solve the inequality 5y+9≤4

The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10

The proof of this statement is constructive, as it will provide a way to explicitly construct a positive integer which is equal to the sum of the positive integers not exceeding it.

To prove this, we will use the following formula:

Let n = the positive integer

Let S = the sum of the positive integers not exceeding n

n = 1 + 2 + ... +n-1 + n

S = 1 + 2 + ... +n-1

Therefore, n = S + n

For example, let n = 5. The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10. Therefore, 5 = 10 + 5, which is true. This proves that for any positive integer, n, it is equal to the sum of the positive integers not exceeding it.

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The coordinates of the point where the chain should attach to the triangle are (3, 4).

Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).

We need to find the coordinates of the point where the chain should attach to the triangle.

The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).

Now, centroid = ((0+3+6)/3, (4+8+0)/4)

=(3, 4)

Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).

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We need to subtract both expressions, then simplify it and make only one expression:

First, subtract both expressions:

Then:

Now, simplify like terms:

Therefore, the result expression is -11x+15y.

Answer:

he needs 9 cans

Step-by-step explanation:

first,

43L/5L

= 8.6 cans

8.6 cans is not logical therefore u need to round up to 9 cans

Answer:

Step-by-step explanation:

Let sharma age be S and Ankit age be A

S = 3a

(s-10) = 5(a-10)

substitute 1 in 2

3a-10 = 5a -50

40 = 2a

a = 20

s = 3 * 20 = 60

Answer:

32.

Step-by-step explanation:

This is an arithmetic sequence with first term a1 = -6 and common difference 2.

an = a1 + d(n - 1)

a20 = -6 + 2(20-1) = 32

Answer:

16c - 7 = 13.32

Step-by-step explanation:

The cost of 16 cookies minus the coupon equal how much he paid

16c - 7 = 13.32

Answer:

16c - 7 = 13.32

Step-by-step explanation:

well, the difference is 39.14 - 38 = 1.14, so that's the tax.

if we take 38 to be the 100%, just the listed price alone, what is 1.14 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 38 & 100\\ 1.14& x \end{array} \implies \cfrac{38}{1.14}~~=~~\cfrac{100}{x} \implies 38x=114\implies x=\cfrac{114}{38}\implies x=3\)

Answer:

There is no photo

Step-by-step explanation:

I cant see the photo therefore I cant help

Answer:

Can u put the answer choices

Step-by-step explanation:

An equation is a collection of variables and constants. The value of x and y for the system of the equation as -2x - 4y = -18 and x = y will be x = 3 and y = 3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given system of equations,

-2x - 4y = -18 and x = y

Substitute, x = y

-2(y) - 4y = -18

-6y = -18

y = 3 and x = 3

Hence "The value of x and y for the system of the equation as -2x - 4y = -18 and x = y will be x = 3 and y = 3".

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Answer:

anser A

Step-by-step explanation:

Let's fill x and y and we'll see which one is right

a) 0 = -3(-7+7)(-7+4)

<=> 0 = 3 * 0 * -3

<=> 0 = 0 => true

b) 0 = -0.5(-7-7)(-7+4)

<=> 0 = -0.5 * -14 * -3

<=> 0 =  -21 => false

c) 0 = (-7-7)(-7-4)

<=> 0 = -154 => false

d) 0 = 2(-7+7)(-7-4)

<=> 0 = 0 => true

so both a and d are right for (-7,0). Now let's for (-4,0)

a) 0 = -3(-4+7)(-4+4)

<=> 0 = 0 => true

d) 0 = 2(-4+7)(-4-4)

<=> 0 = -48 => false

Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

\(d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } \)

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

\(d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} \)

To find the distance between the two complex numbers using the formula

\(d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } \)

where,

\(d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } \)

Answer:

I can't interpret the data the way it is presented.  Are there two columns?  I'll assume "-x2" is really "-x^2."

I've attached a plot of the function.  Check to see which of your points fall on the line.

Step-by-step explanation:

y = -x^2 + 5

Answer:

x = 2 and y = 3

Step-by-step explanation:

To find the x- intercept, let y = 0 in the equation and solve for x

3x + 2(0) = 6

3x + 0 = 6

3x = 6 ( divide both sides by 3 )

x = 2 ← x- intercept

To find the y- intercept, let x = 0 in the equation and solve for y

3(0) + 2y = 6

0 + 2y = 6

2y = 6 ( divide both sides by 2 )

y = 3 ← y- intercept

Using compound interest, it is found that:

a) $1,270.70 will be in the account after 6 years.

b) It will take 17.53 years for the $1000 to double.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, the parameters are given as follows:

\(A(0) = 1000, r = 0.04, n = 12\)

Item a:

Over 6 years, that is t = 6, thus:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}\)

\(A(t) = 1270.7\)

$1,270.70 will be in the account after 6 years.

Item b:

This is t for which A(t) = 2P = 2000, hence:

\(2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}\)

\((1.0033)^{12t} = 2\)

\(\log{(1.0033)^{12t}} = \log{2}\)

\(12\log{(1.0033)} = \log{2}\)

\(t = \frac{\log{2}}{12\log{1.0033}}\)

\(t = 17.53\)

It will take 17.53 years for the $1000 to double.

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Answer:

The answer to your probem is -5.5

Answer:

-1.3n - 7.33 = -0.18

-1.3n = 7.15

n = -5.5

Step-by-step explanation:

Answer:

\(3 > b\)

Step-by-step explanation:

Given

\(a = 1\)

\(c = 2\)

Required

Inequality to measure the length of b

The triangle inequality theorem states that:

\(a + b > c\)

\(a + c > b\)

\(b + c > a\)

On side b, we make use of:

\(a + c > b\)

Substitute values for a ad c

\(1 + 2 > b\)

\(3 > b\)

The inequality is: \(3 > b\)

Answer: -$480

Step-by-step explanation:

The revenue us P*x

now, when P = $40, we have:

X = 14400 - 3*40^2 = 9600

then the revenue is:

9600*$40 = $384000

now, the price increaces by $2 so the new equation is:

X = 14400 - 3*42^2 = 9108

The revenue is:

9109*$42 = $382536

You can see that the revenua is smaller than before.

Now, if we want to calculate the rate of change when p = $40, we need to look at X'(40)

this is:

X´(p) = -3*2*p

then:

X'(40) = -3*2*40 = -120

Theh rate of change of the revenua will be:

X'(40)*$40 = -120*$40 = -$480

The "Explain" step of this part of the problem solving approach is option  C. The "Explain" step is to ensure that the result is reasonable.

In this particular step, the solution is examined critically to ascertain its relevance in the given problem scenario. This aids in detecting possible mistakes, assessing the practicality of the resolution, and guaranteeing that the solution matches the needs of the given problem.

The "Explain" step validates the solution, ensuring accuracy and reliability by reviewing each step. During "Explain", ensure accuracy of solution by identifying errors/mistakes in calculations, formulas or methods used.

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The probability of two planes having no cracks is 0.063 and The probability of no plane having critical cracks is 0.405.

(a) The probability of one plane having a critical crack is 10% or 0.10. The probability of two planes having detectable cracks is (0.21)^2 = 0.0441. The probability of two planes having no cracks is (0.69)^2 = 0.4761. So, the desired probability is 0.10 * 0.0441 * 0.4761 = 0.063.

(b) To find the probability that at least one plane has critical cracks, we can use the complementary probability approach, i.e., finding the probability that no plane has critical cracks and then subtracting it from 1. The probability of no plane having critical cracks is (0.90)^5 = 0.595. So, the desired probability is 1 - 0.595 = 0.405.

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Answer:

\(\omega_1 = \frac{5Rad}{3s}\) and \( \omega_2 = \frac{35Rad}{12s}\)

Step-by-step explanation:

Given that the larger gear is turning at the rate 50rpm. The angular velocity, \(\omega_1\), of the larger gear can be calculated as follows:

\(\omega_1 = \frac{50rev}{m} \) to convert that to secs, we know that 1 rev = 2πRad and 60secs make a min, so we have:

\(\omega_1 = \frac{50rev}{m} \times \frac{2\pi Rad}{1rev} \times \frac{1m}{60s} \)

That gives

\(\omega_1 = \frac{100Rad}{60s}\)

Which gives:

\(\omega_1 = \frac{5Rad}{3s}\)

This is the angular velocity of the larger gear in rads/sec.

In order to get the angular velocity of the smaller gear, we know from the question that both gear are connected to the same belt. This implies that they have the same linear velocity. Thus let us find the linear velocity of the larger gear. This is given by

\(v = r_1 \times \omega_1\) where v stands for linear velocity and \(r_1\) for radius of larger velocity.

We are given the radius of the larger gear as 7ft so we have

\(v = 7ft \times \frac{5Rad}{3s} = \frac{35ft}{3s}\)

To get the angular velocity of the smaller gear, we use

\(v = r_2 \times \omega_2\) where \(r_2\) is the radius of the smaller gear which is given as 4.

Since linear velocity is the same, we have

\( \omega_2 = \frac{35ft}{4 \times 3s}\)

\( \omega_2 = \frac{35Rad}{12s}\)

The locus of all points from which a given segment subtends equal angles is a circle. Therefore:

so:

Divide both sides by 2:

The factors of -18 that sum to 3 are 6 and -3, therefore:

So:

Answer:

42:30

Step-by-step explanation:

10 x 3 = 30

14 x 3 = 42

graph B is the correct answer

We keep X1 constant, then for every 1 unit increase in X2, the Y variable will increase by an estimated 16 units. 98% of the total variation in the dependent variable is explained by the independent variables in the regression model.

The given estimated multiple linear regression equation is Y = 8 + 45X1 + 16X2.

a. Interpretation of the estimated coefficient of X2

In the given estimated regression equation, the estimated coefficient of X2 is 16.

The interpretation of the estimated coefficient of X2 is as follows:

If we keep X1 constant, then for every 1 unit increase in X2,

the Y variable will increase by an estimated 16 units.

b. Interpretation of R2 value

If R^2 (Goodness of Fit Coefficient) is 0.98 in this estimated regression equation,

then it tells that the 98% variability in the Y variable can be explained by the independent variables (X1 and X2) included in the regression model.

In other words, 98% of the total variation in the dependent variable is explained by the independent variables in the regression model.

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Answer:

The cubed root of a number is the number that, when multiplied by itself three times (number x number x number), gives the original number. For example, the cubed root of 27 is 3, as 3 x 3 x 3 = 27. The cubed root of 125 is 5, as 5 x 5 x 5 = 125. Unlike the square root, the cubed root is always positive

Step-by-step explanation:

Answer:

AB is 17 and the midpoint of AB is (-2, - 2.5).

Step-by-step explanation:

The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.

To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.

In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.

Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.

Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.

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