solve for y 3x-7y=21
A. y=-3/7x+21
B. y=3/7x-21
C. y=3/7x-3
D. y=-3/7x+3

The standard form of the given equation f(x) = 6x² − x + 1 is:

[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]

So, f(x) = 6x² − x + 1:

We must convert this to standard form, which is provided by:

Where x² is the co-efficient of the leading term and (h, k) is the curve's vertex (minimum and maximum point).

The formula h = -b/2a can be used to calculate h.

We can find k by determining f(h), as k=f (h).

[tex]\begin{aligned}&k=f\left(\frac{1}{12}\right)=6\left(\frac{1}{12}\right)^2-\frac{1}{12}+1 \\&k=\left(6 \times \frac{1}{141}\right)-\frac{1}{12}+1 \\&k=\frac{1}{24}-\frac{1}{12}+1 \\&k=\frac{1-2+24}{24}=\frac{23}{24}\end{aligned}[/tex]

Therefore, the standard form of the given equation f(x) = 6x² − x + 1 is:

[tex]f(x)=6\left(x-\frac{1}{12}\right)^2-\frac{23}{24}[/tex]

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The correct question is given below:

Write the quadratic function in standard form.

f(x) = 6x² − x + 1

The total distance travelled by the body is 48 meters

According to the question we have been given an equation of the position of  a body moving along x-axis as

                    s = t³ - 12t² + 36t

where,    s = distance in meters

             t = time in seconds

We need to find the total distance traveled by the body from t=0s to t=4s

The formula for the total distance is given as :

            S = |s(1) - s(0)| + |s(2) - s(1)| + |s(3) - s(2)| + |s(4) - s(3)|

Now we will find out the distance travelled in time 0s to 4s

when t = 0s ,  s = (0)³ - 12(0)² + 36*0

                         = 0m

         t = 1s ,  s = (1)³ - 12(1)² + 36*1

                         =  25m

         t = 2s ,  s = (2)³ - 12(2)² + 36*2

                         =  32m

         t = 3s , s = (3)³ - 12(3)² + 36*3

                         = 27m

         t = 4s , s = (4)³ - 12(4)² + 36*4

                         = 16m

Putting the required values in the above formula we get ,

  S = |25-0|+|32-25|+|27-32|+|16-27|

  S = 25 + 7 + 5 + 11 meters

   S = 48 meters

Hence the total distance travelled by the body is 48 meters

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The distance between the two points are-9.87 units.

The distance formula is;

d² = (y₂ - y₁)² + (x₂ - x₁)²

Let the two given points be;

A(x₁, y₁) = (-1,-9)

B(x₂, y₂) = (6, - 16)

Put the values in the formula;

d² = (-16 + 9)² + (6 + 1)²

d² = (-7)² + (7)²

d² =2 (7)²

d = 7√2

d = 7×1.41

d = 9.87

Therefore, the distance between the two points is found as 9.87 units.

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According to the empirical rule, there are a answers of the given statement.

According to the statement

We have to find that the answers of the given statement.

So, For this purpose, we know that the

The empirical rule is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

From the given information:

The mean of 340 grams and a standard deviation of 35 grams.

Then

a) About 68% of organs weight between:

According to the empirical rule:

68% of the information values lie within 1 variance of the mean

95% of the info values lie within 2 variance of the mean

99.7% of the information values lie within 3 variance of the mean

Thus, 68% of the information values consist the range: Mean - 1 variance to Mean + 1 variance.

Using the values of Mean and variance, we get:

Mean - 1 variance = 320 - 20 = 300 grams

Mean + 1 variance = 320 + 20 = 340 grams

This means 68% of the organs will weigh between 300 and 340 grams.

And

b) In order to search out what percentage of organs weight between the given range, we'd like to seek out what proportion far these values are from the mean.

Since, mean is 320 and 280 is 40 but mean, we will write:

280 = 320 - 40

280 = 320 - 2(2)

280 = 320 - 2 Standard Deviations

Similarly,

360 = 320 + 40

360 = 320 + 2 Standard Deviations

So, we've got to inform what percentage of values lie within 2 variance of the mean. in step with the empirical law, this amount is 95%.

So, 95% of the organs weigh between 280 grams and 360 grams.

And

c) From the previous part we all know that 95% of the organs weight between 280 grams and 360 grams.

It is on condition that the distribution is bell shaped. the full percentage under a bell shaped distribution is 100%. So so as to calculate what proportion percentage of values are below 280 and above 360, we'd like to subtract the proportion of values that are between 280 and 360 from 100% i.e.

Percentage valuable outside the range = 100% - Percentage of values inside the range

So,

Percentage of organs weighs but 280 grams or over 360 grams = 100 - Percentage of organs that weigh between 280 grams and 360 grams

Percentage of organs weighs but 280 grams or quite 360 grams = 100% - 95% = 5%

So, 5% of the organs weigh but 280 grams or over 360 grams.

And

D) 300 is 1 variance below the mean and 360 is 2 standard deviations above the mean.

Previously it's been established that, 68% of the info values lie within 1 variance of the mean i.e

From 1 variance below the mean to 1 variance above the mean, the share of values is 68%. Since the distribution is bell shaped and bell shaped distribution is symmetric about the mean, therefore the percentage of values below the mean and above the mean must be the identical.

So, from 68% of the information values that are within 1 variance from the mean, 1/2 them i.e. 34% are 1 variance below the mean and 34% are 1 variance above the mean. Thus, percentage of values from 300 to 320 is 34%

Likewise, data within 2 standard deviations of the mean is 95%. From this half the information i.e. 47.5% is 2 standard deviations below the mean and 47.5% is 2 standard deviations above the mean. Thus, percentage of values between 320 and 360 grams is 47.5%

So,The total percentage of values from 300 grams to 360 grams = 34% + 47.5% = 81.5%

Therefore, 81.5% of organs weigh between 300 grams and 360 grams.

So, According to the empirical rule, there are a answers of the given statement.

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Answer:

Step-by-step explanation:

f(x) = 1/x

In the figure, m ∠ 7 = 100 °. The measure of angle 8 is 80°

An angle is a figure in the Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by the two rays are in the plane where the rays are located. The meeting of the two planes also creates angles. We refer to these as the dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of the intersecting curves.

Angle can also refer to length of a rotation or an angle. This metric represents relationship between a circular arc's length and radius. The arc is centered at the vertex and defined by sides in the case of a geometric angle. When there is a rotation, the arc is defined by any other point and rotation's image, and it is centered at the rotation's center.

Given,

∠7 = 100°

According to the given figure,

∠7+∠8= 180°

100°+ ∠8= 180°

∠8= 180°- 100° = 80°

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Answer:

39 hours

Step-by-step explanation:

52 × 45 = 2340

2340 mins into hours = 39 hours

hope this helps :)

In a triangle of EFG we have ∠E+∠F = 120°,E=(8x-2)° and F=(7x+2)°.

Option B is true and angle of G is 60°.

Given that,

∠E+∠F = 120°

In the figure we have a triangle with EFG.

E=(8x-2)°

F=(7x+2)°

We know

∠E+∠F = 120°

8x-2+7x+2=120

15x=120

x=120/15

x=8

We got x =8

∠E=8[tex]\times[/tex]8-2=62°

∠F=7[tex]\times[/tex]8+2=58°

Now, we know in a triangle all angles are equal to 180°.

∠E+∠F+∠G=180°

62°+58°+G=180°

120°+G=180°

G=180°-120°

G=60°

We have 4 option

a) (7x)° which is false

b) (7x+4)° which is true (7[tex]\times[/tex]8+4=60°)

c)(8x)° which is false

d) (8x+4)° which is false

Therefore, option B is true and angle of G is 60°.

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Answer:

Step-by-step explanation:

comment on the comment section with a complete question I will help you there please

Answer:

x = 10/9

Step-by-step explanation:

Solve:

27^(3x-2) = 81

When solving equations in exponential form make sure the two bases on both sides are the same.

3^3(3x-2) = 3^4

Once the two bases are the same you cancel them out and used its exponent to solve the equation.

3(3x-2) = 4

9x-6 = 4

Add 6 to both sides.

9x-6+6 = 4+6

9x = 10

Divide both sides by 9.

x = 10/9

Therefore x = 10/9.

Answer:

-3 will be on the -x axis n the -6 will be on the -y axis so both will meet at a point.

Step-by-step explanation:

that is all I understand am not sure if I am ryt

The exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

Given,

Melatonin is fast-acting and has a half-life of approximately 30 minutes.

10-milligram tablet is taken.

We need to write an exponential equation to model this after t time periods.

Half-life is the time required for a quantity to reduce to half of its initial value.

The formula is given as:

N(t) = [tex]N_{0} ~(\frac{1}{2})~^\frac{t}{t_{1/2}}[/tex]

Where

N(t) = quantity of the substance remaining

[tex]N_{0}[/tex] =  initial quantity of the substance

[tex]t_{1/2}[/tex] = half-life of the substance

We have,

Half-life = 30 minutes

[tex]N_{0}[/tex] = 10 mg

The exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

Thus the exponential equation to model this after t time periods is:

N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]

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Step-by-step explanation:

if I understand you correctly, then we have the 4 described cards. 3 of these 4 cards are face cards (Jack, Queen, King).

a probability is always desired cases over totally possible cases.

so, for the first pull we have a probability of

3/4 = 0.75

we have 4 total possibilities, and 3 of them are the desired outcome.

for the second pull we have then only 3 cards left (we did not replace the first pulled card). and because the first pulled card was in this scenario a face card, 2 out of these 3 cards are face cards.

so, the probability to pull a face card here is

2/3 = 0.66666...

when we combine these 2 events into one connected event (we are creating event 1 AND event 2), we multiply the probabilities, giving us

3/4 × 2/3 = 6/12 = 1/2 = 0.5

Answer:

15+90=3×18

Step-by-step explanation:

GCF= 5

Considering the greatest common divisor, you obtain:

The greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.

A method to calculate the greatest common factor must follow the following steps:

To find the greatest number of gift bags the party planner can make, you find the greatest common divisor.

To do this, decompose the numbers 96, 36 and 24:

The common factors with the smallest exponent are: 2² and 3

So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12

This means that the greatest number of gift bags that the party planner can make is 12.

To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:

Finally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

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Answer:

[tex]5y - 20 = 0 \\ 5y = 20 \\ y = \frac{20}{5} = 4[/tex]

Answer:

f(1) = 1

f(4) = -2

f(0) = 2

Step-by-step explanation:

y = f(x)

Answer: IK=14

Step-by-step explanation:

IK=IJ+JK

IL=IJ+JL

IL-JL=IJ+JL-JL

IJ=IL-JL

IK=IL-JL+JK

IK=31-25+8

IK=6+8

IK=14

Answer:

7000 panels.

Step-by-step explanation:

Let x be the number of panels produced by Plant B.

Therefore:

Given information:

Create an equation with the given information and defined variables, remembering to write the percentages in their decimal form:

[tex]\implies 0.03(4x) + 0.02x = 980[/tex]

To find the number of panels Plant B produced, solve the found equation for x:

[tex]\implies 0.03(4x) + 0.02x = 980[/tex]

[tex]\implies 0.12x + 0.02x = 980[/tex]

[tex]\implies 0.14x = 980[/tex]

[tex]\implies \dfrac{0.14x}{0.14} = \dfrac{980}{0.14}[/tex]

[tex]\implies x=7000[/tex]

Therefore, Plant B produced 7000 panels.

Answer:

7.112 x [tex]10^{-5}[/tex]

Step-by-step explanation:

You need to re-write the number so that it is 1 or larger but less than 10.  To do that, we need to move the decimal 5 spaces to the right.  The actually number is smaller.  The [tex]10^{-5}[/tex] is telling me how much smaller the number actually is.  To get the number in standard notation I would have to take 7.112 and divide it by 100,000.

Answer:

3:1 = 6:2 = 12:4

Hope this helps :)

Answer:

3.1=12.4

Step-by-step explanation:

12.4

12/12+4=12/16=3/4.

so 3.1=12.4

Answer:

When faced with this question as multiple choice, you can either try to verify that one of the answers is true, or you can try to solve for the answer and compare to the choices. Your challenge during a multiple choice test is to identify the fastest possibility so that you can go on to the next problem.

In this case neither choice takes any significant amount of time. You can verify which equation is satisfied by any two points in the table very quickly.

Or you can notice that the equations are all linear and then take two points and solve for the equation of the line between them.

In either case, answer C quickly reveals itself as correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.

If you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:

  C = πd

  C = π(48 m) = 48π m ≈ 151 m

Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...

  track length = curved length + straight length

  track length = 151 m + 2×96 m = 343 m

The length of the track is 343 meters.

The area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.

The radius of the circular portion is half the diameter, or 24 m. Then the area is ...

  A = πr²

  A = π(24 m)² = 576π m² ≈ 1810 m²

The area of the rectangular portion is the product of length and width:

  A = LW

  A = (96 m)(48 m) = 4608 m²

The enclosed area is the sum of these areas:

  enclosed area = area of circle + area of rectangle

  enclosed area = 1810 m² +4608 m² = 6418 m²

The area enclosed by the track is 6418 square meters.

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.

The perimeter of the composite figure is:

p = 2π · r + 2 · l

p = 2π · (24 m) + 2 · (96 m)

p ≈ 342.796 m

A = π · r² + l · (2 · r)

A = π · (24 m)² + (96 m) · (48 m)

A ≈ 6417.557 m²

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

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The number of street lights that will be needed is 3 street lights.

From the information, it was stated that the city places street lights at equal intervals along a city street beginning 3/8 mile from one end of the street. If the street is 7/8 mile long,

The number of street lights needed will be:

= 7/8 ÷ 3/8

= 7/8 × 8/3

= 7/3

= 3 street lights.

Therefore, the number of street lights that will be needed is 3 street lights.

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The amount Trey invested in Fund B is $8,000.

Profit is a residual income, It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. while return is a total revenue. Profits may be negative, whereas returns, such as wages and interest are always positive.

amount invested in Fund A = $12,000            (given)

profit returned by Fund A =  1% of $12,000    (given)

= 1/100*$12,000

= $120

Let amount invested in Fund B = x                   (assumption)

profit returned by Fund B =  6% of x                 (given)

= 6/100*x

= $ 6x/100

Given that both funds A and B together returned a 3% profit, So the equation we get is

120+6x/100 = 3% of (12,000+x)

(12,000+6x)/100 = 3/100* (12,000+x)

12,000+6x = 3(12,000+x)

12,000+6x = 36,000+3x

6x-3x = 36,000-12,000                       (bringing like terms on same side)

3x = 24,000

x = 24,000/3

x = $8,000

Therefore, we can conclude that the amount Trey invested in Fund B is $8,000  

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Answer: LN=29

Step-by-step explanation:

LN=LM+MN

KM=KL+LM

KM-KL=KL-KL+LM

LM=KM-KL

LN=KM-KL+MN

LN=8-3+24

LN=5+24

LN=29