Step-by-step explanation:
A fence for a rectangular garden with one side against an existing wall is constructed by using 60 feet of fencing.
Perimeter of rectangle (3 sides)= 60 feet
Let 'x' be the width of the wall
[tex]Perimeter = 2(length)+2(width)\\60=2(length)+2x\\\\60-2x=2(length)\\\frac{60-2x}{2} =length\\Length =30-x[/tex]
Formula for the area of the rectangle is
[tex]Area=length \cdot width\\A=length(x)[/tex]
Replace the length we got using perimeter
[tex]A=(30-x)(x)\\A(x)= 30x-x^2[/tex]
To find out the maximum are we take derivative
[tex]A'(x)= 30-2x\\0=30-2x\\-30=-2x\\x=15[/tex]
find out second derivative to check whether x=15 is maximum
[tex]A''(x)=-2[/tex]
second derivative is negative
So, Maximum area at x=15
To find maximum area we plug in 15 for x in A(x)
[tex]A(x)=30x-x^2\\A(15)=30(15)-15^2\\A(15)=225[/tex]
So, maximum area is 225 square feet
01:38:56
What is the scale factor of a triangle with a vertex of A(-6, 4) that has been dilated with a center of dilation at the origin so
the vertex of its image is A'(-24, 16)?
Answer:
Answer: The scale factor of the triangle is 4
Step-by-step explanation:
Football player caught the ball and made a gain of 8 yards on the first play. On the next play the team lost 12 yards. How many years do they need to gain on the next play to get back their original position?
Factorise 18pq-12p
-
Answer:
6p(3q - 2).
Step-by-step explanation:
The GCF ( Greatest Common Factor) of 18pq and 12p is 6p.
So 18pq-12p = 6p(3q - 2).
Please look at the question and answer
Answer:
no . of items = 10
Position of mean = (n+1)/2
= 11/2 = 5.5th item
In the data 5.5 item is the average of 5th and 6th item
median = (x+2+x+4)/2
or 25= (2x+6)/2
or 50 = 2x +6
0r 2x = 44
x =22
Answer:
X=23
Step-by-step explanation:
11,13,15,19,_,_,30,39,46
The middle number is the first dash which is represented by x+2 which is equal to 25
25-2=23 which is x
Dash 2 which is represented by x+4 is equal to 23+4=27
The Price of dried mango is $9 for every 3/4 pound.
what is the price per pound of the dried mango?
$_ per lb
Answer:
12
Step-by-step explanation:
9 ÷3 =3 ×4 that is how to do the problem
6. The amount of time it took four soccer players to run from one goal line to the other is as follows:
Player #1 - 10.4 seconds
Player #2 - 10.1 seconds
Player #3 - 9.9 seconds
Player #4 - 9.4 seconds.
If the data was only accurate to the ones place, which soccer player's time would be different from the others?
A Player #1
B Player #3
C Player #2
D Player #4
Given:
The amount of time it took four soccer players to run from one goal line to the other is:
Player #1 - 10.4 seconds
Player #2 - 10.1 seconds
Player #3 - 9.9 seconds
Player #4 - 9.4 seconds
To find:
Soccer player whose time would be different from the others, if the data was only accurate to the ones place.
Solution:
We need to approximate the time to the ones place.
Player #1 - 10.4 seconds = 10 seconds
Player #2 - 10.1 seconds = 10 seconds
Player #3 - 9.9 seconds = 10 seconds
Player #4 - 9.4 seconds = 9 seconds
Therefore, the time of players 4 is different from others.
Hence, the correct option is D.
if DF = 15 and DE = 6, find EF if E is between D and F?
Answer:
EF=9
Step-by-step explanation:
DF=15
DE=6 EF=9
Write equation 6+x=15
subtract 6 on both sides
x=9 EF=9
Solve the equation below 7a=56
Answer:
a=8
Step-by-step explanation:
So, what is the pattern? For positive integers a and b: (x^a)^b
Answer: (x^b)^a
Step-by-step explanation:
the inverse of a monomial with an exponent raised to another power will give the same product if you flip the exponents.
Here we have a general rule for exponents.
We will find that:
[tex](x^a)^b = x^{a*b}[/tex]
To get this, we can first check it with some values for the exponents.
a = 2
b = 3
[tex](x^2)^3 = (x^2)*(x^2)*(x^2) = (x*x)*(x*x)*(x*x) = x^6 = x^{2*3}[/tex]
Similarly, we can prove it for two general values of a and b:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a)\\b\ times[/tex]
Now each one of these parentheses has a multiplying by itself a times.
So when we write all the x's, we will see that there are a total of b*a x's
Thus we will have:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a) = x^{a*b}[/tex]
If you want to learn more, you can read:
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One week, Caroline earned $183.20 at her job when she worked for 8 hours. If she is paid the same hourly wage, how much would she make the next week if she worked 13 hours?
Answer:
$297.70
Step-by-step explanation:
First, find her hourly wage:
183.20/8
= 22.9
Then, multiply this by 13:
22.9(13)
= 297.7
So, she will make $297.70 next week
Answer:
297.70
Step-by-step explanation:
Read the pdf named "Brain"
2) I have two consecutive numbers. The difference of 4 times the first and 3 times the second number is negative 25. What is the value of your two numbers?
Answer:
31
Step-by-step explanation:
Answer:
Step-by-step explanation
The anwser should be 30 or 37 because 4 times 3 is 12 then plus 25 is 37Which does Not round to 200?
163
266
150
221
Answer:
266
Step-by-step explanation:
Jake has a 1 in 5 chance of winning the egg and spoon race.
What is the probability that he will not win the race?
4/5
subtract 1/5 from 5/5.
Answer:
4/5
Step-by-step explanation:
if he has a 1/5 of winning, the left over chances he has has to be towards losing because we already know his chance of winning, and there is no in between, so the left over is 4/5
Can someone please help me
Answer: (b) 7.8 degrees
Step-by-step explanation: You need to pay attention to the number -8.4. It says the temperature changed by +2.7 degrees an hour for 6 HOURS. Therefore, your equation would be -8.4 + (2.7 * 6).
You have to solve whats in the parenthesis first, so your equation would end up being -8.4 + 16.2 making your answer 7.8 degrees.
A bicycle tire is 28 inches in diameter. Approximately how far does the bicycle move forward each time the wheel goes around? (Use 22/7 as an approximation for .)? i forgot this sorry someone help please
Answer:
Step-by-step explanation:
28x pi=87.96 in
Can someone help me??
Answer:
C
Step-by-step explanation:
−√57 is -7.54983443 repeating but rounded is -7.5 which is smack dab in the middle of integers (numbers) of -7 and -8.
HELP ME PLEASE I NEED THIS <3333
Answer:
214°
Step-by-step explanation:
The arc subtending an angle at the centre are equal, that is
arc ED = 90° and
arc DF = 360° - (90 + 146)° = 360° - 236° = 124°
Thus
arc EDF = arc ED + arc DF = 90° + 124° = 214°
How do I do solving systems by substitution please help
The problem I'm on is x-y=-5 with x+y=1
Please show steps I need an answer before my report card comes in tomorrow
Answer:
I believe the answer is x=-2, and y=3.
Step-by-step explanation:
Given: x-y=-5
Fill in: -2-3=-5
Calculate: -5=5
-------------------------------
Given: x+y=1
Fill in: -2+3=1
Calculate: 1=1
Answer:
x = -2.
y = 3.
Step-by-step explanation:
x-y=-5
x+y=1
From the first equation
x = y - 5
Substitute this in the second equation:
y - 5 + y = 1
2y = 1 + 5 = 6
y = 3.
Substitute this into the second equation:
x + 3 = 1
x = -2.
Round to the nearest thousandth: 4.3218 →
Answer:
4.322
Step-by-step explanation:
You would round up because of 8.
Hope this helps!! :D
Answer:
4.322
Since 8 is greater than 5, you round upwards.
A teacher surveyed all 120 of her students about their lunch and lunch schedule. The teacher asked two questions:
• Do you buy a school lunch or bring lunch from home?
Do you eat during festlunch, second lunch, or third lunch
The results showed the majority of her students eat during second lunch and most students buy a school lunch
Which two way table could be a correct representation of the results?
D
you buy lunch and your teacher asks you how much you brought from home then you divide, simple.
. Bartholomew Jackson is paid $10.56 an hour to knit dog sweaters. He gets paid 1.5 times his normal wages for overtime (over 40 hours per week). If he works 55.5 hours in one week, how much money does he earn
Answer:
$667.92
Step-by-step explanation:
Use the equation (p*1.5)*o=t
the variable p is equal to his hourly pay.
the variable o is equal to hours worked overtime.
the variable t is equal to the total amount of money they will make.
As for the 1.5, this is the way overtime is always calculated, at 1.5 times the rate of your hourly wage.
Back to the question:
the variable p is replaced by his hourly pay, $10.56.
the variable o is replaced by the amount of hours he worked overtime. Now, this part is a bit trickier because the question is designed to confuse you. If his overtime only counts if he works over 40 hours a week, then you need to subtract the 40 from his total amount of hours worked. You should get 15.5 because 55.5-40=15.5. Thus, variable o=15.5.
Lastly, you have to calculate it.
Plug in the variables to get:
($10.56*1.5)*15.5= $245.52
DON'T STOP HERE!!!
Since the question asks for how much he has earned for the week, you have to add this onto his normal salary. This part is easy, just multiply the 40 hours by his pay. So,
40*$10.56= $422.40.
Finally, add the overtime ($245.52) to his normal pay ($422.40).
$422.40+$245.52= $667.92
Which statement describes the inverse of m(x) = x2 – 17x?
Answer:
The correct option is;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
[tex]x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}[/tex]
Which can be simplified as follows;
[tex]x = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2} \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}[/tex]
And further simplified as follows;
[tex]x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}[/tex]
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
[tex]m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex] to increase m⁻¹(x) above the minimum.
Answer:
b
Step-by-step explanation:
edge 2021
Jenny invests $8500 for 3 years in a savings account. She gets 2.3% per year compound interest. How much money will Jenny have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.
Answer:$9,100.09
Step-by-step explanation:
Plz answer this as soon as possible it’s my hw I have to submit it tomorrow.
Answer:
43
Step-by-step explanation:
-2+3×15
45-2
43 is the answer
Translate the following into a verbal expression 3(4-x)+7
Answer:
3 times 4 minus a number, plus 7
3(4 - x) + 7
Consider points R, S, and T.
Point S is in the middle. Point R is below and to the left of point S. Point T is below and to the right of point S.
Which statement is true about the geometric figure that can contain these points?
Are the ratios 3:9 and 21:27 equivalent? Why or why not?
Answer:
Not equivalent
Step-by-step explanation:
Given:
3:9 and 21:27We see that
21:27= 7:9Comparing:
3:9 < 7:9They have same denominator but different numerator, hence they are different
Answer: No
Step-by-step explanation:
No there are not since 3 times 7 = 21 and 9 times 3 = 27. The numbers that are used to multiply for the answers, 7 and 9, are not the same so therefore both ratios are not equivalent.
A line is an undefined term because it
solve for x: -8+22=13x-5-12x
Answer:
x = 19
Step-by-step explanation:
-8 + 22 = 13x - 5 - 12x
switch sides
13x - 5 - 12x = -8 + 22
group like terms
13x - 12x = -8 + 22 + 5
simplify:
x = 19
the difference of six times a number and 7 is -49.
Answer:
6x - 7 = 6(x + 4)
Step-by-step explanation:
The value of the number (n) is -7.
What is an Algebraic Expressions?When we apply the mathematical operations on constants and variables then we get the mathematical statements, these are known as algebraic expressions.The mathematical operators include, division, addition, multiplication and subtraction.Let a number we want to find be n.
Hence, according to the given condition, the equation will be:
⇒ 6n - 7 = -49
⇒ 6n = -42
Dividing both sides by 6, we get:
⇒ n = -7
Therefore, the number that satisfy the algebraic expression is n = -7.
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