Help with math problems

The value of x that makes the equation true is 2.25.

A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modelling is the process of creating a mathematical model. Both applied mathematics and the natural sciences employ mathematical models. The area of operations research is largely concerned with using mathematical models to resolve issues in commercial or military operations.

Using the figure we see that, for the left model we have:

3 (-x) = -3x.

Also, we have 10(1) = 10

Thus the left model has the equation:

-3x + 10

For the right model we have:

5x - 8

Equate the two models:

-3x + 10 = 5x - 8

18 = 8x

x = 2.25

Hence, the value of x that makes the equation true is 2.25.

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The solution to the system 2xy+3=4y 3xy+2=5y is  (x, y) = (22/5, -30/29).

Starting with the first equation:

2xy + 3 = 4y

We can rearrange it to solve for one of the variables in terms of the other:

2xy - 4y = -3

2y(x - 2) = -3

y = -3/(2(x - 2))

Now we can substitute this expression for y into the second equation:

3x(-3/(2(x - 2))) + 2 = 5(-3/(2(x - 2)))

Multiplying both sides by 2(x - 2) to clear the fraction:

-9x + 4(x - 2) = -30

-9x + 4x - 8 = -30

-5x = -22

x = 22/5

Now we can use this value of x to solve for y:

y = -3/(2(22/5 - 2))

y = -30/29

Therefore, the solution to the system is (x, y) = (22/5, -30/29).

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We get abοut 4 minutes if we rοund tο the clοsest minute. The sοlutiοn is thus A. 4 minutes οr sο.

A mathematical nοtiοn knοwn as prοpοrtiοnality describes the relatiοnship between twο quantities that cοnsistently change tοgether. When twο quantities are prοpοrtiοnal, their relatiοnship stays cοnsistent οver time. Tο put it anοther way, if twο variables, A and B, are prοpοrtiοnal, then the ratiο οf A tο B must be cοnstant and can be written as fοllοws:

A/B = k

where k is a ratiο cοnstant. This means that tο keep the ratiο cοnsistent, if οne οf the quantities is multiplied by a certain factοr, the οther quantity must alsο be multiplied by the same factοr.

given

dT/dt = -k (T - Ts)

where T is the οbject's temperature, Ts is the envirοnment's temperature, and k is a prοpοrtiοnality factοr. dT/dt stands fοr the rate οf change οf temperature.

In this instance, the rοοm is currently 70°F and the pοt οf water is οriginally 200°F. We thus have:

dT/dt = -k (200 - 70) = -k(130) (130)

The water's temperature has decreased tο 164°F after 5 minutes. Therefοre, we are aware that t = 5 at T = 164:

[tex]164 = 200e^{(-k*5)[/tex]

calculating k:

[tex]e^{(-5k)} = 164/200 = 0.82[/tex]

-5k = ln(0.82) (0.82)

k = -ln(0.82)/5

We can nοw calculate the time it takes fοr the water tο cοοl tο 150°F using this number οf k:

[tex]150 = 200e^{(-k*t)[/tex]

[tex]e^{(-k*t)}= 150/200 = 0.75-k*t = ln(0.75) (0.75)[/tex]

t = -ln(0.75)/k

By changing the amοunt οf k, we οbtain:

t = -ln(0.75)/(-ln(0.82)/5) ≈ 3.8

We get abοut 4 minutes if we rοund tο the clοsest minute. The sοlutiοn is thus A. 4 minutes οr sο.

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The line goes through the point and has a slope of 4, a y-intercept of -6, and a slope of 4. (0, 6).

The proportion of the increase in the y-value to the change inside the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) and Q := (4,1) on the line.

A line's slope is how steeply it slopes form LEFT to RIGHT. Divide the rise, or vertically increase, by the run, or horizontally start changing, to get the line's gradient.

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The complete question is:

X in graphs the equation y = 4x - 6.

Select all statements about Xin's graph that are true.

a. The graph is a curved line.

b. The line passes through the origin.

c. The line passes through the point (0, 6).

d. The slope of the line is 4.

e. The y-intercept of the line is -6.

Answer:

12 lbs of food per bag

Step-by-step explanation:

To distribute cat food equally into a certain number of bags, we can divide the amount of cat food by the number of bags to get how much food should go in each bag.

60 lbs of food ÷ 5 bags = 12 lbs of food per bag

Answer: If a movie starts at 2:45 PM and has a duration of 2 hours and 10 minutes, what time does it end?

To solve this, we need to add the duration of the movie to the start time and convert it back to the 12-hour clock format.

Adding 2 hours and 10 minutes to 2:45 PM, we get:

2:45 PM + 2 hours + 10 minutes = 4:55 PM

So, the movie ends at 4:55 PM.

Step-by-step explanation:

According to the ratio , the three girls shares are R2000,R3000 and R7000.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here the given total share amount is R12000.

Now the ratio for three girls is 2:3:7.

Total = 2+3+7=12

Now the share amounts are,

=> [tex]\frac{2}{12}\times 12000[/tex] = [tex]2\times1000=R2000.\\[/tex]

=> [tex]\frac{3}{12}\times=3\times1000=R3000[/tex]

=> [tex]\frac{7}{12}\times12000=7\times1000=R7000[/tex]

Hence the three girls shares are R2000,R3000 and R7000.

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Answer: 36 cubes

Step-by-step explanation:

Length x Width x Height

18 x 6 x 9 = 972

3 x 3 x 3 = 27

972 / 27 = 36

Answer:

Step-by-step explanation:

Given functions:

    [tex]r(x)=x^2+5x+14[/tex]

    [tex]c(x)=x^2-4x+5[/tex]

where:

Profit is calculated by subtracting expenses from revenue.

Therefore, the composite function for profit is:

Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.

To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:

[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]

Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.

The number of men needed to complete the same job in 16 days working 6 hours a day is given as follows:

28 men.

The number of men is obtained applying the proportions in the context of the problem.

The rule of three is given as follows:

n/48 = 8/6 x 7/16.

(the time is inverse proportional to the number of men, hence the fractions are inverted).

Thus:

n/48 = 56/96

Applying cross multiplication, the number of men is obtained as follows:

96n = 48 x 56

n = 48 x 56/96

n = 28 men.

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Answer:

74

Step-by-step explanation:

-6(-5-4) - 4(-3-2)

30 + 24 + 12 + 8

= 54 + 12 + 8

= 66 + 8

= 74

The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below

a) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:

1. Replace f(x) with y: y = (x - 2)^3 - 3

Solve for x in terms of y:

a. Add 3 to both sides: y + 3 = (x - 2)^3

b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2

c. Add 2 to both sides: x = (y + 3)^(1/3) + 2

Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2

b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:

So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).

To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).

Combining all of this information, we can sketch the graph of f^-1(x) as shown below:

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Answer:Hello!-47 s the answer :)

Step-by-step explanation:

Answer:

A. (1,2), (2,4), (3,6), (4,8)

Step-by-step explanation:

The 1st number in parenthesis is the number of boxes of popcorn. The 2nd number is the cost.

Answer:

A rotation about the origin 180 degrees means that the pre-image essentially rotates half an actual circle

The rule for 180 degrees rotation is (x,y)-->(-x, -y)

So the points of this quadrilateral are now

(1,3) = (-1, -3)

(4,1)=(-4, -1)

(4,4)=(-4, -4)

(1,4)=(-1,-4)

So it moves from 1st to 3rd quadrant

HOPE THIS HELPS

Thus, the archery set's discounted price is $61.10.

A reduction from the normal or list price. providing clients with a 10% discount. purchasing discounted tickets. (2): a proportionate reduction from an account of debt, typically provided in exchange for cash or quick payment.

The initial cost of the soccer jersey must be multiplied by (100% - 20%) = 80%, or 0.8, to determine the sale price after a 20% discount.

$85.75 x 0.8 = $68.60; Sale Price =Original Price multiplied by (1 - Discount)

Hence, the soccer jersey's retail price is $68.60.

We can apply the formula to get the tennis racket's original cost after just a 55% reduction and a $49.05 sale price:

Original Cost = Discounted Cost (1 - Discount)

Original Price = $49.05 / (1 - 55%) = $49.05 / 0.45 = $109.00

Hence, the tennis racket's original cost is $99.00.

The following formula can be used to determine the discount % for the archer set with just an original cost of $94.00 as well as a sale of $61.10:

Discount = (Original Price - Sale Price) / Original Price x 100%

Discount = ($94.00 - $61.10) / $94.00 x 100% = 35%

Hence, the archery set has a 35% discount.

The following equation can be used to determine the retail price of a archery kit with a 35% reduction and an original cost of $94.00:

Sale Price =Original Price multiplied by (1 - Discount)

Sale Price = $94.00 x (1 - 35%) = $61.10

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The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,

The formula for interest is written as,

I = (PRT)/100

The value of the principal is $2,300 and the amount generated in six months is $2,762. Then the percentage rate is calculated as,

($2,762 - $2,300) = [$2,300 x r x (6/12)] / 100

46,200 = 1,150r

r = 40.17%

The loan's simple interest rate when the loan of $2,300 is taken will be 40.17%.

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Answer:

30 men

Step-by-step explanation:

7 men x 300 days = 2100 man-days  to build 1 house)

(2100 man-days/house) x (1 house/70 days) = 30 men

The area of the triangle ABC is, 9 sq units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The area of a triangle is (1/2)×base×height.

Given, x equals 3 less than 6 which is,

x = (6 - 3).

x = 3.

Now, The base of the triangle is x units and the height is 2x units.

Therefore, The area of the triangle is,

= (1/2)×(3)×2(3).

= 9 sq units.

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The total possible outcomes is 16, the probability that all children are males is 1/16, the probability of having all one gender is 1/8

1. The tree diagram for the sex of the children is as follows:

Child 1: M / F

Child 2: M / F

Child 3: M / F

Child 4: M / F

Possible Outcomes: MMMM, MMMF, MMFM, MFMF, FMFM, FMMF, FMFF, FFFF

There are 2 options for each child, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16.

2. The probability that all children are males is 1/2 x 1/2 x 1/2 x 1/2 = 1/16.

3. The probability of having all one gender of children is the sum of the probability of having all boys and the probability of having all girls. Each of these outcomes has a probability of 1/16, so the total probability is 1/16 + 1/16 = 1/8.

4. The easiest way to solve this problem is to find the probability of having no female children, and then subtract that from 1. The probability of having no female children is (1/2)^4 = 1/16, so the probability of having at least 2 female children is 1 - 1/16 - 1/16 = 7/8.

5. The tree diagram for flipping a coin, rolling a 6-sided die, flipping a coin, and rolling a 3-sided die is as follows:

C / H

/

1-6 1-3

\ /

H / T

The first branch represents the coin flip, the second branch represents the roll of the 6-sided die, the third branch represents the second coin flip, and the fourth branch represents the roll of the 3-sided die.

6. There are 2 options for the first coin flip, 6 options for the second branch, 2 options for the second coin flip, and 3 options for the fourth branch, so the total number of possible outcomes is 2 x 6 x 2 x 3 = 72.

7. The probability of getting only heads on both coin tosses is 1/2 x 1/2 = 1/4. Therefore, the probability of getting only heads on both coin tosses and any result on the dice is 1/4 x 1 = 1/4.

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Answer:

43 degrees

Step-by-step explanation:

85 degrees + 25 = 110 and the angle sum for a right triangle will always equal 180 degrees. The outside angle is 62 degrees, so 62 +70= 132. 180-132 is 48. Now you want to solve the angle sum for the shorter wider triangle. We know one angle is 89 degrees, plus the 48 degrees= 137. Now to find ? do 180-137=43. The missing angle for ? is 43 degrees.

I hope this helps :)

Answer:

onomatopoeia

Step-by-step explanation:

The aacrued amount in the account in 15 years to the nearest dollar is $9,393.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

First,lets convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036

Now, plug in the values

A = P( 1 + r/n )^( n × t )

A = $5,500( 1 + 0.036/2 )^( 2 × 15 )

A = $5,500(1 + 0.018)^(30)

A = $5,500(1.018)^(30)

A = $9,393

Therefore, the accrued amount is $9,393.

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The volume of the box is a function of x, given by:[tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

What is volume ?

Volume is a physical quantity that measures the amount of three-dimensional space that a substance or object occupies. It is usually measured in cubic units, such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

To construct the box, we start with a square piece of cardboard that is 8 inches by 8 inches. We will cut out squares from each corner with side length x inches. This will leave us with a rectangular piece of cardboard with dimensions 8-2x by 8-2x, and we can fold up the sides to form the open box.

The height of the box will be x inches, and the length and width of the base of the box will be 8-2x inches. Therefore, the volume of the box will be:

Volume = Length x Width x Height

Volume = (8-2x) x (8-2x) x x

[tex]Volume = x(64-32x+4x^2)[/tex]

Therefore, the volume of the box is a function of x, given by: [tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

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The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

1. We can use the formula:

distance = rate × time

For the upstream journey:

distance = 4 miles

rate = 2 - r (since Dara is paddling against the current)

time = 4/(2-r) hours

For the downstream journey:

distance = 4 miles

rate = 2 + r (since Dara is paddling with the current)

time = 4/(2+r) hours

We can fill in the table as follows:

                       Distance (mi)    Avg Speed (mph)    Time (h)

With Current:            4                     2+r                    (4)/(2+r)

Against Current:       4                    2-r                       (4)/(2-r)

2. We know that the total time for the round trip is 6 hours:

4/(2-r) + 4/(2+r) = 6

3. Multiplying both sides by the LCD (2-r)(2+r), we get:

4(2+r) + 4(2-r) = 6(2-r)(2+r)

Simplifying, we get:

8 = 12 - 2r²

Rearranging, we get:

r² = 2

Taking the square root of both sides, we get:

r = ±√2

Since the current is flowing in one direction, we take the positive square root:

r = √2 ≈ 1.41 miles per hour

The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².

4. To the nearest hundredth, the rate of the current is approximately 1.41 miles per hour, which is option B: About 1.15 miles per hour (rounded to two decimal places).

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The number of different ways will be 108000.

Permutations are various ways to arrange things in a specific order. It can also be stated as the linear reordering of items in an already ordered set.

A first guess for the number of ways to select a committee consisting of 3 engineers, 2 physicists, and 2 computer scientists from 10 engineers, 5 physicists, and 6 computer scientists could be to simply multiply the number of ways to select each group separately:

10 choose 3 x 5 choose 2 x 6 choose 2

This would give us the number of ways to select 3 engineers out of 10, 2 physicists out of 5, and 2 computer scientists out of 6.

The number of ways can be,

N = ¹⁰C₃ x ⁵C₂ x ⁶C₂

N = 10 x 9 x 8 x 5 x 6 x 5

N = 108000

Therefore, the number of different ways will be 108000.

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