Cost of bench = x
Cost of garden table = x - 50
x - 50 + x = 700
2x - 50 = 700
2x = 750
x = 325
Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table.
A table listing the first few steps in deriving the quadratic formula
In which step did Yvonne first make an error?
The step in which Yvonne first makes an error while solving the quadratic equation by completing the square in step 1.
What is a quadratic equation?A quadratic equation is an equation in which the highest power of the variable is two.
Yvonne is solving the quadratic equation, which is,
6x² +24x +7 =0
He is solving the above equation by completing the square.
The first step to solving this quadratic equation by completing the square is, Take the constant value 7 at the opposite side of the equation as,
6x² +24x = -7
Here, the number seven was a positive number, which we have changed to negative because this number brings the other side of the equation.
In the image attached below, the first step of the Yvonne while solving the equation by completing the square is,
6x² +24x = 7
Here, Yvonne does not change the sign of the number 7 while taking it to another side of the equation.
Hence, the step in which Yvonne first makes an error while solving the quadratic equation by completing the square is step 1.
The table is attached with the answer below
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Rob Herndon, an accountant with Southwest Airlines, wants to retire 50% of
Southwest Airlines bonds by 2028. Calculate the payment Rob needs to make
at the end of each year at 5% compounded annually to reach his goal of paying
off $430,000 in 10 years.
For Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.
What is a future value?A future value refers to a value on a future date based on an assumed growth rate of interest over some period.
The future value can be determined using the FV formula or table.
We can also compute the future value using an online finance calculator as follows:
Data and Calculations:N (# of periods) = 10 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $430,000
Results:
PMT = $34,186.97
Sum of all periodic payments = $341,869.70
Total Interest= $88,130.30
Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.
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Which of these graphs represents a function?
Answer:
Should be W
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.
Hope this helps!!
Question
The temperature in Scranton was -12°F at 10 am. By 1 pm the temperature was 1 °F. What was the difference between
the 10 am and 1 pm temperatures?
Provide your answer below:
degrees Fahrenheit
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Answer:
Step-by-step explanation:
difference=1-(-12)=13°F
The area of rectangle is 2356 square meters. The length is 38 meters. What is the width?
Answer:
62 meters
Step-by-step explanation:
So the area of a rectangle can be defined as: [tex]A = wl[/tex] where A=area, w=width, l=length. So if we plug in the known values we can solve for the unknown, which in this case is the width. So let's plug in the known values:
[tex]2356 m^2 = 38 m * w[/tex]
Divide both sides by 38 m
[tex]62 m = w[/tex]
Rebecca earned $115 in simple interest for 8 months at an annual interest rate of 3%. How much money did she start with in her account?
The amount of money she started with is $5750
How to determine the amount she start with?The given parameters are:
Interest = $115
Rate = 3%
Time = 8 months
The amount she start with (P) is calculated using:
P = I/(RT/12)
This gives
P = 115/(3% * 8/12)
Evaluate the product
P = 115/(0.02)
Divide
P = 5750
Hence, the amount of money she started with is $5750
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What is the volume of the composite figure?
The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid = 4,050 ft³.
How to Find the Volume of a Composite Figure?The composite figure shown is composed of a square pyramid and a rectangular prism. To find the volume of the composite figure, find the volume of the square pyramid and the volume of the rectangular prims respectively.
Volume of the square pyramid = 1/3(B)(h), where:
Base area (B) = (l)(w) = (15)(15)
Base area (B) = (l)(w) = 225 ft³.
h = 9 ft
Volume of the square pyramid = 1/3(225)(9)
Volume of the square pyramid = 675 ft³.
Volume of the rectangular prism = (length)(width)(height)
Volume of the rectangular prism = (15)(15)(15)
Volume of the rectangular prism = 3,375 ft³.
The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid
The Volume of the composite figure = 3,375 + 675
The Volume of the composite figure = 4,050 ft³.
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pls help asap, find the height of the cylinder and round to the nearest tenth
Answer:
h = 2.4
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
271.4 = pi ( 6)^2 *h
271.4 = 36* pi* h
Letting 3.14 = pi
271.4 = 113.04 h
Divide each side by 113.04
271.4 /113.04 = 113.04h/113.04
2.424805379 = h
Rounding to the nearest tenth
2.4 = h
OR if we use the pi button
271.4 = 36 * pi *h
Divide each side by 36 pi
271.4/36pi = h
h=2.3997
Rounding to the nearest tenth
h =2.4
To be competitive for admission to four-year universities (UCF, UF, FSU, FAU, FIU, UCF, USF, etc.) what courses should you try to have each year of high school no matter the intended college major or current status of high school graduation requirements?
Answer:
Ask your guidance counselor or a college admissions counselor
Step-by-step explanation:
Identify the underline place 75.733
The underlined place is tenths.
Rounding off o the tenth place = 75.7.
What is the Nearest Tenth?The tenths of a number is the first digit after a decimal point. To round off a number to the nearest tenth, if the number next to the tenth digit is not up to 5, let it be assumed as 0.
The underlined place is the tenths. Rounding 75.733 to the nearest tenth would give us: 75.7. This is because the next digit close to 7 is 3. It is not up to 5.
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What is the primary importance of benefits 1and 2 as discussed in "the pros and cons of patents"?
Benefits 1 and 2 in the 'Pros and Cons of Patents' significantly throws light on the opportunity of owning a market, and securing funds respectively.
What is the primary importance of benefits 1 and 2?
Benefit 1 of 'Pros and Cons of Patents' is about the possibility of owning a market.
Since the US government will protect your creation for 20 years, you will essentially control the market for that product during that time. For instance, Eli Lilly invented Prozac in 1987 and had the monopoly for 14 years until 2001.
Benefit 2 of 'Pros and Cons of Patents' concerns around attracting and accumulating the sources of funding and investors.
If an invention is not protected, no one will put their money at risk The only way an invention can ensure a return is through patent protection since investors don't care about good intentions; they only care about money.
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Answer:
According to the article, patents allow inventors to “own the market” for their ideas, meaning the US government has deemed the idea original and protected the idea from being reproduced by others for 20 years. This makes the idea more marketable, which allows the inventor to attract investors. These benefits support the idea that patents promote invention.
Step-by-step explanation: edmentum sample answer
Ali rented a truck for one day. There was a base fee of , and there was an additional charge of cents for each mile driven. Ali had to pay when he returned the truck. For how many miles did he drive the truck?
Using a linear function, it is found that he drove the truck for 240 miles.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Researching the problem on the internet, there was a base fee of $18.99, which is the y-intercept, and there was an additional charge of 75 cents for each mile driven, which is the slope, hence the cost function for m miles driven is given by:
C(m) = 18.99 + 0.75m.
He paid $199, hence the number of miles he drove is found as follows:
C(m) = 18.99 + 0.75m.
199 = 18.99 + 0.75m
m = (199 - 18.99)/0.75
m = 240 miles.
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find the volume pls
Answer:
i think it is 340
Step-by-step explanation:
Reciprocal of 3 4/7 that would help
Answer:
fraction form: 7/25
Decimal form: 0.28
Step-by-step explanation:
Find the equations of the following lines.
a) Parallel to 2 + − 3 = 0 and passing through ( −4, 5)
b) Perpendicular to 2 = + 5 and passing through ( −1, 4)
a washer and dryer cost 750 combined the washer cost $50 more than the dryer what is the cost of the dryer?
Answer:
350$ for dryer
Step-by-step explanation:
x = cost of dryer
x + 50 = cost of washer
750 = x + (x + 50)
750 = 2x + 50
700 = 2x
350 = x
Please help! I will give you lots of points!!!
Directions: construct the bisector of the following figures.
Note: please draw them out each on a piece of paper or laptop. Thank you!
A bisector is the required line that divides a given line or an angle into two equal parts. The required construction of the bisectors is shown in the attachment to this answer.
Bisection is the process in which a given line or angle is divided into two equal parts by constructing the required bisector. Thus the steps to bisect the given arcs are stated below:
For figure 1:
Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.Repeat the same process using point B as the center and the same radius as that used in A.Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector.For figure 2:
Open the compass to any radius, using point M as the center draw arcs on the reverse side of the given arc MN.Repeat the same process using point N as the center and the same radius as that used in M.Join the intersections of the arcs on the reverse sides of arc MN by a line. Thus the required bisector.For figure 3:
Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.Repeat the same process using point B as the center and the same radius as that used in A.Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector. The point on arc AB through which the bisector intersects is the required point S. The mid point of arc AB.For figure 4:
Open the compass to any radius, using point A as the center draw arcs on the reverse side of the given arc AB.Repeat the same process using point B as the center and the same radius as that used in A.Join the intersections of the arcs on the reverse sides of arc AB by a line. Thus the required bisector. Repeat the same procedures using points BC.NB: The point of intersection of the bisectors in relation to arc AC is the radius of the given arc.
The required constructions are attached to this answer.
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Use the data tab of the graphing tool to display the data from Luther’s table in a scatter plot, with x representing the number of pitches thrown and y representing the average speed of the pitches. Select the relationship tab to add the best fit linear function to the graph.
What are the equation of the line of best fit and the absolute value of the correlation coefficient?
The equation of the line of best fit is y = -4.75X + 88.6 and the absolute value of the correlation coefficient is 0.906
The equation of the line of best fitThe data values of the question are as follows:
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
To determine the equation of the line of best fit, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 28Sum of Y = 487Mean X = 4Mean Y = 69.5714Sum of squares (SSX) = 28Sum of products (SP) = -133The value of R is: -0.906.The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -133/28 = -4.75
a = MY - bMX = 69.57 - (-4.75*4) = 88.57143
So, we have:
y = -4.75X + 88.57143
Approximate
y = -4.75X + 88.6
Hence, the equation of the line of best fit is y = -4.75X + 88.6
The absolute value of the correlation coefficientIn (a), we have:
The value of R is: -0.906.
This represents the correlation coefficient.
The absolute value is
|R| = 0.906.
Hence, the absolute value of the correlation coefficient is 0.906
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there are 5 trur or fales questions on an exam. how many different ways can a student do the exam if it is forbidden to leave the answer blank
Answer:
32 different ways.
Step-by-step explanation:
There are 2 combinations for each question, and there are 5 questions. Therefore there are [tex]2\times2\times2\times2\times2[/tex] = 32 different ways the student could do the exam.
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Question 3(Multiple Choice Worth 1 points)
(06.05 LC)
Given the following functions f(x) and g(x), solve f[g(7)].
f(x) = 4x + 21
g(x)=2x+2
16
49
85
784
Answer:
C.) 85
Explanation:
Given following:
f(x) = 4x + 21g(x) = 2x + 2While solving these function questions, go from right to left.
Steps:
f[g(7)]f[2(7) + 2]f[16]4(16) + 2185Find the value of z. You must show work to receive full credit.
The value of z from the cyclic quadrilateral as described is; 173/22.
What is the value of z?Since the quadrilateral TUVW is a cyclic quadrilateral, it follows that the opposite angles of the quadrilateral are supplementary and hence, amount to 180.
On this note, 14z -7 +8z = 360
22z -7 = 180
22z = 180 -7
z = 173/22
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Solve the system of equations
1/2x+6y=12
y=x+15
Please I need help. Also if you know the answer could you help me learn how to solve it?
Answer:
x=-12,y=3
Step-by-step explanation:
1/2x+6y=12
y=x+15
since y=x+15
substitute y in first equation, we have
1/2x+6(x+15)=12
open the bracket
1/2x+6x+90=12
1/2x+6x=12-90
x/2+6x= -78
13x/2=-78
13x=2×-78
x=-12
Now x=-12, put x=-12 in the second equation, we have
y=x+15
y=-12+15
y=3
hope it helps
Answer:
x=-8, y=2
Step-by-step explanation:
if 1/2x+6y=12 then 1/2x+y=2 and x+y=1 and y=1-x..if y=1-x then 1-x=x=15 and 2x=16 so x=8 if x=8 then 1/2(8) +6y=12 or 4=6y=12.. then 2y=4 and y=2
9
Given log 103=0.4771 and log 107 = 0.8451, find log 10
9
log 10 49
(Round to four decimal places as needed.)
without using a calculator.
Step-by-step explanation:
rules of the logarithm :
e.g.
log(a×b) = log(a) + log(b)
log10(9) = log10(3×3) = log10(3) + log10(3) =
= 0.4771 + 0.4771 = 0.9542
log10(49) = log10(7×7) = log10(7) + log10(7) =
= 0.8451 + 0.8451 = 1.6902
calculate exact value of 4 1/5-(1 1/9 ×3)
Answer:
Exact form - 13/15
Decimal Form - 0.86
Step-by-step explanation:
Convert the mixed numbers to improper fractions, then find the LCD and combine
For every $8 in their budget, the Parks spend $3 on food. If their weekly
budget is $704, how much do they spend on food each week?
A. $88
B. $192
C. $235
D. $264
Answer:
3÷8
=37.5%
$704x37.5%
=$264
ANSWER D
dexamethasone 4 mg/1 ml is available. the MD orders 6000 mcg. how much will the nurse give? (Round to the tenth)
Answer:
1.5 mL
Step-by-step explanation:
The abbreviation mcg stands for "microgram," or 10^-6 grams. The abbreviation mg stands for "milligram," or 10^-3 grams. The relationship between these is ...
1 mg = 1000 mcg
DoseThe order for 6000 mcg is an order for 6(1000 mcg) = 6(1 mg) = 6 mg. At 4 mg/mL, the quantity of dexamethasone required is ...
(6 mg)/(4 mg/mL) = (6/4) mL = 1.5 mL
The nurse will give 1.5 milliliters of dexamethasone.
rewrite the following expression as a single logarithm 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).
What is the rewritten form of the expression?The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;
2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)
= log {(x+3)²(x-2)^5}/(x-7)³(x²)
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11a.) From the early 1980's through 2012, the number of adults enrolled in Bachelor Degree programs
has steadily increased. In 1983, 10.8 million adults were in enrolled in a Bachelor Degree program while
in 2012, 20.6 million adults were enrolled. Write an approximate linear equation that would model
these data where t = time in years after 1983 and B is the number of adults in millions in the US in a
Bachelor Degree program. (Source: http://nces.ed.gov/)
(a) B = 0.338t+20.6
(b) B = -0.338t+20.6
(c) B = 0.338t - 10.8 (d) B = 0.338t+10.
it's is a if you didn't know
An approximate linear equation that would model these data is:
(a) B = 0.338t+20.6
How to write the linear equation?The general form of a linear equation in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
We are told that In 1983, 10.8 million adults were in enrolled in a Bachelor Degree program while in 2012, 20.6 million adults were enrolled.
Thus:
Rate of increase = (20.6 - 10.8)/(2012 - 1983)
Rate of increase = 9.8/29 = 0.338
Thus, the equation is:
B = 0.338t+20.6
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Common denominator for 16/25 and 13/20
Answer: LCD = 100
Step-by-step explanation:
16/25 = 64/100
13/20 = 65/100
Devon had 40 video games. He sold 2/5 of them at $500 each.
(a) How many video games does he have left?
(b) of the remaining video games, he sold 3/8 of them for $ 7200 altogether and kept the rest for himself
(I) How many video games did Devon keep for himself?
(ii) what was the selling price of a video game?
(c) Calculate the total amount of the money he received from the sale of the video games.
Using proportions, it is found that:
a) He has 24 videogames left.
b - I) He kept 15 videogames for himself.
b - II) The selling price of a videogame was of $800.
c) He received $15,200 from the sale of the videogames.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Item a:
He has 3/5 of 40 videogames left, hence:
3/5 x 40 = 3 x 8 = 24.
He has 24 videogames left.
Item b:
He kept 5/8 of the 24 videogames, hence:
5/8 x 24 = 5 x 3 = 15.
He kept 15 videogames for himself.
He also sold 9 videogames for $7,200, hence the selling price of one of them is:
7200/9 = $800.
Item c:
Earned $7,200 plus 500 for 16, hence:
T = 7200 + 500 x 16 = $15,200.
He received $15,200 from the sale of the videogames.
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