..................................
(90 Points)
(Score for Question 1: ___ of 10 points)
A local newspaper charges $42 per half-page advertisement and $86 per full-page advertisement. Kathryn has a budget of $1192 to purchase 20 advertisements.
• Define a variable for each unknown.
• Write a system of equations to represent the situation.
• How many full-page advertisements does Kathryn purchase?
• Show your work.
• How many half-page advertisements does Kathryn purchase?
Show your work.
Answer:
Let x = number of half-page advertisements
Let y = number of full-page advertisements
[tex]\begin{cases} 42x + 86y = 1192\\ x + y = 20\end{cases}[/tex]
8 full-page advertisements
12 half-page advertisements
Step-by-step explanation:
Definition of variables
Let x = number of half-page advertisements
Let y = number of full-page advertisements
Given information:
cost per half-page advertisement = $42cost per full-page advertisement = $86total budget = $1192number of advertisements to purchase = 20Using the given information, we can write a system of equations:
Equation 1: 42x + 86y = 1192
Equation 2: x + y = 20
To solve the system of equations, rearrange Equation 2 to make x the subject:
⇒ x = 20 - y
then substitute this into Equation 1 and solve for y:
⇒ 42(20 - y) + 86y = 1192
⇒ 840 - 42y + 86y = 1192
⇒ 840 + 44y = 1192
⇒ 44y = 352
⇒ y = 8
Substitute the found value of y into Equation 2 and solve for x:
⇒ x + 8 = 20
⇒ x = 12
Therefore, Kathryn purchased:
8 full-page advertisements12 half-page advertisementswhat is the equation
Answer:
[tex]y = \sin( \frac{2\pi}{3} x) [/tex]
Step-by-step explanation:
The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:
[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]
A small country is comprised of five states, A, B, C, D, and E. The population of each state is given in the following table. Congress will have 57 seats divided among the five states according to their respective populations. Use Jefferson's method with d=32,920 to apportion 57 seats
Based on Jefferson's method and the value of d, the apportionment of the 57 seats will be:
A - 4 seats.B - 5 seats. C - 10 seats.D - 16 seats.E - 22 seats.How will the seats be allocated?This is done by dividing the population of the state by the d value and then rounding this off:
State A:
= 138,352 / 32,920
= 4.2
= 4
State B:
= 181,282 / 32,920
= 5.5
= 5
State C:
= 337,026 / 32,920
= 10.23
= 10
State D:
= 549,634 / 32,920
= 16.6
= 16
State E:
= 729,736 / 32,920
= 22.1
= 22
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Find the equation of the line that is perpendicular to the graph of y=1/6x+3 and passes through (6.-6)
Answer:
y=−6x−36
Step-by-step explanation:
ez math
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.
The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.
The function we have is:
y = ∛(x - 5)
So cubic root is given
Here we notice that when x = 0, we have:
y = ∛-5, this is the y-intercept
And when x = 5 we have:
y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.
Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
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Answer:A
Step-by-step explanation: Edge 2022
what is the first shape
Answer:
The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron
Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x? (1 point) 3 4 13 22
Answer: 3
Step-by-step explanation:
The sine of an angle is equal to the cosine of its complement, so
[tex]4x+10=2x+16\\\\2x+10=16\\\\2x=6\\ \\ x=3[/tex]
find the area of this shape
Answer:
Area of shape is 9.42 units²
Step-by-step explanation:
From the picture we observe:
1. The shape is 3 quarters of circle as one quarter is excluded (note the right angle);
2. The radius of the circle is 2 units.
Use area formula of circle to find the area of given shape:
A = πr², area of circleA = 3πr²/4 = 3*3.14*2²/4 = 9.42 units², area of shapeAnswer:
a = 4pi
Step-by-step explanation:
The formula of finding a area of a circle is "a = piR^2.
Replace the R with the radius which is 2 for this circle.
if f(x)=5^2x-2 and g(x)=x+1, find (f-g) (x)
The function (f-g) (x) is represented as 5^2x - 3 - x .
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)=5^2x-2
g(x)=x+1
Then, the function
(f-g) (x) = 5^2x-2 - (x+1)
Distribute the negative;
(f-g) (x) = 5^2x-2 - x - 1
(f-g) (x) = 5^2x - 3 - x
Hence, the function (f-g) (x) is represented as 5^2x - 3 - x .
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Find f(g(3)) and g(f(-2)).
f(x)=x²-1 and g(x)=2x-3
Answer:
1. 8
2. 3
Step-by-step explanation:
[tex]f(g(3)) \\= f(2(3)-3))\\=f(3)\\=3^2-1\\= 9-1\\=8\\\\g(f(-2))\\= g((-2)^2-1)\\=g(4-1)\\=g(3)\\=2*3-3\\=3[/tex]
What is the area of a rectangle with vertices at (6, −3), (3, −6) , (−1, −2), and (2, 1)? Enter your answer in the box. units²
The area of triangle is 24 sq. units
What is Area of rectangle?Area of rectangle is product of its length to its breadth.
i.e., Area of rectangle = length* breadth
let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)
Using distance formula
AB = √(3-6)²+ (-6 +3)²
AB= √9 + 9
AB= √18
AB= 3√2
now,
BC= √(-1-3)²+ (-2 +6)²
BC = √16 +16
BC = √32
BC =4 √2
Now, Area of rectangle
= AB* BC
= 3√2 *4 √2
= 12*2
= 24 square units
Hence, area of rectangle is 24 sq. units
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An economy package of cups has 690 green cups. If the green cups are 30% of the total package, how many cups are in the package?
The total number of cups in the package is 2300.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here,
Let the total number of cups in the package be x.
Number of green cup = 690
Weightage of green cup in total = 30%
Now,
30% of x = 690
30/100 X x = 690
x = 690 X 100/30
x = 23 X 100
x = 2300
Thus, the total number of cups in the package is 2300.
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The polynomial f(x) has degree 3. Choose each statement that could describe all zeros of f.
The true statements are
(a) -one zero with multiplicity 3(d) -one zero with multiplicity 1 and one zero with multiplicity 2(l) -Three zeros with multiplicity 1Missing information in the question-one zero with multiplicity 3
-one zero with multiplicity 4
-one zero with multiplicity 5
-one zero with multiplicity 1 and one zero with multiplicity 2
-one zero with multiplicity 1 and one zero with multiplicity 3
-one zero with multiplicity 2 and two zeros with multiplicity 1
-one zero with multiplicity 2 and three zeros with multiplicity 1
-Two zeros with multiplicity 2
-Two zero with multiplicity 2 and two zeros with multiplicity 1
-Two zero with multiplicity 2 and three zeros with multiplicity 1
-Two zero with multiplicity 1
-Three zeros with multiplicity 1
-Four zeros with multiplicity 1
-Five zeros with multiplicity 1
How to determine the true statements?The function is given as:
f(x)
And it has a degree of 3
This means that
The total multiplicity of the zeros of the function is 3 It cannot have more than three zeros i.e. it can have 1, 2 or 3 zerosUsing the above highlight as a guide, the true statements are (a), (d),and (l)
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The two triangles are similar What is the value of x? Enter your answer in the box x =
Answ x=59
Step-by-step explanation:
Assuming that Hamid’s revenue is found by multiplying the book price by the number of copies sold, create an equation (in standard form) to model his revenue.
An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is x = ny.
What is an equation?The process of equating one thing with another.
Let Hamid’s revenue is $x and the price of book is $y.
If he sold n number of copies.
Then, the general equation will be x = n * y.
Therefore, an equation of Hamid's revenue will be x = ny.
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(x^4-13x^2+36)/(2x^2+10+12)
Answer:
Step-by-step explanation:
need help with this question im stuck
Answer:
answer is B. 100°
Step-by-step explanation:
if correct please I need brainlist
Answer:
100°
Step-by-step explanation:
Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.
The 80° angle and angle x are opposite each other, so:
x + 80° = 180°
x = 180° - 80°
x = 100°
A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?
The speed of the wind and the speed of the dragon in still air are respectively; 142.5 mph and 7.5 mph
How to calculate the speed?The dragon flew 300 miles with the wind in two hours.
After flying against the wind for two hours, he had made 270 miles of the return trip.
Let s be the speed in still air
Let w be the speed of the wind
Thus;
(s - w) = effective speed against the wind
and
(s + w) = effective speed with the wind
We know that;
distance = time * effective speed
Thus;
2(s + w) = 300
2(s - w) = 270
This can be simplified to get;
s + w = 150 -----(1)
s - w = 135 -----(2)
Add both equations to get;
2s = 285
s = 285/2
s = 142.5 mph.
Then, plane speed in still air is;
142.5 + w = 150
w = 150 - 142.5
w = 7.5 mph is the speed of the wind
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Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5, 5),A(5,5),A, left parenthesis, 5, comma, 5, right parenthesis, comma B(7,5)B(7,5)B, left parenthesis, 7, comma, 5, right parenthesis, C(7,-1)C(7,−1)C, left parenthesis, 7, comma, minus, 1, right parenthesis, and D(5,-1)D(5,−1)D, left parenthesis, 5, comma, minus, 1, right parenthesis.
Given these coordinates, what is the length of side BCBCB, C of this rectangle?
Answer:
The length of the side BC is 6 units.
Step-by-step explanation:
Distance formula: This works for any two points in 2D space with coordinates (x₁, y₁) for the first point and (x₂, y₂) for the second pointIt is the length of the line segment joining two pointsd = [tex]\sqrt{(x_{2} {-} x_{1})^{2} +(y_{2} {-} y_{1})^{2}}[/tex]For the given question:Rectangle ABCD
Coordinates of Point A,B,C,D
[tex]A = ( 5 , 5)B = (7, 5)C = (7 , -1)D = (5 , -1)[/tex]
As we are asked to find the length of side BC, we'll apply the Distance formula on side BC
BC = [tex]\sqrt{(7_ {-} 7)^{2} +(-1 {-} 5)^{2}}[/tex]
= [tex]\sqrt{(0)^{2} +(-6)^{2}}[/tex]
= [tex]\sqrt{ 36}[/tex]
= [tex]6[/tex]
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Please hurry:)
Which of the following is equivalent to…
Answer:
D
Step-by-step explanation:
B is the set of odd numbers greater than 5 and less than 21
Answer:
List method: {7,9,11,13,15,17,19}
Set method: {X:N where N is odd, N>5 and N<21}
The odd numbers greater than 5 and less than 21 are {7, 9,11,13,15,17,19}.
What are odd numbers?Odd numbers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly.
Odd numbers are opposite to even numbers this means that even numbers are numbers that can be divided by 2.
When we say numbers greater than 5 and less than 21 this means 5< x < 21
The odd numbers greater than 5 and less than 21 are ;
{7, 9,11,13,15,17,19}. These odd numbers are greater than 5 and less than 21.
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what is the sign of f on the interval -5/9 < X < 2/3
Note that the sign of f on the interval -5/9 < x < 2/3 is negative. (Option B)
What is the explanation for the above?To determine the sign of f(x) on the interval -5/9 < x < 2/3, we need to evaluate f(x) at a test point within this interval and determine if it is positive or negative.
Since we know that f(x) has zeros at x = -4, x = -5/9, and x = 2/3, we can use these points as our reference to choose test points.
Specifically, since the zeros at x = -5/9 and x = 2/3 are not included in the interval -5/9 < x < 2/3, we can choose any test point within this interval, such as x = 0.
Evaluating f(x) at x = 0, we get:
f(0) = (3(0) - 2)(0 + 4)(9(0) + 5)
= (-2)(4)(5)
= -40
Since f(0) is negative, we can conclude that f(x) is negative on the interval -5/9 < x < 2/3.
Therefore, the sign of f on the interval -5/9 < x < 2/3 is negative
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Full Question:
f(x) = (3x - 2) (x+4) (9x +5) has zeros at x = -4, x = -5/9, and x = 2/3, that is the sign of f on the interval -5/9 < x < 2/3?
what is the least common multiple of the numbers 8 and 12?
A. 24
B. 8
C. 4
D.96
Answer:
A. 24
Step-by-step explanation:
Least common multiple of 8 and 12 = 24
8× 1 = 8 12×1 = 12
8×2 = 16 12×2=24
8×3 = 24
L.C.M (8,12) = 24
The greatest multiple that occurs in both the multiples of 8 and 12, is 24.
Hence, the least common multiple here is 24.
Evaluate the piecewise-defined function for the indicated values. I’m just unsure of how to solve when the value isn’t given directly. Namely, how to solve for b through d
The value of the function at t=0 is 9 , 6<x<7 is -t+5, 1<n<2 is 9, for [tex]m^{2} +1[/tex] is 9.
Given function which is 9 for 0 to 5 , -t+5 for 5 to 8 and [tex]\sqrt{t-1}[/tex] for 8<t<11.
A) We have to find the function at t=0 which is 9 because it lies between 0<=t<5.
B) In this we have to find the value of the function when x=t lies between 6 and 7. is -t+5.
C) In this we have to find the value of Q(n) when n lies between 1 and 2 and the value becomes 9 because it lies between 0 and 5.
D) In this we have to find the function at [tex]m^{2} +1[/tex] when m belongs to [tex]\sqrt{7} and \sqrt{10}[/tex] the value of m lies between 2 and 4 and the value of m square +1 lies between 3 and 5. Hence the value of function at m square plus one is 9.
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For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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GUYS PLEASE HELP WITH THIS PLEASE
Examine how sounds of music are related to trigonometric functions.
What does change of amplitude do? How about frequency?
Using graphs and equations, represent multiple transformations explaining their relevancy to the sound wave
Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
The change of amplitude of a sound wave's amplitude is linked to the change in pressure that occurs due to the wave measured at a given location.
Frequency tells the number of waves that pass a fixed location in a specific time frame.
How does sound waves relate to trigonometric functions?Sound engineers uses the basic laws of trigonometry via sine and cosine graphs.
Note that all sounds can be broken down into a lot of sine waves, as sine waves comes together to form sounds.
Therefore, Trigonometry functions is often employed in taking the measurement of the level or the pitch of a sound wave or musical note.
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10% of an amount is 6.2 . Wirk out the original account
Answer:
the original amount was 62
Step-by-step explanation:
You can use the part over whole formula like this:
[tex]\frac{part}{whole} = ( \frac{6.2}{?} * \frac{10}{100})\\ ? = 62[/tex]
why?
because we know that 10% = 10/100, we can easily find out the answer by cross multiplying
? * 10 (let's use x, instead of ?)
=10x
6.2 * 100
= 620
Now we have an equation that looks like this: 10x = 620
By using the inverse operation tool (dividing each side by 10 to isolate x) we have:
x (or ?) = 62
Determine the rate of change equation by implicitly differentiating with respect to
time t.
x^4+ y^4 = 4y
By the power and chain rules, taking derivatives on both sides with respect to [tex]t[/tex] gives
[tex]4x^3 \dfrac{dx}{dt} + 4y^3 \dfrac{dy}{dt} = 4\dfrac{dy}{dt}[/tex]
or
[tex]4x^3 \dfrac{dx}{dt} + (4y^3-4) \dfrac{dy}{dt} = 0[/tex]
The graphs below have the same shapes. What is the equation for the red graph?
The equation of the red graphed function is: g(x) = 1 - x².
How to Find the Equation of a Graphed Function?Given the graph shown in the attachment below, the graphed function heads downwards, and the x - axis is intercepted at ( 1, 0 ) and (-1,0).
Thus, the x-intercepts, which is the zeros of the function, are: 1 and -1.
So, g(x) = (x + 1)(x -1)
Expand:
g(x) = 1 - x²
The equation of the red graph is: g(x) = 1 - x².
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what is the difference between a relation and function? Classify each of the following as a function, or not a function. State the domain and range
{(1,7),(1,14),(1,21)}
The relation is/isn't a function
Domain _ _ _
Range _ _ _
Leave Unused Fields Blank
Answer:
A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.
In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.
The given relation is not a function as the element 1 is related to 3 different elements in the second set.
Domain={1}
Range={7,14,21}
