Simplify the following expression: 33 + (-5)

Answer:

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

  g(2.95) ≈ 16(2.95 -3) -1 = -1.8

  g(3.05) ≈ 16(3.05 -3) -1 = -0.2

__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

Answer:

121 feet

Step-by-step explanation:

Equation:

484 / 4 = 121

Word Explanation:

If there are 4 sides in a square and the total of all 4 sides is 484, We have to divide 484 by 4 and get 121 feet.

The perimeter of the square fence is P = 88 feet and Tyrone needs 22 feet of fence on each side

The perimeter of a square is given by four times the length of its each side

The equation for the perimeter of the square with the side 'a' is given by

Perimeter of Square = 4a

Given data ,

Let the perimeter of the square be represented as P

Now , the equation will be

Let the side length of the square be a²

The area of the square is A = 484 feet²

Taking square roots on both sides of the equation , we get

A = a²

a² = 484

a = 22 feet

Now , perimeter of the square P = 4a

Substituting the values in the equation , we get

Perimeter of the square P = 4 x 22

Perimeter of the square P = 88 feet

Hence , the perimeter of the square is 88 feet

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Answer: sqrt75 or 8.66

Step-by-step explanation:

The pythagorean theroem states the a^2+b^2=c^2 in this case 5^2+b^2=10^2 where b is the height of the building. So to solve this just simplify

5^2+b^2=10^2

25+b^2=100

b^2=75

\(\sqrt{b}^2\)=\(\sqrt{75}\)

b=8.66

Given that,

Series 1: 3, 5.5, 8..... and series 2: 33/2, 57/2, 81/2.

To find,

The value of n.

Solution,

Let n is the no of terms in both the series.

For 3, 5.5, 8

First term, a = 3 and common difference d = 2.5

Sum of n terms of a series is given by :

\(S=\dfrac{n}{2}(2a+(n-1)d)\)

So,

\(S=\dfrac{n}{2}(2\times 3+(n-1)2.5)\\\\S=\dfrac{n}{2}(6+2.5(n-1))\ ....(1)\)

For 33/2, 57/2, 81/2

First term, a = 33/2 and common difference, d = 12

nth term of a series is given by :

\(a_n=a+(n-1)d\)

For 2nd terms,

\(a_2=\dfrac{33}{2}+(2-1)\times 12\ ....(2)\)

According to question, sum of the first n terms of the arithmetical progression 3, 5.5, 8. .... is equal to the 2nth term of the arithmetic  progression 33/2, 57/2, 81/2

From equation (1) and (2) :

\(\dfrac{n}{2}(6+2.5(n-1))=\dfrac{33}{2}+ 12\\\\\dfrac{n}{2}(6+2.5(n-1))=\dfrac{57}{2}\\\\n(6+2.5(n-1))=57\\\\6n+2.5n^2-2.5n-57=0\\\\2.5n^2+2.5n-57=0\\\\\text{On solving the above quadratic equation, we get the value of x as follows :}\\\\x=4.126,-5.526\)

Neglecting the negative value, we get the value of n = 4.126

or

n = 4

Hence, the value of n is 4.

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

The original fraction is 10/19

Let the fraction be \(\frac{x}{y}\)

Now , according to question

\(\frac{x+2}{y+5}\) =\(\frac{1}{2}\)

⇒ 2(x+2)=y+5

⇒2x-y-1=0-------(1)

and \(\frac{x-4}{y-1}\)=\(\frac{1}{3}\)

⇒3(x-4)=y-1

⇒3x-y-11=0------(2)

subtracting 1 from 2 we get

2x-y-1

3x-y-11

-  +  +

⇒ x=10

putting in (1)

20-y-1=0

y=19

∴ The actual fraction was 10/19

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

Step-by-step explanation:

This problem requires the use of the Pythagorean Theorem to find the lengths of the sides of a piece of property in the shape of a right triangle

Example:

Taylor finds a piece of property in the shape of a right triangle. She finds that the longer leg is 10 m shorter than twice the length of the shorter leg and the hypotenuse is 20 m longer than the longer leg. Find the lengths of the sides of the triangular lot.

Answer:

Obtuse - over 90°

Acute - less than 90°

Right - 90°

Straight - 180°

1. Obtuse

2. Acute

3. Right

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many pairs οf sunglasses must be sοld tο cοver the fixed and variable cοsts in οrder tο reach the break-even pοint.

Assume that X sunglasses must be sοld tο break even.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=>  $9.44 X = $748,374 + $2.19 X

=>  $9.44 X - $2.19 X = $748,374

=>  $7.25 X = $748,374

=>  X = $748,374 / $7.25

=>   X = 103,184

Therefοre, fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

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Let x be the amount loaned at 5% annual interest, then the rest of the loan, $23,500 - x, is loaned at 6% annual interest.

The interest earned from the loan at 5% annual interest is 0.05x, and the interest earned from the loan at 6% annual interest is 0.06($23,500 - x) = $1,410.00 - 0.06x.

The total interest earned is given as $1,280.00, so we can set up the equation:

0.05x + (1,410 - 0.06x) = 1,280

Simplifying and solving for x, we get:

0.05x + 1,410 - 0.06x = 1,280

-0.01x = -130

x = 13,000

Therefore, $13,000 was loaned at 5% annual interest, and $10,500 ($23,500 - $13,000) was loaned at 6% annual interest.

dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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Answer:

3.5 ounces

Step-by-step explanation:

Answer:

Thousandths.

Step-by-step explanation:

The third decimal place, which is three places after the decimal point is called as the thousandths place.

The number 5 is at the thousandths place.

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

D

Step-by-step explanation:

a nickel = 5 and 5 x 40 = 200 so it would be 2.00

Answer:

I REALLY DON'T KNOW IM DOIN IT FOR THE POINTS

Step-by-step explanation:

The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

Answer:

1 = 81 degrees

2 = 99 degrees

3 = 81 degrees

4 = 99 degrees

5 = 81 degrees

6 = 99 degrees

7 = 81 degrees

Answer:

Step-by-step explanation:

1 = 81 degrees

2 = 99 degrees

3 = 81 degrees

4 = 99 degrees

5 = 81 degrees

6 = 99 degrees

7 = 81 degrees

Answer:

6/30

Step-by-step explanation:

20 percent of 30 is 6 ^_^

Hello

        S        a         T

2a + 6  /            /
          /             /       a + 17
        /             /
   V          a         U

you want ST = VU (it's good) and SV = TU (not good)

2a + 6 = a + 17

2a - a = 17 - 6

a = 9

Answer:

6

Step-by-step explanation:

If each grid represents the amount of fuel in each car, each grid means that there is 1 car.

There are 6 tanks of fuel in total, or 6 cars in total.

Answer:

The answer is\sqrt{13}

Step-by-step explanation:

Let's take this problem step-by-step:

If a line is parallel to each other:

 ⇒ their slope must be equal

Thus the line parallel to: \(y=\frac{3}{4}x-4\)

 ⇒ that line's slope: 3/4

The point-slope form is: \((y-y_1)=m(x-x_1)\)

Let's put that line into the point-slope form:

 \((y-7)=\frac{3}{4}(x+1)\)  <== Answer

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Answer:

\(y - 7 = \frac{3}{4} (x+1)\)

Step-by-step explanation:

We are given the equation y = 3/4x-4, and we want to write an equation of a line that is parallel to y=3/4x-4, and that also passes through (-1, 7), in point-slope form.

Point-slope form is written as \(y-y_1=m(x-x_1)\), where \(m\) is the slope, and \((x_1, y_1)\) is a point

If two lines are parallel to each other, it means they have the same slope.

The line y = 3/4x-4 is written in the form slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 3/4 is in the place of where m is, 3/4 is the slope of this line.

It is also the slope of our new line.

So we can substitute 3/4 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=\frac{3}{4} (x-x_1)\)

Now, we need to replace the values of \(x_1\) and \(y_1\) with a point.

Since we are given (-1, 7), and that it passes through the line, it means that we can use its values in the equation.

Note that we have subtraction in this equation, so when we use a negative number, we still write the subtraction sign in front of the minus sign the negative number has. Just because the number is already negative doesn't mean we ignore the minus sign the formula gives.

\(y-7=\frac{3}{4} (x--1)\)

We can simplify this equation, as --1 is the same as +1.

\(y-7=\frac{3}{4} (x+1)\)

The given inequality shows that the values of "x" that satisfy this inequality are all the numbers between 1.25 and 1.5, excluding 1.25 and 1.5.

What is inequality?

In mathematics, inequality refers to a statement that compares the relative size or value of two expressions or quantities. This is typically represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to).

The inequality "1.25 < x < 1.5" represents a range of values for the variable "x". In this scenario, the variable "x" must be a real number greater than 1.25 and less than 1.5. This means that the values of "x" that satisfy this inequality are all the numbers between 1.25 and 1.5, excluding 1.25 and 1.5.

Hence, the given inequality shows that the values of "x" that satisfy this inequality are all the numbers between 1.25 and 1.5, excluding 1.25 and 1.5.

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Answer:

Y = 6

Step-by-step explanation:

Answer:

The volume of the cylinder is given by the formula: V = πr^2h, where r is the radius and h is the height. In this case, the height is equal to the diameter of the hemisphere (which is also the diameter of the paperweight), so we have:

V = π * 9^2 * (2 * 9) = 904π cm^3

The volume of the cone is given by the formula: V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the height is equal to the diameter of the hemisphere, and the radius is half the diameter, so we have:

V = (1/3)π * (9/2)^2 * (2 * 9) = 188π cm^3

To estimate the volume of the hemisphere, we find the average of the volumes of the cylinder and cone:

V = (904π + 188π) / 2 = 546π cm^3

If the radius of the hemisphere is 12 cm, its diameter is 2 * 12 = 24 cm.

If the radius of the hemisphere is x m, its diameter is 2 * x m.

If the radius of the hemisphere is 12.004 ft, its diameter is 2 * 12.004 = 24.008 ft.

If the diameter of the hemisphere is 12 cm, its radius is 12 / 2 = 6 cm.

If the diameter of the hemisphere is x m, its radius is x / 2 m.

If the diameter of the hemisphere is 12.004 ft, its radius is 12.004 / 2 = 6.002 ft.

Answer: A

Step-by-step explanation:

I did it already

Answer:

A

Step-by-step explanation: