We know that
• The gardener used at most 56 feet of fencing.
,• The length of the fence is four feet longer than the width.
Remember that the perimeter of a rectangle is defined by
[tex]P=2(w+l)[/tex]Now, let's use the given information to express as inequality.
[tex]2(w+l)\leq56[/tex]However, we have to use another expression that relates the width and length.
[tex]l=w+4[/tex]Since the length is 4 units longer than the width. We replace this last expression in the inequality.
[tex]\begin{gathered} 2(w+w+4)\leq56 \\ 2(2w+4)\leq56 \\ 2w+4\leq\frac{56}{2} \\ 2w+4\leq28 \\ 2w\leq28-4 \\ 2w\leq24 \\ w\leq\frac{24}{2} \\ w\leq12 \end{gathered}[/tex]The largest width possible is 12 feet.
Now, we look for the length.
[tex]\begin{gathered} 2(12+l)\leq56 \\ 24+2l\leq56 \\ 2l\leq56-24 \\ 2l\leq32 \\ l\leq\frac{32}{2} \\ l\leq16 \end{gathered}[/tex]Therefore, the largest measure possible for the length is 16 feet.Anna rolls a die and then flips a coin. Identify the tree diagram which displays the outcomes correctly.
Let:
1 = Get a 1
2 = Get a 2
3 = Get a 3
4 = Get a 4
5 = Get a 5
6 = Get a 6
H = Get heads
T = Get tails
The set of all possible outcomes of the experiment is:
[tex]\begin{gathered} S=\mleft\lbrace(1,H\mright),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),\ldots \\ \ldots(5,H),(5,T),(6,H),(6,T)\} \end{gathered}[/tex]Therefore, the only tree diagram which displays the outcomes correctly is the one in the option A.
Help me out with details
Answer:
The numbers are proportional with each other. If you were to divide the length on the table by the corresponding width, you'd get the same answer each time(0.6)
find a point slope equation for a line containing the given point and having the given slope y-y1 = m (x-x1 )7. (7, 0), m = 48. (0,9), m = -2
We have the following:
7. (7.0), m = 4
replacing:
[tex]\begin{gathered} y-0=4\cdot(x-7) \\ y=4x-28 \end{gathered}[/tex]8. (0,9), m = -2
[tex]\begin{gathered} y-9=-2\cdot(x-0) \\ y=-2x+9 \end{gathered}[/tex]What is 5x100? Pls tell me
We want to calculate;
[tex]5\times100=500[/tex]Thus the answer is 500.
Solve 15 - 8x > 3 - 2x and write the solution in interval notation.O Interval notation solution:O No solution
Add 8x to both sides
[tex]\begin{gathered} 15-8x+8x>3-2x+8x \\ 15>3+6x \end{gathered}[/tex]Subtract 3 from both sides
[tex]\begin{gathered} 15-3>3-3+6x \\ 12>6x \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{12}{6}>\frac{6x}{6} \\ 2>x \\ x<2 \end{gathered}[/tex]Interval notation solution: x < 2
Determine the end behavior for each function below. Place the letter(s) of the appropriatestatement(s) on the line provided. A. As x approaches ∞o, y approaches ∞oB. As x approaches -œo, y approaches œC. As x approaches ∞o, y approaches -∞0D. As x approaches -c0, y approaches -00
Solution:
From the given graphs,
The first graph is the absolute function graph.
Which can be expressed in the form
[tex]y=-|x|[/tex]Since the leading coefficient is negative,
The end behavior of the graph is
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow-\infty[/tex]Hence, the answers are C and D
The second graph is a quadratic graph of the form
[tex]y=x^2[/tex]Since the leading coefficient is positive
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are A and B
The third graph is a cubic function that can be expressed in the form
[tex]y=-x^3[/tex]The leading coefficient is negative.
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are C and B
If you pay Php 38,500.00 at the end of 3 years and 3 months to settle an obligation of Php 35,800. What simple interest rate was used?
Mr. Jones owned his car for 12 years. The car has 169,344 miles recordedon the odometer. What is the average number of miles driven per year?
total distance travelled by the car is 169344 miles, for 12 years,
the distance travelled in 1 year is
[tex]=\frac{169344}{12}=14112[/tex]so the average number of miles der
How do I do I calculate the curve of best fit with the following data points given?
To determine the curve of best fit, let's look at the x-intercepts of the curve.
Based on the graph, the x-intercepts are at x = -7 and x = -1.
Since -7 and -1 are the x-intercepts, we can say that the factors of this curve are:
[tex](x+7)(x+1)[/tex]Now, we can also see that the graph is opening downward, therefore, the leading coefficient of the equation of this graph must be negative. For this, we will multiply the factors above by -1.
[tex]-(x+7)(x+1)[/tex]All we have to do now is multiply the factors above in order to get the curve of best fit.
[tex]-(x^2+x+7x+7)[/tex]Combine similar terms like x and 7x.
[tex]-(x^2+8x+7)[/tex]Then, distribute the negative sign.
[tex]-x^2-8x-7[/tex]Therefore, the curve of best fit is y = -x² - 8x - 7.
B(q-L)--------- =3. its all divided by h but I don't. hunderstand how to solve for q
Given the equation below,
[tex]\frac{B(q-L)}{h}=r[/tex]Solving for q, by making q the subject of formula from the above equation
Multiply both sides by h
[tex]\begin{gathered} h\times\frac{B(q-L)}{h}=r\times h \\ B(q-L)=rh \end{gathered}[/tex]Divide both sides by B
[tex]\begin{gathered} \frac{B(q-L)}{B}=\frac{rh}{B} \\ (q-L)=\frac{rh}{B} \end{gathered}[/tex]Add L to both sides
[tex]\begin{gathered} q-L+L=\frac{rh}{B}+L \\ q=\frac{rh}{B}+L \end{gathered}[/tex]Hence, the answer is
[tex]q=\frac{rh}{B}+L[/tex]2xy^2-x^2Evaluate where x=2 and y=5is that first step correct and what would be the order of operations from there
To evaluate this , replace the terms with the numbers as
2 xy^2 - x^2
[tex]2xy^2-x^2[/tex][tex]2\cdot2\cdot5^2-2^2[/tex][tex]4\cdot5^2-4[/tex][tex]4\cdot25\text{ - 4}[/tex][tex]100-4=96[/tex]Solve the following quadratic function by factoring f(x) = x2 – X – 12 Enter the number that belongs in the green box. x = 4; x = [?] Enter
The given function is
[tex]f(x)=x^2-x-12[/tex]To solve it by factoring, we have to look for two numbers whose product is 12 and whose difference is 1. Those numbers are 4 and 3.
[tex]f(x)=(x-4)(x+3)=0[/tex]Then, we use the zero property
[tex]\begin{gathered} x-4=0\rightarrow x=4 \\ x+3=\rightarrow x=-3 \end{gathered}[/tex]Hence, the answer is -3.I need to know if this is the correct answer
Answer:
Correct
Explanation:
Given the function:
[tex]5x+3y=15[/tex]To confirm if the graph is correct, find the x and y-intercepts of the function.
x-intercept
When y=0
[tex]\begin{gathered} 5x+3(0)=15 \\ 5x=15 \\ x=\frac{15}{5}=3 \end{gathered}[/tex]• The x-intercept is (3,0).
y-intercept
When x=0
[tex]\begin{gathered} 5(0)+3y=15 \\ 3y=15 \\ y=\frac{15}{3}=5 \end{gathered}[/tex]• The y-intercept is (0,5)
These are the intercepts on the shown graph.
Your graph is correct.
Tyra works as a hostess. She earns $6.75 per hour and works 35 hours a week. She also earns an average of $200 per week in tips. How much will Tyra earn in a year? A. $436 B. $5,235 C. $22,685 D. $27,300
Answer:
C. $22,685
Step-by-step explanation:
(35x6.75+200)x52(weeks in a year)=$22,685
Determine if it is a true proportion. Please choose the correct letter
Given the equation:
[tex]\frac{\frac{3}{5}}{\frac{14}{2}}=\frac{\frac{1}{2}}{\frac{35}{6}}[/tex]Let's determine if the proportion is a true proportion.
If the proportionis true, it means the ratio on both sides if the equality are equal.
Now, let's find the ratios.
For the first ratio:
[tex]\begin{gathered} \frac{\frac{3}{5}}{\frac{14}{2}} \\ \\ =\frac{3}{5}\div\frac{14}{2} \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =\frac{3}{5}\times\frac{2}{14} \\ \\ =\frac{3}{5}\times\frac{1}{7} \\ \\ =\frac{3\times1}{5\times7} \\ \\ =\frac{3}{35} \end{gathered}[/tex]For the second ratio:
[tex]\begin{gathered} \frac{\frac{1}{2}}{\frac{35}{6}} \\ \\ =\frac{1}{2}\div\frac{35}{6} \\ \\ \text{ Flip the fraction on the right and change the division symbol to mutilication:} \\ =\frac{1}{2}\times\frac{6}{35} \\ \\ =\frac{1\times6}{2\times35} \\ \\ =\frac{6}{70} \\ \\ =\frac{3}{35} \end{gathered}[/tex]After simlifying, we have:
[tex]\frac{3}{35}=\frac{3}{35}[/tex]Since the equation is true, we can say the proortion is true because it has a constant ratio.
the table below gives the side lengths and surface areas of different cubes.
Given
Relationship between sides and surface areas
Find
Conclusion from the table
Explanation
From the table we can see that sides double in 1st, 2nd and 4th case
So comparing them
When side =1 then Surface area = 6 cm sq
When side = 2 then Surface area = 24 cm sq
Here we can see that when the side doubles, the surface area quadruples
Similar result is obtained when in relation of side = 2 and side 4
Final Answer
When the side doubles, the surface area quadruples
option (a) is correct
Help ! its not a test i just don't understand!!
An important rule before subtracting fractions, you must first make them have a common denominator. The common denominator is the LCM (Least Common Multiple) of the two different denominators.
You may use this formula:
[tex]\frac{a}{b}=\frac{(a)(\frac{c}{b})}{c}[/tex]We get,
a.) 9/12 - 1/2 ; The LCM of 12 and 2 is 12.
[tex]\frac{9}{12}-\frac{1}{2}=\text{ }\frac{9}{12}-\frac{(1)(\frac{12}{2})}{12}=\text{ }\frac{9}{12}-\frac{(1)(6)}{12}=\frac{9}{12}-\frac{6}{12}[/tex][tex]\frac{9}{12}-\frac{6}{12}=\frac{3}{12}[/tex]Therefore, the difference of 9/12 - 1/2 is 3/12. You shade letter B.
It is known that the events ANB are mutually exclusive that p(a)=0.60 and p(b)=0.16
The probability of two mutually exclusive events to happen simultaniously can be described as below:
[tex]P(A\text{ and }B)=P(A)\cdot P(B)[/tex]We can replace the terms above with the probabilities to determine the answer for this problem.
[tex]P(A\text{ and }B)=0.6\cdot0.16=0.096[/tex]The probability of both events happening simultaneously is 0.096.
A cyclist rides her bike at a speed of 15 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers. Speed: Distance traveled in 5 hours:
Given: The cyclist rides her bike at a speed of 15 miles per hour
To Determine: The speed in kilometers per hour and the kilometers cycles in 5 hours
Solution
Please note that 1 miles equal to 1.6kilometers. Let us convert 15miles to kilometers as shown below
[tex]\begin{gathered} 1miles=1.6kilometers \\ 15miles=15\times1.6kilometers \\ 15miles=24kilometers \end{gathered}[/tex]Therefore the speed of 15miles per hour is equivalent to 24kilometers per hour
The kilometers travelled in 5 hours would be
[tex]\begin{gathered} distance=speed\times time \\ speed=24kilometers-per-hour \\ time=5hours \\ distance=24\times5 \\ distance=120kilometers \end{gathered}[/tex]Hence, the speed in kilometers per hour is 24 kilometers per hour,
And the kilometers travelled in 5 hours is 120 kilometers
Find the area ofa cirde with a circumference of 50.24 units,
Step 1
Find radius r , from circumference
circumference = 50.24
[tex]\begin{gathered} \text{Circumference = 2 }\pi\text{ r} \\ \pi\text{ = 3.142} \\ 50.24\text{ = 2 x 3.142r} \\ 50.24\text{ = 6.284r} \\ r\text{ = }\frac{50.24}{6.284} \\ r\text{ = 7.99} \end{gathered}[/tex][tex]\begin{gathered} \text{Area = }\pi r^2 \\ =3.142\text{ x 7.99 x 7.99} \\ =\text{ 200.58} \end{gathered}[/tex]A curve has equation x3 - 5x2 + 7x - 2dyDifferentiate the function to obtaindxa) Find the x coordinates of the points where = 0 and hence the coordinates of thed.xturning points on the curve.dyb) With the aid of a table consider the sign of on either side of the turning points,dxdetermine whether the turning points are maximum or minimum points.c) Sketch the curve showing the turning points clearly and label any other points ofinterest.
SOLUTION
Write our the function given
To differentiate the function, we apply the differentiation rule
[tex]y=x^n,\frac{dy}{dx}=nx^{n-1}[/tex]Hence
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{Then} \\ \frac{d}{dx}\mleft(x^3-5x^2+7x-2\mright) \end{gathered}[/tex]Then Apply the sum and difference rule for derivative, we have
[tex]\begin{gathered} =\frac{d}{dx}\mleft(x^3\mright)-\frac{d}{dx}\mleft(5x^2\mright)+\frac{d}{dx}\mleft(7x\mright)-\frac{d}{dx}\mleft(2\mright) \\ =3x^2-10x+7-0 \\ =3x^2-10x+7 \end{gathered}[/tex]For dy/dx =0,we have
[tex]3x^2-10x+7=0[/tex]solve quadratic equation, we have
[tex]\begin{gathered} 3x^2-3x-7x+7=0 \\ 3x(x-1)-7(x-1)=0 \\ (3x-7)(x-1)=0 \end{gathered}[/tex]Equation each factor the zero, we have
[tex]\begin{gathered} 3x-7=0,x-1=0 \\ 3x=7,x=1 \\ x=\frac{7}{3},1 \end{gathered}[/tex]Hence
The x coordinates are
x= 7/3 and x=1
To obtain the coordinate of the turning point, we substitute into the equation given
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{for x=7/3} \\ y=(\frac{7}{3})^3-5(\frac{7}{3})^2+7(\frac{7}{3})-2 \end{gathered}[/tex]Then by simplification, we have
[tex]y=-\frac{5}{27}[/tex]Then, one of the turning point is
[tex](\frac{7}{3},-\frac{5}{27})[/tex]Then, we substitute the other value of x,
[tex]\begin{gathered} \text{for x=1} \\ y=x^3-5x^2+7x-2 \\ y=(1)^3-5(1)^2+7(1)-2 \\ y=1-5+7-2 \\ y=1 \\ \text{turning point =(1,1)} \end{gathered}[/tex]Therefore the other turning point is (1,1)
The turning point are (7/3, -5/27) and (1,1)
what are the coordinates for the location of the center of the merry-go-round?
Given the coordinates of the following locations
[tex]\begin{gathered} Q(4,-2) \\ R(2,-4) \\ S(0,2) \end{gathered}[/tex]From the question we have that the distance of the point are equal so we will have;
[tex](x-4)^2+(y+2)^2=(x-2)^2+(y+4)^2=(x-0)^2+(y-2)^2[/tex]Solving equation 1 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-8x+16+y^2+4y+4=x^2+y^2-4y+4_{} \\ -8x+8y=-16 \\ \text{Divide through by 8} \\ -x+y=-2 \\ x=y+2 \end{gathered}[/tex]Solving equation 2 and 3 simultaneously we will have
[tex]\begin{gathered} x^2-4x+4+y^2+8y+16=x^2+y^2-4y+4 \\ -4x+12y=-16 \\ \text{Divide through by 4} \\ -x+3y=-4 \\ x=3y+4 \end{gathered}[/tex]Thus , to solve for y we have;
[tex]\begin{gathered} y+2=3y+4 \\ 2-4=3y-y \\ -2=2y \\ y=\frac{-2}{2}=-1 \end{gathered}[/tex]Substitute y to find x
[tex]\begin{gathered} x=y+2 \\ x=-1+2=1 \end{gathered}[/tex]Hence the coordinates of the center of the merry-go-round is ( 1, - 1)
The second option is the correct option
To solve the rational equation2. 3-x+65X+25how can the expressionX+2be rewritten usingthe least common denominator?
The expression given is:
[tex]\frac{2}{x}+\frac{3-x}{6}[/tex]The Least Common Denominator (L.C.D) of the expression is the product of the denominator:
[tex]6\times x=6x[/tex]Since
[tex]\frac{2}{x}+\frac{3-x}{6}=\frac{5}{x+2}[/tex]Then, we can multiply both the numerator and denominator with the L.C.D of 6x:
[tex]\begin{gathered} \frac{5}{x+2} \\ \\ \frac{5}{x+2}\times\frac{6x}{6x} \\ \\ \frac{30x}{6x(x+2)} \end{gathered}[/tex]Therefore, the final answer is: Option B
Patrick is buying rabbits. This graph shows how the total cost depends on the number of rabbits purchased.
Using the graph provided, we must find how many rabbits correspond to a cost of $20.
To find the number of rabbits, we look for the value $20 on the vertical axis, then we follow a horizontal line to the curve, and then we go down vertically to the horizontal axis. We find that the number of rabbits is 5.
We see that we have a linear relationship between the number of rabbits and its cost. If 5 rabbits cost $20, each rabbit costs $20/5 = $4 (we can also find this value looking at the graph).
Using the cost of each rabbit, we have that:
• 5 rabbits cost $4 * 5 = $20,
,• 8 rabbits cost $4 * 8 = $32,
,• 12 rabbIts cost $4 * 12 = $48.
Answer
5 rabbits cost $20,
8 rabbits cost $32,
12 rabbIts cost $48.
In the first episode of a reality show, contestants had to spin two wheels of fate. Spinning the first wheel determined the remote location where contestants would reside for the duration of the season. Spinning the second wheel determined which "bonus survival tool" they would be allowed to bring, along with a few other necessary items. A tent Matches Desert 4 1 Rainforest 3 1 Mountain peak 1 1 What is the probability that a randomly selected participant spun the second wheel and landed on a tent given that the participant spun the first wheel and landed on mountain peak? Simplify any fractions.
Answer:
1/2
Explanation:
Taking into account the table, we know that 2 participants spun the first wheel and it landed on a mountain peak and 1 of those participants spun the second wheel and landed on a tent. So, we can calculate the probability as:
[tex]P=\frac{1}{2}[/tex]Because there are 2 people on a mountain peak and for one of them landed on a tent.
Therefore, the answer is 1/2
I dont understand how the answer is 1/3. how do you calculate that answer????
1/3
Explanation:To convert repeating decimals to fraction, we need to represent it with a variable
let n = 0.3333...
Multiply the above by 100:
100n = 33.3333...
The 3 dots after the 3333 means the numbers continues; hence indicating a repeating decimal
n = 0.3333 ...equation 1
100n = 33.3333 ...equation 2
subtract equation 1 from 2:
100n - n = 33.3333 - 0.3333
100n - n = 99n
99n = 33
divide both sides by 99:
99n/99 = 33/99
n = 1/3
Therefore, 0.3 repeating decimal in fraction is 1/3
(word sentence) Pooky eats three cans of cat food each day. How long will 27 cans of food last?
ANSWER:
9 days
Solution:
[tex]\frac{27\text{ cans}}{3\text{ cans per day}}\text{ = 9 days}[/tex]Answer: The 27 cans of food will last 9 days since 27 ÷ 3 = 9.
Step-by-step explanation:
Find the area of a triangle ABC when c = 15 m, a = 20 meters, and b = 10 meters.
Recall Heron's Formula to find the area of a triangle with sides a, b and c.
We define a new quantity s given by:
[tex]s=\frac{a+b+c}{2}[/tex]Then, the area of the triangle is given by the formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]For a=20, b=10 and c=15 we have:
[tex]s=\frac{20+10+15}{2}=22.5[/tex]Then, the area of the triangle is:
[tex]\begin{gathered} A=\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)} \\ =\sqrt{22.5(2.5)(12.5)(7.5)} \\ =\frac{75\sqrt{15}}{4} \\ =72.61843774... \\ \approx72.6 \end{gathered}[/tex]Therefore, the exact answer is:
[tex]A=\frac{75\sqrt{15}}{4}[/tex]And the approximate area of the triangle ABC when c=15m, a=20m and b=10m is 72.6 m^2.
Simplify the following expression.(3x – 5)(4 – 9x) + (2x + 1)(6x2 + 5)O12.3 – 21.12 - 671 - 15O12 x3 – 21–2 + 671 - 1512r 3 + 21,2 – 675 + 15O12 x3 + 21x2 + 67x + 15Submit
The Solution:
Given the expression below:
[tex]\mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright)[/tex]We are required to simplify the above expression.
[tex]\begin{gathered} \mleft(3x-5\mright)\mleft(4-9x\mright)+\mleft(2x+1\mright)\mleft(6x^2+5\mright) \\ 3x(4-9x)-5(4-9x)+2x(6x^2+5)+1(6x^2+5) \end{gathered}[/tex]Clearing the brackets, we get
[tex]\begin{gathered} 12x-27x^2-20+45x+12x^3+10x+6x^2+5 \\ 12x^3+6x^2-27x^2+12x+45x+10x-20+5 \end{gathered}[/tex][tex]12x^3-21x^2+67x-15[/tex]Therefore, the correct answer is
[tex]12x^3-21x^2+67x-15[/tex]Which shows how to use similar right triangles to find the equation of the line through (0,6) and any point (x,y), on the line?
By the given triangles in the figure, you can notice that the following proportion must be equal, because the involved sides are congruent:
[tex]\frac{y-b}{x-0}=\frac{m+b-b}{1-0}[/tex]In the left side, side of triangle with length y - b, divided by side with length x, must be equal to the quotient between side with length m + b - b and side with length 1.
Solve the previous equation for y, just as follow:
[tex]\begin{gathered} \frac{y-b}{x}=m \\ y-b=mx \\ y=mx+b \end{gathered}[/tex]