What is the greatest common factor of 28 and 60

Answer:

0.05 oz

Step-by-step explanation:

Usually, the greatest number that is allowed for approximation, assuming that the number itself is obtained by approximation, is the greatest possible error of it.

It is usually half the place value of the last digit of the number.

Here we are given [tex]4\frac{1}{2}[/tex] oz which is equal to [tex]4.5[/tex] oz. The last digit is 5 which is at the tenth place (0.1) so the greatest possible error for this would be its half.

[tex]\frac{0.1}{2}[/tex] = 0.05 oz

Answer:

4

Step-by-step explanation:

-3.5/-0.875 = 4

Answer:

The answer is 4 or C

Step-by-step explanation:

Since its a negative-negative equation, the result is a positive number. So take this equation as 3.5/0.875. Your result will be four or C. Hope this helps!

Answer:

for value 36

c makes the perfect square

x2 - 12x +36

= x2 - 2*6x +6^2

= (x-6)^2 #

Answer:  The required value of c is 36.

Step-by-step explanation:  We are given to find the value of c so that the following expression becomes a perfect square trinomial :

[tex]E=x^2-12x+c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of c, we proceed as follows :

[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]

So, for E to be a perfect square trinomial, we must have

[tex]c-36=0\\\\\Righatrrow c=36.[/tex]

Thus, the required value of c is 36.

answer is 2nd equation

30x 6/100x6=180/600

Answer:x=12

Step-by-step explanation:

5x+9-3x=18+15

First of all, in the case of a equation that has one vatiable having one power ,you need to bring all the variable together in one side.

5x-3x=18+15-9

0r,2x=18+6

Or,2x=24

Or,x=24/2

Or,x=12

So it's the solution..

To solve the equation 5x + 9 - 3x = 18 + 15, you simplify both sides of the equation to get 2x + 9 = 33. Then, you isolate x by subtracting 9 from both sides to get 2x = 24, and further divide by 2 to get x = 12. Therefore, x = 12 is the solution.

The question requires the solution for the equation 5x + 9 - 3x = 18 + 15. To start solving this, first simplify both sides of the equation. The left side simplifies to 5x - 3x + 9, which equals 2x + 9. The right side simplifies to 18 + 15, which equals 33.

So, 2x + 9 = 33. To isolate x, subtract 9 from both sides of the equation, and you'll get 2x = 24. Then divide both sides by 2, and you'll get x = 12.

This means that the solution to the equation 5x + 9 - 3x = 18 + 15 is x = 12.

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Answer:

2,085

Step-by-step explanation:

multiply 3 by 600 then 90 then 5 and then u add them all and u get ur answer

The correct answer is 12

Set up a ratio and then solve. See paper attached. (:

Final answer:

H varies directly as L, and using the constant of direct variation from the given values (H=20 when L=50), we calculated the value of H to be 12 when L is 30.

Explanation:

The concept we are dealing with here is direct variation, which means we can set up a proportion based on the relationship that H varies directly as L. Given that H=20 when L=50, we can determine the constant of variation k by dividing H by L (H = k*L), which gives us k = 20/50 or k = 0.4. With the constant of variation, we can then find the value of H when L=30.

To do this, we use the formula for direct variation again with our constant k and the new value of L:

H = k * L = 0.4 * 30 = 12

Therefore, when L is 30, H is 12.

Answer:

y = -x - 2.

Step-by-step explanation:

The function rule that describes the patter in the table is: y = -x - 2.

To prove that, we're going to test each given point:

For x= -2 ⇒  y = -(-2) - 2 = 0  ✅

For x = -1 ⇒ y = -(-1) - 2 = -1 ✅

For x = 0 ⇒ y = -(0) - 2 = -2 ✅

For x = 1 ⇒ y = -(1) - 2 = -3 ✅

For x = 2 ⇒ y = -(2) - 2 = -4 ✅

Then, we have just proved that the function rule that describes the patter in table is y = -x - 2

Answer:

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

5x^3/x^3(7+x)

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

Answer:

A. 1/x = 2/6

Step-by-step explanation:

Given the sides of the smaller parallelogram:

1 in and 2 in

Given the sides of the bigger parallelogram:

x in and 6 in

By Comparison of similar sides

I.e. the slant sides (1in and x in) and the base (2in and 6in) of both parallelogram.

1/x = 2/6

Hence, the scale factor proportion for the enlargement is 1/x = 2/6.

Solving further to get the value of x

Simplify both sides

1/x = ⅓

Multiply both sides by x

1/x * x = ⅓ * x

1 = ⅓x

Multiply both sides by 3

1 * 3 = ⅓x * 3

3 = x

So x = 3 in

Answer:

A. 1/x = 2/6

Step-by-step explanation:

9+1/2x=35

x=52

hope this helps

Answer:

Vertical= 61.43 miles

Horizontal=43.02 miles

Step-by-step explanation:

We use the trigonometric ratios for a right angled triangle to calculate the components.

The vertical is the adjacent while the horizontal is the opposite.

The vertical is calculated as follows:

V= 75 Cos 35° =61.43 Miles

The magnitude of the horizontal H is calculated as follows:

H= 75 Sin 35° = 43.02 miles

Final answer:

Using trigonometric functions, the horizontal component of the ship's journey is found to be 61.44 miles to the east, and the vertical component is 43.02 miles to the north.

Explanation:

A ship leaving port sails for 75 miles in a direct 35° north of due east. To find the magnitude of the vertical and horizontal components, one can use trigonometric functions based on the angle provided. The horizontal (east) component can be found using the cosine function, and the vertical (north) component can be calculated using the sine function.

To calculate the horizontal (east) component: Horizontal Component = 75 miles * cos(35°) = 75 * 0.8192 = 61.44 miles.

To calculate the vertical (north) component: Vertical Component = 75 miles * sin(35°) = 75 * 0.5736 = 43.02 miles.

Therefore, the ship’s vertical component of movement is 43.02 miles to the north, and the horizontal component is 61.44 miles to the east.

1. Only constraint 2 would be met if 18 pairs of leather boots and 36 pairs of running  shoes were ordered.

2. Only constraint 1 would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

Data and Calculations:

Total pairs of shoes required = 48 pairs

Running shoes required (r) = 2 of leather boots

Leather boots required (b)= 1/2 of running shoes

Constraint 1:

The total pairs of different shoes required:

Running shoes = 32r

Leather boots = 16b

Total pairs = 32r + 16b = 48

Constraint 2:

Ratio equation:

Running shoes = 2r

Leather boots = b

Equation = 2r + b = 48

Thus, Constraint 2 satisfies the first order, while Constraint 1 satisfies the second order. The two constraints do not satisfy the two orders.

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Amanda needs 48 pairs of shoes total, with twice as many running shoes as leather boots. Constraint 1 is x + y = 48, and constraint 2 is y = 2x. An order of 18 boots and 36 running shoes meets only constraint 2, while 12 boots and 36 running shoes meet both constraints.

Amanda needs to order a total of 48 pairs of shoes, with twice as many pairs of running shoes as leather boots. To set up the equations, let x represent the number of pairs of leather boots and y represent the number of pairs of running shoes.

Constraint 1:

The total number of pairs of shoes:

x + y = 48

Constraint 2:

The ratio of the number of running shoes to leather boots:

y = 2x

To check which constraints are met by given orders:

1. For 18 pairs of leather boots (x = 18) and 36 pairs of running shoes (y = 36):

Using constraint 1: 18 + 36 = 54. This does not meet constraint 1.

Using constraint 2: 36 = 2(18). This meets constraint 2.

2. For 12 pairs of leather boots (x = 12) and 36 pairs of running shoes (y = 36):

Using constraint 1: 12 + 36 = 48. This meets constraint 1.

Using constraint 2: 36 = 2(12). This meets constraint 2.

The value of n and the distance from Point B to Point C cannot be determined without specific coordinates for these points. Given that B is the midpoint between points A and C, the x-coordinate for Point B should be n/2. The distance between the points would be calculated using the distance formula derived from the Pythagorean Theorem.

To calculate the distance between points in a graph, we typically use the distance formula, which is derived from the Pythagorean Theorem. From our given information, Point A lies on the y-axis and has the same y-coordinate as Point B. Point C is graphed at (n, -3). Given that the distance is the same from Point B to both points A and C, this implies that Point B is the midpoint between Points A and C. The coordinates of the midpoint are obtained by averaging the x and y coordinates of the two points. Therefore, the x-coordinate of Point B must be n/2.

The distance from Point B to Point C (or similarly to Point A) can be obtained using the distance formula: sqrt((x2−x1)² + (y2−y1)²), where x1, y1 are the coordinates of one point and x2, y2 are the coordinates of the other point.

However, without concrete values for some of these points in the given equation, we cannot provide a specific numerical value for the distance or n. This calculation depends specifically on the placement of the points on the graph.

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Answer:

y = -2x + 1

Step-by-step explanation:

Then any equation of the form y = -2x + b, b≠1 will create a system with no solution.  Hence the values of m and b are m = -2, b ≠ 1.

hope i helped

Answer:

Option B and E

Step-by-step explanation:

As we know a system of two parallel lines has no solution.

In other words two lines having same slope will have no solution.

In this question equation of one line is

y = -2x + b

So another line having same slope (-2) will have no solution.

Option B and E are the correct options.

For this case we must subtract the following expression:

[tex](-2x ^ 2 + 9x-3) - (7x ^ 2-4x + 2) =[/tex]

We must bear in mind that:

[tex]- * + = -\\- * - = +[/tex]

We rewrite the expression:

[tex]-2x ^ 2 + 9x-3-7x ^ 2 + 4x-2 =[/tex]

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of major is placed:

[tex]-2x ^ 2-7x ^ 2 + 9x + 4x-3-2 =\\-9x ^ 2 + 13x-5[/tex]

Answer:

[tex]-9x ^ 2 + 13x-5[/tex]

Answer: [tex]=-9x^2+13x-5[/tex]

Step-by-step explanation:

First, you need to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Then, to subtract the polynomials given, the first step is to distribute the negative sign:

[tex](-2x^2+9x-3)-(7x^2-4x+2)=-2x^2+9x-3-7x^2+4x-2[/tex]

And finally, you need to add the like terms.

With this procedure,  you get the following result:

[tex]=-9x^2+13x-5[/tex]

We must find the slope of the graph first, we can do this by finding two perfect points and inputting those points into the formula y2 - y1/x2 - x1

Perfect point #1: (0,1)

Perfect point #2: (2,5)

As mentioned above, input these numbers into our formula.

5-1 = 4

2 - 0 = 2

4/2 = 2

So, the slope of the graph is 2.

Now, we must find the y-intercept which can be found based on where the line intersects with the y-axis. As we can see, the line intersects at (0,1) therefore the y-intercept of the graph is 1.

We now form a linear equation:

y = 2x + 1

However, since this is linear equality graph we will replace the equal sign with an inequality symbol. The inequality symbol we can use is based on the direction of the shaded area. If shaded up, we use the "greater than symbol", if down then we use the "less than symbol".

The line also matters, if the line is dotted we use the normal inequality symbol, but if it is straight then we use one of the "equal to" inequality symbols.

As for our graph, we have a dotted line with the shaded area upwards. Therefore, we will be using the greater than symbol and not a "equal to" symbol.

So, our answer would be y > 2x + 1

Answer:

19600

Step-by-step explanation:

140 squared = 140 x 140 = 19600

Answer:

0

Step-by-step explanation:

Integers are counting numbers, opposite of counting numbers, and 0.

Here is your answer in the picture

Answer:

6

Step-by-step explanation:

Divide -12/-2 to get 6.

Simplify -12\div -2−12÷−2 to 66.

Answer:

Part 1) [tex]24,000(0.908)^{5}> 15,000[/tex]

Part 2) No

Step-by-step explanation:

step 1

Let

x ----> the time in years

y ----> the area of the forests is square miles

we know that

The equation that represent this situation is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

we have

[tex]a=24,000\ mi^{2}[/tex]

[tex]b=100\%-9.2\%=90.8\%=90.8/100=0.908[/tex]

substitute

[tex]y=24,000(0.908)^{x}[/tex]

The inequality that represent the situation is

[tex]24,000(0.908)^{x}> 15,000[/tex]

step 2

Verify if the state will be  able to keep their funding from the nonprofit wildlife organization in 5 years

For x=5 years

[tex]24,000(0.908)^{5}> 15,000[/tex]

[tex]14,813> 15,000[/tex] ----> is not true

therefore

The state will be not able to keep their funding from the nonprofit wildlife organization in 5 years

Answer:

24,000(0.908) > 15,000; no

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

The 40 is the adjacent side of the triangle that can be drawn and the 9 is the opposite side.

The hypotenuse =  sqrt (40^2 + 9^2) = 41.

sine = opp/hyp = 9/41 = 0.2195.

cosine = 40/41 = 0.9756.

tangent = 9/40 =0.2250.

cosec = 1/ sine =  41/9 = 4.5556.

secant = 1  / cosine = 41/40 = 1.0250.

cotangent = 1 / tangent =  40/9 = 4.4444.

The decimal forms are  correct to the nearest ten thousandth.

The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.

The three sides of the right-angled triangle are:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ =  Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Tan θ = Perpendicular/Base or Sin θ/Cos θ

Cot θ = Base/Perpendicular or 1/tan θ

Sec θ = Hypotenuse/Base or 1/cos θ

Cosec θ = Hypotenuse/Perpendicular or 1/sin θ

According to the Pythagoras theorem, we can say that in a right-angled triangle:

Hypotenuese² = Base² + Perpendicular²

We have to find the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.

With the angle being θ, we have drawn a figure of the case. (attached)

In the right-angled triangle AOB, with respect to angle θ,

Hypotenuse: AO, Perpendicular: AB, and Base: BO

First we derive the value of AO, using the Pythagoras theorem,

AO² = AB² + BO² = 9² + 40² = 81 + 1600 = 1681 = 41²

∴ AO = 41 units.

Now we find the value of the six trigonometric functions, with respect to the angle θ.

sin θ = Perpendicular/Hypotenuse = AB/AO = 9/41

cos θ = Base/Hypotenuse = BO/AO = 40/41

tan θ = sin θ/cos θ = (9/41)/(40/41) = 9/40

cot θ = 1/tan θ = 1/(9/40) = 40/9

sec θ = 1/cos θ = 1/(40/41) = 41/40

cosec θ = 1/sin θ = 1/(9/40) = 40/9.

∴ The values of the six trigonometric functions are:

sin θ = 9/41, cos θ = 40/41, tan θ = 9/40, cot θ = 40/9, sec θ = 41/40, cosec θ = 41/9.

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Answer:

ALL REAL NUMBERS

Step-by-step explanation:

Any quadratic function is ALWAYS R.

To identify geometric figures in a diagram, know the definitions and characteristics of each shape like a circle, triangle, and rectangle. By recognizing these characteristics, you can determine which shapes are in the diagram.

In order to identify which geometric figures are drawn in a diagram, you need to know the basic definitions and characteristics of geometric shapes. For instance, a circle is a figure in which all points are equidistant from a single point in the center. A triangle is a figure formed by three straight lines. A rectangle has four sides and all the angles are right angles. A square is a special type of rectangle where all four sides are equal. By identifying these various characteristics, you can determine which geometric shapes are represented in the diagram.

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Answer:

It is b.

Step-by-step explanation:

When x is negative x^5 will also be negative.

f(x) = x^5 - 3x^3 + 2x + 4

As x  --> -∞ x^5 will  be the main factor for f(x) --->  -∞ .

Similarly  x^5 will have the greatest influence when x ---> ∞, so f(x) ---> ∞.

Answer:

b

Step-by-step explanation:

The end behaviour is what happens when x gets larger and positive ( right hand end ) or larger and negative ( left hand end ) Tis is called the end behaviour as x → + ∞ and x → - ∞ respectively

For a polynomial the end behaviour is determined by the term of greatest degree.

For the given function

f(x) = [tex]x^{5}[/tex] - 3x³ + 2x + 4 ← degree 5 polynomial

The leading coefficient is positive

• Odd degree, positive leading coefficient, then

as x → - ∞, f(x) → - ∞

as x → + ∞, f(x) → + ∞

----------------------------------------------------------------------

• Odd degree, negative leading coefficient, then

as x → - ∞, f(x) → f(x) → + ∞

as x → + ∞, f(x) → - ∞

Answer:

Beena = 19 years old

Seema = 28 years old

Step-by-step explanation:

Beena = x

Seema = x + 9

x + 9 + 10 = 2x

19 + x = 2x

2x - x = 19

x = 19

Answer:

x = 10

Step-by-step explanation:

The axis of symmetry is the vertical line that passes through the vertex.  We can readily see that the x-coordinate of the vertex is 10.

Therefore, the axis of symmetry here is x = 10.

Answer:

D=[tex]\sqrt{(147-30\sqrt{10}}[/tex]

Step-by-step explanation:

Here we are required to find the distance between two coordinates. We will use the distance formula to find the distance

The distance formula is given as

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here we are given two coordinates as

[tex](6,5\sqrt{5} ) , (4,3\sqrt{2} )[/tex]

Substituting these values in the Distance formula given above we get

[tex]D=\sqrt{(6-4)^2+(5\sqrt{5} -3\sqrt{2}) ^2}[/tex]

[tex]D=\sqrt{(2)^2+(5\sqrt{5})^2+(3\sqrt{2})^2-2*5\sqrt{5}*3\sqrt{2}}\\[/tex]

[tex]D=\sqrt{4+125+18-2*15\sqrt{10}}\\D=\sqrt{147-30\sqrt{10}}\\[/tex]

Hence this is our answer

answer :

2 square of 3 is the answer

step-by-step explanation :

[tex]\sqrt({x} _{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} \\\\\sqrt({4} - 6})^{2} + (3\sqrt{2} - 5\sqrt{2} )^{2} \\\\= \sqrt(-2})^{2} + (-2\sqrt{2} )^{2} \\\\\\= \sqrt4 + 8 \\\\\\\\\\= \sqrt12 \\\\\\\\= 2\sqrt{3}[/tex]

The average rate of change in f(x) over the interval [1, 5] is -1

Hi! Let me help you to understand this problem. Here we have the following function:

[tex]f(x) = 17-x[/tex]

We need to compute the Average Rate of Change (ARC) in [tex]f(x)[/tex] over the interval [tex][1, 5][/tex]. So what is the average rate of change of a function? In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:

So:

[tex]ARC=m=-1[/tex]

This can also be calculated as:

[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ \\ ARC=\frac{17-5-(17-1)}{5-1} \\ \\ ARC=-1[/tex]