12 x 3.4x - 5.4x - x

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

14 ) x + 37 + 37 = 180

or , x + 74 = 180

or , x = 180 - 74

or , x = 106

9514 1404 393

Explanation:

1) 2x^2 -5x -3 = 0 . . . . standard form equation

To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.

  -6 = (1)(-6) = (2)(-3)

The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.

If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...

  (ax +p)(ax +q)/a . . . . . factored form of the quadratic

  (2x +1)(2x +(-6))/2 . . . .fill in the values we know

  (2x +1)(x -3) . . . . . . .  factor 2 from the second binomial

So, the factored form of the quadratic equation is ...

  (2x +1)(x -3) = 0 . . . . factored form equation

__

2) f(x) = x^2 +7x +10 . . . . standard form quadratic function

Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...

  f(x) = (x +2)(x +5) . . . . . . factored form quadratic function

The leading coefficient is 1, so we have no further work to do.

Roots, x-intercepts, zeros

The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)

Solutions

Often, we are interested in solving the equation ...

  f(x) = 0

For that equation, the solutions are the zeros or x-intercepts or roots. The graph attached also shows solutions for ...

  f(x) = 4

Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the roots, x-intercepts, or zeros are not solutions to this equation.

The tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate, After 20 minutes, the amount of salt in the tank is still 50 grams.

In order To calculate the amount of salt in the tank after 20 minutes, we basically use the formula:  Salt (in grams) = (Amount of salt in the tank x Time) / Total volume.So, after 20 minutes, the amount of salt in the tank is:  (50 grams x 20 minutes) / 240 liters = 8.33 grams.    

As we can see, both methods produce the same result, confirming that the amount of salt in the tank after 20 minutes is still 50 grams. since the rate of pumping in salt water is equal to the rate of pumping out salt water, so the total amount of salt remains the same.

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A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number of grams of salt in the tank after 20 minutes

Answer:

The simple interest is calculated by multiplying the principal amount by the interest rate and the number of years.

Simple Interest = Principal x Interest Rate x Time

The simple interest on Boden's account is:

800 x 3.2% x 4 = 800 x 0.032 x 4 = $256

To find the total amount in the account after 4 years, we add the interest to the principal:

800 + 256 = $1056

So, Boden's account will have $1056 after 4 years.

Answer:

Revolution traveled by me = 30π ft.

Revolution traveled by my friend = 20π ft.

Difference between revolutions = 10π ft.

Step-by-step explanation:

In one revolution, I travel 2π(15) = 30π ft., and my friend travels 2π(10) = 20π ft., so my revolution is 30π - 20π, or 10π, ft. longer than my friend's revolution.

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

Your answer would be 7/20 or 0.35.

The correct derivative expressions of the given ones are -

\($1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0\)

\($2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =\)\($\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8\)

\($3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20\)

It is given that -

\($\int\limits^3_8 {f(x)} \, dx = 6\\\)

and

\($\int\limits^3_8 {g(x)} \, dx\)

The correct statements of the given are -

\($1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0\)

\($2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =\)\($\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8\)

\($3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20\)

Therefore, the correct derivative expressions of the given ones are -

\($1.\;\;\int\limits^3_3 {f^{2} (x)} \, dx = 0\)

\($2.\;\int\limits^3_8 {g(x)-f(x)} \, dx =\)\($\int\limits^3_8 {g(x)} \, dx - \int\limits^3_8 {f(x)} \, dx = -2 - 6 = -8\)

\($3.\;\;\int\limits^3_8 {4f(x)} \, dx - \int\limits^3_8 {2g(x)} \, dx = 24 - 4 = 20\)

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Answer:

  C.  ∫(f·g)dx = -12 is incorrect

Step-by-step explanation:

You want to know which of the integral expressions is incorrect given ...

\(\displaystyle \int_3^8{f(x)}\,dx=6\ \ \text{ and }\int_3^8{g(x)}\,dx=-2\)

Expression A has the same value for upper and lower limits of the integral. The area being integrated has zero width, so its value will be zero, as shown in expression A.

Expression E has the limits reversed from those in expression B, so the value of that integral will be the opposite of the value shown for B. Both of these integral expressions (B, E) are correct.

The integral of a sum is the sum of the integrals. This is shown in expressions B, D, and E, all of which are correct.

In general, the integral of a product will have no relation to the product of integrals. Hence expression C is NOT necessarily correct.

<95141404393>

The probability current corresponding to the wave function ψ(r,t) = r e^(ikr) is S = (m r^2 / ℏk) r^.

To calculate the probability current, we start with the expression S = (2m/ℏ) Im[ψ^* ∇ψ - ψ ∇^*]. Given the wave function ψ(r,t) = r e^(ikr), we need to calculate the gradient (∇) and the complex conjugate (∗) of ψ. The gradient of ψ can be computed as ∇ψ = (∂/∂x, ∂/∂y, ∂/∂z) (r e^(ikr)). Applying the derivatives, we obtain ∇ψ = (e^(ikr) + ikr e^(ikr)) (cosθ, sinθ, 0), where θ is the angle between the position vector r and the x-y plane.

The complex conjugate of ψ, ψ^*, is obtained by taking the complex conjugate of each term in ψ. Therefore, ψ^* = r e^(-ikr). Similarly, we calculate ∇^* = (e^(-ikr) - ikr e^(-ikr)) (cosθ, sinθ, 0).

Now we substitute these expressions into the formula for the probability current S. After simplification, we get S = (m r^2 / ℏk) r^, where r^ = (sinθ cosφ, sinθ sinφ, cosθ) is the unit vector in the direction of r.

In summary, the probability current corresponding to the given wave function ψ(r,t) = r e^(ikr) is S = (m r^2 / ℏk) r^. This expression represents the magnitude and direction of the probability current associated with the particle described by the wave function.

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

the weight of the substance after 28 years is 8 grams.

We have that the half life of a substance is defined as the time required for the substance to decrease by half

The formula for calculating the half - life of a material is given as;

\(N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }\)

Where

Substitute into the formula

N(t) = 128 × (0. 5) ^28/ 7

N (t) = 128 × ( 0. 5) ^ 4

N(t) = 128 × 0. 0625

N(t) = 8 grams

Thus, the weight of the substance after 28 years is 8 grams.

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We can use the power series expansion of the exponential function e^(-x) to evaluate the sum of the series:

e^(-x) = ∑(n=0 to infinity) (-1)^n (x^n) / n!

Setting x = 3/2, we get:

e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^n / n!

Multiplying both sides by (3/2)^2 and simplifying, we get:

(9/4) e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

Comparing this with the given series, we can see that they differ only by a factor of (-1) and a shift in the index of summation. Therefore, we can write:

∑(n=0 to infinity) (-1)^n (2n) (3/2)^(2n) / (2n)!

= (-1) ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

= (-1) ((9/4) e^(-3/2))

= - (9/4) e^(-3/2)

Hence, the sum of the series is - (9/4) e^(-3/2).

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The total tons of trash that was thrown away by the people is 3.9 tons.

The first step is to convert pounds to tons

1 pound  = 0.0005 tons

40 x 0.0005 = 0.02 tons

The second step is to multiply 0.02 by 195

0.02 x 195 = 3.9 tons

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In rectangular form, the given equation is expressed as y = 2x, which represents a straight line passing through the origin with a slope of 2. The graph of this equation in rectangular coordinates is a straight line with a positive slope.

The polar equation r = 2 cot(θ) csc(θ) represents a graph that is symmetric about the x-axis and has vertical asymptotes at θ = 0 and θ = π.

To convert the polar equation r = 2 cot(θ) csc(θ) to rectangular form, we can use the trigonometric identities cot(θ) = cos(θ) / sin(θ) and csc(θ) = 1 / sin(θ).

Substituting these identities into the equation, we have r = 2(cos(θ) / sin(θ))(1 / sin(θ)). Simplifying further, we get r = 2 cos(θ) / sin²(θ).

To convert to rectangular form, we can use the relationship between polar and rectangular coordinates: x = r cos(θ) and y = r sin(θ).

Substituting these equations into the polar equation, we have

y = 2x sin²(θ) / cos(θ).

Simplifying the equation, we get y = 2x tan(θ).

The rectangular equation y = 2x represents a straight line passing through the origin with a slope of 2.

It means that for every unit increase in x, y increases by 2 units. The line is symmetric about the origin and has a positive slope.

As x approaches infinity or negative infinity, y also approaches infinity or negative infinity, respectively.

When sketching the graph, we draw a line passing through the origin with a slope of 2.

The line extends indefinitely in both directions, and all points on the line satisfy the equation y = 2x.

The graph does not intersect the y-axis and has no x-intercept.

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Answer: 42.5

Step-by-step explanation:

Answer:

52.5, it’s asking for measure d not x, measure d is equal to measure b

Step-by-step explanation:

a=3x, b=x+10,

3x+x+10=180

4x=170

x=42.5

b/d=42.5+10

b/d=52.5

Answer:

Jamie has a  foot plank that he needs to cut into 1/9 pieces.

15 ÷ 1/9 = 135  

135 x 1/9 = 15

Step-by-step explanation:

we are 95% confident that the true mean difference between the amount of mail-order purchases and the amount of internet purchases lies between -$23.09 and $9.29.

Step 1: Find the critical value that should be used in constructing the confidence interval.

Since the sample sizes are small (n1=9, n2=13), we will use the t-distribution for the interval estimate. The degrees of freedom is calculated using the formula:

df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1 - 1) + ((s2^2/n2)^2)/(n2 - 1)]

Plugging in the values gives:

df = [(27.75^2/9 + 25.75^2/13)^2] / [((27.75^2/9)^2)/(9 - 1) + ((25.75^2/13)^2)/(13 - 1)] ≈ 17.447

Using a t-table with 17 degrees of freedom and a confidence level of 95%, we find the critical value to be 2.110.

Step 2: Calculate the point estimate of the difference between the means.

The point estimate of the difference between the means is:

1x - x2 = $72.10 - $79.00 = -$6.90

Step 3: Calculate the confidence interval.

The formula for the confidence interval for the difference between two population means is:

(1x - x2) ± tα/2 * sqrt[s1^2/n1 + s2^2/n2]

Plugging in the values gives:

(-$6.90) ± 2.110 * sqrt[27.75^2/9 + 25.75^2/13] ≈ (-$23.09, $9.29)

Therefore, we are 95% confident that the true mean difference between the amount of mail-order purchases and the amount of internet purchases lies between -$23.09 and $9.29.

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184,219,440 ways.

What is contestant?

A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.

There are 570 contestants, and any one of them can win the first prize.

One of the remaining 569 people can receive the second prize.

Third may be assigned to any of the remaining 568.

We can accomplish this in 570*569*568 ways

= 184,219,440 ways.

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Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.

In the given question, we have to find the speed of each.

Two trains going in opposite directions leave at the same time.

One train tavels 15 mph faster than the other.

In 6 hours the trains are 630 miles apart.

Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.

Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.

So, find the distance covered by the first vehicle in 6 hours by using the formula

Distance = Speed × Time

So the distance D(1) is;

D(1) = s*6

D(1) = 6s

So the distance D(2) is;

D(2) = (s+15)*6

D(2) = 6s+90

Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.

D(1)+D(2) = 630

Puttimg the value of D(1) and D(2)

6s+6s+90=630

Simplifying

12s+90=630

Subtract 90 on both side we get

12s=540

Divide by 12 on both side we get

s=45 mph

So the value of speed of the faster vehicle

s+15 = 45+15

s+15 = 60 mph

Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.

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Answer:

tulips= 56

and  daffodils= 93

Step-by-step explanation:

Step one:

given data

number of tulips = 56

ratio of tulips to daffodiis= 3:5

total ratio= 3+5= 8

Step two:

Required

The number pf daffodiis

let us apply the part to all aproach

the total flowers can be found bellow

let the total be x

3/8=56/x

cross multiply

3x=56*8

3x=448

divide both sides by 3

x=448/3

x=149.3

=149 approx.

The total flowers is 149

the number of daffodils is =149-56=93

tulips= 56

and  daffodils= 93

Answer:

21 tuilps : 35 daffodils

Step-by-step explanation

There are 3 : 5  = 3+5=8

3= tulips

5=daffodils

8 parts of the bed                    

=

3/8*56 = 21 (tuilips)

5/8*56 = 35(daffodils)

Thus we have 21 tuilips and 35 daffadils (21:35)

Answer: 1) -5.8

Step-by-step explanation:

in order to solve the problem you have to put it together:

9x-5 = 14x+24

then go from there : subtract 24 on both sides , then subtract 9x on both sides , that’ll leave you with : -29 = 5x

so from there we divide , giving us x= -5.8

The equation that represents china growth function  is

P(t) = 1.39 * ( 1.006)ⁿ.

What is a function?

function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

The initial population = 1.39 billion in 2013

Growth rate  = 0.6%

Let a be the initial population

Let b be the growth rate

Let n be the elapsed year from 2013

Let the population in nay year be P(t)

Then equation is

P(t) = a * ( b )ⁿ

P(t) = 1.39 * ( 1.006)ⁿ

∴ The equation P(t) represents the growth function of china

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The equation for the circle in the graph is:

(x + 2)² + (y + 2)² = 0.5625

A circle whose center is at the point (a, b) and has a radius of R units can be written as:

(x - a)² + (y - b)² = R²

Here we can see in the graph that the center of the circle is at the point (-2, -2), and we also can see that the radius of the circle is 0.75 units, then the equation for the circle in the graph will be:

(x - (-2))² + (y - (-2))² = 0.75²

We can simplify that to get:

(x + 2)² + (y + 2)² = 0.5625

That is the equation.

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Answer:

37.68

Step-by-step explanation:

C= Pie x C

C = 3.14 x 12

37.68 cm

Step-by-step explanation:

Circumference =?

π = 3.14

d = 12

Circumference = πd

Substitute values into the given equation

\(c = 3.14 \times 12 \\ c = 37.68 \: cm\)

Ur solution is in the attachment.

Answer:

d)  ? = 5

e)   ? = -2x

f)    ? = x

Step-by-step explanation:

d) 20 = (4)(?)

    20/4 = ?

     5 = ?

    Check:

    20 = 4*5

e)   -14x = (7)(?)

     -14x/7 = ?

      -2x = ?

      Check:

      -14x = 7*-2x

f)    x³ =x² (?)

      x³/x² = ?

      x³⁻² = ?

      x¹ = ?

       x = ?

      Check:

     x³ = (x²)(x)      

To solve this problem, we need to use combination which is statistical tool to determine the number of ways an event may occur. The combination to select a 5 a side team from 12 students is 792.

This a mathematical technique that is used to determine the number of possible arrangements in a collection of items where the way they're arranged does not matter.

Data;

The combination for this would be

\(C = ^1^2C_5 = 792\)

The combination to select a 5 a side team from 12 students is 792.

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Answer:

Center  = (1,2)  radius = 2

Step-by-step explanation:

I used Demos to graph the circle.

Then I added two line to find the center of the circle

The radius is 2

Answer:

answer is 30 pls mark me branilest