Answer:
x = 0 , π
Step-by-step explanation:
[tex]-4 \sin x = 1 - cos^2 x[/tex]
Rewrite it by using the identity [tex]\sin^2x + \cos^2x = 1[/tex][tex]=> -4\sin x = \sin^2x[/tex]
Add 4sin x to both the sides.[tex]=> -4\sin x + 4\sin x = sin^2x + 4\sin x[/tex]
[tex]=> \sin^2x + 4\sin x = 0[/tex]
Take sin x common from the expression in L.H.S.[tex]=> \sin x(\sin x + 4)=0[/tex]
Here , we can get two more equations to find x.
1) [tex]\sin x(\sin x + 4)=0[/tex]
Divide both the sides by sin x[tex]=> \frac{\sin x(\sin x + 4)}{\sin x} = \frac{0}{\sin x}[/tex]
[tex]=> \sin x + 4 = 0[/tex]
Substract 4 from both the sides.[tex]=> \sin x + 4 - 4 = 0 - 4[/tex]
[tex]=> \sin x = -4[/tex]
[tex]=> x = No \; Solution[/tex]
2) [tex]\sin x(\sin x + 4)=0[/tex]
Divide both the sides by (sin x + 4)[tex]=> \frac{\sin x(\sin x + 4)}{\sin x + 4} = \frac{0}{\sin x + 4}[/tex]
[tex]=> \sin x = 0[/tex]
[tex]=> x = 0 \; , \pi[/tex] over interval [0 , 2π).
Write and solve an inequality that represents the number of days driven without the warning light coming on. Explain clearly what the solution to the inequality means in the context of this situation.
Answer:
0.6x < 12.5
x < 20.83 days
Step-by-step explanation:
Diego's family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Write an inequality that represents the number of days Diego's father can drive the car without the warning light coming on. Explain each part of your inequality
Car fuel capacity = 14 gallons
Fuel capacity that shows warning light = 1.5 gallons
Fuel capacity without warning light = Car fuel capacity - Fuel capacity that shows warning light
= 14 gallons - 1.5 gallons
= 12.5 gallons
Fuel used per day = 0.6 gallons
Let
x = number of days Diego's father can drive the car without the warning light coming on
The inequality is
0.6x < 12.5
Solve for x
x < 12.5/0.6
x < 20.83 days
Write each equation in function notation, then solve the function for the given value.
(i.e. Find the Function and Solution)
y = -2/5x + 3/8 when c = 1/3
Given:
The equation is:
[tex]y=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
To find:
The function notation for the given equation and then solve the function for the value [tex]x=\dfrac{1}{3}[/tex].
Solution:
We have,
[tex]y=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
Substitute [tex]y=f(x)[/tex] in the given equation to find the function notation of it.
[tex]f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
Substituting [tex]x=\dfrac{1}{3}[/tex], we get
[tex]f(\dfrac{1}{3})=-\dfrac{2}{5}(\dfrac{1}{3})+\dfrac{3}{8}[/tex]
[tex]f(\dfrac{1}{3})=-\dfrac{2}{15}+\dfrac{3}{8}[/tex]
[tex]f(\dfrac{1}{3})=\dfrac{-16+45}{120}[/tex]
[tex]f(\dfrac{1}{3})=\dfrac{29}{120}[/tex]
Therefore, the function notation is [tex]f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex] and the value of the function at [tex]x=\dfrac{1}{3}[/tex] is [tex]\dfrac{29}{120}[/tex].
Helppp quick! That’s the question^ please help guysss
Answer:
The slope represents the cost per gallon for heating oil while the y-intercept represents the fee for heating oil.
Find the quotient of
x3−4x2−4x+16x−2
Answer:
x^2 - 2x - 8.
Step-by-step explanation:
Using long division:
x - 2)x^3 - 4x^2 - 4x + 16( x^2 - 2x - 8 <------ Quotient
x^3 - 2x^2
-2x^2 - 4x
-2x^2 + 4x
- 8x + 16
-8x + 16
............
f(x) = 2x-1
What kind of shift is represented?
Hi there!
»»————- ★ ————-««
I believe your answer is:
A vertical shift down one unit.
»»————- ★ ————-««
Here’s why:
A chart showing the rules of function transformations are shown. The equation shown is the parent function of '2x' that is shifted 1 unit down. If the number was inside the x [like (x - 1)] it would be a horizontal transformation. Since it's outside we would consider it to be a vertical shift.»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Find the length of the arc
Answer:
33 ft
Step-by-step explanation:
C = 2 r [tex]\pi[/tex]
The length of the arc is [tex]\frac{18\pi }{360}[/tex] × 210 ≈ [tex]\frac{18*22*210}{360*7}[/tex] = 33 ft .
a sphere has a radius of 6 centimeters. what is the volume of the sphere?
Question
A sphere has a radius of 6 centimeters. What is the volume of the sphere
Given:
r = 6 cm
Formula:
V = (4/3)πr
Solution:
V = (4/3)πr
V = (4/3)(3.14)(6)
V = 25.12 cm³
Final Answer:
25.12 cm³
A bank account starts with $3.00. The amount in the account doubles every year .
Answer:
Step-by-step explana
multiply it by 2 or sdd itself to it
The account will have $1536.007 after 9 years.
Part A:
To express the total amount of money A(t) in the account after 7 years, we can use the formula:
A(t) = P[tex](2^t)[/tex]
where:
A(t) is the total amount in the account after t years,
P is the initial amount in the account (starting with $3.00 in this case),
t is the number of years.
Substituting the values into the formula, we get:
A(t) = 3 ([tex]2^7[/tex])
A(t) = 3 x 128
A(t) = 384
Therefore, the total amount of money in the account after 7 years is $384.
B) To find out after how many years the account will have $1536.007, we need to solve the equation:
1536.007 = 3 [tex](2^t)[/tex]
Dividing both sides of the equation by 3, we get:
512.0023333333 = [tex]2^t[/tex]
Taking the logarithm (base 2) of both sides, we have:
log2(512.0023333333) = t
t = 9.000317.
Therefore, the account will have $1536.007 after 9 years.
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ2
Holly cuts 2 ribbons into tenths for a craft project how many 1/10 size ribbons does she have
Answer:
Holly would have 20 1/10 sized ribbons.
Step-by-step explanation:
One whole ribbon would equal out to 10, this number multiplied by 2 would be 20. Therefore meaning she should have 20 1/10 sized pieces of ribbon.
if a/4=2/3, then (a-4)/4 would equal
a. -2/3
b. -1/3
c. 0
d. 1/3
Answer:
b. -1/3
Step-by-step explanation:
a/4=2/3
a=8/3
(a-4)/4
(8-12)/12
=-4/12
=-1/3
Answer:
-1/3
Step-by-step explanation:
a/4=2/3
Multiply each side by 4
a/4 *4=2/3 *4
a = 8/3
(a-4)/4
(8/3 - 4) /4
Getting a common denominator
(8/4 - 12/3) /4
(-4/3)/4
-1/3
find -15(-8)
A. 120
B. 80
C. -23
D. -120
Answer:
A
Step-by-step explanation:
-15(-8)
=+(15*8)
=120
So, the ans is A
The bars of a histogram should be shown in increasing order. true or false
Answer:
false it can be in any order but must be according to the set of data
Montraie is driving on a long road trip. He currently has 13 gallons of gas in his car.
Each hour that he drives, his car uses up 1 gallon of gas. How much gas would be in
the tank after driving for 6 hours? How much gas would be left after t hours?
Answer:
7 gallons
Step-by-step explanation:
Montraie is driving on a long road trip
He currentlyhase 13 gallons of fuel in his car
Each hour that he drives, he uses up 1 gallon of fuel
Therefore the amount of gas that would be left after 6 hours can be calculated as follows
= 13-6
= 7
Hence there will be 7 gallons of fuel left
=
move numbers to the lines to complete the sentence about the image A’B’C’D .
line segment A’B has the length of (blank) units , the line segment C’D’ has a length of (blank) units
2. 3. 4. 5. 6. 8.
Answer:
first blank- 2 second blank- 3 1/2 or 4 may be 3 too
Step-by-step explanation:
well when you look at the shape you can go from a to b and count the blocks which it would be 2
and you would want to do the same thing with C,D
Please help. I am very confused about this problem.
jzgsgßiqhwgwgah I don't know
Answers:
number of sides = 15regular polygon name = regular 15-gon=======================================================
Explanation:
If 156 degrees is the interior angle measure, then 180-156 = 24 is the exterior angle measure.
Divide 360 over this to find that 360/24 = 15
This means the regular polygon has 15 sides.
I'm using the idea that if n is the number of sides, then 360/n is the exterior angle measure. So 180 - (360/n) is the interior measure.
how do you translate "six more than x is equal to four." as a equation.
Answer:
6>x=4
hope that helps!
please mark brainiest<3
Find the volume of the cube, if one face of the cube has an area of
121 sq.m.
Answer:
1331 m^2
Step-by-step explanation:
To find the volume of the cube, we should first find the length of one side's edge. The square root of 121 (the face area) gives us our edge length, 11.
Now, to find the volume of the whole cube, we use the equation V=11^3, and our result is 1331.
Last question of the day :)
Answer:
yehshjdjejrdjjej3u Rudd ixjje
who understands this sum?
Answer:
$31728
Step-by-step explanation:
sorry if I'm wrong
Find the measure of angle A
Answer:
This is an isosceles triangle, meaning it has 2 congruent angles and one other angle.
Looking at this triangle, we know that ∠B = ∠C.
∠B = 57 degrees
All the angles in a triangle add up to 180, so you need to subtract the two values from 180 to get ∠A.
∠A = 180 - 57 - 57
= 66 degrees
Hope this helps!
George rolls a six sided die. What is the possibility that he rolls a 1 or a prime Number.
Answer:
1: 16.7%
prime number: 50%
Step-by-step explanation:
divide the numbers
Answer:
2/3
Step-by-step explanation:
There are 6 possible numbers
all of the prime numbers from 1 to 6 are
2, 3, 5 ( plus 1 because this problem is counting 1 along with the prime numbers)
That is 4 numbers
4 out of 6 numbers
so there is a 4/6 or 2/3 chance that George will roll a 1 or a prme number
Please help fast!! What is the range of the scores shown in the stem and leaf plot
95
40
58
37
Answer:
37
Step-by-step explanation:
Highest take the lowest
95-58=37
The area of the pacific ocean is more than 60 million square miles. What is that in scientific notation?
Answer: 6.0 x 10^7
Step-by-step explanation:
60000000 = 6.0 x 10^7
Part A: Estindlate the solution from the graph. -
Part B: What is the equation of each line in the system? blue line: _ and red line:
Answer:
Part A
The estimated solution of the graph is (37/29, -30/29)
Part B
The equation of the blue line is y = 0.6·x - 1.8
The equation of the red line is y = (-4/3)·x + 2/3
Step-by-step explanation:
Part A
From the given graph, we have two lines, one red and one blue line, intersecting in Quadrant IV
Given that the equation of the lines are also required, we find the solution of the graph, through the equation of the lines as follows;
The points through which the blue line passes are (-2, -3), and (3, 0)
The slope of the blue line, [tex]m_b[/tex] = (0 - (-3))/(3 - (-2)) = 0.6
Therefore, we have;
y - 0 = 0.6·(x - 3)
∴ The equation of the blue line is y = 0.6·x - 1.8
The approximate points through which the red line passes are (-1, 2) and (-2.5, 4)
The slope of the red line, [tex]m_r[/tex] = (4 - 2)/((-2.5) - (-1)) = -4/3
Therefore, we have;
y - 2 = (-4/3)·(x - (-1)) = (-4/3)·x - 4/3
∴ The equation of the red line is y = (-4/3)·x - 4/3 + 2 = (-4/3)·x + 2/3
y = (-4/3)·x + 2/3
The solution for the graph is the point where the y-values are equal
Therefore, wat the solution point, y = y, and 0.6·x - 1.8 = (-4/3)·x + 2/3
0.6·x + 4/3·x = 1.8 + 2/3
x = (1.8 + 2/3)/(0.6 + (4/3)) = 37/29 ≈ 1.28
At the solution of the graph, y = 0.6 × (37/29) - 1.8 = -30/29
Therefore, the estimated solution of the graph is (37/29, -30/29)
Part B
From the above solution of the graph, we have;
The equation of the blue line: y = 0.6·x - 1.8
The equation of the red line: y = (-4/3)·x + 2/3
A company has designed its new packaging for products to be shaped liked the prism shown. If the cost of packaging is $0.03 per square inch, find the total cost of the package shown. (10 inches horizontally, 4 inches vertically, and 4 inches on the side)
Answer:
$5.76
Step-by-step explanation:
We solve using the formula of the area of a rectangular prism
A = 2(LW + LH + WH)
The dimensions of the package are given as: 10 inches horizontally, 4 inches vertically, and 4 inches on the side
=2 × (4 × 10 + 4 × 10 + 4 ×4)
=192 square inches
If the cost of packaging is $0.03 per square inch, the total cost of the package is calculated as:
1 square inch = $0.03
192 square inches = x
Cross Multiply
= 192 × $0.03
= $5.76
Stuck on this one. I can’t remember the process to get the answer
Find the volume of a regular square pyramid with base edge 10 ft. and height 12 ft.
120 ft
75ft?
400 ft
D 300 ft?
Answer:
V = 400 ft^3
Step-by-step explanation:
The area of the base of this regular square pyramid is (10 ft)^2, or 100 ft^2.
Recalling that the area of a pyramid is V = (1/3)(base area)(height), in this case we get V = (1/3)(100 ft^2)(12 ft) = 400 ft^3
Find the area of the equilateral triangle when the base is 2.0 cm and the top angle is 50°
Answer:
There is an error in the question.
All angles in an equilateral triange are 60º
PLEASE HELP QUICKLY!!! Use the following image to answer the questions below:
HELP PLZZZZZZZ ITS FOR A TESTTT
Answer:
x = 9 , y = 27
Step-by-step explanation:
Given that the given polygons are similar , So their corresponding sides will be proportional .
Look at the base sides . They are 32 & 24. So the , ratio of sides is ,
=> Ratio = 32/24 = 4/3 .
This ratio will be same for all sides .
So that ,
=> x - 1 / 6 = 4/3
=> 3x - 3 = 24
=> 3x = 27
=> x = 9
Similarly ,
=> y + 1 / 21 = 4/3
=> 3y + 3 = 84
=> 3y = 81
=> y = 27
So the correct choice is last option .
