Use the pythagorean theorem to find ad and dc. then find ac using addition. show your calculations.

Answer:

754.27

Step-by-step explanation:

Use coumpound interest formula A=p(1+r)^t

Convert 5% into a decimal (move decimal over to times to the left making it .05)

Plug in numbers A=3500(1+.05)^4

Then you get $4254.27

Subtract by priciple of 3500 and you get left with 754.27

Answer: (e) (i) To represent the inequalities graphically on a coordinate plane, you can use a scale of 2cm to represent 5 units on each axis. To shade the unwanted regions, you can start by drawing the coordinate plane and labeling the x and y axes. Then, you can graph the inequalities by plotting the lines and shading the regions that do not satisfy the inequalities.

(b) 2x + 3y ≤ 30

This inequality represents a line with the equation 2x + 3y = 30. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.

(c) x - 2y ≥ -10

This inequality represents a line with the equation x - 2y = -10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or above the line satisfy the inequality.

(d) y ≤ -2x + 10

This inequality represents a line with the equation y = -2x + 10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.

The set of points that satisfy all three inequalities is the area that is not shaded in the graph.

(ii) To find the maximum number of rabbits the farmer can buy, we need to find the coordinates of the vertex of the feasible region.

The coordinates of the vertex of the feasible region is (x,y) the point where the line 2x+3y=30 and x-2y=-10 intersects.

We can substitute the x-2y=-10 into the 2x+3y=30 equation

2x+3y=30

2x+3y+2y=-10

2x+5y=-10

x=-5y+10

substituting this into one of the equation we have

2(-5y+10)+3y=30

-10y+20+3y=30

-7y=10

y= -10/7

substituting this into x = -5y+10 we have

x = -5(-10/7)+10 = 15

the maximum number of rabbits the farmer can buy is 15

Step-by-step explanation:

Answer:

Geometric proofs can be written in one of two ways: two columns, or a paragraph. A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof, we'll learn the two-column method.

Step-by-step explanation:

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If f(x) = 2x + 5 and three-halves are inverse functions of each other, then the equation is mc^(005)- is 3/2.

If two functions are inverses of each other, then their graphs are reflections of each other across the line y = x. This means that if we start with the graph of one function and reflect it across the line y = x, we will get the graph of the other function.

In this case, the graph of f(x) is a line with a slope of 2 and a y-intercept of 5. When we reflect this graph across the line y = x, we get the graph of the inverse function, which is three-halves.

We know that three-halves(8) = 3, so the equation is mc^(005)- is 3/2.

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Answer:

Step-by-step explanation:

[Already answered]

Answer:

x/7 + 9 = 6

Step-by-step explanation:

Hope this helps! Please give brainliest!

For each increase of one unit on the x-axis (the horizontal axis), the amount on the y-axis (the vertical axis) increases by the slope of the line.

Slope is the amount of change in the y-axis that occurs as a result of a one-unit change in the x-axis. It is also known as the rise over run.

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right. If the slope is zero, the line is horizontal.

The slope of a horizontal line is zero, and the slope of a vertical line is undefined because the x or y coordinate does not change as the other changes.

Therefore, the slope of a line represents the amount by which the value on the y-axis increases for every increase of one unit on the x-axis

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Answer: (h,k) (-1, -8)

Step-by-step explanation:

Answer:

The vertex will be (1,8)

Step-by-step explanation:

hope it helps have a great day!!!

We need to add 4 blue marbles to the bag to make the probability of drawing a blue marble 1/2.

Currently, there are two blue marbles out of a total of eight marbles in the bag, so the probability of drawing a blue marble is 2/8 or 1/4.

Let x be the number of blue marbles we need to add to the bag. After adding x blue marbles, there will be a total of 2 + x blue marbles in the bag, out of a total of 8 + x marbles.

We want the probability of drawing a blue marble to be 1/2, so we can set up the equation:

(2 + x) / (8 + x) = 1/2

Multiplying both sides by (8 + x), we get:

2 + x = (8 + x) / 2

Multiplying both sides by 2, we get:

4 + 2x = 8 + x

Subtracting x from both sides, we get:

4 + x = 8

Subtracting 4 from both sides, we get:

x = 4

Therefore, we need to add 4 blue marbles to the bag to make the probability of drawing a blue marble 1/2.

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There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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The standard form of the given number is  (5 × 10⁻³)/6.

The standard form of 0.005/6 is:

Therefore, the standard form of the given number is  (5 × 10⁻³)/6.

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Answer:

I think it's -0.4 but tell me if I'm wrong

Starting with the first term οf the sequence, which is 13. As a result, the sequence's fοurth term is -2.

The given sequence starts with the first term, which is 13. The term-tο-term rule is 'take away 5', which means we need tο subtract 5 frοm the previοus term tο get the next term in the sequence.

Sο, tο find the secοnd term, we subtract 5 frοm the first term, which gives us 13 - 5 = 8.

Tο find the third term, we subtract 5 frοm the secοnd term, which gives us 8 - 5 = 3.

Tο find the fοurth term, we subtract 5 frοm the third term, which gives us 3 - 5 = -2.

Hence, the sequence's fοurth term is -2.

Overall, we can use the given term-tο-term rule tο find any term in the sequence by applying it successively tο the previοus term.

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Answer:

54 inches

Hope this helps! :)

Step-by-step explanation:

Answer:

30 dollars

Step-by-step explanation:

40% of 100 = 40. 40% of 50 = 20. 50-20 = 30.

Answer:

79.94

Step-by-step explanation:

Answer:

79.94 is the answer to this. ps bills suck

Partial derivative with respect to\(X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ\)

Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)

The first partial derivatives of the function F(X,Y) = X2Y - 3Y2 + X/(X + Y)2 + XY2e-XZ can be found by taking the partial derivative with respect to each of the variables X and Y separately.
For the partial derivative with respect to X, we have:
Partial derivative with respect to X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ
For the partial derivative with respect to Y, we have:
Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)
This completes the calculation of the first partial derivatives of the function F(X,Y).
The first partial derivatives of the functions are given below:

\(F(x, y) = x^2y - 3y^2\)

The first partial derivative with respect to x,

Fx (x, y) = 2xy

The first partial derivative with respect to y,\(Fy (x, y) = x^2 - 6yW = xy^2 e^-xz\)

The first partial derivative with respect to x,

\(Wx (x, y, z) = y^2e^-xz - x^2y^2e^-xz\)

The first partial derivative with respect to y, Wy (x, y, z) = 2xye^-xz

The first partial derivative with respect to z, \(Wz (x, y, z) = -xy^2e^-xz\)

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The slope between the points p(3, y) and q(x, -5) is given as -7/3. To determine one possible value for x and y, we can use the slope formula, which states that the slope (m) between two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points p(3, y) and q(x, -5), we can plug in the values into the slope formula:

-7/3 = (-5 - y) / (x - 3)

To find one possible value for x and y, we can solve this equation for x.

Multiply both sides of the equation by (x - 3) to eliminate the denominator:

-7(x - 3) = -3(-5 - y)

Expand and simplify:

-7x + 21 = 15 + 3y

Rearrange the equation:

7x - 3y = -6

This equation represents the relationship between x and y for any point on the line with a slope of -7/3 passing through the points p(3, y) and q(x, -5).

We can assign any arbitrary value to either x or y and solve for the other variable. For example, if we set x = 0, we can solve for y:

7(0) - 3y = -6
-3y = -6
y = 2

Therefore, one possible value for x is 0 and one possible value for y is 2.

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

59

Step-by-step explanation:

It goes to 59 because the number in the decimals place is a 0, for 0-4 you round down and for 5-9 you round up.

Answer:

59

Step-by-step explanation:

Although the hundredths number is 9, it will be turned into 1 tenth. Unfortunately, 1 is not high enough to be added to the whole number so it becomes 0. In the end, the answer is 59

Answer:

y = 7x - 4

Step-by-step explanation:

To solve the equation of this line ( in point - slope form ) we would have to first identify the slope. If we are given the points ( 0, - 4 ) and ( 1, 3 ) then through the change in y / change in x, we can calculate the value of this slope. Take a look at the steps below;

\(( 0, - 4 ), ( 1, 3 )\\\\Slope = y2 - y1 / x2 - x1,\\\\Slope = - 4 - 3 / 0 - 1,\\Slope = - 7 / - 1\\Slope = 7 / 1\\\\Slope = 7\)

Now that we have the slope of this line, we have assume part of the equation of this line ( that passes through the points ( 0, - 4 ) and ( 1, 3 ) );

\(y = mx + b -\\m = slope, b = y - intercept\)

Plug in the value of slope for " m " in y = mx + b, and determine the y - intercept by plugging in x as 0 and y as - 4, given the point ( 0, - 4 );

\(- 4 = 7 * ( 0 ) + b,\\- 4 = 0 + b,\\b = - 4\)

From this information, we can say that the equation of this line is y = 7x - 4;

Solution, y = 7x - 4

Answer:

The anwser would be 51 i think

Step-by-step explanation:

if im right ls makr brainliest

Answer:51

Step-by-step explanation:

Answer:

8(3v+3w-2)=(8×3v+8×3w-8×2)

Step-by-step explanation:

8×3v=24v.

8×3w=24w. [24v+24w-16]=(8×3v+8×3w-2×8)

8×(-2)=-16.

The sum of the angle measures of the polygon is 540°, the value of x is 5.

The sum of the angle measures of the polygon is 540°.

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180°. = 3× 180°= 540°

If a polygon has x sides, then the sum of its angle measures can be found using the formula:

Therefore, for a polygon with x sides, the equation becomes:

⇒(x-2) * 180° = 540°

Solving for x, we get:

⇒x = (540° + 360°) / 180° + 2

⇒x = 3 + 2

⇒x = 5

So, the polygon has 5 sides.

Therefore, the value of  x is 5.

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Answer:

3ab

Step-by-step explanation:

i hope you don't want to know how i did this :)

Answer:

Solution given:

Since the given triangle is isosceles and right angled triangle

perpendicular [p]=base[b]=x

hypotenuse [h]=6

we have

by using Pythagoras law

p²+b²=h²

x²+x²=6²

2x²=36

x²=36/2

x²=18

x=\(\sqrt{18}\)

x=\(\bold{3\sqrt{2}}\)

The length of side x in simplest radical form with a rational denominator is \(3\sqrt{2}\)

Given the following data:

To determine the length of side x in simplest radical form with a rational denominator, we would apply Pythagorean's Theorem:

Mathematically, Pythagorean's Theorem is given by this formula:

\(c^2 = a^2 + b^2\)

Substituting the given parameters into the formula, we have:

\(6^2 = x^2 + x^2\\\\36=2x^2\\\\18=x^2\\\\x=\sqrt{18} \\\\x=3\sqrt{2}\)

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Answer:

3000

Step-by-step explanation:

it is very simple as the number's hundredth place is more than 5 , hence , it will be rounded up to nearest greater number.

in our case, it is 3000

Answer: 52 seconds.

Step-by-step explanation:

|-3| + 23 = 26. 26 x 2 = 52.