Write the absolute value in the form x-b=c where b is a number and c can be either number or expression

The smallest integer 160 needs to be multiplied by to give a square number is 15.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The smallest integer 160 needs to be multiplied by to give a square number;

60 x 15= 900

Hence,

The square root of 900= 30

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Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

Answer:

yes because it goes through the origin and has a constant rate is the correct answer hope it helps you :)

Answer:

A shows all possible combinations

Step-by-step explanation:

Answer:

1/3 and 21

Step-by-step explanation:

 hope it helped  :)

1m = 1000mm

15m = 15000mm

1 L = 1000 mL

0.75 L = 750 mL

Answer:

These should be the correct conversions:

15m =15000mm

0.75 L = 750 mL

Step-by-step explanation:

Commutative property of addition

Changing the order of addends does not change the sum.

For example:

For the problem

we have that the order of the addends does not alter the result:

We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

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We get: v - h + k - s = Ce^(-s/2) or y - x - (h - k) = Ce^(-(x-h-s)/2).

This is the general solution to the original differential equation, in terms of h, k, and C.

To solve the differential equation

dy/dx = (x-y-1)/(x+y+1)

       dy/dx = dv/ds + k

       x - y - 1 = h + s - v - k - 1 = s - v + (h - k - 1)

        x + y + 1 = h + s + v + k + 1 = s + v + (h + k + 1)

        dv/ds + k = [(h + s - v - k - 1) - (s - v + (h - k - 1))] / [(h + s + v + k + 1) -

        (s + v + (h + k + 1))]

       dv/ds + k = [(2h - 2k - 2)s - 2v] / [-2]

       or

       dv/ds = (v - h + k - s) / 2

        dv/ds = du/ds

        and the equation becomes:

        du/ds = -u/2

        v - h + k - s = Ce^(-s/2)

        or

        y - x - (h - k) = Ce^(-(x-h-s)/2)

This is the general solution to the original differential equation, in terms of h, k, and C.

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Step-by-step explanation:

(18+12√5)(9-6√5)

18(9-6√5)+12√5(9-6√5)

162-108√5+108√5-360

162-360

-198

hope this helps you.

The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle. The area of the triangle is 90 units².

The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle.

\(\rm{ Area \triangle = \dfrac{1}{2} \times base \times height\\\)

For the given triangle if the hypotenuse is assumed as the base, and the altitude is assumed as the height of the triangle, then the area of the triangle will be,

Area of the triangle = 0.5 × 15 units × 12units

                                 = 90 units²

Hence, the area of the triangle is 90 units².

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Step-by-step explanation:

There are 60 * 60 * 24 =  86400 seconds in a day

if the light flashes 5 times every 10 seconds, that means it flashes once every 2 seconds.

It follows the flashes in a day are 86400 / 2 = 43200

The statement "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g is false because, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.

Random assignment in an RCT can help to reduce selection bias, but it does not guarantee the absence of coverage bias.

Coverage bias can occur if the participants who are enrolled in the trial do not represent the population to which the results will be generalized.

For example, if the trial only includes participants who are healthier or more compliant than the typical patient, the results may not be applicable to the broader population.

Therefore, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.

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Answer:

-4.9, negative four and eight ninths, four and seven tenths, 490%

Step-by-step explanation:

4 7/10 =approx. 4.7

-4 8/9 = -4.888889

490% = 4.9

-4.9

Answer:

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon and Decagon

Answer:

1.Regular Polygons.

2.Irregular Polygons.

3.Concave Polygons.

4.Convex Polygons.

5.Trigons.

6.Quadrilateral Polygons.

7.Pentagon Polygons.

8.Hexagon Polygons.

Step-by-step explanation:

Explanation:

The graph of y = -3/5x + 9 is a straight line, so to graph the function we need to identify two points of the line.

Then, we can find two points if we give a value to the variable x and calculate the value of y as:

If x = 5 then:

y = (-3/5)x + 9

y = (-3/5)*5 + 9

y = -3 + 9

y = 6

If x = 10 then:

y = (-3/5)*10 + 9

y = -6 + 9

y = 3

Therefore, we have the points (5, 6) and (10, 3), so the graph of the line is:

Answer:

Step-by-step explanation:

The gradient of the line 3y-12x+7=0 is; 4.

According to the question;

We are responsible to determine the gradient of the line 3y-12x+7=0.

To do this; we must rewrite the equation 3y-12x+7=0 in the slope-intercept form as follows;

3y-12x+7=0

3y = 12x - 7

y = 4x -7/4

By comparison with; y = mx + c;

where, gradient/slope is m;

The gradient/slope of the line 3y-12x+7=0 is; 4.

Therefore, The two solutions are x₁ = -0.5 and x₂ = -1.0. The correct answers are x = -1.0 and x = -0.5.

To solve the equation 2x(x + 1.5) = -1, follow these steps:
1. Distribute the 2x: 2x^2 + 3x = -1.
2. Rearrange the equation to make it quadratic: 2x^2 + 3x + 1 = 0.
3. Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 2, b = 3, and c = 1.
4. Calculate the discriminant: Δ = b^2 - 4ac = 3^2 - 4(2)(1) = 9 - 8 = 1.
5. Calculate the two solutions: x₁ = (-3 + √1) / 4 and x₂ = (-3 - √1) / 4.

Therefore, The two solutions are x₁ = -0.5 and x₂ = -1.0. The correct answers are x = -1.0 and x = -0.5.

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Intermediate value theorem: The theorem states that if a continuous function f defined on a closed interval [a, b], which takes values f(a) and f(b) at endpoints of the interval, then it also takes any value between f(a) and f(b). Bolzano's theorem: Bolzano's theorem states that if a continuous function f(x) has different signs at two points in the closed interval [a, b], then there must be at least one point c in that interval such that f(c) = 0.

Proof of intermediate value theorem using Bolzano's theorem:Let g = f - y, where y is a constant function. Now, g(a) = f(a) - y and g(b) = f(b) - y. If y is chosen such that y = f(a) and y = f(b) has different signs, then g(a) and g(b) will have different signs.So, by Bolzano's theorem, there exists a c between a and b such that g(c) = 0 or f(c) - y = 0 or f(c) = y. As y is any number between f(a) and f(b), f(c) takes all values between f(a) and f(b).Thus, the intermediate value theorem is proved.20. (a) Mean value theorem: It states that if f is a continuous function on a closed interval [a, b] and differentiable on (a, b), then there exists a point c in (a, b) such that f'(c) = [f(b) - f(a)]/[b - a].(b) Using mean value theorem to prove:i) sin x < x for x > 0Let f(x) = sin x. Now, f(0) = 0 and f'(x) = cos x. As cos x is a continuous function on the closed interval [0, x] and differentiable on (0, x), there exists a c in (0, x) such that cos c = [cos x - cos 0]/[x - 0] or cos c = sin x/x or sin c < x. As sin x < sin c, the required inequality sin x < x for x > 0 is proved.ii) ln(1 + x) < x for x > 0t f(x) = ln(1 + x). Now, f(0) = 0 and f'(x) = 1/(1 + x).  Hence, the required inequality ln(1 + x) < x for x > 0 is proved.(c) Deduction e^-x sin x < x/1 + 2 for x > 0As 1 + 2 > e^2, dividing by e^x > 0, we get e^-x < 1/e^2. Hence, (e^-x/1 + 2) < e^-x/e^2.Now, sin x < x, so -x < -sin x and e^-x > e^-sin x.So, \((e^-x sin x) < (xe^-sin x)\) and\((e^-x sin x) < (xe^-x/e^2)\) or e^-x sin x < x/1 + 2 for x > 0.21.

Given f is a continuous function on [a, b] and twice differentiable on (0, 2), such that f(0) = 0, f(1) = 1 and f(2) = 2.Using the mean value theorem, there exists a point c in (0, 2) such that f'(c) =\([f(2) - f(0)]/[2 - 0] or f'(c) = 1.\) As f is twice differentiable on (0, 2), f' is continuous on (0, 2) and differentiable on (0, 2) and by Rolle's theorem, there exists a point d in (0, 2) such that f''(d) = 0. As f'(c) = 1 and f'(0) = 0, we have f''(d) = 1/c. Therefore, there exists a point to in (0, 2) such that\(f^2(xo) = 0.\)

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Stephanie's bill was $12.60.

To calculate Stephanie's bill, we need to find what fraction of Jack's bill her bill was. Since Stephanie's bill is a fraction of Jack's bill, we can use proportions to solve for the unknown value. Let x be Stephanie's bill, then we can write the equation:

x = (1/2) * 25.20

Simplifying, we get:

x = 12.60

Therefore, Stephanie's bill was $12.60.

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The simple interest formula allows us to calculate the interest earned or paid on a loan. According to this formula, the amount of interest is given by I = C · i · t, where C is the principal, i is the annual interest rate in decimal form, and t is the period of time expressed in years.

Where:

• I = interest

• C= initial capital

• t = time in years

• i =annual interest

From the problem we have

The loans for Keen and Kyle differ in time so we will calculate the interest of both loans

To find the difference, we subtract the interest values that Keen and Kyle paid to Mrs. Cruz.

To establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese,

In a dairy factory, the best study that would be a reliable source of evidence is a randomized controlled trial (RCT).In an RCT, the participants are randomly assigned to two or more groups,

where one group receives the intervention (in this case, cheese packaged with thicker material) and the other group receives the standard treatment (cheese packaged with the usual material).

To ensure the reliability of the study, the RCT should be conducted in a double-blind manner, where neither the participants nor the researchers know which group is receiving the intervention. This will prevent any bias that may influence the results.

The participants should also be selected carefully to ensure that they represent the target population of the study. In this case, the participants should be cheese consumers or distributors who are interested in the shelf life of the cheese.

By comparing the shelf life of the cheese packaged with thicker material to that packaged with the usual material, the RCT can establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese.

The results of the study can then be used to inform the dairy factory's packaging practices and improve the shelf life of their cheeses.

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Answer:

Heeeeey :)

Step-by-step explanation:

The point that is 1/4 of the way from A=37 to B=13 is located at 31 on the number line.

To find the location of a point that is 1/4 of the way from A to B on a number line, we can use the following formula:

P = A + (1/4)(B - A)

where P is the location of the point we are trying to find.

In this case, A = 37 and B = 13. So, we can substitute these values into the formula:

P = 37 + (1/4)(13 - 37)

P = 37 + (1/4)(-24)

P = 37 - 6

P = 31

Therefore, the location of the point that is 1/4 of the way from A=37 to B=13 on the number line is 31. We can confirm this by checking that the distance between A and P is one-fourth the distance between A and B, and similarly, the distance between P and B is three-fourths the distance between A and B.

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Step-by-step explanation:

To  do this equation, we could put it in terms of algebra, lets say the large chocolate bars are represented by L and the small bars by S

April

4S + 6L = $16.50

Bill

4S + 3L = $11.25

Looking at this, we can see that the difference between the two purchases is that Bill bought three less large chocolate bars, this means the difference in total cost equals three large chocolate bars. Using this knowledge.

$16.50 minus $11.25 = $5.25

$5.25 = Three Large Bars

Divide this by three to get the cost of one large bar.

$1.75 is the cost of one single large bar.

Answer:

April: 4x+6y=16.5

Bill: 4x+3y=11.25

solving the two equations simultaneously will give you y=1.75

Answer:

1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The joint equations of diagonals are;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Step-by-step explanation:

The equations are;

x² - 7·x + 6 = 0......................(1)

y² - 14·y + 40 = 0.................(2)

Factorizing equation (1) and equation (2) , we get

x² - 7·x + 6 = (x - 6)·(x - 1) = 0

Which are vertical lines at points x = 6 and x = 1

For equation (2) , we get

y² - 14·y + 40 = (y - 10)·(y - 4) = 0

Which are horizontal lines at point y = 4 and y = 10

The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The points of intersection of the equations are;

(1, 4), (1, 10), (6, 4), and (6, 10)

The end point of the diagonals are;

(1, 10), (6, 4) and  (1, 4), (6, 10)

The slope of the diagonals are;

(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5

The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)

y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5

5·y = 56 - 6·x

The other diagonal is therefore;

y - 4 = 6/5×(x - 1)

y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5

5·y = 6·x + 14.

The joint equations of diagonals are therefore;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Answer:

- 3/5

Positive

Step-by-step explanation:

when plotting on a number line, you will start with the first term listed in the equation, in this case it is -3/5

then, if the next term is positive, you will move to the right (aka positive direction), but if the next term is negative then you will move to the left (aka negative direction)

in this question, the next term is positive, so you will move in the positive direction

slope of this line is -3.

Given table:

X, -5 y, 16

X, -4 y, 13

X, -3 y, 10

X, -2 y, 7

slope m = y2 - y1 / x2 - x1

Take any two points (-5,16) and (-4,13).

slope m = 13 - 16 / -4 - (-5)

= -3/-4+5

= -3/1

= -3

Therefore slope of this line is -3.

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