 3n(200)
Equation = 600n
B. Number of fruit flies after 3 days
Number of fruit flies after 3 days = 600(3).
Number of fruit flies after 3 days = 1800 fruit flies
Find the solutions to $x^2 + 64 = 0.$[tex]Find the solutions to $x^2 + 64 = 0.$[/tex]
Answers
Answer:
x=8i,\:x=-8i
Step-by-step explanation:
x^2+64-64=0-64
x^2=-64
x=\sqrt{-64},\:x=-\sqrt{-64}
x=8i,\:x=-8i
3. Miss. Mead pays Miss. Adams $160.00 per week. She works 40 hours per week. Miss. Adams
was idle for 4 hours and 30 minutes during one week. How much did Miss. Mead pay for idle
time?
SHOW
a. $16.00 b. $18.00 c. $22.00 d. $24.00
Answers
Answer:
B. $18.00
Step-by-step explanation
160/4 divide 160 by 4 to see how much Miss Adams makes and hour
She makes $4 an hour
multiply this ($4) by her idle time (4.5) hours to get $18
The graph of function f is shown. Function g is represented by the table. Which statement correctly compares the two functions?
Answers
Answer:
Option (A)
Step-by-step explanation:
Graph of function 'f' represents,
x - intercept of the function 'f' → (1, 0)
y - intercept of the function → (0, 6)
As x-approaches ∞, value of the function approaches (-2)
Points in the given table is for the another function 'g'
x - intercept of the function 'g' → (1, 0) [For x - intercept, y = 0]
y - intercept of the function 'g' → (0, 3) [For y - intercept, x = 0]
As x approaches ∞, value of function 'g' approaches (-1).
Therefore, x - intercepts of both the functions are same but end behavior are different when x → ∞.
Option (A) will be the answer.
A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth.
Answers
This is a problem using the Pythagorean theorem.
The square of the length required is 122 + 122 + 302 = 1188
The length is the square root of this number; I will leave it to you to extract the square root.
Answer:
34.47
Step-by-step explanation:
I need help on this can someone help
Answers
Answer:
1:3
Step-by-step explanation:
[tex]3:9\\= 1: 3[/tex]
Answer:
1 : 3
Step-by-step explanation:
pears : apples
3 9
Divide each side by 3
3/3 9/3
1 : 3
Simplify:
[tex] \frac{ {a}^{5} {b}^{8} }{ {a}^{4} {b}^{10} } [/tex]
HELP! answer if you can !
Answers
In general, (x^n1)/(x^n2)=x^(n1-n2). So the simplified version is a*(b^-2)=a/(b^2).
Answer:
a^5b^8/a^4b^10
= a^5-4 b^8-10
= a^1 b^-2
= a/b^2
I hope this helps
if u have question let me know in comments ^_^
Solve the equation for x
Answers
Answer:
the answer is 5
Step-by-step explanation:
2x/5 - 9 = -7
2x/5 = -7 + 9
2x/5 = 2
2x = 2 * 5
2x = 10
x = 10/2
x = 5
Answer:
x = 5
Step-by-step explanation:
2
--- x - 9 = -7 add 9 both sides
5
2
--- x - 9 + 9 = -7 + 9
5
2
--- x = 2 multiply both sides by 5
5
2
5 * --- x = 2 * 5
5
2x = 10
x = 10 / 2
x = 5
A pyramid has a square base with an area of 169 ft.² what is the perimeter of the base of the pyramid
Answers
Answer:
52
Step-by-step explanation:
Square root of 169 is 13.
SInce it is a square all sides are same length. So you could do 13x4 or 13+13+13+13. Both will equal to 52.
The perimeter of the base of the pyramid is 52 square feet.
Given that,
The pyramid contains a square base having an area of 169 square feet.
We know that,
Area of the square = side^2
169 = side^2
So, the side is 13 feet.
So, the perimeter should be
= 4 × sides
= 4 × 13
= 52 feet
Therefore, we can conclude that The perimeter of the base of the pyramid is 52 square feet.
Learn more about the square here: brainly.com/question/14198272
Plz help with this question! What is 1/3 * 3/5 * 5/7 ... * 97/99
Answers
Answer:
Step-by-step explanation:
(1/3)*(3/5)*(5/7)*.......*(93/95) * (95/97) * (97/99)
The denominator of each fraction will cancel out the numerator of the next fraction.
Take a close look
Therefore the result is 1/99
HOPE IT HELPS!!
The product of the geometric series is 1/99.
The product is a geometric series with first term 1/3 and common ratio 2/3. The number of terms is 49. The sum of the series is 1/99.
Here's the explanation:
A geometric series is a series where each term is multiplied by a constant value to get the next term. The constant value is called the common ratio.
In this case, the first term is 1/3 and the common ratio is 2/3. This means that each term is multiplied by 2/3 to get the next term.
The number of terms in the series is 49. This means that there are 49 terms in the series, starting with 1/3 and ending with 97/99.
The sum of the series is 1/99. This can be found using the formula for the sum of a geometric series:
S = a × (1 - [tex]r^{n}[/tex]) / 1 - r
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/3, r = 2/3, and n = 49. Substituting these values into the formula, we get:
S = (1/3) × (1 - (2/3)49) / 1 - (2/3) = 1/99
Therefore, the product is 1/99.
Learn more about geometric series here: brainly.com/question/30264021
#SPJ2
Write an expression to represent the product of 6 and the square of a number plus 15.
Answers
Answer:
6x^2 + 15
Step-by-step explanation:
We don't know what the square of a number is, so we represent it as x^2
The first part tells us to find the product of 6 and the square of a number, so
6x^2
The second part tells us to add 15 so,
6x^2 + 15
The expression that should be represented is [tex]6x^2 + 15[/tex]
Given that
The product of 6.The square of number + 15.Based on the above information,
Let us assume the number should be x
So, from the above information, the expression should be [tex]6x^2 + 15[/tex]
Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]
Learn more about the equation here:brainly.com/question/21105092?
help me with guys plzzzzz
Answers
Answer:
C
Step-by-step explanation:
So the lion weighs more than the ant right?
And we wish to figure out how much greater the lion's weight is compared to the ant's weight.
So only thing we have to do is divide.
[tex]\frac{1 * 10^5}{2*10^-3} = \frac{10^5}{2*10^-3} = \frac{10^8}{2} = 50000000 = 5 * 10^7[/tex]
Answer:
5×10^7
Step-by-step explanation:
2×10^-3 1×10^5
(1×10^5)/(2×10^-3)=
5×10^7
to scheck :(2*10^-3)(5*10^7)=(1*10^5)
If area of a rhombus is 336 cm and one of its diagonal is 14 cm, find its perimeter.
Answers
Answer:
The perimeter of the Rhombus is 100 cm
Step-by-step explanation:
First of all, we will need to find the length of the other diagonal.
let’s call the diagonals p and q
Mathematically, the area of the Rhombus is;
pq/2 = Area of Rhombus.
Let’s call the missing diagonal p
So;
(p * 14)/2 = 336
14p = 672
p = 672/14
p = 48 cm
Now, we can find the perimeter of the Rhombus using these diagonals.
Mathematically;
P = 2 √(p^2 + q^2)
Substituting these values, we have;
P = 2 √(14)^2 + (48^2)
P = 2 √(2500)
P = 2 * 50
P = 100 cm
The perimeter of the rhombus is the sum of its side lengths
The perimeter of the Rhombus is 100 cm
The length of one of its diagonal is given as:
[tex]p= 14[/tex]
And the area is given as:
[tex]A = 336[/tex]
Assume the other diagonal is q.
The area of the rhombus is represented as:
[tex]A = \frac{pq}2[/tex]
So, we have:
[tex]336 = \frac{14q}2[/tex]
This gives
[tex]336 = 7q[/tex]
Divide both sides by 7
[tex]48 = q[/tex]
Rewrite as:
[tex]q = 48[/tex]
The perimeter (P) of the rhombus is calculated as:
[tex]P =2\sqrt{p^2 + q^2[/tex]
So, we have:
[tex]P =2\sqrt{48^2 + 14^2[/tex]
Evaluate the squares
[tex]P =2\sqrt{2500[/tex]
Take positive root of 2500
[tex]P =2 \times 50[/tex]
[tex]P =100[/tex]
Hence, the perimeter of the Rhombus is 100 cm
Read more about areas and perimeters at:
https://brainly.com/question/14137384
Nan left her house at 1 p.m. driving at a constant speed of 40 miles perhour. If she continues at that same speed for the entire trip, she will reach
her destination at 4:45 p.m. If Nan were to drive 10 miles per hour faster,
how much quicker would she arrive?
Answers
Answer:
45 minutes faster
Step-by-step explanation:
Distance:
40 x 3.75 = 150
If travel 50 miles/h:
150/50 = 3
3.75 - 3 = 0.75 of hour
45 minutes
Hope that helped!!! k
This table represents a quadratic function.
What is the value of “a” in the function’s equation?
A. -1/2
B. 1/2
C. 2
D. 1
Answers
Answer:
I think 1/2 is the ans
Step-by-step explanation:
quadratic function equation
would help
What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Answers
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
find the sum of partial fraction for x^4/(x-1)(x²-4)
Answers
Answer:
see attachment
Step-by-step explanation:
4x +16 x+4
Simplify your answer as much as possible.
Answers
Answer:
20x+4
Step-by-step explanation:
The like terms here are 4x and 16x .
This will give us the answer 20x.
As there is no other like term for 4, we just add it in 20x.
This gives us the final answer of 20x+4.
Thankssssss :)))))))
solve for x 7(x+2) =6(x+5)
Answers
Answer:
16
Step-by-step explanation:
Distribute 7 into x and 2, which gets you 7x+14. Then distribute 6 into x and 5, which is 6x+30. 7x-6x= x, 30-14=16 so there’s your answer.
Answer:
Step-by-step explanation:
7x + 14 = 6x + 30
x + 14 = 30
x = 16
reduce 63/72 to its lowest terms
Answers
Answer:
7/8
Step-by-step explanation:
63 ÷ 9/72 ÷ 9
= 7/8
Answer:
7/8
Step-by-step explanation:
63/9 = 7
72/9 = 8
then:
63/72 = 7/8
Please please please help
Answers
Answer:
m = 4
Step-by-step explanation:
9/6=6/m
9m = 36
m = 4
Evaluate the function below at x=7. Then enter your solution rounded up to 2 decimal places. 1500•1.09^x
Answers
Answer:
Value of the function will be 2742.06
Step-by-step explanation:
Given function is,
f(x) = 1500(1.09)ˣ
By substituting the value of x we can find the value of the given function.
For x = 7,
f(7) = 1500(1.09)⁷
= 1500(1.828)
= 2742.0587
≈ 2742.06
Value of the function will be 2742.06
-5/6 + 1 2/9
Can some one help me out?
Answers
Answer:
[tex]2 \frac{4}{9} [/tex]
[tex] = \frac{ - 5}{6} + 1 \frac{2}{9} [/tex]
[tex] = \frac{ - 5}{6} + \frac{11}{9} [/tex]
[tex] = \frac{ - 5 \times 2 + 11 \times 1}{9} [/tex]
[tex] = \frac{ - 10 + 9}{9} [/tex]
[tex] = \frac{-1}{9} [/tex]
Type the correct answer in the box. Use numerals instead of words.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
5.75 cm
The area of the shape is
square centimeters.
Answers
Answer:
35 cm squared
Step-by-step explanation:
Triangle area = bxh 2 = 5.75 x 8 / 2 = 23
Trapezium Area = a+b /2 x h = 8 + 4 /2 x 2 = 12
23 + 12 = 35
Hope that helped!!! k
Explanation:
Find the area of trapezoid:
A = (8 + 4)2/2 = (12 x 2)/2 = 24/2 = 12
Find the area of the triangle:
A = (8 x 5.75)/2 = 4 x 5.75 = 23
Find the area of the whole shape:
A (trapezoid) + A (triangle) = A (whole shape)
12 + 23 = 35 = A (whole shape)
Answer ASAP, will give brainliest!!
Answers
Answer:
Step-by-step explanation:
77; The formula to calculating the area of a trapezoid is (a+b)/2 * c. a+b are the 2 parallel lines, and c is the height or the altitude. So, it is (10+12)/2 * 7, which is 22/2 * 7 = 11*7=77 :)
1 person = 40 min = 1 bag, 4 person = ? min = 1575 bags
Answers
Answer:
15 750 minStep-by-step explanation:
4 person = 1575 bags
1 person = 1575:4 = 393.75 bags
40 min = 1 bag
393,75 bags = 40 min•393,75 = 15 750 min
Enter a counterexample for the conclusion. If x is a prime number, then x + 1 is not a prime number. A counterexample is x = .
Answers
2 is prime and 3 is also prime
Answer:
x = 2
Step-by-step explanation:
If x is a prime number, then x + 1 is not a prime number.
A counterexample is x = 2.
x = 2
2 is prime
x + 1 = 2 + 1 = 3
3 is also prime