Determine the equation of the linear function that generates the following table of values.

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

[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]

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]

The area of the border around the pool is determined as 145.97 ft².

Diameter of the circle = 20 ft

Radius of the circle = 10 ft

Area = π(10²) = 314.16 ft²

A = 40 ft x 20 ft = 800 ft²

Pool area = 314.16 ft² + 800 ft² = 1,114.16 ft²

Diameter of the circle = 20 ft + 1ft + 1 ft = 22 ft

Radius of the circle = 11 ft

A = π(11²) = 380.13 ft²

A = 22 ft x 40 ft = 880 ft²

Total area = 880 ft² + 380.13 ft² = 1,260.13 ft²

Area 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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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]

The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

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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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)

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:

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.

Answer:

[tex]\huge\boxed{\sf 49\ inches}[/tex]

Step-by-step explanation:

Length of the ladder = 4 feet 1 inch

We know that,

So,

4 feets = 12 × 4 inches

4 feets = 48 inches

So,

= 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]

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.

All 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.

The number of people who plays only footfall will be 15. The percentage of the class plays only football will be 15.79%.

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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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.

Answer:

c

Step-by-step explanation:

This is a fact. (See attached image)

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°

The true statement is that only line A is a well-placed line of best fit

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

Line B

For 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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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]

Answer:

Option 1: 4(2y - 4x) -1

Step-by-step explanation:

Hello!

Given:

Plug in the values for x and y into each equation and see which one outputs 15.

The only option that works is the first option.

Answer:

[tex]4 (2y-4x)-1[/tex]

Step-by-step explanation:

Given:

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]

[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

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

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

Using a right-angled triangle the value of Cos C is  24/25 and Sin A is 20/29.

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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Answer:

the probability= 2/6=1/3

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

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

The length of the flagpole is x - 5  yards

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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Answer:

Retype your question. That question made me nauseous

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^