Find the solution to the system of equations: x 3y = 7 and 2x 4y = 8 1. isolate x in the first equation: 2. substitute the value for x into the second equation: 3. solve for y: 4. substitute y into either original equation: 5. write the solution as an ordered pair:

Answer:

The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

Answer:

Part 1) Option B. y = 10x + 45

Part 2) The score is 95

Step-by-step explanation:

Linear equation that best describes the given model

Let

x ---> number of hours students spent studying

y ---> their score on the test

Looking at the line that was fit to the data to model the relationship

The slope is positive

The y-intercept is the point (0,45)

For x=1, y=55 ----> point (1,55)

Find the slope

The formula to calculate the slope between two points is equal to

substitute the points (0,45) and (1,55)

Find the equation of the line in slope intercept form

we have

substitute

Part 2) Estimate the score for a student that spent 5 hours studying.

For x=5 hours

substitute in the linear equation and solve for y

Answer:

[tex]12.50 \space\ h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

[tex]\boxed {12.50 \times h = 2500.75}[/tex]

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = [tex]\frac{2500.75}{12.50}[/tex]

  = 200.6 hours

Answer: 12.50h = 2500.75

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

goal:tan^5x=tanx(sec²x-2sec²x+1)

proof: from l.h.s to r.h.s

tan^5x=(tanx)^5=((tanx)(tan²x)(tan²x))

from trigonometry identity

(tan²x)=sec²x-1

tan^5x=(tanx(sec²x-1)(sec²x-1))

=(tanx(sec^4x-sec²x-sec²x+1))

=(tanx(sec^4x-2sec²x+1))

proved

Answer:

6 Meters

Step-by-step explanation:

If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.

a=v/t ->>> 6= 36/t

The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,

B) Number of peaches=7,number of apples=3,

C) Number of red token=10, number of blue token=6,green tokens=4,

D)Number of golf balls=13, number of tennis balls=2.

We are required to find the following probabilities:

A) Probability of getting red marble=Number of red marbles/ Total marbles.

=3/12

=1/4

=0.25

B) Probability of getting peaches=Number of peaches/Total fruits.

=7/10

=0.7

C) Probability of getting green tokens=Number of green tokens/Total tokens

=4/20

=1/5

=0.2

D)Probability of getting golf balls= Number of golf balls/ Total balls.

=13/15

=0.867

The sequence will be from C-A-B-D.

Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

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The values that exist two standard deviations above and below the mean are 681 and 265.

The given parameters exist:

Mean = 473

Standard deviation =104

The values above and below the mean exist calculated utilizing:

[tex]$x=\bar{x} \pm n \sigma$[/tex]

In this case n = 2.

So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]

The value above is:

x = 473 + 2 [tex]*[/tex] 104 = 681

The value below is:

x = 473 - 2 [tex]*[/tex] 104 = 265

Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.

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We conclude  the hypothesis test as Alternative Hypothesis if the data would be very unusual if the original assumption about our parameter were correct.

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Using the normal distribution, it is found that:

a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.

b. 5.7% of male sailors requires custom uniform pants.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 32.6, \sigma = 1.3[/tex]

For item a, the percentile is the p-value of Z when X = 34.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (34.1 - 32.6)/1.3

Z = 1.15

Z = 1.15 has a p-value of 0.875.

Hence 87.5th percentile.

For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:

X = 36:

Z = (36 - 32.6)/1.3

Z = 2.62

Z = 2.62 has a p-value of 0.996.

X = 30:

Z = (30 - 32.6)/1.3

Z = -2

Z = -2 has a p-value of 0.023.

0.996 - 0.023 = 0.943.

Hence the proportion who requires an special order is:

1 - 0.943 = 0.057.

5.7% of male sailors requires custom uniform pants.

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The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The area of triangle A = 1728 square feet

The base length of the triangle b = 72 feet

Let h be the height of the triangle

Area = (1/2)b×h

1728 = (1/2)72×h

h = 48 feet

Half of the 72 is 72/2 = 36

As we know,

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Applying trigonometric ratio:

tan(x) = 48/36

tan(x) = 1.333

x = 53.13 degrees

Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

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Using proportions, it is found that:

A. The vegetables weigh 66 pounds.

B. 0.5 pints are dispensed after 25 seconds.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:

W = 16 x 4.125 = 66 pounds.

Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:

A = 25 x 0.16 = 4 gallons.

Each gallon has 8 pints, hence the number of pints dispensed is:

4/8 = 0.5 pints.

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From the given information, a exists jointly proportional to b and c.

then [tex]$$a \propto b c$[/tex]

Therefore, the value of a exists 2.

Given, a exists jointly proportional to b and c.

[tex]$$a \propto b c$[/tex]

Taking K as the constant of proportionality.

a = K b c

For b = 8 and c = 9, the value of a = 4

4 = K(8)(9)

4 = 72 K

Dividing the equation by 72, we get

[tex]$K=\frac{1}{18}[/tex]

Using the value of K in the equation:

[tex]$a=\frac{b c}{18}[/tex]

Substitute the values of b = 2 and c = 18, in the above equation

[tex]$a=\frac{2 \times 18}{18} \\[/tex]

a = 2

Therefore, the value of a exists 2.

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Answer:

  32.4 inches

Step-by-step explanation:

Sam wants the increase to be 8% of 30 inches.

The amount of increase Sam wants in his waist size is ...

  8% × 30 in = 0.08×30 in = 2.4 in

Adding the wanted increase to his present size would make Sam's waist size be ...

  30 in + 2.4 in = 32.4 in

Sam wants his waist size to be 32.4 inches.

__

Additional comment

The larger size can also be computed from ...

  30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches

Answer: 2 and 3, or 3 and 2

Step-by-step explanation:

a + b = 5 so a = 5 - b

Substitute a = 5 - b into ab = 6; (5 - b)b =  6

5b - [tex]b^{2}[/tex] = 6

[tex]b^{2}[/tex] - 5b + 6 = 0

(b - 2)(b - 3) = 0

So b is either 2 or 3

So a is either 3 or 2 depending on what b is

The second store offered the better buy at the price of $92.00.

What is better buy?

Better buy refers to the lowest price out of the prices offered by the three stores.

In order to determine the lowest price, the no discount price of the first store needs to be compared to the prices of  two other stores, bearing that after-discount price is the pre-discount price multiplied by 1 minus the discount rate.

First store price=$95.00

Second store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$115

discount rate=20%

Second store after-discount price=$115*(1-20%)

Second store after-discount price=$92.00

Third store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$105

discount rate=10%

Third store after-discount price=$105*(1-10%)

Third store after-discount price=$94.50

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By critically observing the graph, we can infer and logically deduce the following points:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

By critically observing the graph which models the changes in temperature over a specific period of time (in years), we can infer and logically deduce the following points:

In conclusion, there are four (4) points of intersection on this graph.

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The deductible mileage cost has reduced by 2.16%

What is a percentage change?

A percentage change  compares the difference between the new amount and the old amount to the old amount.

I mean the percentage change is the new deductible mileage cost minus the old deductible mileage cost divided by the old deductible mileage cost

New deductible mileage cost= 57.5 cents

Old deductible mileage cost= 56 cents

percentage decrease=(56-57.5)/57.5

percentage decrease=-2.61%

The negative sign in -2.61% means that there was a percentage decrease in deductible mileage cost by 2.61%

In essence, the deductible mileage cost has been reduced by 2.16%

Hundredth of a percent means two decimal places.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).

iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.

In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:

5 · a - 7 · b = - 20

- 3 · a = - 20

Whose solution is a = 20 / 3 and b = 160 / 21.

ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.

iii) Now we find the coordinates of the intercepts of the line:

x-Intercept

(20 / 3) · x = - 20

x = - 3

y-Intercept

(160 / 21) · y = - 20

y = - 21 / 8

iv) We can find two alternative solutions by using multiples:

20 · x + (160 / 7) · y = - 60

140 · x + 160 = 420

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Answer:

OK

Let x=the number

2x=double the number

2x+5=the doubled number increased by 5

And we are told that this equals -47

sooooo

2x+5=-47 subtract 5 from each side2x=-47-5=-52

2x=-52

x=-26------the number

CK

2*(-26)=-52

-52 increased by 5=-52+5=-47

-47=-47

Hope this helps- Clara ☆*: .｡. o(≧▽≦)o .｡.:*☆

Step-by-step explanation:

❄ Hi there,

let us start by letting the number be r. The problem tells us that r is doubled and then increased by 2.

This is what it looks like –

[tex]\triangleright \ \sf{2r+2}[/tex]

Also the result is 14 more than 5r.

We end up with an equation that looks like this –

[tex]\triangleright \ \sf{2r+2=14+5r}[/tex]

To find the number we should solve the equation for r –

[tex]\large\begin{gathered} \sf{2r+2=14+5r} . \ Solve \ for \ r: \\ \sf{2r-5r+2=14}\\ \\ \sf{-3r+2=14}\\\sf{-3r=14-2}\\\sf{-3r=12}\\\sf{-r=4}\\\sf{r=-4}\end{gathered}[/tex]

❄

Answer:

16u²

Step-by-step explanation:

It is a regular parallelogram

we have points (3, 4) and (4, 0).

we also have the origin which is (0, 0) and the difference between (0, 0) and (4, 0) on the x axis is 4 and since it is a regular shape, that means the top right corner = (3, 4) + (4, 0), so it is (7, 4). we know the base is 4 now. the vertical height = (7, 4) - (1, 0) which is (6, 4). now we are looking at difference in y. which is between (4, 0) and (6, 4), so the difference is 4.

now we just do 4 x 4 since it is bh and you get 16 units ²

Answer:

[tex]\frac{263}{999}[/tex]

Step-by-step explanation:

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

From the question we can say that the Hexagon has three shapes inside it,

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

An equilateral triangle is shown inside a square.

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

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Answer:

Regular Hexagon

Regular Pentagon

Square

Equilateral Triangle

Step-by-step explanation:

E2020 Geometry B!! :3

The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.

The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.

So in the given question, the perimeter of the fence required = 1200 meters.

Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,

Perimeter = 2l + 3w

1200 = 2l + 3w

Thus, let l be equal to 300, we have;

1200 = 2(300) + 3w

1200 - 600 = 3w

w = 200

Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.

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Answer:

9

Step-by-step explanation:

when you divide 576 by 9 you get 64 which is a perfect cube

cbrt(64) = 4

so your answer is 9

By using subtraction of yellow areas from the entire squares, the areas of the inscribed shapes are listed below:

The areas of the inscribed shapes can be easily found by subtracting the yellow areas from the square, in order to find the value of green areas. Now we proceed to find the result for each case by using area formulae for triangles:

Case A

A = 6² - 0.5 · (3) · (6) - 0.5 · (3) · (6)

A = 36 - 18

A = 18 units

Case B

A = 6² - 4 · 0.5 · (2) · (4)

A = 36 - 16

A = 20 units

Case C

A = 6² - 0.5 · 6² - 0.5 · 6 · 2

A = 36 - 18 - 6

A = 12 units

Case D

A = 6² - 2 · 0.5 · 6 · 4

A = 36 - 24

A = 12 units

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Answer:

x - 14.95 = 12.48

x = 27.43

Step-by-step explanation:

The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

For given question,

We have been given a function f(x) = 6 + 9x² - 6x³

We need to find the local maximum and local minimum of the function  f(x)

First we find the first derivative of the function.

⇒ f'(x) = 0 + 18x - 18x²

⇒ f'(x) = - 18x² + 18x

Putting the first derivative of the function equal to zero, we get

⇒ f'(x) = 0

⇒ - 18x² + 18x = 0

⇒ 18(-x² + x) = 0

⇒ x (-x + 1) = 0

⇒ x = 0    or    -x + 1 = 0

⇒ x = 0     or    x = 1

Now we find the second derivative of the function.

⇒ f"(x) = - 36x + 18

At x = 0 the value of second derivative of function f(x),

⇒ f"(0) = - 36(0) + 18

⇒ f"(0) = 0 + 18

⇒ f"(0) = 18

Here, at x=0, f"(x) > 0

This means, the function f(x) has the local minimum value at x = 0,  which is given by

⇒ f(0) = 6 + 9(0)² - 6(0)³

⇒ f(0) = 6 + 0 - 0

⇒ f(0) = 6

At x = 1 the value of second derivative of function f(x),

⇒ f"(1) = - 36(1) + 18

⇒ f"(1) = - 18

Here, at x = 1, f"(x) < 0

This means, the function f(x) has the local maximum value at x = 1,  which is given by

⇒ f(1) = 6 + 9(1)² - 6(1)³

⇒ f(1) = 6 + 9 - 6

⇒ f(1) = 9

So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.

Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

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