Answer:
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
Step-by-step explanation:
Given
A is the set of integers greater than - 7 and less than - 3
B={c, h, j, k, v, y}
For set A:
The integers greater than -7 will be -6,-5 ....
As the set has integers less than -3, the set will be:
[tex]A = \{-6,-5,-4\}[/tex]
Cardinalities:
Cardinality is the number of elements in the set.
So,
[tex]n(A) = 3\\n(B) = 6[/tex]
Now for the statements:
-6 ∈ A True as -6 is a member of set A
-14 ∈ A False as -14 is not a member of A
k ∈ B True
Q∈B False
Hence,
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
write the equation of the line in standard form passing through (2,-4) with a slope of -7
Answer:
7x+Y=-2
Step-by-step explanation:
(y-y1)=m(x-x1)
(Y+4)=-7(x-2)
Y+4=-7x+2
Y+7x=2-4
7x+Y=-2
Write an equivalent addition expression to : -10 – (-4)
Answer:
-6
Step-by-step explanation:
-10-(-4)=-1+4=-6
Hope this helps plz mark brainliest ;D
Determine an expression for dy
dx given that x = sin3
(t)andy = cos3
(t)
Answer:
[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]
Step-by-step explanation:
Recall that using the chain rule we can state:
[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]
And similarly:
[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]
now notice that we can find [tex]cos(t) = \sqrt[3]{y}[/tex] from the expression for y,
and [tex]sin(t) = \sqrt[3]{x}[/tex] from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]
What is the equation of the line that passes through the point (5,2) and has a slope
of -3/5
Answer:y = -0.6x + 5
Step-by-step explanation:
Answer:
yessir the one on top is right btw
Step-by-step explanation:
hope this helped
The leg of a right triangle is 2 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle?
2 units
6 units
Square root of 12 units
Square root of 20 units
Answer:
its 6 units
Step-by-step explanation:
Answer:
Square root of 20
I really hope i'm right sorry in advanced if i'm not
While on vacation, Jorge and Jackie traveled to Bryce Canyon National Park in Utah. They were impressed by the different elevations at the viewpoints along the road. The graph describes the elevations for several viewpoints in terms of the time since they entered the park. The graph represents a function E(t). Part A:Describe why the graph represents a function. Part B:Identify the domain in range of the function.
Answer:
timeline
Step-by-step explanation:
the table shows the same time I don't have your phone you u you y you can get a hold of y have a lot to do it you got a
The domain and range provides a definition for a graph
Part A: The graph represents a function because a vertical line drawn from the horizontal crosses the graph only once
Part B. Domain: 0 ≤ t ≤ 30
Range: 7000 < f(t) ≤ 9,300
Reason:
Part A: The reason why the graph represents a function is that a function is a one to one relationship that maps each element of the set known as the domain to exactly one element of the set which is the range of the function
Therefore, a vertical line drawn on the graph of a function crosses the graph only once, such that one input cannot have two outputs
Which gives that the graph is a function, given that all the vertical lines from the horizontal axis crosses the graph f(t) at exactly one point
Part B
Domain:
The domain of a function are the possible input values of the function
In the graph, the possible values of the time, t are; 0 ≤ t ≤ 30
The domain of the function is 0 ≤ t ≤ 30
Range:
The range of a function are the possible output values of the function
The range of the given function f(t) are; from approximately 7,000 feet to approximately 9,000 feet, which gives;
The range of the function: 7000 < f(t) ≤ 9,300
Learn more here:
https://brainly.com/question/24508506
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What is the unit rate if the candy is $7.80 for 2 pounds?
Answer:
= 3.9 candy per pound
Step-by-step explanation:
This is a fraction equal to
7.8 candy ÷ 2 pounds
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2
7.8 candy ÷ 2
________
2 pounds ÷ 2
=
3.9 candy
_______
1 pound
=
3.9 candy
_______
pound
= 3.9 candy per pound
Based on the pattern in the table, what is the value of a?
Powers of 2
Value
2 Superscript negative 1
One-half
2 Superscript negative 2
One-fourth
2 Superscript negative 3
one-eighth
2 Superscript negative 4
StartFraction 1 Over 16 EndFraction
2 Superscript negative 5
StartFraction 1 Over 32 EndFraction
2 Superscript negative 6
a
Negative 64
Negative 12
StartFraction 1 Over 16 EndFraction
StartFraction 1 Over 64 EndFraction
Answer:1/64
Step-by-step explanation: I got it right
Based on the pattern in the table, the value of a is StartFraction 1 Over 64 EndFraction.
What are Exponents?Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.
Given is a pattern, which is the powers of 2.
The first term is 2⁻¹ = 1/2
The second term is 2⁻² = 1/ 2² = 1/4
The third term is 2⁻³ = 1 / 2³ = 1/8
The fourth term is 2⁻⁴ = 1 / 2⁴ = 1/16
The fifth term is 2⁻⁵ = 1/ 2⁵ = 1/32
The sixth term is 2⁻⁶ = 1/ 2⁶ = 1/64
So the value of a is 1/64.
Hence the value of a is 1/64.
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A submarine started at the surface of the water and
was moving down at –15 kilometers per
minute
toward the ocean floor. The submarine traveled at
this rate for 52 minutes before coming to rest on the
ocean floor. What is the depth of the ocean floor?
Answer:
The depth of the Ocean Floor is -780 kilometers
Step-by-step explanation:
The answer is -780 because -15 multiplied by 52 equals -780.
Use this picture and help please
Answer:
This would be 55 degrees because the sum of angles A, B and C = 180 degrees
Drag the phrases into the box to match each expression.
Answer:
theres no image
Step-by-step explanation:
ANSWER QUICK PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
case a) y=1/3x+8
case b) y=-3x+28
Step-by-step explanation:
case a)
parallel lines has the same slope, then, the searched line has the form:
[tex]y=\frac{1}{3} x +b[/tex]
Now, in order to find b, we must use the given point (6,10). By substituying this point into the last equation, one has
[tex]10=\frac{1}{3} 6+b\\10=\frac{6}{3} +b\\10=2+b\\b=10-2\\b=8[/tex]
Then, the line equation is y=1/3x+8
case b)
the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line, that is
[tex]m=-\frac{1}{\frac{1}{3} } \\m=-3[/tex]
Hence, the searched line has the form y=-3x + b. Now, in order to find the y-intercept b, we must use the given point (6,10). Therefore,
[tex]10=-3(6)+b\\10=-18+b\\b=10+18\\b=28[/tex]
Hence, the searced equation is y=-3x+28
y= -2x+8
what is the value of y when 0 is the value of x?
Not sure what you mean but will be explaining about y = 0 and x =0 anyway.
So for x = 0, that means the value of x is 0.
y = -2(0)+8
y=0+8
y=8
So when x = 0, the value of y is 8 (y = 8) or we can write (0,8)
For y = 0, that means the value of y is 0.
0=-2x+8
-8=-2x
-2x=-8
x=4
So when y = 0, x = 4. We can write as (4,0)
what kind of graph is this?
Answer:
Linear
General Formulas and Concepts:
Types of Graphs
LinearQuadraticExponentialCubicSquare rootCube rootStep-by-step explanation:
Whenever the graph is a straight line (either a diagonal or a horizontal, NOT a vertical line), it will always be linear.
The ______ identity is 1.
Answer:
I believe its ,multiplication
Step-by-step explanation:
because any number you multiply be one is one
mark brainliest if correct please
Answer:
multiplication
Step-by-step explanation:
Cause of Peter griffen
Who can help me with this for algebra 2
i need helppp!!
worth 10 points
Answer:
I think that it is 120 but not sure
Step-by-step explanation:
sorry if wrong
Worth 75 points!! Need help with calculus
1. Determine the intervals on which each function is increasing or
decreasing
(a) f(x) = x^3 - 11/2x^2 - 4x
Answer:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]
And we want to determine the intervals for which the function is increasing or decreasing.
We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.
To find the critical points, we need to find the first derivative and then solve for the x. So:
[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]
Differentiate:
[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]
Set the derivative equal to 0 and solve for x:
[tex]0=3x^2-11x-4[/tex]
Factor:
[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]
Zero Product Property:
[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]
Therefore, our critical points are -1/3 and 4.
We can thus sketch the following number line:
<————-(-1/3)——————————————(4)—————>
Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.
For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:
[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]
The result is positive.
Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).
For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:
[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]
The result is negative.
Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).
And finally, for greater than 4, we can use 5:
[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]
The result is positive.
Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.
Therefore:
[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]
In interval notation:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
How do you do these two questions?
Answer:
(x − π)⁷ / 5040
(x − 1)³ / 16
Step-by-step explanation:
Taylor series expansion of a function is:
f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(x₀) / n! (x − x₀)ⁿ
where f⁽ⁿ⁾(x₀) is the nth derivative evaluated at x₀.
For the first problem, f(x) = sin x and x₀ = π. We want the seventh degree term, so n = 7.
The seventh degree term is therefore: f⁽⁷⁾(π) / 7! (x − π)⁷
Find the seventh derivative of sin x:
f(x) = sin x
f⁽¹⁾(x) = cos x
f⁽²⁾(x) = -sin x
f⁽³⁾(x) = -cos x
f⁽⁴⁾(x) = sin x
f⁽⁵⁾(x) = cos x
f⁽⁶⁾(x) = -sin x
f⁽⁷⁾(x) = -cos x
Evaluated at π, f⁽⁷⁾(x) = 1. So the seventh degree term is (x − π)⁷ / 5040.
For the second problem, f(x) = √x and x₀ = 1. We want the third degree term, so n = 3.
The third degree term is therefore: f⁽³⁾(1) / 3! (x − 1)³
Find the third derivative of √x:
f(x) = √x
f⁽¹⁾(x) = ½ x^-½
f⁽²⁾(x) = -¼ x^-³/₂
f⁽³⁾(x) = ⅜ x^-⁵/₂
Evaluated at 1, f⁽³⁾(x) = ⅜. So the third degree term is (x − 1)³ / 16.
Please Help ASAP IT'S DUE TODAY!!
140 ÷ 20 = 7
7 × 15 = 105
24
6 1/2
I need to find the slope.
Answer:
The slope is 3/2
Could someone please guide me towards solving side x I know I have to use trig but I'm completely lost
Answer:
x = 33.13 units
Step-by-step explanation:
Let the altitude of the triangle be h units.
[tex] \sin 65 \degree = \frac{h}{31} \\ \\ 0.906307787 = \frac{h}{31} \\ \\ h = 0.906307787 \times 31 \\ \\ h = 28.0955414 \\ \\ \cos \: 32 \degree = \frac{h}{x} \\ \\ 0.8480480962 = \frac{28.0955414}{x} \\ \\ x = \frac{28.0955414}{0.8480480962} \\ \\ x = 33.1296556 \\ \\ x \approx 33.13 \: units[/tex]
Answer:
x = 23.7926Step-by-step explanation:
Step 1
Find the length of vertical line segment, lets call it h. Use function cos
h/31 = cos 66°h = 31 * cos 66° = 31*0.4067 = 12.6077Step 2
Find x using another function, sin
h/x = sin 32°x = h / sin 32°x = 12.6077 / 0.5299x = 23.7926There are 7 students in a class: 2 boys and 5 girls.If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?
Answer:
two sevenths
Step-by-step explanation:
Chad bought 1 box of raisins. He gave 1/6 of it to one brother, 1/4 to another brother, and he kept the rest for himself. What fraction did he keep?
Write the answer in the simplest form
Answer:
He kept 7/12 of the box.
Step-by-step explanation:
We add and convert both 1/6 and 1/4 because we cant add fractions with unlike denominators.
1/6 = 2/12 | 1/4 = 3/12
then add.
2/12 + 3/12 = 5/12.
we subtract this from a whole, which is 12/12.
12/12 - 5/12 = 7/12
he keeps 7/12 of the box
hope this helped!
Lines
AB
and
CD
are straight lines. Find x and y. Give reasons to justify your solutions.
Answer:
x = 18
y = 54°
Step-by-step explanation:
m<MON = 90° (given)
m<MOA = 72° (given)
m<AON + m<MOA = m<MON (Angle Addition Postulate)
m<AON + 72° = 90° (Substitution)
Subtract 72° from each side
m<AON = 90° - 72°
m<AON = 18°
m<AOD = 18° + 2x
m<BOC = 3x
m<AOD = m<BOC (vertical angles)
18 + 2x = 3x (Substitution)
Subtract 2x from each side
18 = 3x - 2x
18 = x
x = 18.
72° + y + 3x = 180° (angles on a straight line)
Plug in the value of x
72 + y + 3(18) = 180
72 + y + 54 = 180
126 + y = 180
Subtract 126 from both sides
y = 54
Which of these shows the following expression factored completely? 6x2 – 13x +5
Answer:
B
Step-by-step explanation:
That's my guess.
Answer:
C
Step-by-step explanation:
Can anyone thats really extremely excellent at math, history and english please help me out with my questions. Truly need help. Please only answer if you know how to. ( Just click on my name and go to my questions) answer.
Answer:
Meeeeeeeeeeeeeeeeeeeeeee
answer pls hurry need this asap
Answer:
y=-6x-8
Step-by-step explanation:
well first of all the line passes through (0,-8) ehich would give you a y-int of -8, to find the slope of y=mx+b you could do rise/run. fi you found a point and counted down to another point it'd be -6, then count the run it'd be 1, -6/1 equals -6
Write an equation in point-slope form and slope-intercept form for the line.
passes through (6, -6), slope = 5
Answer:
y = 5- 36
Step-by-step explanation:
6 is the x
-6 is the y
y=mx+b
so m times x, m is the slope
5 times 6 is 30
-6=30+b
so -36
y=5x-36
SORRY IF IM WRONG I TRIED