First, let's find the area circular sector:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
r = radius = 7cm
θ = angle (in radians) = 5/6 π
so:
[tex]\begin{gathered} A=\frac{7^2(\frac{5}{6}\pi)}{2} \\ A=\frac{245}{12}\pi \end{gathered}[/tex]Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:
[tex]\begin{gathered} At=\frac{1}{2}s^2\cdot\sin (\theta) \\ \end{gathered}[/tex]where:
s = one of the equal sides = 7
θ = angle = 150
so:
[tex]\begin{gathered} At=\frac{1}{2}(7^2)\sin (150) \\ At=\frac{49}{4} \end{gathered}[/tex]Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:
[tex]Area_{\text{ }}of_{\text{ }}the_{\text{ }}white_{\text{ }}region=\frac{245}{12}\pi-\frac{49}{4}=51.9cm^2[/tex]Help me with/ #2 plsUsing the graphs what are the solutions to the following systems
Explanation:
The graph shows a ine crossing the parabola. The solution of the systems is the point where both system of equations intersect.
The line crosses the parabola at two point:
At x = 2, y = 2
This point is applicable to both. Since both have same values at this point, (2, 2) is one of the solution
At x = -2, y = -6
Both graphs have this point . This shows point (-2, -6) is also a solution
Hence, the solutions of the systems are (2, 2) and (-2, -6)
Give Line SV parallels Line TU and Triangle SVX =~ Triangle UTXProve: VUTS is a parallelogramWrite a Paragraph Proof.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the proof are as follows:
Since
[tex]\begin{gathered} \bar{SV}\text{ is parallel to} \\ \bar{TU} \end{gathered}[/tex]and
[tex]\text{Triangle SVX }\cong\text{ Triangle UTX}[/tex]Then,
[tex]VX\cong\text{ XT ( by }CPCTC\text{ ) }[/tex]CPCTC means corresponding parts of congruent triangles are congruent
and
[tex]UX\text{ }\cong XS\text{ ( by CPCTC)}[/tex]Thus,
VUTS is a parallelogram since diagonals of a parallelogram bisect each other
i need help with math
A. ∠4 is congruent to ∠5; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
D. ∠2 and ∠3; True.
What are the properties of angles of parallel lines?On a common plane, two parallel lines do not intersect.As a result, the characteristics of parallel lines with respect to transversals are given below.Angles that correspond are equal.Vertical angles are equal to vertically opposite angles.Interior angles that alternate are equal.The exterior angles that alternate are equal.For the give question;
Two line are cut by the transversal.
∠1 = 90.5° and ∠7 = 89.5°
Thus the result for the given statement are-
A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
∠6 = ∠7 = 89.5°.(correct)
D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.
Thus, the result for the given statement are found.
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From the entrance, most people will go straight to the roller coaster or straight to the tower. The distance from the entrance to the roller coaster is 461m, and the distance from the entrance to the tower is 707 m. If the paths to these two attractions are separated by a 41o angle, how far apart are the roller coaster and the tower?
The given situation can be illustrated as follow:
In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:
[tex]x^2=(461)^2+(707)^2-2(461)(707)\cos 41[/tex]By simplifying the previous expression, you obtain:
[tex]\begin{gathered} x^2=220409.5413 \\ x=\sqrt[]{220409.5413} \\ x\approx469.5 \end{gathered}[/tex]Hence, the distance between the tower and the roller coaester is approximately 469.5m
i need to find the independent variable and dependent and make a equation and find the output when input=10
The given situation is about the value of quarters and the number of quarters. If we think this through, we would deduct that the value of quarters depends on the number of quarters there are, for example, if there are 4 quarters, then the value is 1 dollar, and so on.
Hence,
The independent variable is the number of quarters.
The dependent variable is the value of the quarters.
The equation would be v = 0.25n.
If the input is 10, it means n = 10.
[tex]v=0.25n=0.25\cdot10=2.5[/tex]The output would be 2.5.
Alex has a box of chocolates which are all
flavoured with either caramel or raspberry.
The possible outcomes of Alex picking two
chocolates at random are shown in the tree
diagram below.
If both chocolates are the same flavour, what
is the probability that they are both
raspberry?
Give your answer as a fraction in its simplest
form.
Probability that they are both raspberry = 5/33
From the question, we have
probability that they are both raspberry = 5/12*4/11
=5/33
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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A rental car company charges 23.95 per day to rent a car and $0.08 for every mile driven. Nathan wants to rent a car, knowing that:He plans to drive 400 miles.He has at most $440 to spend.Which inequality can be used to determine x, the maximum number of days Nathan can afford to rent for while staying within his budget?
Answer
Explanation
The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)
Charge based on number of days = (23.95) (x) = (23.95x) dollars
Charge based on the number of miles = (0.08) (400) = 32 dollars
(The total charge on the car) ≤ 440
23.95x + 32 ≤ 440
23.95x + 32 - 32 ≤ 440 - 32
23.95x ≤ 408
Divide both sides by 23.95
(23.95x/23.95) ≤ (408/23.95)
x ≤ 17.04
Hope this Helps!!!
In the rectangle below, FH = 4x – 2, EG= 5x-12, and m ZIGF = 53º.Find El and m ZIFE.EFBEI =Хm LIFE =HG
Answer:
The length EI is;
[tex]EI=19[/tex]The measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]Explanation:
Given the rectangle in the attached image.
Given;
[tex]\begin{gathered} FH=4x-2 \\ EG=5x-12 \\ m\angle IGF=53^{\circ} \end{gathered}[/tex]Recall that the length of the diagonals of a rectangle are equal so;
[tex]\begin{gathered} FH=EG \\ 4x-2=5x-12 \end{gathered}[/tex]solving for x, we have;
[tex]\begin{gathered} 4x-2=5x-12 \\ 12-2=5x-4x \\ x=10 \end{gathered}[/tex]Since we have the value of x, let us substitute to get the length of diagonal EG;
[tex]\begin{gathered} EG=5x-12 \\ EG=5(10)-12=50-12 \\ EG=38\text{ units} \end{gathered}[/tex]Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;
[tex]\begin{gathered} EI=\frac{EG}{2}=\frac{38}{2} \\ EI=19 \end{gathered}[/tex]Therefore, the length EI is;
[tex]EI=19[/tex]To get the measure of angle IFE;
[tex]m\angle IGF=m\angle IFG=53^{\circ}[/tex]Reason: base angles of an isosceles triangle are equal.
So;
[tex]m\angle IFE+m\angle IFG=90^{\circ}[/tex]Reason: Complementary angles.
Substituting the value of angle IFG;
[tex]\begin{gathered} m\angle IFE+53^{\circ}=90^{\circ} \\ m\angle IFE=90^{\circ}-53^{\circ} \\ m\angle IFE=37^{\circ} \end{gathered}[/tex]Therefore, the measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]The graph of f(x) = StartRoot x EndRoot is reflected across the y-axis to create the graph of function g. How do the domains of f and g compare?The domains of f and g are both x ≥ 0.The domains of f and g are both all real numbers.The domain of f is x ≥ 0, while the domain of g is x ≤ 0.The domain of f is x ≤ 0, while the domain of g is x ≥ 0.
Step-by-step explanation:
Given that f(x) is reflected across the y-axis to create the graph of function g.
i.e. f is reflected on the line x=0
Hence x will become -x in g.
When domain of f is x>=0 the domain of g can only be x less than or equal to 0.
Hence answer is option 3,The domain of f is x ≥ 0, while the domain of g is x ≤ 0
Answer:
The third one
Step-by-step explanation:
Shelly is rolling a six-sided number cube and recording her results in a chart.Number ofRollsNumber ofTimesLanded on 1Number ofTimesLanded on 2Number ofTimesLanded on 3Number ofTimesLanded on 4Number ofTimesLanded on sNumber ofTimesLanded on 6100141714192019200304237332731300SO54495252600971031051119599AWhich is BEST supported by the data in the chart?А when viewing the data for rolling a one, as the number of rolls Increases, the experimental probability becomes closer to equal to the theoretical probability.when viewing the data for rolling a two, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.When viewing the data for rolling a four, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.When viewing the data for rolling a sbc, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.BСD
We will have the following:
The expression that best describes the information is:
*When viewing the data for tolling a one, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.
Please help me!!!!!!!
Answer:
B. (19/24)
Step-by-step explanation:
1 1 5
------ + ------ + -------
4 8 12
1(6) 1(3) 5(2)
------ + ------ + -------
4(6) 8(3) 12(2)
6 3 10 19
------ + ------ + ------- = -------
24 24 24 24
I hope this helps!
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Question
Each equation represents a proportional relationship. Choose the equations for which the constant of proportionality is 14.
Responses
A y = 0.25xy = 0.25x
B 4y = x4y = x
C y = 4xy = 4x
D 32y = 8x32y = 8x
E 14y = 2x
Answer:
its B
Step-by-step explanation: just took the test
Hi I need help with this question. Melissa starts with four packages of balloons and 8 single balloons. Her brother gave her 20 more balloons and three more packages. She now has twice the number of balloons she started with. Write and solve an equation to find how many balloons are in a package. How many balloons did Melissa start with?
Okay, here we have this:
Let's take the packages as (x), so we obtain:
Melissa Starts with: 4x+8 ballons (1)
Her brother gave her: 3x+20 ballons (2)
And as she now has twice the number of balloons she started with. This mean that:
2(4x+8)=(3x+20)+(4x+8)
Let's clear x in this equation:
8x+16=3x+20+4x+8
8x+16=7x+28
8x-7x=28-16
x=12
Finally we obtain that in a package are 12 ballons, now let's calculate How many balloons did Melisa start with?:
Remember that Melissa Starts with: 4x+8 ballons, so replacing x with 12, we obtain that Melissa Starts with: 4(12)+8=48+8=56.
Finally we obtain that Melissa Starts with 56 ballons.
the store bought a bike from the factory for$ 99 and sold I to Andre for $117 what percentage was the markup?
EXPLANATION
Let's see the facts:
Bike Price: $99
Sold Price: $117
The percentage is given by the following relationship:
[tex]\text{Percentage: }\frac{\text{Selling price per unit}-Cost\text{ price per unit}}{Cost\text{ price per unit}}\cdot100[/tex]Replacing terms:
[tex]\text{Percentage =}\frac{117-99}{99}\cdot100[/tex][tex]\text{Percentage = 18.18\%}[/tex]Answer: The markup was 18.18%
Hi this is one of my exit ticket problem can you solve it please.
The triangles that are similar is A and B
Please help. I am not sure how to go about this.
Solution:
(a) Given the functions:
[tex]\begin{gathered} f(x)=x-4 \\ \\ g(x)=x+4 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(x+4) \\ \\ f(x+4)=x+4-4 \\ \\ f(g(x))=x \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} g(f(x))=g(x-4) \\ \\ g(x-4)=x-4+4 \\ \\ g(f(x))=x \end{gathered}[/tex]Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.
ANSWER: f and g are inverse of each other.
(b) Given:
[tex]\begin{gathered} f(x)=-\frac{1}{3x},x0 \\ \\ g(x)=\frac{1}{3x},x0 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(\frac{1}{3x}) \\ \\ f(\frac{1}{3x})=-\frac{1}{3(\frac{1}{3x})} \\ \\ f(g(x))=-x \end{gathered}[/tex]Also,
[tex]\begin{gathered} g(f(x))=g(-\frac{1}{3x}) \\ \\ g(-\frac{1}{3x})=\frac{1}{3(-\frac{1}{3x})} \\ \\ g(f(x))=-x \end{gathered}[/tex]ANSWER: f and g are not inverses of each other.
Given the polynomial P(x)= x^3 + 10x^2 + 25xa. List all of the potential rational roots b. Find and list all the actual roots of P(x), and the multiplicity of each root
a)
In order to find the list of all potential rational roots, let's find the factors of the division between the constant term and the leading term.
Since the constant term is zero, so the only potential rational root in the list is 0.
b)
Since the constant term is zero, so 0 is a root of the polynomial. Then, let's factor it to find the remaining roots:
[tex]\begin{gathered} x^3+10x^2+25x=0 \\ x(x^2+10x+25)=0 \\ x^2+10x+25=0 \end{gathered}[/tex]Solving this quadratic equation using the quadratic formula, we have:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2+10x+25=0 \\ a=1,b=10,c=25 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-10+\sqrt[]{100-100}}{2}=\frac{-10+0}{2}=-5 \\ x_2=\frac{-10-0}{2}=-5 \end{gathered}[/tex]Therefore the actual roots of P(x) are:
0 (multiplicity 1) and -5 (multiplicity 2).
Use the Distributive Property to simplify the following expression.8(x+4)
Given the expression:
8(x + 4)
Let's simplify using distributive property.
Use distributive property to distribute 8 into x + 4:
8(x) + 8(4)
Evaluate:
8x + 32
ANSWER:
8x + 32
Convert the following expressions to simplify fraction or integer. If it is not a real number, enter none
We are given the expression:
[tex]8^{\frac{2}{3}}[/tex]To get the answer, we will have to apply exponents rules
The rule is:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a}^b[/tex]Thus
we will have
[tex]8^{\frac{2}{3}}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]Therefore,
The answer is 4
Sarah is saving money to go on a trip. She needs at least $1975 in order to go. Sarah is mowing lawns and walking dogs to raise money. She charges $25 each time he mows a lawn and $15 each time she walks a dog. I have to Define the variables for the problem and Write an inequality to model this problem
We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;
Let x represent the number times she mows a lawn;
Let y represent the number of times she walks a dog;
The inequality can be modelled thus;
[tex]25x+15y\ge1975[/tex]Can you please give me a step by step explanation/solution. Thanks
The Perimeter of a Rectangle
Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:
P = w + w + l + l
Or, equivalently
P = 2w + 2l
Hermann was calculating the perimeter of a rectangle and built the expression:
P = x + x + 4x + 4x feet
Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.
a) We'll draw a rectangle with such dimensions:
b) Assuming the base is the length and the height is the width, the relationship between the base and the height is
4x / x = 4
This means the base is four times the height
c) We are given the perimeter as P = 60 feet.
We need to solve the equation
x + x + 4x + 4x = 60
Simplifying:
10x = 60
Dividing by 10:
x = 60/10
x = 6 feet
The base is 4x = 24 feet.
The base of Herman's rectangle is 24 feet
The height of Herman's rectangle is 6 feet
identify the reflection of the figure with vertices P (2, -12), Q (-3, 13), and R (-5, - 15) across the x-axis.
EXPLANATION:
We are given the following coordinates for a figure on the coordinate plane;
[tex]\begin{gathered} P(2,-12) \\ Q(-3,13) \\ R(-5,-15) \end{gathered}[/tex]To reflect any figure or any set of coordinates across the x-axis, we shall apply the rule;
[tex](x,y)\rightarrow(x,-y)[/tex]Note that the x-coordinate remains the same whereas, the y-coordinate changes its sign.
Imagine folding a graph page in two equal halves along the horizontal axis. You'll observe the y-coordinates will switch sides from top to bottom (positive to negative) or bottom to top (negative to positive). The x-coordinate remains the same since moving the folded page does not affect values along the horizontal line.
Therefore, for the vertices given, the reflection across the x-axis would be;
[tex]P(2,-12)\rightarrow P^{\prime}(2,12)[/tex][tex]Q(-3,13)\rightarrow Q^{\prime}(-3,-13)[/tex][tex]R(-5,-15)\rightarrow R^{\prime}(-5,15)[/tex]ANSWER:
The coordinates of the reflection across the x-axis therefore will be;
[tex]\begin{gathered} P^{\prime}(2,12) \\ Q^{\prime}(-3,-13) \\ R^{\prime}(-5,15) \end{gathered}[/tex]Find the prime factorization of 54 from least to greatest; then write it using exponents.
The prime factorization of 54 is
54 = 2 × 3 × 3 ×3
Using the exponential form of the prime factorization that is
54 = 2 × 3³
The selling price of a refrigerator is $548.90. If the markup is 10% of the dealer's cost, what is the dealer's cost of the refrigerator?
Answer
Dealer's cost = $499
Explanation
The markup percent is given as
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent}[/tex]Markup percent = 10%
Selling Price = 548.90 dollars
Cost = ?
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent} \\ \text{10 = }\frac{548.90\text{-(Cost)}}{Cost}\times100\text{ percent} \\ 0.1=\frac{548.90-\text{Cost}}{\text{Cost}} \\ \text{Cross multiply} \\ 0.1(\text{Cost) }=548.90-\text{Cost} \end{gathered}[/tex]0.1 (Cost) + Cost = 548.90
1.1 (Cost) = 548.90
Divide both sides by 1.1
Cost = (548.90/1.1)
Cost = 499 dollars
Hope this Helps!!!
Pl3ase help me with Geometry. right angles and perpendicular angles
(Question 3)
Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that
[tex]\bar{DB}=\bar{BE}[/tex]Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,
[tex]\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=\frac{30}{2} \\ \rightarrow x=15 \end{gathered}[/tex]We know that
[tex]AE=x+21[/tex]We'll just have to plug in the value of x we calculated to find the lenght of AE
[tex]AE=15+21\rightarrow AE=36[/tex]Therefore, AE = 36
(Question 4)
Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that
Therefore, RS = 5
The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w
Step 1
Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?
Step 2
[tex]\begin{gathered} l=\frac{a}{w} \\ l=\frac{6x^2y+4y^2x}{2xy} \end{gathered}[/tex][tex]\begin{gathered} factorize \\ l=\frac{2xy\left(3x+2y\right)}{2xy} \end{gathered}[/tex]Thus;
[tex]l=3x+2y[/tex]Answer;
[tex]l=3x+2y[/tex]I don't know if -32 is greater or less than 15
Answer: -32 is less than 15.
Step-by-step explanation: 15 is greater than zero therefore it is not a negative number. -32 is less than 0 therefore it is a negative number. Negatives will always be less than positives.
I need help with this problem.It say solve the following inequalities and graph it on the Number Line.
Given the inequality:
[tex]13>-4x-7[/tex]• You can solve it as follows:
1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:
[tex]13+(7)>-4x-7+(7)[/tex][tex]20>-4x[/tex]2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):
[tex]\begin{gathered} \frac{20}{-4}<\frac{x}{-4} \\ \\ -53. You can rewrite the solution in this form:[tex]x>-5[/tex]• In order to graph the solution on the Number Line, you can follow these steps:
1. Since the symbol is:
[tex]>[/tex]You need to draw an open circle over the number -5.
2. Draw a line from the circle to the right.
Then, you get:
Hence, the answer is:
• Solution:
[tex]x>-5[/tex]• Number Line:
Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total interest is $220, how much is invested in each savings account?
A account 8% B account 12%
A+$450 = B (1)
Ax8% +Bx12%= $220
Ax0.08 + Bx0.12 = 220
Now we replace (1) on B:
Ax0.08 + (A+450)x0.12 = 220
Ax0.08 + Ax0.12 + 54 = 220
Ax0.2 = 166
A= 830.
Now we replace the value of A on equation (1):
830 + 450 = B
B = 1280
Question #2Several points are plotted on the graph. Which of the plotted points on the graph represent the zeros of the function:f (x) = (x^2+ 2x- 8) (x – 6)
Given function is:
[tex]f(x)=(x^2+2x-8)(x-6)[/tex]Now put f(x)=0
[tex]\begin{gathered} (x^2+2x-8)(x-6)=0 \\ (x^2+2x-8)=0,(x-6)=0 \\ x-6=0 \\ x=6 \end{gathered}[/tex]so the first point is (6,0) now for another points:
[tex]\begin{gathered} (x^2+2x-8)=0 \\ (x^2+4x-2x-8)=0 \\ x(x+4)-2(x+4)=0 \\ (x+4)(x-2)=0 \\ x=-4,2 \end{gathered}[/tex]So the points are (-4,0) and (2,0) and(6,0)
Hence the correct options are 1,2 and 4.