step 1
Find out the area of the complete pie
[tex]A=pi*r^2[/tex]r=30/2=15 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}[/tex]Remember that the area of a complete circle, subtends a central angle of 360 degrees
so
Applying proportion
Find out the area for a central angle of 42 degrees
[tex]\begin{gathered} \frac{225pi}{360^o}=\frac{x}{42^o} \\ \\ x=\frac{225p\imaginaryI}{360^{o}}*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}[/tex]The answer is 82.43 ft21/ (gg^2 e^5)^2 Write your answer with only positive exponents
ANSWER
[tex]\frac{1}{g^6e^{10}}[/tex]EXPLANATION
In the denominator, we have the product of g and g². The product of two powers with the same base is the base raised to the sum of the exponents,
[tex]\frac{1}{(gg^2e^5)^2}=\frac{1}{(g^{2+1}e^5)^2}=\frac{1}{(g^3e^5)^2}[/tex]Now, we also have the power of a product. The exponents can be distributed into the multiplication,
[tex]\frac{1}{(g^3e^5)^2}=\frac{1}{(g^3)^2(e^5)^2}[/tex]And finally, for both g and e, we have the power of a power. The result is the base raised to the product of the exponents,
[tex]\frac{1}{(g^3)^2(e^5)^2}=\frac{1}{g^{3\cdot2}e^{5\cdot2}^{}}=\frac{1}{g^6e^{10}}[/tex]Hence, the simplified expression is,
[tex]\frac{1}{g^6e^{10}}[/tex]Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which number line represents all of the possible weights, in pounds, of apples Patricia can keep in her store?
Given:
The bins can hold no more than w(b) < 200 pounds.
The crate can hold no more than w(c) < 50 pounds.
The number of bins is n(b) = 3.
The number of crates is n(c) = 2.
The objective is to find the correct number line for the graph.
Explanation:
The maximum quantity of bins can be calculated as,
[tex]\begin{gathered} Q(b)The maximum quantity of crate can be calculated as,[tex]\begin{gathered} Q(c)To find the maximum store capacity:The maximum store capacity can be calculated as,
[tex]undefined[/tex]which portion must be true?
The two figures are similar
Using the similarity theorem
The only true proportion is
[tex]\frac{8}{2}\text{ = }\frac{x}{y}[/tex]As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines. What is the same? What is different?
If the line of the graph is vertical then the slope of the graph is zero. The coordinate of the y-value will never change on vertical lines.
What are vertical lines?The vertical line is a line that is parallel to the y-axis. A vertical line can be defined as a line on the coordinate plane where all the points on the line have the same x-coordinate. A form of test employed in relation is the vertical line test. Any kind of vertical line equation lacks a y-intercept. The vertical line test is used to determine whether or not the given relation is a function. The vertical line is another name for the vertical bar. A mathematical sign is an upright slash. Depending on the context, it may be used to represent a certain kind of logic or an operation. The vertical line is the line that runs along the y-axis.
To know more about vertical lines, visit:
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Need help with solving equations and also need help understanding what moves to the lowest variable term mean.
An equation is a mathematical expression that contains an equal sign. The objective of an equation is usually to determine the value of an unkown variable, commonly referred to x or y. In order to do that, however, we need to isolate the variable on the left side and this has to be done in a way that mantains the balance in the equation. This means that whatever operation we do on one side we have to perform the same exact operation on the other side. Let's take a look at an example.
[tex]3x+9=x+40[/tex]For this equation we have the unknown variable x, which is the value we want to find. Our goal is to isolate the variable on the left side, however we can see that there is one x on the right side, the first step will be to move this to the left side, this is what means to move the lowest variablem term first, because if we were to move "3x", which is the highest variable term, we would have to perform more steps to solve the equation.
To move the term "x" from the right to the left we need to subtract both sides by "x", this is because when we subtract "x-x" on the right side, the result will be 0 and we will be left with unkown variables only on the left. Let's check this out:
[tex]\begin{gathered} 3x+9-x=x+40-x \\ 3x-x+9=x-x+40 \\ 2x+9=40 \end{gathered}[/tex]As we can see by doing so we eliminated the variable on the right side. Now we want to remove the 9 from the left side, we will have to perform a similar operation by subtracting 9 from both sides.
[tex]\begin{gathered} 2x+9-9=40-9 \\ 2x=31 \end{gathered}[/tex]Now we have only a variable term on the left side, but it still being multiplied by 2 and we don't want that, so we have to divide both sides by 2.
[tex]\begin{gathered} \frac{2x}{2}=\frac{31}{2} \\ x=\frac{31}{2} \end{gathered}[/tex]With this we achieved the goal of the equation, which was to find the value of x. In short we always want to isolate the variable on the left side and to do that we will have to perform the inverse operation of the other terms in both sides of the equation, if a term is adding we need to subtract on both sides, if it is multiplying we need to divide on both sides and so on. We have to do that first with the term that contains the letter of lowest value, like we did with this one.
A freight train is carrying goods across the country. The distance it has traveled directly with the number of gallons of fuel it has used. See the graph below
1) To find how many miles per gallon that freight train makes is to find a rate. We can find it in two ways, either by setting a proportion or by finding the slope.
2) Note that this direct variation depicted by the graph is proportional. Therefore, let's find the slope by picking two points:
[tex]\begin{gathered} (200,50),(400,100) \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{100-50}{400-200}=\frac{50}{200}=\frac{1}{4} \end{gathered}[/tex]3) Thus, the answers are:
Some roads in the Rocky Mountains have a rise of 7 feet for every 100 horizontal feet.What is the slope of such roads?
Let's begin by listing out the information given to us:
The road rises by 7 feet every 100 horizontal feet
The equation becomes:
Slope (m) = Δy/Δx = 7/100 = 0.07
Slope (m) = 0.07
Hello, I need help writing a recursive formula for these I’m struggling bad
1) Notice that:
[tex]\begin{gathered} 3=\frac{30}{10}, \\ \frac{3}{10}=\frac{3}{10}, \\ \frac{3}{100}=\frac{\frac{3}{10}}{10}. \end{gathered}[/tex]Therefore the recursive formula for the first sequence is:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]2) Notice that:
[tex]\begin{gathered} 11=14-3, \\ 8=11-3, \\ 5=11-3. \end{gathered}[/tex]Therefore the recursive formula for the second sequence is:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]Answer:
Left sequence:
[tex]\begin{gathered} a_1=30, \\ a_n=\frac{a_{n-1}}{10}\text{ for }n\geq2. \end{gathered}[/tex]Right sequence:
[tex]\begin{gathered} a_1=14, \\ a_n=a_{n-1}-3\text{ for }n\geq2. \end{gathered}[/tex]
If Rosa is at most 27 years old. What symbol does at most refer to less than greater than less than or equal to greater than or equal to
The correct answer is less than or equal to because at most 27 years means that Rosa's highest age is 27.
3. If the mZLKI - 174º and KR bisects LLKI, then find the mLLKR.
R
E
K
87°
1740
0740
90°
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1:
[tex]undefined[/tex]Answer:
87°
Step-by-step explanation:
Angle bisector:Angle bisector is a ray that divides an angle into two congruent angles.
∠LKR = ∠LKJ ÷ 2
= 174° ÷ 2
= 87°
What is the missing reason for The third step in the proof below
Solution
The image below contain the solution
. Compare: what is greater 5/3 or 9/16
hello
between 5/3 and 9/16, 5/3 is greater than 9/16
[tex]\frac{5}{3}>\frac{9}{16}[/tex]3.What are the coordinates of the center and the length of the radius of the circle whose equation is(x + 1)^2 + (-5)^2 = 16?
The general equation of circle with centre (h.k) and radius r is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Simplify the equation to obtain the centre and radius of circle.
[tex]\begin{gathered} (x+1)^2+(y-5)^2=16 \\ (x-(-1))^2+(y-5)^2=(4)^2 \end{gathered}[/tex]So center of circle is (-1,5) and radius 4.
Suppose the booster club is raising money to help offset the cost of a trip.You make $10 per door wreath sold and $2 per candy bar sold. The clubwants to raise at least $400.00. Write an inequality to represent thissituation.
Let the number of door wreath sold is x.
Let the number of candy bar sold is y.
The inequality can be represented as,
[tex]10x+2y\ge400[/tex]Thus, the above inequation gives the required inequality.
Translate this sentence into an equation.The product of 5 and Julie's height is 80.Use the variablej to represent Julie's height.
ANSWER:
5 x j = 80
STEP-BY-STEP EXPLANATION:
The sentence as an equation would be the multiplication of j and 5 equal to 80, just like this:
[tex]5\times j=80[/tex]How to solve this problem step by step in depth. I have no idea how to solve this
Answer
[tex]f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5}[/tex]Explanation
The given function is
[tex]f(x)=-5x-4[/tex]Let y = f(x), this implies
[tex]y=-5x-4[/tex]Now, make x the subject of the formula
[tex]\begin{gathered} y=-5x-4 \\ 5x=-y-4 \\ \text{To get x, we divide both sides by 5} \\ \frac{5x}{5}=\frac{-y-4}{5} \\ \\ x=\frac{-y-4}{5} \end{gathered}[/tex]Since f(x) = y, then x = f⁻¹(y)
[tex]\begin{gathered} f^{-}^{1}\mleft(y\mright)=\frac{-y-4}{5} \\ \therefore f^{-1}(x)=\frac{-x-4}{5} \end{gathered}[/tex]The above inverse function can be rewritten as follows
[tex]\begin{gathered} f^{-1}(x)=\frac{-x}{5}-\frac{4}{5} \\ f^{-1}(x)=\frac{-1}{5}x-\frac{4}{5} \end{gathered}[/tex]A gift box for a shirt has a length of 60 centimeters, a width of 30 centimeters, anda height of 10 centimeters. Find the surface area of the gift box.
A rectangular box has six faces. The surface area is given by the sum of the area of those faces. Parallel faces have the same area, therefore, we just need to calculate the area of three of them and multiply by 2. The surface area of our gift box is:
[tex]\begin{gathered} S=2(60\times30+60\times10+30\times10) \\ =2(1800+600+300) \\ =2(2700) \\ =5400 \end{gathered}[/tex]The surface area of the box is 5400 cm².
i don’t understand this very well, i think growth and decay but not sure
She bought the bike by 3,000 six years ago, we are assuming the value of her mountain bike depreciated 20% each year
1 year
3,000*20% = 600
2year
3,000-600 = 2,400*20% = 480
3year
2,400-480 = 1920*20% = 384
4 year
1920-384= 1,536*20% = 307.2
5 year
1,536-307.2= 1,228.8*20% = 245.76
6year
1,228.8 - 245.76 = 1,043.04*20% = 208.608
1,043.04 - 208.608 =834.432
Rounded to the nearest dollar
= 834
solve equation 10 - 25x = 5 what is the value of x
ANSWER
x = 1/5
EXPLANATION
We are given the equation:
10 - 25x = 5
To find the value of x, first we subtract 10 from both sides of the equation:
10 - 25x - 10 = 5 - 10
10 - 10 - 25x = 5 - 10
-25x = -5
Now, divide both sides by 5:
=> x = -5 / -25
x = 1/5
That is the value of x.
solve the equation. check your solution 1/3 (2b+9) =2/3 (b+9/2)
The equation to solve is:
[tex]\frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2})[/tex]We use distributive property [a(b+c)=ab+ac], simplify and solve for b:
[tex]\begin{gathered} \frac{1}{3}(2b+9)=\frac{2}{3}(b+\frac{9}{2}) \\ \frac{2}{3}b+3=\frac{2}{3}b+3 \end{gathered}[/tex]From here, we can't solve.
It is the same equation.
No Solution.
I need this practice problem from my prep guide answered and explained
To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.
[tex]8x^2+9y^2-16x-9y=-2[/tex]Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.
[tex]\begin{gathered} (8x^2-16x)+(9y^2-9y)=-2 \\ 8(x^2-2x)+9(y^2-y)=-2 \\ 8(x^2-2x+1)+9(y^2-y+\frac{1}{4})=-2+8+9(\frac{1}{4}) \end{gathered}[/tex]Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.
[tex]8(x-1)^2+9(y-\frac{1}{2})=\frac{33}{4}[/tex]To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.
[tex]\begin{gathered} \mleft(\frac{4}{33}\mright)(8)(x-1)^2+\mleft(\frac{4}{33}\mright)(9)(y-\frac{1}{2})=\mleft(\frac{4}{33}\mright)\mleft(\frac{33}{4}\mright) \\ \frac{32\mleft(x-1\mright)^2}{33}+\frac{12(y-\frac{1}{2})}{11}=1 \end{gathered}[/tex]Find the X-Intercept and the y-intercept of 4x- 5y = 15X-Intercept:???Y-intercept: ???help
The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
the first drop down answers are 18,10,7,14the second drop down box options are 16.5,30.5,44.5the third options are 2.5, 1.5, 1,3 the fourth options are 14n, 18n, 7n, 10nthe fifth options are each movie tickets cost the same amount, there is a service fee for buying tickets online, the cost increase as tge number of tickets increase, the leaste amount of tickets you cab buy is 1
Answer:
Recursive formula:
a_n = a_n-1 + 14,
a_1 = 16.5
Explicit formula: a_n = 14(n - 1) + 16.5
Each movie costs the same amount.
Explanation:
Looking at the numbers we see that each next term a_n is 14 added to the previous term, a_n-1 and the first term a_1 is 16.5; therefore, we can say
[tex]\begin{gathered} a_n=a_{n-1}+14, \\ a_1=16.5 \end{gathered}[/tex]
the line L3 is perpendicular to 3x-y+2=0 .find the gradient of L3
Answer:
[tex]-\frac{1}{3}[/tex]Explanation:
Here, we want to get the gradient of the line L3
The equation of a straight line can be expressed as:
[tex]y\text{ = mx + b}[/tex]where m is the gradient (slope) and b is the y-intercept (the y-value when x = 0)
Now,let us write the equation of the first line in the slope-intercept form
Mathematically, we have this as:
[tex]\begin{gathered} 3x-y\text{ + 2 = 0} \\ y\text{ = 3x + 2} \end{gathered}[/tex]The gradient of the first line is 3
Now,let us get the gradient of the second line L3
Mathematically, when two lines ae perpendicular, the product of their gradients (slopes) equal -1
Thus, we have it that:
[tex]\begin{gathered} m_1\text{ }\times m_2\text{ = -1} \\ 3\text{ }\times m_2\text{ = -1} \\ m_2\text{ = -}\frac{1}{3} \end{gathered}[/tex]evaluate the expression 0.03^3
The given expression is,
[tex]0.03^3[/tex]So, expanding we have,
[tex]0.03^3=0.03\times0.03\times0.03=\text{0}.000027[/tex]Find the equation of the line containing the points (42.3,82) and (42.8,94) more
Let's remember that the equation of a line always has the form:
[tex]y=m\cdot x+b[/tex]where "m" and "b" are constant numbers that we must find. Now, let's find "m" first. "m" is called the slope of the line, and it represents the relationship between the changes in y (second component) and the changes in x (first component). So it isn't surprising that we can compute it by:
[tex]m=\frac{94-82}{42.8-42.3}=\frac{12}{0.5}=24[/tex]Having calculated "m", we know that, (for the point (42.3,82) must lie in the line)
[tex]82=24\cdot(42.3)+b[/tex]Then,
[tex]b=82-24\cdot(42.3)=933.2[/tex]This implies that the equation of our line is
[tex]y=24\cdot x-933.2[/tex]Here is a graph of the line:
Comment: Our line is represented with a red color.
what is the driving distance from the hospital to City Hall
Coordinate of the Hospital = (-6, -4)
Coordinate of City Hall = (0,0)
[tex]\begin{gathered} \text{Distance betw}en\text{ two points = }\sqrt[]{(x_2-x_{1)^2+}(y_2-y_1)^2} \\ \\ =\sqrt[]{(0-(-6))^2+(0-(-4))^2} \\ =\sqrt[]{(0+6)^2+(0+4)^2} \\ =\sqrt[]{6^2+4}^2 \\ =\sqrt[]{36\text{ +16}} \\ =\sqrt[]{52} \\ =2\sqrt[]{13}\text{ or 7.21} \end{gathered}[/tex]Use the Distributive Property to rewrite each expression without parentheses.1. 6(x+3)2. 5(y-4)3. - 7(m-1)4. 9(3x + 2)5. -3(7 +3p)6. 1 (8x-10)
The distributive property states:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]so:
[tex]\begin{gathered} 6(x+3)=6\cdot x+6\cdot3=6x+18 \\ 5(y-4)=5\cdot y-5\cdot4=5y-20 \\ -7(m-1)=-7\cdot m-7\cdot(-1)=-7m+7 \\ 9(3x+2)=9\cdot3x+9\cdot2=27x+18 \\ -3(7+3p)=-3\cdot7-3\cdot3p=-21-9p \\ 1(8x-10)=1\cdot8x+1\cdot10=8x-10 \end{gathered}[/tex]The midpoint of AB is M(5,1). If the coordinates of A are (3,6), what are thecoordinates of B?
We have a segment AB of which we know the coordinates of A(3,6) and the midpoint M(5,1).
We have to find the coordinates of B.
We know that the coordinates of the midpoint M are the average of the coordinates of the endpoints A and B, so we can write:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ 2\cdot x_M=x_A+x_B \\ x_B=2x_M-x_A \end{gathered}[/tex]Now we have the x-coordinate of B in function of the x-coordinates of A and M.
The same can be calculated for the y-coordinate:
[tex]y_B=2y_M-y_A[/tex]Then, we can replace and calculate:
[tex]\begin{gathered} x_B=2x_M-x_A \\ x_B=2\cdot5-3 \\ x_B=10-3 \\ x_B=7 \end{gathered}[/tex][tex]\begin{gathered} y_B=2y_M-y_A \\ y_B=2\cdot1-6 \\ y_B=2-6 \\ y_B=-4 \end{gathered}[/tex]Then, the coordinates of B are (7,-4).
Answer: B = (7,-4)
A committee must be made up of two students from grades 9, 10, or 11, and another two students from grade 12. How many different committees can be made? Explain and show all of your work.
to make the committee