Answer:
Hello,
Step-by-step explanation:
I suppose the question is to solve the equation.
[tex]Remember:\\\\sin(a)-sin(b)=2cos(\dfrac{a+b}{2} )*sin(\dfrac{a-b}{2} )\\cos(a)-cos(b)=2sin(\dfrac{a+b}{2} )*cos(\dfrac{b-a}{2} )\\\\\\sin(2a)+cos(4a)=cos(2a)+sin(4a)\\\\\Longleftrightarrow sin(4a)-sin(2a)=cos(4a)-cos(2a)\\\\\Longleftrightarrow 2cos(\dfrac{4a+2a}{2})*sin(\dfrac{4a-2a}{2})=2cos(\dfrac{4a+2a}{2})*sin(\dfrac{2a-4a}{2})\\\\\Longleftrightarrow cos(3a)*sin(a)=cos(3a)*(-sin(a))\\\\\Longleftrightarrow 2cos(3a)*sin(a)=0\\\\[/tex]
[tex]sin (a)=0\ or\ cos(3a)=0\\\\\boxed{k\in\ \mathbb{Z}\ : a=k*\pi\ or\ a=\dfrac{(2k+1)*\pi}{2} }\\[/tex]
What’s the answer to this?
Answer:
[tex]f(3x)=9x^2-3[/tex]
Step-by-step explanation:
One is given the following function:
[tex]f(x)=x^2-3[/tex]
One is asked to evaluate the function for ([tex]f(3x)[/tex]). Substitute ([tex]3x[/tex]) in place of ([tex]x[/tex]) then simplify. Remember that a number raised to an exponent is the same as that number times itself the number of times that the exponent indicates. One can apply this logic here while simplifying,
[tex]f(x)=x^2-3[/tex]
[tex]f(3x)=(3x)^2-3[/tex]
[tex]f(3x)=(3x*3x)-3[/tex]
[tex]f(3x)=(9x^2)-3[/tex]
[tex]f(3x)=9x^2-3[/tex]
A lottery ticket has a grand prize of $41.7 million. The probability of winning the grand prize is .000000023. Determine the expected value of the lottery ticket. (Round your answer to 3 decimal places.) Expected value
Answer:
000023 because if we take three 0's we can get 000023 and 417 million
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 4:
Of the three functions {f(x), g(x), h(x))} featured on the graph below (on the following page), rank the functions in order of greatest rate of growth to least.
9514 1404 393
Answer:
g, h, f
Step-by-step explanation:
A graph of two exponential curves will have the one with the least growth rate crossing under the one with the greater growth rate. Here, f(x) is shown crossing under g(x) and is on its way to a point of intersection with h(x). So, f(x) has the least growth rate.
g(x) and h(x) start out at about the same level, but g(x) curves upward faster, indicating it has the higher growth rate.
In order from greatest to least growth rate, the functions are ...
g(x), h(x), f(x)
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Step-by-step explanation:
How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??
The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.
O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.
O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.
Answer:
B. The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.
Step-by-step explanation:
just did the test
Graph the line.
Y=-1/4x+4
give a coordinates of the Vertex y =(x + 2)
.
squared - 1
Given:
The equation of a parabola is:
[tex]y=(x+2)^2-1[/tex]
To find:
The coordinates of the vertex of the given equation.
Solution:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex.
We have,
[tex]y=(x+2)^2-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1[/tex]
[tex]h=-2[/tex]
[tex]k=-1[/tex]
We know that the vertex of the parabola is (h,k).
Therefore, the vertex of the given equation is (-2,-1).
How many square inches of sheet metal are used to make the vent transition shown? (The ends are open.)
Answer:
Area of the metal sheet required = 364 square inches
Step-by-step explanation:
Area of the metal sheet required = Surface area of the lateral sides of the vent transition
Since, lateral sides of the vent is in the shape of a trapezoid,
Therefore, surface area of the vent = 4(Surface area of one lateral side)
= [tex]4[\frac{1}{2}(b_1+b_2)h][/tex]
Here, [tex]b_1[/tex] and [tex]b_2[/tex] are two parallel sides and [tex]h[/tex] is the distance between these parallel sides.
Surface area of the vent = [tex]4[\frac{1}{2}(8+5)14][/tex]
= 364 square inches
Therefore, area of the metal sheet required = 364 square inches
1
) Solve the equation
(85) for n.
8n
n =
?
Answer:
n = -10
Step-by-step explanation:
1 / 8^n = 8^5^2
We know that 1/a^b = a^-b
We also know that a^b^c = a^(b*c)
8^-n = 8^(5*2)
8^-n = 8^(10)
Since the bases are the same, the exponents are the same
-n = 10
n = -10
The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)∀x ∃y(x+y≥0)
The domain of a set is the possible input values the set can take.
It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers
Given that: ∀x ∃y(x+y≥0)
Considering x+y ≥ 0, it means that the values of x + y are at least 0.
Make y the subject in x+y ≥ 0
So, we have:
[tex]\mathbf{y \le -x}[/tex]
There is no restriction as to the possible values of x.
This means that x can take any real number.
Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.
Read more about domain at:
https://brainly.com/question/15110684
At what rates did she invest?
$1500 invested at___%
$800 invested at ____%
Answer:
4% and 5% respectively
Step-by-step explanation:
Let the intrest rate be x in the first account at x% and (x+1)% in the second account.
ATQ, 100=(x)*1500/100+(x+1)*800/100
x=4.
A man purchased a magazine at the airport for $2.69. The tax on the purchase was $0.13. What is the tax rate at the airport? The tax rate is %. (Round to the nearest percent as needed.)
We need to find the percent, let's start but making the equation.
The price is 2.69
The tax cost is 0.13
So what percent of 2.69 is = 0.13.
Equation: X/100 x 2.69 = 0.13
Multiply each side by 100 so we can get x alone with the price: 2.69x = 13
Now to get x alone, we must divide both sides by 2.69: x = 4.8
Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.
I hope this helps! :)
What is the product?
(-2a² + s) (5a^2 - 6s)
Answer:
10a²+17a²s-6s²
Step-by-step explanation:
(-2a²+s)(5a²-6s)
= -10a²+12a²s+5a²s-6s²
= -10a²+17a²s-6s²
Answer:
b
Step-by-step explanation:
This is Some next level Geometry
Step-by-step explanation:
Measure of Angle 1 is 115 due to corresponding angles postulate
Measure of Angle 2 is 65 is linear pair postulate.
La'Vonn rolled a die 100 times. His results are below. What is the relative frequency for La'Vonn rolling a 3?
Answer:
.15
Step-by-step explanation:
Which of the following phrases are expressions?
6-1>L,
-6k = -8,
1/4<3/8,
3 + 5
Answer:
-6k = -8 is an expression
A and C are inequalities
D is arithmetic
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
A. because the system of equations actually has only one solution
B. because the system of equations actually has no solution
C.because the graphs of the two equations overlap each other
D. because the graph of one of the equations does not exist
9514 1404 393
Answer:
C. because the graphs of the two equations overlap each other
Step-by-step explanation:
When a system of linear equations has an infinite number of solutions, the equations are "dependent." That means they both describe the same line. The graph will appear to be one line because the lines overlap each other.
__
Additional comment
The Desmos graphing calculator lets the texture of the graph be varied, so we can see that the two lines overlap. In the attached, one equation is graphed as a dotted red line, the other as a solid blue line.
How much does college tuition cost? That depends, of course, on where you go to college. Construct a weighted average. Using the data from "College Affordable for Most," estimate midpoints for the cost intervals. Say 46% of tuitions cost about $4,500; 21% cost about $7,500; 7% cost about $12,000; 8% cost about $18,000; 9% cost about $24,000; and 9% cost about $31,000. Compute the weighted average of college tuition charged at all colleges.
Answer:
0.127
Step-by-step explanation:
nine times a number
Answer:
if we do 9 times a number that will be
9x
Answer:
9x
Step-by-step explanation:
9 times a number (a variable) = 9x
PLS HELP
Evaluate the piecewise function at the indicated values from the domain
==========================================================
Explanation:
Piecewise functions are admittedly a bit confusing at first if you aren't familiar with them.
However, they aren't too bad. Effectively we have two functions going on depending on what the input is.
If the input x is less than 0, then we go for the top row and say [tex]f(x) = x^2[/tex]
OR
If the input x is greater than 0, then we go for the bottom row to say [tex]f(x) = \sqrt[3]{x}[/tex]
-------------------------------
In this case, the input is x = -8. So we go for the first row since this x value satisfies x < 0.
We would then say:
[tex]f(x) = x^2\\\\f(-8) = (-8)^2\\\\f(-8) = 64\\\\[/tex]
Which points us to choice A as the final answer.
Answer:
f(-8) = 64
Step-by-step explanation:
Input -8 into one of the formulas (either will work) and the answer should be 64. therefore, if x is -8, f(-8) would equal 64.
Help me with this question for 10 points please
9514 1404 393
Answer:
(a) 10 cm
Step-by-step explanation:
Since C is the midpoint of AB, the triangle shown is 1/4 of the rectangular area shown. When the tank is sitting horizontally on its 100 cm side, the water height will be 1/4 of the 40 cm height of the tank. It will be 10 cm.
__
More elaborate explanation
Triangle area = 1/2(AD)(AC) = 1/2(AD)(1/2(AB)) = 1/4(AD)(AB)
Whole tank area = (AD)(AB)
So, the triangle area is 1/4 the whole tank area. When the tank is tipped back to horizontal, the water area will still be 1/4 the whole tank area, so will be ...
water area = (1/4(AD))(AB)
and the height will be 1/4(AD) = 1/4(40 cm) = 10 cm
whats 5 + 5 i need help my iq is 1 i need help pls pls pls pls
Answer:
Here are some activities you can do to improve various areas of your intelligence, from reasoning and planning to problem-solving and more.
Memory activities. ...
Executive control activities. ...
Visuospatial reasoning activities. ...
Relational skills. ...
Musical instruments. ...
New languages. ...
Frequent reading. ...
Continued education.
A sample of 50 elements from a population with a standard deviation of 20 is selected. The sample mean is 150. The 90% confidence interval for is: a.165.0 to 185.0. b.146.4 to 153.6. c.145.3 to 154.7. d.171.8 to 188.2.
Answer:
c.145.3 to 154.7.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.
The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.
Thus the correct answer is given by option c.
a) __m=10km 25m =___km
b) __m=__km__m=1.5 km
Example :
a) 7250m= 7km 250m = 7.250km
Please help me
Answer:
a) 10,025 m = 10km 25m = 10.025 km
b) 1,500 m = 1 km 500 m = 1.5 km
Answer:
a) 10025m = 10km 25m = 10.025km
b) 1500m = 1km 500m = 1.5km
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion.
Unit conversion is the conversion between different units of measurement for the same quantity.
1 km = 1000 m
Solve:
a)
10km 25m = 10×1000 + 25 = 10025 m10km 25m = 10 + 25/1000 = 10.025 kmb)
1.5km = 1 + 0.5 × 1000 = 1km 500m1.5km = 1.5 × 1000 = 1500mHope this helps!! :)
Please let me know if you have any questions
A line passes through the point (5,6) and is parallel to the line given by the equation y = 2x - 12. Which of these is an equation for the line? O A. y-5=-264-6) B. y - 6 = -2(x - 5) C. y + 6 = 2(x + 5) D. Y- 6 = 2(x - 5)
Answer: D
Step-by-step explanation:
(lines parallel to each other have the same slope)
slope = m = 2
y = mx + b, (5,6)
6 = 2(5) + b
6 = 10 + b
b = -4
y = 2x - 4
y - 6 = 2(x - 5)
y - 6 = 2x - 10
y = 2x -4
If a(x + 1) + b(x − 1) − 2 = 0 for all real x, then a =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Answer:
D) 1
Step-by-step explanation:
using the distributive property we have ax+a+bx-b-2=0. because the equation is true for all real x, ax=-bx. this means a-b-2=0 and a=-b. a-b-2=0 becomes a=b+2. then we substitute a for -b and get -b=b+2 which becomes 2b=-2 so b=-1. since a=-b, a=1
Given f(x) = 4x - 3 and g(x) = 9x + 2, solve for (f + g)(x).
[tex]\\ \sf\longmapsto (f+g)(x)[/tex]
[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]
[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]
[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]
[tex]\\ \sf\longmapsto 13x-1[/tex]
Answer:
13x - 1
Step-by-step explanation:
f(x) + g(x) = 4x - 3 + 9x + 2
f(x) + g(x) = 4x+9x + 2 - 3
f(x) + g(x) = 13x - 1
Basketball A basketball player makes 8 of 12 free throws
in the first game of the season. If she shoots with the same
accuracy in the second game, how many of the 15 free
throws she attempts will she make?
If (3a+4b)=16 and ab=4, find the value of (9a^2+16b^2).
Answer:
160
Step-by-step explanation:
(3a+4b) = 16
ab = 4
Square (3a+4b)
(3a+4b)(3a+4b) = 16^2
9a^2 + 12ab+12ab+16b^2 = =256
9a^2 +16b^2 +24ab=256
9a^2 +16b^2 +24ab - 24 ab=256 -24ab
9a^2 +16b^2 =256- 24ab
We know ab = 4
9a^2 +16b^2 =256- 24*4
9a^2 +16b^2 =256- 96
9a^2 +16b^2 =160
At which values of x does the function Fx) have a vertical asymptote? Check
all that apply.
F(x) =
2/3x(x - 1)(x + 5)
I A. -1
B. 2
C. 1
D. -5
E. 0
F. 3
9514 1404 393
Answer:
C, D, E
Step-by-step explanation:
Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...
x = 0 ⇒ x = 0 . . . . . . choice E
x -1 = 0 ⇒ x = 1 . . . . . choice C
x +5 = 0 ⇒ x = -5 . . . choice D
find the value of the trigonometric ratio
