16 factory workers made 40 pieces in a certain amount of time. How many workers are needed to make (1) 20, (2)25 and (3)100 pieces in the same amount of time, assuming each worker works at the same rate?

The following equation has infinite many solutions

3(2x+1)=2(1+3x)+1

Step-by-step explanation:

An equation has infinite solutions if there is same constant on both sides of the equation.

We will check each equation one by one to find the equation with infinite solutions.

So,

3(2x+1)=2(1+3x)+1

[tex]3(2x+1)=2(1+3x)+1\\6x+3 = 2+6x+1\\6x +3 = 6x +3\\6x-6x+3 = 3\\3 = 3[/tex]

3(2x+1)=2(1+3x)-1

[tex]3(2x+1)=2(1+3x)-1\\6x+3 = 2+6x-1\\6x+3=1+6x\\6x-6x+3 = 1\\3 = 1[/tex]

3(2x-1)=2(1+3x)-1

[tex]3(2x-1)=2(1+3x)-1\\6x-3 = 2+6x-1\\6x-3 = 1+6x\\6x-6x-3 = 1\\-3 = 1[/tex]

3(2x+1)=2(3+2x)-3​

[tex]3(2x+1)=2(3+2x)-3​\\6x+3 = 6+4x-3\\6x+3 = 3+4x\\6x-4x+3 = 3\\2x+3 = 3[/tex]

The following equation has infinite many solutions

3(2x+1)=2(1+3x)+1

Keywords: Solution of equation, Linear equation

Learn more about linear equation at:

#LearnwithBrainly

Answer:

Yes (6,3) is a solution

Step-by-step explanation:

It because both of the lines that are shaded intercepted so it works for both

Answer:

[tex]l(AB)=5\ units[/tex]

is the distance between the point A and point B.

Step-by-step explanation:

Let

A ≡ (x₁, y₁) ≡ (-9 , -8 )

B ≡ (x₂, y₂) ≡ (-6 , -4 )

Now by Pythagoras  Distance formula we have

a² + b² = c²

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}\\\\l(AB) = \sqrt{((-6--9)^{2}+(-4--8)^{2} )}\\\\l(AB)=\sqrt{(3)^{2}+(4)^{2}  }\\\\l(AB) =\sqrt{25} \\\\l(AB) = 5\ units[/tex]

Answer

c= √(a² + b²)

c=√( -6  –  -9 )² + ( -4 –  -8 )²

Step-by-step explanation:

Answer:

[tex]3y^2[/tex]

Step-by-step explanation:

Given:

To find the GCF of [tex]3y^2\ and\ 24y^3[/tex] using prime factorization.

Writing each in prime factors:

3 = 1 [tex]\times[/tex] 3

24 = 1 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex]2 [tex]\times[/tex] 3

Now, GCF of 3 and 24 is 3

[tex]y^2=1\times y\times y[/tex]

[tex]y^3=1\times y\times y\times y[/tex]

GCF of [tex]y^2[/tex] and [tex]y^3[/tex] is [tex]y\times y=y^2[/tex].

Therefore, the overall GCF of the two terms is [tex]3y^2[/tex]

Answer:

y=3x

Step-by-step explanation:

The slope of this graph is 3.

Answer:

51

Step-by-step explanation:

add them altogether then times by 3

The final factored expression using the GCF is: 14x+63=7(2x+9)

To factor the expression 14x + 63 using the Greatest Common Factor (GCF), let's first find the GCF of the numerical coefficients 14 and 63. The largest number that divides both 14 and 63 without a remainder is 7, making it the GCF.

Next, we divide each term by the GCF:

14x divided by 7 is 2x

63 divided by 7 is 9

Now that we have divided each term by the GCF, we can write the original expression as a product of the GCF and the simplified expression:

14x + 63 = 7(2x + 9)

This expression is fully factored as the product of the GCF (7) and the binomial (2x + 9).

The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + n

Option C

Solution:

Given Sequence is 3, 4, 5, 6, 7, ...

Let us the check the each option which can form the above sequence

a) a= 2n

[tex]\begin{array}{l}{\text {For } n=0, a=2 \times(0)=0} \\\\ {\text {For } n=1, a=2 \times(1)=2} \\\\ {\text {For } n=2, a=2 \times(2)=4}\end{array}[/tex]

We get a sequence 0, 2, 4 which does not satisfy the given sequence

b) a= 2-n

[tex]\begin{array}{l}{\text {For } n=0, a=2-0=2} \\\\ {\text {For } n=1, a=2-1=1} \\\\ {\text {For } n=2, a=2-2=0}\end{array}[/tex]

We get a sequence 2, 1, 0 which does not satisfy the given sequence

c) a= 3+n

For n = 0, a = 3 + 0  = 3

For n = 1, a = 3 + 1  = 4

For n = 2, a = 3 + 2 = 5

For n = 3 , a = 3 + 3 = 6

For n = 4, a = 3 + 4 = 7

Which satisfy the given sequence

Hence, c) is the correct option

The closed linear form of the sequence 3, 4, 5, 6, 7, ... is a = 3 + n, which matches option C. The pattern in the sequence indicates that the nth term can be expressed as 3 + (n - 1). Therefore, the answer is option A: a = 2 + n.

To find the closed linear form, we identify the pattern in the sequence. The sequence starts at 3 and increments by 1 for each subsequent term. Hence, the nth term (an) can be expressed as:

an = 3 + (n - 1)

an = 2 + n

Therefore, the closed linear form of the given sequence is option A: a = 2 + n.

The expression will be  y =8*2 or y = (48/6)*2

Step-by-step explanation:

The direct proportion is given if y varied directly as x

y∝x

When the proprtionality symbol is removed, a proportionality constant is introduced.

y = kx

as we know y = 48 when x = 6

[tex]48 = k * 6\\k = \frac{48}{6}\\k = 8[/tex]

The equation will be:

y = 8x

So when x=2

y = 8*2

y = 16

Hence,

The expression will be  y =8*2 or y = (48/6)*2

Keywords: Proportion, Direct proportion

Learn more about proportion at:

#LearnwithBrainly

To find the value of y when x is 2 in a direct variation, use the constant of variation k found from the given values (y = 48 when x = 6), which is 8 in this case, and multiply it by 2 to get y = 16.

If y varies directly as x, this means that y can be expressed as y = kx, where k is the constant of variation. Given that y = 48 when x = 6, we can find the value of k by substituting these values into the direct variation equation:

k = y/x = 48/6 = 8

Now that we have k, we can find the value of y when x is 2:

y = kx = 8 x 2 = 16

Therefore, the expression to find the value of y when x is 2 is y = 8 x 2.

Answer:

[tex]\displaystyle [3\frac{1}{3}, -2][/tex]

Step-by-step explanation:

{2x + 3y = ⅔

{3x - 4y = 18

¾[3x - 4y = 18]

{2x + 3y = ⅔

{2¼x - 3y = 13½

____________

[tex]\displaystyle \frac{4\frac{1}{4}x}{4\frac{1}{4}} = \frac{14\frac{1}{6}}{4\frac{1}{4}} \\ \\[/tex]

[tex]\displaystyle x = 3\frac{1}{3}[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]-2 = y[/tex]

I am joyous to assist you anytime.

The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.

To solve the system of equations:

we can use the method of substitution or elimination. Let's use elimination in this case:

First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:

Next, we add the two equations together to eliminate y:

8x + 12y + 9x - 12y = 8/3 + 54

17x = 54 + 8/3

17x = 54 + 2.6667

17x = 56.6667

Now we divide both sides by 17 to solve for x:

x = 56.6667 / 17

x = 3.3333

With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:

2x + 3y = 2/3

Substitute x:

2(3.3333) + 3y = 2/3

6.6666 + 3y = 2/3

3y = 2/3 - 6.6666

3y = -6.0000

Now divide both sides by 3 to solve for y:

y = -6.0000 / 3

y = -2.0000

The solution to the system is x = 3.3333 and y = -2.0000.

Answer:

36792.2133

Step-by-step explanation:

36792+0.2+0.0133=36792.2133

Answer:

m∠NQP=74°

Step-by-step explanation:

we know that

The measure of the interior angles in a triangle must be equal to 180 degrees

In this problem

In the triangle NPQ

m∠N+m∠P+m∠Q=180°

we have

m∠N=(2x)°

m∠P=(34)°

m∠Q=(2x+2)°

substitute the values

[tex](2x)\°+(34)\°+(2x+2)\°=180\°[/tex]

solve for x

[tex](4x+36)\°=180\°[/tex]

[tex]4x=180-36[/tex]

[tex]4x=144[/tex]

[tex]x=36[/tex]

Find the measure of angle NQP

we know that

m∠NQP=m∠Q=(2x+2)°

substitute the value of x

m∠NQP=(2(36)+2)=74°

Answer:

The missing part is given below.

500=(2xL)+(__2__x_90___)

500=2L+__180_____

_320__=2L

_320____ divided by 2=L

_160____=L

Step-by-step explanation:

Given:

Perimeter of Rectangle = 500 feet

Width = 90 feet

Length = L

Solution:

[tex]\textrm{Perimeter of Rectangle} = 2(Length + Width)\\\\\textrm{On substituting the given values in it we get}\\500 = 2\times L + 2\times 90\\\\500 - 180 =2\times L\\320 =2\times L\\\\\frac{320}{2}=L\ ....................... (\textrm{320 divided by 2}) \\160 = L[/tex]

Final answer:

To find the length of the garden, the formula for the perimeter of a rectangle is used (P = 2L + 2W), where the perimeter is 500 feet and the width is 90 feet. By substituting these values and solving for L, we find that the length of the garden is 160 feet.

Explanation:

Finding the Length of a Garden

To find the length of a rectangular garden when you know the perimeter and the width, you can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P stands for the perimeter, L is the length, and W is the width. The student has provided that the width (W) of the garden is 90 feet and the perimeter (P) is 500 feet.

Substituting the values we know into the formula, we get:

500 = 2L + 2(90)

Now, we solve for the length (L) by following these steps:

First, do the multiplication: 500 = 2L + 180

Next, subtract 180 from both sides to isolate the term with L: 320 = 2L

Finally, divide both sides by 2 to solve for L: 160 = L

Therefore, the length of the garden is 160 feet.

The percent decrease in the mass of Finley's pumpkin after carving is approximately 40.55%.

To calculate the percent decrease in the mass of Finley's pumpkin after carving, use the following formula:

Percent Decrease = ((Original Mass - New Mass) / Original Mass) 100%

First, let's find the decrease in mass.

Decrease in Mass = Original Mass - New Mass = 6.56 kg - 3.9 kg = 2.66 kg

Then, calculate the percent decrease:

Percent Decrease = (2.66 kg / 6.56 kg) 100% = 40.55%

The percent decrease in the mass of the pumpkin after carving is approximately 40.55%.

Answer:

[tex]A_{5} = 1875[/tex]

Step-by-step explanation:

The geometric sequence is represented by

[tex]A_{n} = 5 \times A_{n - 1}[/tex] .......... (1) and [tex]A_{1} = 3[/tex]

So, [tex]A_{2} = 5 \times A_{2 - 1} = 5 \times A_{1} = 5 \times 3 = 15[/tex]

{Putting n = 2}

Again, putting n = 3 in equation (1), we get

[tex]A_{3} = 5 \times A_{2} = 5 \times 15 = 75[/tex]

Again, putting n = 4 in equation (1), we get

[tex]A_{4} = 5 \times A_{3} = 5 \times 75 = 375[/tex]

Again, putting n = 5 in equation (1), we get

[tex]A_{5} = 5 \times A_{4} = 5 \times 375 = 1875[/tex] (Answer)

Answer:

$3.60

Step-by-step explanation:

25+20=45 (because you need the tax of both)

0.8(45)=3.60 (finding the tax amount)

Answer:

$1.40

Step-by-step explanation:

1.75-(1.75×.2)

1.75-.35

1.4

Answer:

$1.40

Step-by-step explanation:

100% - 20% = 80%

Therefore, Multiply $1.75 by 80% to get this week's price of orange

$1.75 x 80% = $1.40 per pound

Answer:

B is the answer at least i think also are you in gaca? if so webmail me my name is Angela Petersen

Ms. Brown has been reading for 18 weeks so far.

To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.

Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]

Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.

Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]

Now, we can solve for ( x ) by cross-multiplying:

[tex]\[ 2 \times x = 3 \times 12 \][/tex]

[tex]\[ 2x = 36 \][/tex]

Divide both sides by 2 to solve for ( x ):

[tex]\[ x = \frac{36}{2} \][/tex]

[tex]\[ x = 18 \][/tex]

So, Ms. Brown has been reading for 18 weeks so far.

complete question given below:

Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?

Answer:  monday

Step-by-step explanation:

Answer:

1. For x is x=5y+30 and for y is y=1/5x−6

2. For x is x=5y−45 and for y is y=1/5x+9

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s 35 because 9*5 is 45 and 80-45 is 35

Answer: Option A, Option B, Option D.

Step-by-step explanation:

Let's check each option.

A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]

B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]

C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]

D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]

Then, the correct options are: Option A, Option B, Option D.

Answer:

-8/15

Step-by-step explanation:

8*-3/15*5

=-24/75

= -8/15

Answer:

It will be answer choice D.

Step-by-step explanation:

It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late.

The linear equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late is (y = 0.5x + 10).

Given :

According to the given, data x represent the number of minutes her normal commute takes when she leaves on time.

Let y be the total time taken by Jade after 5:00 pm to reach home. So, the linear equation that represents the given situation is:

[tex]\rm y = \dfrac{1}{2}x+10[/tex]

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/11897796

Answer:

Explanation:

1. Name the angle of inclination of the line joining p to the origin α.

2. Find the relation between the coordinates of the point (x,y)

When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).

As per the definition of the tangent trigonometric ratio you have:

From which you can clear y:

Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.

Answer:

Damien will receive a change of [tex]\$4.69[/tex]

Step-by-step explanation:

Given:

Pair of jeans = $33

Sales tax = 7%

Money paid as Sales tax = 7% of sale done on pair of jeans  = [tex]\frac{7}{100}\times \$33 = \$2.31[/tex]

Total amount paid = 40

We need to find the amount he will receive back

Amount receive back can be calculated by Total amount paid minus Amount for pair of jeans minus money paid as Sales Tax

Change amount received = Total amount paid - Amount for pair of jeans - money paid as Sales Tax = [tex]\$40 - \$33-\$2.31 = \$ 4.69[/tex]

Hence Damien will receive a change of [tex]\$4.69[/tex]