Step-by-step explanation:
when means of more than two groups are to be compared, ANOVA is perferred
Rewrite in simplest terms: -7(5v-10)-7v
Answer: -42v + 70
Step-by-step explanation: You’d multiply -7 with the figures in the brackets, then you’d group like terms then subtract -7v from -35v.
1. -35v + 70 - 7v
Negative multiplied by negative is a positive
2. -35v - 7v + 70
Group like terms
3. -42v +70
Subtract
Hope this was helpful
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{-7(5v - 10) -7v}[/tex]
[tex]\huge\textbf{Solving for your equation:}[/tex]
[tex]\mathbf{-7(5v - 10) -7v}[/tex]
[tex]\huge\textbf{Distribute -7 within the parentheses:}[/tex]
[tex]\mathbf{= -7(5x) -7(-10) - 7v}[/tex]
[tex]\mathbf{= -35v + 70 - 7v}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{= (-35v - 7v) + (70)}[/tex]
[tex]\mathbf{= -35v - 7v + 70}[/tex]
[tex]\mathbf{= -42v + 70}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{-42v + 7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Assume that when human resource managers are randomly selected, 41% say job applicants should follow up within two weeks. If 6 human resource managers are randomly selected, find the probability that at lease 2 of them say job applicants should follow up within 2 weeks
Answer:
the probability= 2/6=1/3
Three packages weigh
1/1/12
pounds, 43
pounds. What is the average weight, in pounds, of the packages?
A. 2.14
B. 2.85
C. 4.75
D. 8.55
Answer:
B. 2.85
Step-by-step explanation:
to find the average of multiple numbers, we add them together and divide by the number of values we combined
for example: the average of 1, 2, and 3:
1 + 2 + 3 = 6
6 / 3 (because there were 3 numbers) = 2
so, this average would be 2.
Let's add the weights (I have changed these into a denominator of 20, so that they can be easily added. Let me know if you need clarification on how I did so)
1 1/2 pounds, 4 3/4 pounds, 2 3/10pounds
1 1/2 = 1 10/20
4 3/4 = 4 15/20
2 3/10 = 2 6/20
1 10/20 + 4 15/20 + 2 6/20 = 7 31/20
7 31/20 = 8 11/20
8 11/20 = 8.55
8.55 / 3 = 2.85
so, the average weight of these packages is 2.85 [pounds]
hope this helps! ^u^
What is the solution to this equation?
-1/5(x+1 1/4)=-2 1/2
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{1}{5}\left(x+1\frac{3}{4}\right)=-2\frac{1}{2} \end{gathered}$}[/tex]
Multiply both sides of the equation by 20, the lowest common denominator of 5,4,2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{4+3}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Add 4 and 3 to get 7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4\left(x+\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Use the distributive property to multiply −4 times x 4/7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-4\times\left(\frac{7}{4}\right)=-10(2\times2+1) } \end{gathered}$}[/tex]
Multiply −4 by 4/7.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(2\times2+1) \ \ \to \ \ [Multiply \ 2\times2] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10(4+1) \ \ \to \ \ [Add] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=10\times5 \ \ \to \ \ [Multiply] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x-7=-50 } \end{gathered}$}[/tex]
Add 7 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-50+7 \ \ \to \ \ [Add] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-4x=-43 } \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{-43}{-4} } \end{gathered}$}[/tex]
The fraction [tex]\bf{\frac{-43}{-4}}[/tex] can be simplified to [tex]\bf{\frac{43}{4}}[/tex] by removing the negative sign from the numerator and denominator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=\frac{43}{4} } \end{gathered}$}[/tex]
simplify
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{x=10\frac{3}{4} \ \ \to \ \ \ Answer } \end{gathered}$}[/tex]
{ Pisces04 }Answer:
[tex]\sf c)\ x=10\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sf -\dfrac{1}{5}\left(x+1\dfrac{3}{4}\right)=-2\dfrac{1}{2}[/tex]
Step 1: Convert the mixed numbers into improper fractions.
[tex]\sf -\dfrac{1}{5}\left(x+\dfrac{4\times1+3}{4}\right)=-\dfrac{2\times2+1}{2}\implies -\dfrac{1}{5}\left(x+\dfrac{7}{4}\right)=-\dfrac{5}{2}[/tex]
Step 2: Distribute -⅕ through the parentheses.
[tex]\sf-\dfrac{1}{5}(x)+-\dfrac{1}{5}\left(\dfrac{7}{4}\right)=-\dfrac{5}{2}\\\\\implies -\dfrac{1}{5}x-\dfrac{7}{20}=-\dfrac{5}{2}[/tex]
Step 3: Rewrite the equation with a common denominator of 20.
[tex]\sf -\dfrac{1\times4}{5\times4}x-\dfrac{7}{20}=-\dfrac{5\times10}{2\times10}\\\\\implies -\dfrac{4}{20}x-\dfrac{7}{20}=-\dfrac{50}{20}[/tex]
Step 4: Multiply both sides by 20.
[tex]\sf 20\left(-\dfrac{4}{20}x\right)-20\left(\dfrac{7}{20}\right)=20\left(-\dfrac{50}{20}\right)\\\\\implies -4x-7=-50[/tex]
Step 5: Add 7 to both sides.
[tex]\sf -4x-7+7=-50+7\\\\\implies -4x=-43[/tex]
Step 6: Divide both sides by -4.
[tex]\sf \dfrac{-4x}{-4}=\dfrac{-43}{-4}\\\\\implies x=\dfrac{43}{4}[/tex]
Step 7: Convert the answer back into a mixed number.
[tex]\sf x=\dfrac{43}{4}\implies x=\dfrac{40+3}{4}\implies x=10\dfrac{3}{4}[/tex]
In a class of 95 students, 48 play basketball, 35 play football and 32 play neither basketball or football. What percentage of the class plays only football?
Need answers ASAP thank you so much
The number of people who plays only footfall will be 15. The percentage of the class plays only football will be 15.79%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
In a class of 95 students, 48 play basketball, 35 play football and 32 play neither basketball nor football.
Let x be the number of student who plays basketball as well as football.
48 – x + x + 35 – x + 32 = 95
115 – x = 95
x = 20
The number of people who plays only footfall will be
⇒ 35 – 20
⇒ 15
Then the percentage of the class plays only football will be 15.79%.
⇒ 15/95 × 100
⇒ 15.79%
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Two equations are given below:
m + 5n = 20
m = n − 4
What is the solution to the set of equations in the form (m, n)?
(3, 7)
(0, 4)
(5, 1)
(2, 6)
Answer:
(0,4)
Step-by-step explanation:
Because the problem gives you the value of what m would equal in terms of n you would substitute n - 4 for m in the equation above, resulting in:
n - 4 + 5n = 20
6n - 4 = 20
6n = 24
n = 4
Now that you know n = 4, you already can see that the answer would be (0,4), however to check you can substitute 4 for n into the second equation.
m = 4 - 4
m = 0
Because this results in m = 0, that tells you that (0,4) is the right answer.
Answer:
(0, 4)
Step-by-step explanation:
So you can solve the equation by substitution. The solution of a systems of equations, is when they both intersect, or when the (x, y) values are exactly equal, which is why I can substitute the m of the second equation into the first equation, because I'm looking for when they're equal, and that is when m is going to be equal in both equations, as well as the n value.
original equation:
m + 5n = 20
substitute n-4 as m in the equation
(n-4) + 5n = 20
simplify:
6n-4 = 20
add 4 to both equations
6n = 24
divide both sides by 6
n = 4
Now to find m, simply substitute 4 as n in either equation:
Original equation:
m = n - 4
substitute 4 as n
m = 4-4
m=0
so m=0, and n=4, so the solution in the form (m, n) = (0, 4)
How many hours would it take Natalie if she worked alone?
If A = (10, 4) and B = (2, 19) what is the length of AB
Hello,
Answer:
The length of AB is 17
Step-by-step explanation:
[tex]AB = \sqrt{(x_{B} -x_{A} ) {}^{2} + (y_{B} -y_{A} ) {}^{2} } [/tex]
[tex]AB = \sqrt{(2 - 10) { }^{2} + (19 - 4) {}^{2} } [/tex]
[tex]AB = \sqrt{( - 8) {}^{2} + (15) {}^{2} } [/tex]
[tex]AB = \sqrt{64 + 225} [/tex]
[tex]AB = \sqrt{289} [/tex]
[tex]\boxed{AB = 17}[/tex]
Pay as you go Pay only $6 each time you work out Regular Deal Pay $50 a month and $2 each time you work out All-in-one price! Pay just $100 per month for unlimited use of our great facilities 1. Carlo thinks he will go to the gym about 20 times a month. Which of these options is the least expensive for Carlo? Show how you determined your answer.
Answer:
Regular Deal
Step-by-step explanation:
Pay as you go
Pay only $6 each time you work out
Regular Deal
Pay $50 a month and $2 each time you work out
All-in-one price!
Pay just $100 per month for unlimited use of our great facilities
1. Carlo thinks he will go to the gym about 20 times a month. Which of these options is the least expensive for Carlo? Show how you determined your answer.
For 20 visits to the gym:
Pay as you go:
20 × $6 = $120
Regular Deal
$50 + 20 × $2 = $50 + $40 = $90
All-in-one price!
$100
Answer:
The best deal is for 20 visits per month is: Regular Deal
Same directions as question #1
Sn = ( -1 )n + 1
The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.
How to depict the information?The formula for finding the nth term in an arithmetic sequence given as:
= a + (n - 1)d
Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:
= (-1)n + 1
= (-1)5 + 1
= (-1)6
= -6
Here is the complete question:
Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.
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Simplify the following expression.
‐3 + 7(a – 3b – 1) – 4(10 – a + 2b)
Answer:
11a − 29b − 50
Step-by-step explanation:
Subtract 7 from − 3
7a − 21b − 10 − 40 + 4a − 8b
Add 7a and 4a
11a - 21b - 10 - 40 - 8b
Subtract 8b from -21b
11a - 29b - 10 - 40
Subtract 40 from -10
11a - 29b - 50
Answer:
11a - 29b - 50
Explanation:
⇒ ‐3 + 7(a – 3b – 1) – 4(10 – a + 2b)
distribute inside parenthesis
⇒ -3 + 7a - 21b - 7 - 40 + 4a - 8b
collect like terms
⇒ 7a + 4a - 21b - 8b - 3 - 7 - 40
add or subtract like terms
⇒ 11a - 29b - 50
Find n in this equations: 9P(n,5)=P(n,3).P(9,3)
[tex]\begin{aligned}&9P(n,5)=P(n,3)\cdot P(9,3)\\&9\cdot\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot\dfrac{9!}{6!}\\&\dfrac{n!}{(n-5)!}=\dfrac{n!}{(n-3)!}\cdot7\cdot8\\&\dfrac{1}{(n-5)!}=\dfrac{56}{(n-3)!}\\&(n-4)(n-3)=56\\&n^2-3n-4n+12-56=0\\&n^2-7n-44=0\\&n^2-11n+4n-44=0\\&n(n-11)+4(n-11)=0\\&(n+4)(n-11)=0\\&n=-4 \vee n=11\end[/tex]
[tex]n[/tex] can't be negative, therefore [tex]n=11[/tex]
Answer:
Step-by-step explanation:
9P(n,5)=P(n,3).P(9,3)
9n(n-1)(n-2)(n-3)(n-4)=n(n-1)(n-2)×9×8×7
(n-3)(n-4)=8×7
(n²-4n-3n+12)=56
(n²-7n+12)=56
n²-7n+12-56=0
n²-7n-44=0
n²-11n+4n-44=0
n(n-11)+4(n-11)=0
(n-11)(n+4)=0
n=11,-4
n=-4(rejected as n is a natural number.)
Hence n=11
Insert a rational number and an irrational number between √2 and √3
Answer:
1.5
π/2
Step-by-step explanation:
√2 ≈ 1.41
√3 ≈ 1.73
1.5 is a rational number (15/10) that is in between.
π/2 ≈ 1.57 is an irrational number that is in between.
If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q —> p?
O the original conditional statement
O the inverse of the original conditional statement
O the converse of the original conditional statement
O the contrapositive of the original conditional statement
Jennifer works 3 1/2 hours each morning at the clinic. How many routine physicals could she complete in one morning? (Routine physical=1/3hr)
A. 4
B.9
C. 10
D. 11
Answer:
C
Step-by-step explanation:
Total Work hours = 3 1/2 hours
One routine physical routine requires: 1/3 hours.
Number of routines can be completed = Total work hours / Time required for one physical routine
= [tex]3\frac{1}{2} / \frac{1}{3}\\=\frac{7}{2} /\frac{1}{3} \\=\frac{7}{2} *3\\[/tex]
= 10.5 routines.
In this case, we are unable to complete half a routine (0.5), so we will choose the highest possible whole number, in this case, its 10 routines.
A ladder is 4 feet and 1 inch tall. How tall is it in inches
Answer:
[tex]\huge\boxed{\sf 49\ inches}[/tex]
Step-by-step explanation:
Length of the ladder = 4 feet 1 inch
We know that,
1 feet = 12 inchesSo,
4 feets = 12 × 4 inches
4 feets = 48 inches
So,
Length of the ladder:= 48 inches + 1 inch
= 49 inches
[tex]\rule[225]{225}{2}[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
If a ladder is 4 feet and 1 inch tall, how tall is it in inches?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\boxed{\begin{minipage}{7cm} \\ The length of this ladder is 4 feet and 1 inch.\\The measure of one foot is 12 inches. \end{minipage}}[/tex]
Thus,
[tex]\fbox{The measure of 4 feet is 12*4=48 inches.}[/tex]
We add 1 inch more.
[tex]\bf{48+1=49\;inches}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{The\;ladder\;is\;49\;inches\;long.}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
In general, in y-asin[k(x-d)]+c the equation of the axis of the curve is determined by
the value of
a) d
b) k
c) c
d) a
Answer:
c
Step-by-step explanation:
This is a fact. (See attached image)
I need help please. Trying to get my HS diploma. I did not graduate :(
Which of the following functions are continuous?
Answer:
B. I, II, and III
Step-by-step explanation:
A function is continuous if it is defined everywhere and its graph can be drawn without lifting the pencil. That is, at every point, the limit from the left and the limit from the right must equal each other and the function definition at the point.
Looking at choicesAll polynomial functions with real coefficients are continuous everywhere. (Choices I and II.) They have no discontinuities.
Rational functions will have a discontinuity wherever the denominator is zero. Here, the one rational function has a denominator of x^2+1, which is always positive (never zero). The given rational function is continuous everywhere (Choice III.)
All of the functions in the problem statement are continuous: I, II, and III.
if two men dig a well in 12 days how many days will it take 8 men to dig the same well if they work at the same rate
Answer:
3 days
Step-by-step explanation:
Time taken by 2 men to dig the well = 12 days
Therefore, Time taken by 1 man to dig the well = 2 * 12 = 24 days
So, Time taken by 8 men to dig the well = 2 * 12/8 days = 3 days
Answer:3 days
Step-by-step explanation: 2 people dig well=12 days right
1 person equal 2x12=24 days
8 people 2x12/8=3
hs and Equations: Practice
Question 2 of 5
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Determine the equation for the quadratic relationship graphed below.
у
-2
6
2
4
-6
✓
Submit
X+
X
Reset
Answer:
Retype your question. That question made me nauseous
What is the sequence equation 8, 17, 35, 71, 143
Answer:
Step-by-step explanation:
What you do is multiply the previous number and add 1 to get the next answer.
Equation An = 2(An-1)+1
n = The Term
Please solve
Will mark Brainly
Answer:
x = 23
Step-by-step explanation:
5x - 9 and 2x + 60 are corresponding angles and are congruent , so
5x - 9 = 2x + 60 ( subtract 2x from both sides )
3x - 9 = 60 ( add 9 to both sides )
3x = 69 ( divide both sides by 3 )
x = 23
whats the length of the flagpole in yards?
The length of the flagpole is x - 5 yards
How to determine the length of the flagpole?The area of the flagpole is given as:
Area = x^2 - 10x + 25
Expand the expression
Area = x^2 - 5x -5x + 25
Factorize the expression
Area = (x - 5)(x - 5)
Express as squares
Area =(x - 5)^2
The area of a square is
Area = Length^2
So, we have:
Length = x - 5
Hence, the length of the flagpole is x - 5 yards
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A bulldozer does 4,500 j of work to push a mound of soil to the top of a ramp that is 15 m high. the ramp is at an angle of 35° to the ground. how much force did the bulldozer apply to the mound of soil? round your answer to two significant figures. 300 n 370 n 520 n
The bulldozer will apply 520n of force to the mound of soil if the top of a ramp is 15 m high and ramp is at an angle of 35° to the ground.
Given Work = 4500 j , Height of top of a ramp is 15m , the ramp is at an angle 35° to the ground.
Work is the . product of the force vector and displacement vector.
[tex]W=F . x[/tex]
It is the multiplication of magnitudes of the vectors and the vectors and the cosine of the angle between them.
W=F * cos ∅
Displacement of the soil is 15 m . The force is parallel to the ramp. So the angle between the vectors is 90°-35°=55°.
Plugging in the values and solving for F:4500 J =F(15 m)( cos55 °)
F=523N
rounded to the significant figures the force is 520 n.
Hence bulldozer needs to apply force of 520 N.
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Answer:
520N
Step-by-step explanation:
HOW DO I SOLVE THIS?
Answer:
∠ EGF = 64°
∠ DGE = 26°
Step-by-step explanation:
• ∠ EGF + 90° + 26° = 180° [angles in a triangle add up to 180°]
⇒ ∠ EGF = 180° - 90° - 26°
⇒ ∠ EGF = 64°
• ∠ DGE + ∠ EGF = 90° [as shown in the diagram]
⇒ ∠ DGE + 64° = 90°
⇒ ∠ DGE = 90° - 64°
⇒ ∠ DGE = 26°
A swimming pool is shaped like the figure below. Each end is a semicircle, and the length and
width of the rectangle are 40 feet and 20 feet, respectively. If there were a -foot-wide cement
border around the pool, what would be the area of the border?
The area of the border around the pool is determined as 145.97 ft².
Area of the pool
Diameter of the circle = 20 ft
Radius of the circle = 10 ft
Area of circular portion:Area = π(10²) = 314.16 ft²
Area of rectangular portionA = 40 ft x 20 ft = 800 ft²
Pool area = 314.16 ft² + 800 ft² = 1,114.16 ft²
Overall area which include 1 foot borderDiameter of the circle = 20 ft + 1ft + 1 ft = 22 ft
Radius of the circle = 11 ft
Area of circular portion:A = π(11²) = 380.13 ft²
Area of rectangular portion:A = 22 ft x 40 ft = 880 ft²
Total area = 880 ft² + 380.13 ft² = 1,260.13 ft²
Area of the borderArea of border = Total area - pool area
Area of border = 1,260.13 ft² - 1,114.16 ft²
Area of border = 145.97 ft²
Thus, the area of the border around the pool is determined as 145.97 ft².
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Carmen drew line A and line B in the two scatter plots shown. one scatter plot contains 12 points indicating a negative correlation and line A, which passes through the middle of points, with 6 above and 6 below, touching none of them; the other scatter plot contains 12 points indicating a positive correlation and line B, which passes through four of the points and sits above the other 8 points. Which statement is true? Both line A and line B are well-placed lines of best fit. Only line A is a well-placed line of best fit. Only line B is a well-placed line of best fit. Neither line A nor line B are well-placed lines of best fit.
The true statement is that only line A is a well-placed line of best fit
How to determine the true statement?The scatter plots are not given. However, the question can still be answered
The features of the given lines of best fits are:
Line A
12 points in totalNegative correlationPasses through the 12 points with 6 on either sidesLine B
12 points in totalPositive correlationPasses through the 12 points with 8 and 4 in either sidesFor a line of best fit to be well-placed, the line must divide the points on the scatter plot equally.
From the given features, we can see that line A can be considered as a good line of best fit, because it divides the points on the scatter plot equally.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A right triangle ABC has complementary angles A and C.
Using a right-angled triangle the value of Cos C is 24/25 and Sin A is 20/29.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
A right triangle ABC has complementary angles A and C.
Using a right-angled triangle if Sin A = 24/25 then the other side =7
Therefore Cos C = 24/25
Similarly,
Using a right-angled triangle if Cos C = 20/29 then the other side =21
Therefore Sin A = 20/29
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Which of these expressions equal 15 when x = and y=3? Circle
all that apply.
4 (2y-4x)-1
(x²+1)+2x+3y
4x²+2y³-10
xy+3+20x
Answer:
Option 1: 4(2y - 4x) -1
Step-by-step explanation:
Hello!
Given:
x = 0.5y = 3Plug in the values for x and y into each equation and see which one outputs 15.
4(2y - 4x) -14(2(3) - 4(0.5)) - 14(6 - 2) - 14(4) - 116-115(x² + 1) + 2x + 3y(0.5² + 1) + 2(0.5) + 3(3)1.25 + 1 + 911.254x²+2y³-104(0.5²) + 2(3³) - 104(0.25) + 2(27) - 101 + 54 - 1055 - 1045xy+3+20x(0.5)(3) + 3 + 20(0.5)1.5 + 3 + 104.5 + 1014.5The only option that works is the first option.
Answer:
[tex]4 (2y-4x)-1[/tex]
Step-by-step explanation:
Given:
[tex]x =\dfrac{1}{2}[/tex][tex]y=3[/tex]To find which expressions equal 15, substitute the given values of x and y into the expressions and evaluate:
[tex]\begin{aligned}4(2y-4x)-1 &= 4 \left(2(3)-4 \left(\dfrac{1}{2}\right)\right)-1\\& = 4 \left(6-2\right)-1\\& = 4 \left(4\right)-1\\& = 16-1\\& = 15\\\end{aligned}[/tex]
[tex]\begin{aligned}(x^2+1)+2x+3y & = \left(\left(\dfrac{1}{2}\right)^2+1\right)+2 \left(\dfrac{1}{2}\right)+3(3)\\& = \left(\left\dfrac{1}{4}+1\right)+1+9\\& = \dfrac{5}{4}+1+1+9\\& = \dfrac{45}{4}\end{aligned}[/tex]
[tex]\begin{aligned}4x^2+2y^3-10 & = 4\left(\dfrac{1}{2}\right)^2+2(3)^3-10\\& = 4\left(\dfrac{1}{4}\right)+2(27)-10\\& = 1+54-10\\& = 45\end{aligned}[/tex]
[tex]\begin{aligned}xy+3+20x & = \left(\dfrac{1}{2}\right)(3)+3+20\left(\dfrac{1}{2}\right)\\& = \dfrac{3}{2}+3+10\\& = \dfrac{29}{2}\end{aligned}[/tex]
Therefore, the only expression that equals 15 is:
[tex]4(2y-4x)-1[/tex]
A rectangular vegetable garden will have a width that is feet less than the length, and an area of square feet. If x represents the length, then the length can be found by solving the equation:
x(x-2)=48
What is the length, x, of the garden?
The length is blank feet.