Let the cost of surfing lesson be x and the cost of Parasiling be y
From the question, both surfing lesson and parasailing cost $130
Hnece;
x + y = 130 ---------------------------(1)
From the question, 25 people take surfing lesson and 30 pupil went for parasailing and a total of $3, 650 was collected
Hence;
25x + 30y = 3650--------------------------------(2)
We can now solve equation (1) and (2) simultaneously
Using elimination method,
multiply through equation(1) by 30
30 x + 30 y = 3900 ------------------(3)
subtract equation(1) from equation (3)
5x = 250
divide both-side of the equation by 5
x = 50
substitute x = 50 into equation (1) and then solve for y
x + y = 130
50 + y = 130
subtract 50 from both-side of the equation
y = 130 - 50
y =80
Therefore, the discount price of Surfing lesson is $50 while the discount price for parasailing is $80
ANSWER IMMEDIATELY PLEASE Identify the number of roots each polynomial has.Number one. 3x^4-2x^2+17x-4Number two. 12x^5+x^7-8+4x^2Number 3. 15+6x
Step 1
The degree of the leading term determines how many roots a polynomial has. Examine the highest-degree term of the polynomial – that is, the term with the highest exponent. That exponent is how many roots the polynomial will have. So if the highest exponent in your polynomial is 2, it'll have two roots; if the highest exponent is 3, it'll have three roots; and so on. A polynomial with a leading degree of 5 has 5 roots.
Step 2
[tex]\begin{gathered} Leading\text{ term 3x}^4 \\ Number\text{ of roots 4} \end{gathered}[/tex][tex]\begin{gathered} Leading\text{ term x}^7 \\ Number\text{ of roots 7} \end{gathered}[/tex]
[tex]Number\text{ of roots 1}[/tex]
I need help on my math
To simplify the expression 19+(11+37), solve first the expression inside the parenthesis:
[tex]11+37=48[/tex]Then:
[tex]19+(11+37)=19+48[/tex]Finally, add 19 and 48:
[tex]19+48=67[/tex]Therefore:
[tex]19+(11+37)=67[/tex]a transformation where a figure is flipped over a line1. dilation2.translation3.refelction4rotation
The answer is reflection
If 15 people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
There are 105 handshakes that take place at the meeting.
To find the number of handshakes, we can use a formula that counts the number of combinations of two items from a set of n items.
The formula is:
[tex]n * (n - 1) / 2[/tex]
In this case, n is the number of people, which is 15.
So, we plug in 15 into the formula and get:
[tex]15 * (15 - 1) / 2[/tex]
Simplifying, we get:
[tex]15 * 14 / 2[/tex]
Multiplying, we get:
[tex]210 / 2[/tex]
Dividing, we get:
[tex]105[/tex]
Based on the information marked in the diagram, AABC and _DEF must becongruent.A. TrueB. False
Given:
Two right triangles ABC and DEF are given.
In which AB = DE
Required:
Find the triangles ABC and DEF must be congruent, true, or false.
Explanation:
In triangle ABC and DEF
[tex]\begin{gathered} AB=DE\text{ \lparen Given\rparen} \\ \angle A=\angle D\text{ \lparen90}\degree) \\ \angle C=\angle F \end{gathered}[/tex]Thus the triangles must be congruent.
Final Answer:
Option A is true.
What is 2.078 rounded to the hundredths place?
2.078 rounded to the hundredths place is 2.08.
After the decimal, the 0 is the tenth place, the 7 is the hundredth place, and the 8 is the thousandth place. To round to the hundredths place, we look at the number after the 7. Since it his higher than 5, we increase the 7 by 1, to give us a final answer of 2.08.
triangle PQR with vertices P(6,-6) Q(9,-7) and R(7,-4) what is the area in square units of triangle PQR
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
P(6,-6)
Q(9,-7)
R(7,-4)
A = ?
Step 02:
To solve the exercise we must know the length of the sides.To solve the exercise we must know the length of the sides.
A = (b * h) / 2
side PR = b
side PQ = h
[tex]d\text{ = }\sqrt[]{(x2-x1)^{2}+(y2-y1)^{2}}[/tex][tex]b\text{ = }\sqrt[]{(7-6)^2+(-4-(-6))^2}[/tex][tex]b=\text{ }\sqrt[]{1+4}=\sqrt[]{5}=2.236[/tex][tex]\begin{gathered} h\text{ = }\sqrt[]{(9-6)^{2}+(-7-(-6))^{2}} \\ h\text{ = }\sqrt[]{9+1}=\sqrt[]{10}=3.162 \end{gathered}[/tex]Step 03:
A = (2.236*3.162) / 2 = 3.5355
The answer is:
3.54 ft²
Divide:7/4 ÷ 8/732/4949/3217/3281/32
7/4 ÷ 8/7
To divide fraction multiply the first fraction by the reciprocal of the second fraction:
7/4 x 7/8 = (7x7) / (4x8) = 49/32
A 8 kg eagle is flying up in the sky. You pull out your GPE gun and are able to tell that the bird has a GPE of 2,352 J. How high must the birdbe? (remember the bird is on Earth)
Energy = work per unit time
Energy = workdone / time
energy = mgh
m = 8kg
E = 2352J
since the bird is on the earth, definitely the gravitational force will be acting on it
g = 10m/s^2
2352 = 8 x 10 x h
2352 = 80 x h
2352 = 80h
divide both sides by 80
2352/80 = 80h/80
29.4 metres = h
h = 29.4 metres
The answer is 29.4 metres
Concrete costs $105 per cubic yard. Plato is making a rectangular concrete garage
floor measuring 33 feet long by 15 feet wide by 6 inches thick. How much will the
concrete cost?
A. $311850
B. $9.17
C. $962.50
D. $247.50
The cost of concrete is $311850.
According to the question,
We have the following information:
Concrete costs $105 per cubic yard. Plato is making a rectangular concrete garage floor measuring 33 feet long by 15 feet wide by 6 inches thick.
We know that the following formula is used to find the volume of cuboid:
Volume of cuboid = 33*15*6
Volume of cuboid = 2920 cubic yard
Now, to find the total cost for concrete, we will multiply the volume of concrete with the cost of concrete per cubic yard.
Cost of concrete = 2920*105
Cost of concrete = $311850
Hence, the correct option is A.
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[tex]f(x) = 2( {x})^{2} + 5 \sqrt{(x + 2} [/tex]the domain for f(x) is all real numbers greater then or equal to _____.
the domain for f(x) is all real numbers greater than or equal to -2.
Remember in the real number domain we can't have negative values inside the square root because they are not defined.
May I please get help with figuring out each triangle
Equilateral Triangle : All sides of triangle are equal
Issoceles Triangle : Only two sides of triangle are equal
Scalene Triangles : No sides of triangle are equal
In triangle A;
Sides of triangle are 8, 8, 4
Since two sides are equal i.e. both are of 8 unit
Thus, two sides are equal
Therefore triangle A is issoceled triangle.
Triangle 2
In the triangle,
All angles are equal which provides that all sides are equa
Therefore, Triangle B is an equilateral triangle
Triangle C;
In the given triangle one is of 90 degree
Since, all the angles areq different so, no two sides are equal
Therefore, triangle C is Scalene
Triangle D
In the given triangle as;
All four sides are equal, thus the triangle is an equilateral triangle
Equilateral triangle
Answer :
.
cost of a parent is $159.95 markup is 20% tax is 3%
that Solving for the retail price of a parrot with 20% markup and 3% taxes
We want to know the retail price of a parrot if it costs us $159.95 , knowing that we want to obtain 20% of profit and we're getting taxed 3%
Firts, we have to calculate the 20% of the original value ($159.95), and add that up. Then, we calculate the 3% of that value ($159.95 + 20% markup) and add it up, asl following:
[tex]\begin{gathered} 159.95\times\frac{20}{100}=31.99\rightarrow159.95+31.99=191.94 \\ 191.94\times\frac{3}{100}=5.76\rightarrow191.94+5.76=197.70 \end{gathered}[/tex]Thus, the retail price of the parrot, with 20% markup and 3% taxes, should be $197.70
Find the measure of indicated angle. Round to the 10th.
29.6 °
Explanation
we have a right triangle( a triangle with an angle of 90°), so we can use a trigonometric function
so
Step 1
a) Let
[tex]\begin{gathered} \text{angle}=\text{ ?} \\ \text{ hypotenuse( the longest side)= 23} \\ adjacent\text{ side= }20 \end{gathered}[/tex]so, we need to use a function that relates those values, it is
[tex]\begin{gathered} \cos \emptyset=\frac{adjacen\text{t side}}{\text{hypotenuse }} \\ \text{where }\emptyset\text{ is the angle} \end{gathered}[/tex]b) replace the values in the function and solve for the angle
[tex]\begin{gathered} \cos \emptyset=\frac{adjacen\text{t side}}{\text{hypotenuse }} \\ \cos \text{ ? =}\frac{20}{23} \\ \text{ inverse cosine in both sides } \\ \cos ^{-1}(^{}\cos \text{ ?) =}\cos ^{-1}(\frac{20}{23}) \\ \text{ ? = }29.59\text{ \degree} \\ \text{rounded to 10th} \\ \text{ ? = }29.6\text{ \degree} \end{gathered}[/tex]therefore, the answer is
29.6
I hope this helps you
Find the area A of the polygon with the given vertices. A(-5,-2) , B(4,-2), C(4,-7), D(-5,-7)A=
The area of the polygon is 45 square units.
From the question, we have
The given points make a rectangle with length AB and width AD.
Distance of AB = 4 - (-5) = 9
Distance of AD = -2 - (-7) = 5.
Area = length x width
Area = 9 x 5 =45 square units.
Area of Rectangle:
The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter. The area of a square will, however, be equal to the square of side-length in the case of a square because all of its sides are equal.
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Given the following diagram, find the required measures.Given: /|| mm24 = 105° and m26 = 50°
The question gives us the following parameters:
[tex]\begin{gathered} m\angle4=105\degree \\ m\angle6=50\degree \end{gathered}[/tex]Recall that the sum of angles on a straight line is 180 degrees. This means that:
[tex]\begin{gathered} m\angle3+m\angle4=180\degree \\ \therefore \\ m\angle3=180-m\angle4=180-105 \\ m\angle3=75\degree \end{gathered}[/tex]Recall that the sum of angles in a triangle is 180 degrees. Thus, we have:
[tex]\begin{gathered} m\angle2+m\angle3+m\angle6=180\degree \\ \therefore \\ m\angle2=180-m\angle3-m\angle6=180-75-50 \\ m\angle2=55\degree \end{gathered}[/tex]The SECOND OPTION is correct.
can you help me please? what is the area of this arrow?
Given
Graph
Procedure
Let's calculate the area of the figure as the sum of the area of the rectangle plus the area of the triangle.
Let's first calculate the area of the rectangle.
[tex]\begin{gathered} A_r=lw \\ A_r=10\cdot4 \\ A_r=40 \end{gathered}[/tex]Now let's calculate the area of the triangle.
[tex]\begin{gathered} A_t=\frac{1}{2}\cdot b\cdot h \\ A_t=\frac{1}{2}\cdot7\cdot6 \\ A_t=21 \end{gathered}[/tex]The total area would be
[tex]\begin{gathered} A_T=A_t+A_r \\ A_T=40+21 \\ A_T=61 \end{gathered}[/tex]The area of the arrow would be 61 sq in
What is the total sum of the interior degree of this polygon?What is the value of x?What is the measure of angle T
we are given a polygon with 6 sides, therefore, is a hexagon. The interior angles of a hexagon always add up to 720 degrees.
Using the expression and the given angles, we can construct the following relationship:
[tex](x+80)+135+(x+50)+130+(x+75)+115=720[/tex]Solving the operations we get:
[tex]3x+585=720[/tex]Now we solve for "x" first by subtracting 595 to both sides:
[tex]\begin{gathered} 3x=720-585 \\ 3x=135 \end{gathered}[/tex]Now we divide by 3:
[tex]x=\frac{135}{3}=45[/tex]Therefore, x = 45.
Now we use the expression for angle T:
[tex]\angle T=x+50[/tex]Replacing the value of x, we get:
[tex]\angle T=45+50=95[/tex]Therefore, angle T is 95 degrees.
ms sandlers wants to display his american flag in a triangular case.The height is 8.5 in.the base is 14 2/5 in.what is the area of a triangular case
Here, we want to get the area of the triangular case
Mathematically, this is half the product of the base and the height of the case
We have this as;
[tex]undefined[/tex]DeShawn has $53. He needs at least $76 to buy the jacket he wants. How much more money does he need for the jacket?[tex]x + 76 \geqslant 53[/tex][tex]X - 53 \geqslant 76[/tex][tex]X + 53 \leqslant 76[/tex][tex]X + 53 \geqslant 76[/tex][tex]X \geqslant 23[/tex][tex]X \geqslant 129[/tex][tex]X \geqslant - 26[/tex][tex]X \leqslant 23[/tex]can you please walk me though to the right answer thank you
Based on the given situation, we can define the following expression
[tex]x+53\ge76[/tex]"at least" indicates that we have to use "greater than or equal to".
Let's solve for x
[tex]\begin{gathered} x\ge76-53 \\ x\ge23 \end{gathered}[/tex]Hence, he needs $23 more to buy the jacket.The answers are[tex]\begin{gathered} x+53\ge76 \\ x\ge23 \end{gathered}[/tex]4x – 2y = 20-8x + 4y = -40
We have the system of equations:
[tex]\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}[/tex]We can tell that the equations are linear combination of each other: if we multiply the first equation by -2 we get the second equation.
[tex]\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}[/tex]So in fact we have only one equation and two unknowns, so there are infinite solutions to this system.
We can write the solution as:
[tex]\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}[/tex]Answer: the system has infinte solutions, expressed in the line y=-2x+10.
9 The Social Security number contains nine digits, if the form of 000-00-0000. How many differentSexial Security numbers can be formed using any numerals from 0 to 9?
Each digit has 10 possible values (the numbers from 0 to 9), so in order how many different numbers can be formed, we need to multiply the number of possible values of each digit.
If we have 9 digits, and each digit has 10 possible values, we need to multiply the number 10 by itself 9 times, that is:
[tex]N=10^9[/tex]So the number of different social security numbers is 10^9 (1,000,000,000, one billion)
Remembers since the number is negative to think about what number multiplied by 12 three times
Given:
The number is negative to think about what number multiplied by 3 times give a -125.
Required:
To find the number.
Explanation:
Let the number be x.
[tex]\begin{gathered} x\times x\times x=-125 \\ \\ x^3=-125 \\ \\ x=\sqrt[3]{-125} \\ \\ x=(-5) \end{gathered}[/tex]Final Answer:
The number is -5.
A triangle with area of 28 square inches has a height that is two less than four times the base. Find the base and the height of the triangle. Base is _ inches Height is __ inches
We write the following equations from the data of the statement of the problem:
• the area of the triangle is A = 28,
,• the height h and the base b are related by the following equation:
[tex]h=4b-2[/tex]The formula for the area of the triangle:
[tex]A=\frac{1}{2}\cdot b\cdot h\text{.}[/tex]Replacing the data of the problem in the equation above:
[tex]28=\frac{1}{2}\cdot b\cdot(4b-2).[/tex]We rewrite the equation in the following way:
[tex]\begin{gathered} 2\cdot28=b\cdot(4b-2), \\ 56=4b^2-2b, \\ 4b^2-2b-56=0. \end{gathered}[/tex]We have a quadratic equation for the length of base b, the solutions to this equation are:
[tex]b=4\text{ and }b=-\frac{7}{2}\text{.}[/tex]Because b is the length of one side of the triangle, and lengths are positive quantities, we must select the positive value of b, so we have:
[tex]b=4.[/tex]Replacing this result in the equation for the height, we get:
[tex]h=4b-2=4\cdot4-2=16-2=14.[/tex]Answer
• Base is ,4, inches,
,• Height is, 14, inches.
The charge to rent a trailer is $15 for up to 2 hours plus $8 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.9 hours, 3 hours, and 8.7 hours. Then graph all orderedpairs, (hours, cost), for the function,fa. What is the cost to rent a trailer for 2 9 hours?$b. What is the cost to rent a trailer for 3 hours?$c. What is the cost to rent a trailer for 8.7 hours?$d. What is the cost to rent a trailer for 9 hours?
Answer:
Explanation:
Given that the cost to rent a trailer for 2 hours is $15
[tex]\begin{gathered} C(h)=15 \\ \text{for} \\ 0$8 for an hour or a portion of an hour, we have:[tex]\begin{gathered} C(h)=8(h-2)+15 \\ =8h-1 \end{gathered}[/tex]These gives us the piecewise function:
[tex]undefined[/tex]2 groups of students group a and group B have the age distributions shown below which statement about the distributions is true
The ages of the students of groups A and B are displayed in the histograms.
For group A
We can determine the number of students per age by looking at the bars of the histogram
2 are 15 years old
5 are 16 years old
6 are 17 years old
5 are 18 years old
2 are 19 years old
The total students for group A is
[tex]\begin{gathered} n_A=2+5+6+5+2 \\ n_A=20 \end{gathered}[/tex]To calculate the average age on group a you have to use the following formula
[tex]X^{\text{bar}}=\frac{\Sigma x_if_i}{n}[/tex]Σxifi indicates the sum of each value of age multiplied by its observed frequency
n is the total number of students of the group
For group A the average value is
[tex]\begin{gathered} X^{\text{bar}}_A=\frac{(15\cdot2)+(16\cdot5)+(17\cdot6)+(18\cdot5)+(19\cdot2)}{20} \\ X^{\text{bar}}_A=\frac{340}{20} \\ X^{\text{bar}}_A=17 \end{gathered}[/tex]The average year of group A is 17 years old.
To determine the Median of the group, you have to calculate its position first.
[tex]\begin{gathered} \text{PosMe}=\frac{n}{2} \\ \text{PosMe}=\frac{20}{2} \\ \text{PosMe}=10 \end{gathered}[/tex]The Median is in the tenth position. To determine the age it corresponds you have to look at the accumulated observed frequencies:
F(15)=2
F(16)=2+5=7
F(17)=7+6=13→ The 10nth observation corresponds to a 17 year old student
F(18)=13+5=18
F(19)=18+2=20
The median of group A is 17 years old.
For group B
As before we can determine the number of students per age by looking at the bars of the histogram
2 are 15 years old
3 are 16 years old
4 are 17 years old
5 are 18 years old
6 are 19 years old
The total number of students for group B is
[tex]\begin{gathered} n_B=2+3+4+5+6 \\ n_B=20 \end{gathered}[/tex]The average age of group B can be calculated as
[tex]\begin{gathered} X^{\text{bar}}_B=\frac{\Sigma x_if_i}{n} \\ X^{\text{bar}}_B=\frac{(2\cdot15)+(3\cdot16)+(4\cdot17)+(5\cdot18)+(6\cdot19)}{20} \\ X^{\text{bar}}_B=\frac{350}{20} \\ X^{\text{bar}}_B=17.5 \end{gathered}[/tex]The average age for group B is 17.5 years old
Same as before, to determine the median you have to calculate its position in the sample and then locate it:
[tex]\begin{gathered} \text{PosMe}=\frac{n}{2} \\ \text{PosMe}=\frac{20}{2} \\ \text{PosMe}=10 \end{gathered}[/tex]The median is in the 10nth position, to determine where the 10nth student is located you have to take a look at the accumulated frequencies:
F(15)=2
F(16)=2+3=5
F(17)=5+4=9
F(18)=9+5=14 →The 10nth observation corresponds to a 18 year old student
F(19)=14+6=20
The median of group B is 18 years old
So
[tex]\begin{gathered} X^{\text{bar}}_A=17 \\ X^{\text{bar}}_B=17.5_{} \\ Me_A=17 \\ Me_B=18_{} \end{gathered}[/tex]The mean and median of group B are greater than the mean and median from group B. The correct choice is the first one.
Write a cosine function for the graph.
The correct option A: y = -4 cos Ф/4, is the cosine function for the graph.
Define the term cosine function?The ratio between the angle's adjacent leg and the hypotenuse when it is regarded as a leg of a right triangle is a trigonometric function for an acute angle.
One of the three fundamental trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.Y=cos(x) has its greatest value when x = 2nπ, wherein n is an integer. Y=cos(x) has a lowest value for x= π+2nπ , wherein n is an integer.For the given graph,
cosine function: y = -4 cos Ф/4.
In which, -4 is the amplitude (maximum displacement from the x axis).
Negative sign shows, the displacement is taken along negative y-axis.
And, Ф/4 is the phase angle.
Thus, the cosine function for the graph is y = -4 cos Ф/4.
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Answer:
b. [tex]\displaystyle y = -4cos\:4\theta[/tex]
Step-by-step explanation:
[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ \\ \\ y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
For each ordered pair, determine whether it is a solution to 7x + 4y = -23(x,y) (2,6) it is a solution yes or no(-5,3) it is a solution yes or no(6-7) it is a solution yes or no(-1,-4) it is a solution yes or no
To do this, first plug the values of x and y into the given equation. If you get a true statement, the ordered pair will be a solution to the equation, otherwise, it won't.
So, for the ordered pair (2,6) you have
[tex]\begin{gathered} 7x+4y=-23 \\ 7(2)+4(6)=-23 \\ 14+24=-23 \\ 38=-23 \end{gathered}[/tex]Since the proposition is false, then the ordered pair (2,6) is not a solution to the equation.
For the ordered pair (-5,3) you have
[tex]\begin{gathered} 7x+4y=-23 \\ 7(-5)+4(3)=-23 \\ -35+12=-23 \\ -23=-23 \end{gathered}[/tex]Since the proposition is true, then the ordered pair (-5,3) is a solution to the equation.
For the ordered pair (6,-7) you have
[tex]\begin{gathered} 7x+4y=-23 \\ 7(6)+4(-7)=-23 \\ 42-28=-23 \\ 14=-23 \end{gathered}[/tex]Since the proposition is false, then the ordered pair (6,-7) is not a solution to the equation.
Finally, for the ordered pair (-1,-4) you have
[tex]\begin{gathered} 7x+4y=-23 \\ 7(-1)+4(-4)=-23 \\ -7-16=-23 \\ -23=-23 \end{gathered}[/tex]Since the proposition is true, then the ordered pair (-1,-4) is a solution to the equation.
Which of the following is equivalent to a whole number?v25v10v40
The v means a root, so the only whole number is
[tex]\sqrt{25}=5[/tex]Question 4 Find the Area of the Shaded Region Below 5"
Given data:
The given figure is shown below.
The area of the shaded region is,
[tex]\begin{gathered} A=(20)(10)-2\pi(5)^2 \\ =200-50\pi \\ =42.92\text{ sq-inches} \end{gathered}[/tex]Thus, the area of the shaded region is 42.92 sq-inches.