Answer:
x = 1 mStep-by-step explanation:
Area of pool:
6*4= 24 m²Area of walkway:
(6+2x)(4 +2x) - 24 =24 + 12x + 8x + 4x² - 24 =4x² + 20xIf the areas are equal, then:
4x² + 20x = 24x² + 5x - 6 = 0x = (-5 ±√25+24)/2x = (-5 ± 7)/2x = 1 and x = -6 (excluded as negative)Final answer:
To find the value of x when the area of the walkway equals the area of the pool, set up an equation and solve for x. The value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
Explanation:
To find the value of x when the area of the walkway equals the area of the pool, we need to set up an equation. The area of the pool is the length multiplied by the width, which is 6 meters multiplied by 4 meters, or 24 square meters. The area of the walkway is the total area of the larger rectangle minus the area of the pool.
The total area of the larger rectangle is the length plus twice the width, all multiplied by the width. So, the area of the walkway is x(6 + 2x - 4). Setting the area of the walkway equal to the area of the pool gives us the equation: x(6 + 2x - 4) = 24.
To solve this equation, we can first simplify it by distributing the x through the parentheses: 6x + 2x^2 - 4x = 24. Combining like terms, we have 2x^2 + 2x - 24 = 0. To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us 2(x + 6)(x - 2) = 0. So either (x + 6) = 0 or (x - 2) = 0. Solving for x, we find that x = -6 or x = 2.
Since we are dealing with width, the negative solution x = -6 is not applicable. Therefore, the value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
y=-4x+2 y=6x-8 in substitution ordered pairs
Answer:
(1, -2).
Step-by-step explanation:
y=-4x+2
y=6x-8
Substitute y = 6x - 8 in the first equation
6x - 8 = -4x + 2
10x = 10
x = 1
So y = 6x - 8
= 6(1) - 8
= -2.
The pair should be (1, -2).
Given information:The equation is y=-4x+2 and y=6x-8
Calculation of pairs:here we Substitute y = 6x - 8 in the first equation
So,
6x - 8 = -4x + 2
10x = 10
x = 1
Now
y = 6x - 8
= 6(1) - 8
= -2.
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Darren has a piece of wood that is 7 in by 8 in. Explain how he can divide this large rectangle into two small rectangles
Answer:
Cut it in half so that the two pieces are each 7 in by 4 in.
Alvin’s age is three times Elga’s age. The sum of their ages is 20. What is Elga’s age?
Answer:
Elga's age is 5.
Step-by-step explanation:
3x=y
x+y=20
-------------
x+3x=20
4x=20
x=20/4
x=5
3(5)=15
y=15
x=5, y=15
Find f'(x) for f(x)=cos^2(5x^3).
d/dx cos^2(5x^3)
= d/dx [cos(5x^3)]^2
= 2[cos(5x^3)]
= - 2[cos(5x^3)] * sin(5x^3)
= - 2[cos(5x^3)] * sin(5x^3) * 15x^2
= - 30[cos(5x^3)] * sin(5x^3) * x^2
Explanation:
d/dx x^n = nx^(n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)
Step-by-step explanation:
f(x) = cos²(5x³)
f(x) = (cos(5x³))²
Use chain rule to find the derivative:
f'(x) = 2 cos(5x³) × -sin(5x³) × 15x²
f'(x) = -30x² sin(5x³) cos(5x³)
If desired, use double angle formula to simplify:
f'(x) = -15x² sin(10x³)
Maine has one of the lowest sales tax rates in the country. If an item costs $40, you will pay $2 in sales tax. What percent of sales tax will you pay?
You will pay 5% sales tax.
Step-by-step explanation:
Given,
Cost of item = $40
Sales tax = $2
Percent of sales tax = [tex]\frac{Sales\ tax}{Cost\ of\ item}*100[/tex]
[tex]Percent\ of\ sales\ tax=\frac{2}{40}*100\\Percent\ of\ sales\ tax=\frac{200}{40}\\Percent\ of\ sales\ tax=5\%[/tex]
You will pay 5% sales tax.
Keywords: sales tax, division
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What is the fewest number of transformations needed to take pre-image ABCD to image A'B'C'D'?
(photo attached)
I really need help!
Answer:
2 transformations
Step-by-step explanation:
1)Reflection
2) Rotation 180 degrees clockwise
2. The sequence 5, 20, 35, 50….. shows the number of sit ups Margie did each week, starting with her first week of the new year.
(a) What is the recursive rule for the sequence?
(b) What is the explicit rule for the sequence?
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]
Step-by-step explanation:
The form of the recursive rule of an arithmetic sequence sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where
[tex]a_{1}[/tex] is the first term in the sequence[tex]a_{n}[/tex] the nth term in the sequence [tex]a_{n-1}[/tex] the term before the nth term n is the term numberd is the common difference between each two consecutive termsThe form of the explicit rule of nth term of an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first termd is the common difference between each two consecutive terms∵ The sequence is 5, 20, 35, 50, ….......
∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15
∴ The sequence is an arithmetic sequence with a common
difference 15
∵ The form of the recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]
∵ First term = 5
∵ d = 15
∴ [tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
∵ The form of the explicit rule of nth term of an arithmetic
sequence is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 5 and d = 15
- Substitute these values in the rule
∴ [tex]a_{n}=5+(n-1)15[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=5+15n-15[/tex]
- Add like terms
∴ [tex]a_{n}=15n-10[/tex]
(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]
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Mika placed $4200 in a savings account which compounds interest continuously at a rate of 2.3%. How much will she have in the account after 3 years? Round to the nearest dollar.
Answer:
$4,500
Step-by-step explanation:
4,200e^3(.023)
Simplify: 8x - (14 +4x)
Answer:
4x-14
Step-by-step explanation:
8x-(14+4x)
8x-14-4x
8x-4x-14
4x-14
harry, regan and kelan share £450 in the ratio 2 : 5 : 3 . how much money does kelan get?
Answer:
Kelan gets 135 Euros.
Step-by-step explanation:
First of all you add up the ratio getting 10, with 10 you divide it from 450 getting 45. Then you multiply 3 (Kelan's Part) by 45 getting your answer. Tell me if this helped, i'd appreciate knowing.
This question is based on simple mathematics. Therefore, the answer is £135.
Given:
Harry, regan and kelan share £450 in the ratio 2 : 5 : 3.
We have to determined the money would kelan get.
According to questions,
First of all, adding up the ratios.
We get,
2+5+3 = 10
Regan and kelan share £450. So divided £450 by 10, and solve it further.
We get,
[tex]\dfrac{450}{10} = 45[/tex]
Now, multiplying 45 by 3 (Kelan's part).
We get,
[tex]45\times3= 135[/tex]
Therefore, the money that kelan get is £135.
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I NEED FAST HELP!!!!!!!!!!!!!!!!!!!
Answer:
The student is expected to spend 15.4 hours doing homework
Step-by-step explanation:
The scattered plot shows there is a close correlation between the variables. A line of best fit will go through the 'center' of the points. Since we are not required to find an exact line, we'll draw it in red color as shown below
To know the equation of that line, we must take two clear points of it from the graph. We'll pick (28,4) and (4,25)
The equation of a line, given two points (a,b) and (c,d) is
[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]
Using the selected points
[tex]\displaystyle y-4=\frac{25-4}{4-28}(x-28)[/tex]
Simplifying and computing results, the equation is
[tex]\displaystyle y=-\frac{7}{8}x+\frac{57}{2}[/tex]
Using that equation, we can predict how many hours the students will spend doing homework if they spend 15 hours watching TV
[tex]\displaystyle y=-\frac{7}{8}(15)+\frac{57}{2}[/tex]=15.4 hours
So the student is expected to spend 15.4 hours doing homework
Please answer this correctly
Answer: 12:40
Step-by-step explanation:
Answer:
12:40 PM
Step-by-step explanation:
By the time the plane arrives in Minnesota, the time is already 13:40 or 1:40 PM (eastern time). From eastern time to central time, the time decreases by 1 hour. 1:40 PM - 1 hour is 12:40 PM.
Need help with this math problem
z = 37°
Step-by-step explanation:
The exterior angle theorem says that the sum of two internal angles is equal to the exterior angle
In this case the sum of z and z+4 will be equal to z+41
Writing mathematically
[tex]z + z+ 4 = z + 41\\2z+4 = z + 41\\2z -z = 41 -4\\z = 37[/tex]
Hence
z = 37°
Keywords: Angles, Triangles
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What is the slope of the line of the best fit for this scatter plot?
What is the equation of the line of the best fit?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line
m = [tex]\frac{6-7}{4-2}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 8) ⇒ c = 8
y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of line
Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]
[tex]m=\frac{(6-7)}{4-2)}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]
[tex]y-7=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+7[/tex]
[tex]y=\frac{-1}{2}x+8[/tex]
Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function.
5000(1.07)t = B
Answer the questions below:
a) What does the 5000 represent?
b) What is the annual percentage rate?
c) How much money will Sue have after 5 years?
a) 5000 represents the initial amount that Sue invested in a money market account
b) The annual percentage rate is 7%
c) Sue will have $7012.76 after 5 years
Step-by-step explanation:
The exponential growth function is [tex]f(t)=P(1+r)^{t}[/tex] , where
r is the rate of growth in decimalP is the initial amountt is the timeSue invests in a money market account. The balance of the account in dollars after t years can be represented by the function [tex]5000(1.07)^{t}=B[/tex]
∵ The function is [tex]5000(1.07)^{t}=B[/tex]
∵ The form of the exponential growth function is tex]f(t)=P(1+r)^{t}[/tex]
- By comparing the two functions
∴ P = 5000
∵ P is the initial amount
∴ The initial amount is 5000
a) 5000 represents the initial amount that Sue invested in a money market account
∵ [tex](1+r)^{t}=(1.07)^{t}[/tex]
∴ 1 + r = 1.07
- Subtract 1 from both sides
∴ r = 0.07
∵ r is the annual rate in decimal
∵ 0.07 × 100% = 7%
∴ The annual rate is 7%
b) The annual percentage rate is 7%
∵ t = 5
- Substitute the value of t in the function
∴ [tex]5000(1.07)^{5}=B[/tex]
∴ B = 7012.76
c) Sue will have $7012.76 after 5 years
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Original price of a hotel: $240.00 per night.
You are staying four nights because then you get a 25% discount.
State and local taxes and 'resort fee' add up to a 29% surcharge.
How much will you pay for four nights?
Answer:
$ 929
Step-by-step explanation:
Given: Original price of stay in hotel= $240 per night
Discount= 25%
Total taxes and fee = 29%
Now, finding the price of stay for four night.
Using unitary method to solve:
As we know original price of hotel stay per night is $240
∴ Price of four night stay at original price is [tex]240\times 4 = \$ 960[/tex]
Next, 25% discount given on the price of four night stay.
∴ [tex]960 - \frac{25}{100} \times 960 = 960 - 240[/tex]
= [tex]\$ 720[/tex]
∴Price of four night hotel stay after discount is [tex]\$ 720[/tex]
Now, 29% taxes and fees been added to the price.
Price of hotel stay after discount + Taxes paid.
[tex]720 + ( \frac{29}{100} \times 720) = 720 + 209[/tex]
= [tex]\$ 929[/tex]
∴ [tex]\$ 929[/tex] is the price to be paid for four night stay at hotel after discount and taxes.
A line has a slope of 8 and includes the points (1, z) and (2,8). What is the value of z?
The value of z is zero
Step-by-step explanation:
The slope is the steepness of the line.
The formula for slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]
Here
(x1,y1) = (1,z)
(x2,y2) = (2,8)
So,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]
The value of z is zero
Keywords: slope, Line
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Please help quick will give brainliest
Answer:
a(1) = 8, a(n + 1) = a(n) + 5
Checking this:
a(2) = a(1) + 5 = 8 + 5 = 13
a(3) = a(2) + 5 = 13 + 5 = 18
a(4) = a(3) + 5 = 18 + 5 = 23
a(5) = a(4) + 5 = 23 + 5 = 28
the quotient of a number and -7, decreased by 2, is 10
Answer:
The number is -84.
Step-by-step explanation:
-x/7-2=10
-x/7=10+2
-x/7=12
-x=12*7
-x=84
x=-84
A number is chosen at random from the first 100 positive integers. Find the probability that the number is either even or
a perfect square
3/5
11/20
1/20
Answer:
[tex]\frac{11}{20}[/tex]
Step-by-step explanation:
Total no. of possible outcome= 100 (from 1 to 100)
total no. of favorable outcome= 60 (50 even and 5 odd perfect square)
Hence PROBABILITY=[tex]\\\frac{55}{100}[/tex]
=[tex]\frac{11}{20}[/tex]
Lashonda worked for 13 hours each day for 5 days. Then the next day she worked 6 hours. How many hours did Lashonda work in all?
Answer: 71 hours
Step-by-step explanation:
Write the three digit number for 500+30+8
please solve much appreciated
Answer:
Two equivalent fractions with whole numbers may be 180/150, or 6/5The height of the tree is 39.6 feet.Explanation:
The diagram provides the proportion of the heights to the shadows:
[tex]\frac{x}{33}=\frac{1.8}{1.5}[/tex]From that you are asked (i) to simplify the fraction of the right side to one with whole numbers.
You can do that in two steps by multiplying both numerator and denominator by 10:
[tex]\frac{1.8\times 10}{1.5\times 10}=\frac{180}{150}[/tex]You can simplify that fraction if you divide by the greatest common factor of 180 and 150, which is 30:
[tex]\frac{180/30}{150/30}=\frac{6}{5}[/tex]The second part (ii) asks to find the height of the tree, that is x. To solve for x you can multiply both sides by the denominator of the fraction on the left and then simplify:
[tex]\frac{x}{33}=\frac{6}{5}\\ \\ x=\frac{6\times 33}{5}\\ \\ x=\frac{198}{5}=39.6[/tex]
Thus, the height of the three is 39.6 feet.
Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.
Answer:
The proof is given below.
Step-by-step explanation:
Given: ( the correct question and ans is as follow )
sin (x + y) = 3sin ( x - y)
To Prove
tan x = 2 tan y
Proof:
[tex]\sin (x+y) = 3\sin (x-y)[/tex]
Using the identities
[tex]\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\[/tex]
we get
[tex]\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y[/tex]
Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get
[tex]3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}[/tex]
The Bridal Shop bought a dress from a supplier for $105 wholesale and applied a 65% markup to the price. If a 7.5% sales tax were added after a 20% discount was used, what would be the total cost to purchase the dress? A $146.20 B $149.00 C $158.48 D $160.17
Answer:
The correct answer is 149.00.
Step-by-step explanation:
Part = Percent • Whole
Adding a 65% markup to the original price of 105 is simply multiplying the price by the decimal form of the markup, then adding that to the original price. Next, you would find 20% of your sum by multiplying the sum by 0.20. Then you would find 7.5% of that and add this to the price.
Solve:
105 • 0.65 = 68.25 Find 65% of 105
105 + 68.25 = 173.25 Add the markup to the price
173.25 • 0.20 = 34.65 Find the discount of the new price
173.25 - 34.65 = 138.60 Subtract discount from price
138.60 • 0.075 = 10.395 Find sales tax of new price (Or round to 10.40)
138.60 + 10.395 = 148.995 Add sales tax to new price (Or 149)
Because money only goes to the hundredths place, we can either start rounding to that place in the second to last step - rounding 10.395 to 10.40 - or we can round our answer - 148.995 rounds to 149. Either way, we will still get an answer of $149.00.
Hope this helps.
♥A.W.E.S.W.A.N.♥
Answer:
B $149.00
Step-by-step explanation:
105 * 1.65 = 173.25 (100%+ 65%) Price with the markup
173.25 *0.80 138.60 (Price after 20% discount .The price will be the 80%)
138.60 * 1.075 = 148.995 (price with 7.5 sales tax.)
Concession stand made a profit of $135 on Saturday and lost $12 on Sunday how much profit did the concession stand make
Answer:
123
Step-by-step explanation:
135 - 12 = 123
The concession stand made $123
What is profit and loss?Profit and loss are the terms used to identify whether a deal is profitable or not. We use these terms very often in our daily lives. If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit. If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss.
When, in a transaction, the selling price is greater than the cost price, it means we earn a profit.
When, in a transaction, the cost price is greater than the selling price, it means we incur a loss.
Given:
profit on saturday = $135
loss on sunday = $12
So,
the total profit concession stand made= $135 + (-$12)
= $135 - $12
= $123
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What is the equation of the line that is perpendicular to and
has the same y-intercept as the given line?
y=x+1
y= x+5
y = 5x + 1
y= 5x + 5
I don’t know how to fine the square root
Answer:
Look the square root up on the internet.
Step-by-step explanation:
Angelica was at target and saw that a pair of slippers was $15. She also noticed that there is a 30% off sale on all slippers. What is the cost (sale price) of the slippers after the discount?
The cost of slippers is $10.5 after discount.
Step-by-step explanation:
Given,
Price of slippers = $15
Sale = 30%
Amount of discount = 30% of price of slippers
[tex]Amount\ of\ discount=\frac{30}{100}*15\\Amount\ of\ discount=\frac{450}{100}\\Amount\ of\ discount=\$4.5[/tex]
Sale price = Price of slippers - amount of discount
[tex]Sale\ price=15-4.5\\Sale\ price=\$10.5[/tex]
The cost of slippers is $10.5 after discount.
Keywords: percentage, subtraction
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To find the cost of the slippers after the 30% discount, multiply the original price by 30% and subtract the discount from the original price. The cost of the slippers after the discount is $10.50.
Explanation:To find the cost of the slippers after the 30% discount, first calculate the amount of the discount by multiplying the original price by 30% (or 0.30).
Discount = $15 × 0.30 = $4.50
Next, subtract the discount from the original price to find the sale price:
Sale Price = $15 - $4.50 = $10.50
Therefore, the cost of the slippers after the discount is $10.50.
Which of the following is approximately equal to the product of the multiplication problem below?
18/4 × 20/17
A.
10
B.
7
C.
5
D.
4
Answer:
5
Step-by-step explanation:
We have: [tex]$ \frac{18}{4} \times \frac{20}{7} $[/tex]
Simplifying we get: [tex]$ 18 \times \frac{5}{7} $[/tex]
⇒ [tex]$ \frac{90}{17} $[/tex]
This is equal to 5.2 ≅ 5.
So, Option C - 5 is the answer.