Last year, Craig had 10 records.
Now, he has 12 records.
What is the percent increase?
The percent increase is given by
[tex]\%\: increase=\frac{\text{new value-old value}}{\text{old value}}\times100[/tex]In this case,
Old value = 10 records
New value = 12 records
[tex]\begin{gathered} \%\: increase=\frac{\text{new value-old value}}{\text{old value}}\times100 \\ \%\: increase=\frac{12-10}{10}\times100 \\ \%\: increase=\frac{2}{10}\times100 \\ \%\: increase=20 \end{gathered}[/tex]Therefore, there is a 20% increase in his record collection.
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.
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)
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]
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]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:
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]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]What is the missing reason for The third step in the proof below
Solution
The image below contain the solution
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]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.
I need help with finding the area and perimeter of the letter o
Check below, please.
1) In this question, we're going to remember two concepts: The perimeter is the sum of the lengths of each segment of each letter.
2) So let's start counting each tiny square so that we can get to know the length.
The letter "L" is actually, with this typography, two rectangles:
So, the perimeter (2P) is equal to:
2P =15 +15 +7+3+3+10+3
2P= 56 units
As for the area:
Using the Rectangle formula, then we can write down the area as:
Area:
[tex]\begin{gathered} A=l\cdot w \\ A_1=3\cdot15=45u^2 \\ A_2=10\cdot3=30u^2 \\ A_L=30+45=75u^2 \end{gathered}[/tex]3) In this letter "O" we can divide it into two trapezoids, and two parallel rectangles:
Note that we need to find the length of those corners shaped like triangles, we can use the Pythagorean Theorem, considering the "rise over run" and write:
[tex]\begin{gathered} a^2=3^2+2^2 \\ a^2=9+4 \\ a^2=13 \\ \sqrt[]{a^2}=\sqrt[]{13} \\ a=3.6 \end{gathered}[/tex]So the Perimeter can be written:
[tex]\begin{gathered} 2P=3.6+3.6+3.6+3.6+5+5+12+12+12+12+3+3 \\ 2P_O=78.4 \end{gathered}[/tex]And for the area, we can find the area of those two trapezoids and two rectangles writing this:
[tex]\begin{gathered} A_O=2(\frac{(B+b)h}{2})+2(w\times l) \\ A_O=2(\frac{(9+3)3}{2})+2(12\times3)_{} \\ A_O=108u^2 \end{gathered}[/tex]4) And now, finally the letter "u":
For the corners let's assume they are triangles, and then we can write the following since those corners are like hypotenuses:
[tex]\begin{gathered} a^2=5^2+2^2 \\ a^2=25+4 \\ a=\sqrt[]{29}\approx5.4 \end{gathered}[/tex]And for the inclined lower part of the letter "u", we can write:
[tex]\begin{gathered} a^2=1^2+2^2 \\ a=\sqrt[]{5}\approx2.2 \end{gathered}[/tex]Therefore, we can write the Perimeter as:
[tex]\begin{gathered} 2P=2(5.4)+2(2.2)+4+3(2)+4(13) \\ 2P_U=77.2 \end{gathered}[/tex]And for the area, we can see from bottom to top: One trapezoid, a par of parallelograms, and two rectangles. Hence, we can write:
[tex]\begin{gathered} A_U=\frac{(B+b)h}{2}+2(l\cdot w)+2(l\cdot w) \\ A_U=\frac{(6+4)3}{2}+2(2\cdot2)+2(2\cdot13) \\ A_U=75u^2 \end{gathered}[/tex]5) So, each letter by area and perimeter:
[tex]\begin{gathered} A_L=75u^2 \\ 2P_L=56u \\ -- \\ A_O=108u^2 \\ A_O=78.4u \\ -- \\ A_U=75 \\ 2P_U=77.2 \end{gathered}[/tex]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]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.
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.
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]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 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.
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]. 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]Can anyone help me? I don't know the answer.
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
What is the rectangle?
A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex] plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.
Area of rectangle = Length × Width
Here given that,
[tex]L=\frac{7}{8}m[/tex]
[tex]W=\frac{3}{4}m[/tex]
So,
Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]
[tex]=\frac{21}{32}m^2[/tex]
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
To know more about the rectangle
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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
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.
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]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°
A spinner with 10 equally sized slices has 10 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice? Write your answer as a fraction in simplest form. Explanation Check U 00 00 X. S ? Esp E D 5 E [2]
Step 1
Given;
Step 2
The probability of an event is given as;
[tex]P(event)=\frac{Required\text{ number of events }}{Total\text{ number of events}}[/tex][tex]\begin{gathered} Required\text{ number of events=Yellow slice=10} \\ Total\text{ number of events= 10 slices} \end{gathered}[/tex]Thus,
[tex]P(yellow\text{ slice\rparen=}\frac{10}{10}=1[/tex]Answer;
[tex][/tex]Daryl loaned his friend $2,500 to help him with his business. If his friend pays Daryl back in one year with 15% simple interest how much will he owe Daryl all together?
Answer:
$2875
Explanation
Given
Principal P = $2,500
Rate R = 15%
Time T = 1year
Get the interest on $2500
Simple Interest = PRT/100
Simple Interest = 2500 * 15 * 1/100
Simple Interest = 25*15
Simple Interest = $375
Amount owed altogether = Pricipal + Interest
Amount owed altogether = $2500 + $375
Amount owed altogether = $2875
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]
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.
Jennie has $300 and spends $15.What percent of her money is spent?
ok
Total money = $300
money spend = $15
300 ---------------------- 100
15 ---------------------- x
x = (15 x 100)/300
x = 1500/300
x = 5
Jennie spent 5% of her money
To solve it, use a rule of three. $300 is 100%, so we need to calculate which percent is $15 of the total amount.
In a rule of three, it's necessary to use cross multiplication and then division.
That's why I multiplied 15 by 100 and then I divided by 300.
15 is 5% of $300
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