(x - 12)(x + 5)/(x - 3)³≤0

Answer:

The lace is 36 cm long and 1 cm = 10 mm. So, 36 cm = 360 mm.

He can cut the lace into 18 mm pieces, so he can cut 360 mm / 18 mm = 20 pieces of 18 mm lace from the 36 cm lace.

Answer:

1 cm - 25 miles

4 cm - 25 x 4 = 100 miles

The required distance is 100 miles.

Answer: 3

Hope this helps :)

Step-by-step explanation:

1+2+3+4+5=15

15/5=3

The square root of the numbers are 2. 45, 2. 65, 2. 82, 3 and 3. 16 respectively.

The square root of a number is described as the factor that when multiply by itself would give the original

It is represented with the symbol, "√".

To determine the square root of a number is to find the opposite of the square of that same number.

It is also described as the number having the value of its power or exponent as 1/2

From the information given, we have to determine the square root of the numbers,  we have;

a. √6

The square root of the number is 2. 45

b. √7

The square root of the number is 2. 65

c. The square root of 8

√8 = 2. 82

c. The square root of 9

√9 = 3

d. The square root of 10

√10 = 3. 16

Hence, the square root is the opposite of squaring the number

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Answer:

Step-by-step explanation:

Answer:

4x + 36 = 100

Step-by-step explanation:

Considering how you have already earned 36 points, there will be no variable for it present. The x stands for the amount of times you go see a movie in the theater.

Answer:

You need to see 16 more movies to earn 100 points.

Step-by-step explanation:

you earn 4 advantage points every time you see a movie at the theater.

You need to earn 100 points to get a free movie pass.

Currently, you have 36 advantages points.

If you watch m movies you get = 4m points

You have 36 points so you need = 100 - 36 more points

So the equation will be = 4m = 100 - 36    [after combining like term]

4m = 64 [divide both side by 4]

m = 16

You need to see 16 more movies to earn 100 points.

Answer: The answer to the computation 348 + 598 is 946.

Step-by-step explanation:

To obtain an estimate for the computation 348 + 598, we can round the two numbers to the nearest ten.

348 rounded to the nearest ten is 350

598 rounded to the nearest ten is 600

So, our estimate for the sum of 348 + 598 is 350 + 600 = 950

Using a calculator, the actual computation is 348 + 598 = 946

Our estimate of 950 is 4 more than the actual answer of 946. This means that our estimate is slightly higher than the actual answer. This is not a big difference and it is reasonable as the numbers are rounded to nearest 10.

Answer:

Nose inglés lo siento xdddddddddddddddddddddd

The border should be 6 inches wide.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, A picture is to be put on a poster board that is 18 in. by 22 in. there is to be an even amount of poster board around the picture, the area of the picture is 192 in.²

Let the marginal space left is x in

Therefore,

(18-x)(22-x) = 192

396 -18x - 22x + x² = 192

x² - 40x + 204 = 0

Factorizing the expression, we get,

x = 34 or x = 6

(Note :- Neglecting 34 because 34 is grater than the dimensions given)

Therefore, the marginal space is 6 inches.

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F(x) = x³ on the interval [-2, 1], x = -2 and x = 1, the absolute maximum value is 1 and the absolute minimum value is -8.

A function's critical numbers are the independent variable values at which the function is not continuous, or when the derivatives are equal to 0 or undefined.

1. For the function f(x) = x³ on the interval [-2, 1], the critical numbers are x = -2 and x = 1. The absolute maximum value is 1 and the absolute minimum value is -8.

2. For the function f(x) = x² - 2x² + 3 on the interval [-1, 2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -2.

3. For the function f(x) = 5 - 2x on the interval [-1,2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -3.

4. For the function f(x) = x² - 3x² on the interval [-1, 3], the critical numbers are x = -1, x = 0, and x = 3. The absolute maximum value is 0 and the absolute minimum value is -3.

5. For the function f(x) = 2cosx + x on the interval [0,2], the critical numbers are x = 0 and x = 2. The absolute maximum value is 3 and the absolute minimum value is -1.

6. For the function f(x) = 3x³ - 20x³ on the interval [-2, 2], the critical numbers are x = -2 and x = 2. The absolute maximum value is -4 and the absolute minimum value is -32.

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Answer:

length = 6 cm , breadth = 4 cm

Step-by-step explanation:

the area (A) of the large rectangle = length × breadth

here length = 12 cm and breadth = 4 + x , then

A = 12(4 + x) cm²

the area (A) of the smaller rectangle = x(x + 2)

given area of larger is 4 times area of smaller then

12(x + 4) = 4x(x + 2) ← distribute parenthesis on both sides

12x + 48 = 4x² + 8x , that is

4x² + 8x = 12x + 48 ( subtract 12x + 48 from both sides )

4x² - 4x - 48 = 0 ( divide through by 4 )

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

but x must be greater than zero, so x = 4

dimensions of smaller rectangle are

length = x + 2 = 4 + 2 = 6 cm

breadth = x = 4 cm

Answer:

A rational consumer is an economic concept that presupposes that when making a choice, consumers will always focus primarily on the maximisation of their private benefits. In decision making, rational consumers select the option that will bring the most utility and satisfaction to them.

The required value of y for the angle is 18.

The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

By Corresponding angles

7x = 3x + 36

4x = 36

x = 9

And

Angle in straight line

(6y + 9)+(3x+36) = 180

(6y + 9)+(27+36)

6y + 72 = 180

6y = 108

y = 18

Thus, required value of y is 18.

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Answer:

[tex]\boxed{x^2 - x - 6}[/tex]

Step-by-step explanation:

If a is the root of a polynomial then x-a is a factor of that polynomial

Since - 2 is a root, x -(-2) = x + 2 is a factor

Since 3 is a root, x - 3 is a factor

Multiplying the factors of a polynomial gives you the polynomial equation

So the polynomial equation is

[tex](x + 2)(x-3)[/tex]

Apply FOIL method:
[tex](x + 2)(x-3) \\\\= x\cdot x+ x\left(-3\right)+2x+2\left(-3\right)\\\\= x^2 -3x + 2x -6\\\\x^2 - x - 6\\\\Answer: \boxed{x^2 - x - 6}[/tex]

The amount of the discount, in dollars and cents is $14.77

Total amount paid for the ticket = $32

Percentage discount = 30% of x

Percentage processing fee = 5%

Total amount paid = x - (30% of x) + 5% of x

32 = x - 0.3x + 0.05x

32 = 0.65x

divide both sides by 0.65

x = 32/0.65

x = 49.23076923076923

Approximately,

x = $49.23

Therefore,

Percentage discount = 30% of x

= 0.3 × $49.23

= $14.769

Approximately,

$14.77

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Answer:18,9

Step-by-step explanation:

9x1=9 9x2=18

The ratio for each product, so that they can be compared to the new brand, is given as follows:

The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.

Hence, for the products in this problem, the ratio of protein to carbs is applied by the division of the amounts of protein by cards.

For each product, the ratios are obtained as follows:

Hence they can be compared to the new product, as all the ratios have a denominator of one.

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statement CBA ≅ TWR is true.

The theorem that states that two triangle is congruent when there three corresponding sides are equal and all three corresponding angles are also equal.

given, triangle ABC and Triangle RWT both are right-angled.

we examined that three corresponding sides of ABC is equal to the corresponding sides of RWT and same for the three corresponding angles.

we measured, right angle A = right angle R

base length AB = base length RW

hypotenuse BC = hypotenuse WT

Side length AC = side length RT

angle C = angle T

angle B = angle W

as per the properties of congruence theorem ABC and RWT are congruent.

hence the statement CBA ≅ TWR is true.

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3/2 does not have any factors because it is a fraction and factors are integers that can divide a number evenly. Only integers can have factors, fractions cannot.

Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.

A number is considered to be a factor if the division of that number by that number results in no residue. If we get a product when we multiply two whole numbers, then the numbers we are multiplying are factors of the product since they are divisible by the product. In other words, we get a product when we multiply two whole numbers. Multiplication and division are the two techniques that may be used to discover factors.

Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.

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Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

The z score for a student who received a score of 310 is 0.75

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The z score shows by how many standard deviation the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that the eighth-grade math test is Normal, (282, 40), hence mran = 282, stand. deviation = 40

For a score of 310:

z = (310 - 282) / 40 = 0.75

The z score is 0.75

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The angles forming the triangle must be equal to prove that they are parallel.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given here: AX/AB=XY/BC=AY/AC

Thus the triangles are similar (ΔAXY≈ABC)

Therefore ∠x=∠B & ∠Y=∠C , so we can conclude that the two lines (XY||BC)

Hence, The angles forming the triangle must be equal to prove that they are parallel.

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Answer:

Step-by-step explanation:

Problem 1

The resolution formula for arcseconds is 1 radian = 206265 arcseconds.

To convert 1.22 radians to arcseconds, we can use the conversion ratio of 1 radian = 206265 arcseconds: 1.22 radians x 206265 arcseconds/radian = 252438.3 arcseconds

Problem 2

a. Literal equation: D = (Wavelength / (2* arcsecond))

Variable to solve for: D (diameter of camera lens)

b. Chlorophyll reflects green light. The wavelength of green light on the electromagnetic spectrum is approximately 550 nanometers.

c. D = (Wavelength / (2* arcsecond))

D = (550 x 10^-9 meters / (2* 6 x 10^-6 radians))

D = (550 x 10^-9 meters / 12 x 10^-6 radians)

D = (550 / 12) x 10^-9 meters / 10^-6 radians

D = 45.83 x 10^-3 meters or 0.04583 meters

Problem 3

The graph would have wavelength in nanometers on the x-axis and diameter of lens or mirror in meters on the y-axis.

The graph would start at 100 nanometers and end at 10,000 nanometers on the x-axis and the y-axis would start at 0 and end at the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond.

The graph would show that as the wavelength increases, the diameter of the lens or mirror needed to obtain a resolution of 1 arcsecond would decrease. At a wavelength of 10,000 nanometers (10 microns), the diameter of the camera would be 0.04583 meters.

The spatial resolution of a telescope depends on the size of the telescope's aperture and the wavelength of light being detected.

The spatial resolution of a telescope has an inverse relationship with the wavelength of light being detected and the telescope's diameter. As the wavelength increases, the spatial resolution decreases, and as the diameter of the telescope increases, the spatial resolution increases.

The spatial resolution for our eyes is about 1 arcminute.

Spatial resolution is related to remote sensing in that it refers to the ability of a sensor to distinguish between two objects that are close together. A higher spatial resolution allows for more detailed information to be gathered from an image.

The GOES (Geostationary Operational Environmental Satellite) detects weather patterns, temperature, humidity, and other atmospheric conditions. It uses remote sensing technology to gather and transmit data to meteorologists for weather forecasting and monitoring.

Answer:

Problem 1 - If 1 radian = 206265 arcseconds, what is the resolution formula for arcseconds? Convert 1.22 Radian to arcseconds using ratio. Show your work with units.

Problem 2 - A biologist wants to study deforestation with a satellite camera with a pixel resolution of 10 meters/pixel, which at the orbit of the satellite corresponds to an angular resolution of 6 arcseconds. You have already determined the value for arc seconds from problem number one. To measure the loss of plant matter, she detects the reflection by the ground of chlorophyll, which is the most intense at a wavelength of ___________ (1 nanometer = 10-9 meters) [Use the Electromagnetic Spectrum Below to fill in the blank]. To determine the wavelength, use the electromagnetic spectrum visible light section; what color should chlorophyll reflect? Determine the wavelength using the diagram below. Calculate: What is the diameter of the camera lens that will ensure this resolution at the orbit of the satellite?

There are several steps you need to show for calculating the diameter of the camera lens to receive full credit for problem 2

a. Write the literal equation for the problem. What variable are you solving for? It would help if you manipulated the formula to solve this problem. Show your manipulation in steps.

How to solve literal equations help here.

b. What color should chlorophyll reflect? _____________ Where is the wavelength on the spectrum as far as nanometers? ___________ (this is the wavelength you will use for calculation). Not everyone will have the same wavelength, but it should be similar.

c. Use your literal equation and solve the diameter of the camera lens (You should show all work, and your answer should have one significant figure with units in your response). Circle the answer.

Problem 3 –Since you have already determined the diameter of a lens required for an object with your nanometers from problem #2, you can use this direct relationship to determine the necessary diameter to 10 microns (10 microns = 10,000 nanometers). Choosing the diameter of the lens depends on the wavelength. It would help if you constructed a graph showing the diameter of the lens or the mirror in meters needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 200 nanometers to infrared wavelengths of 10 micrometers.

Question: Construct a graph that shows the diameter of a lens or mirror needed to obtain a resolution of 1 arcsecond from far-ultraviolet wavelengths of 100 nanometers to infrared wavelengths of 10 microns (10,000 nanometers). From orbit, a human subtends an angle of 1 arcsecond and emits infrared energy at a wavelength of 10 microns. How large would the camera be to resolve a human by his heat emission?

To solve this problem, you will need to determine

1. Set up graph: Which variable would be on X and Y? Which variable is dependent/independent? Use units!

2. Label the graph with the appropriate scale, including a title.

3. Plot point versus draw a line of best fit starting at zero to determine the answer.

1. What does the spatial resolution of a telescope depend on?

2. The spatial resolution of a telescope is proportional to the wavelength of light being detected divided by the telescope's diameter. Is this a direct or inverse relationship? How does that relate to wavelength versus lens diameter?

3. What is the spatial resolution for our eyes?

4. How is spatial resolution related to remote sensing? (from Module 3 reading assignment)

5. How is the GOES satellite related to this lesson? What exactly does the GOES detect?

When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

Answer:  48 square inches

Step-by-step explanation:

To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.

area of triangle L x W = 6x4=24

area of rectangle LxW =6x4=24

24+24=48

The radius of the cylinder is 1.59 centimeters.

Remember that for a cylinder of radius R and height H, the volume is given by the formula:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is 76cm, and the volume is 600cm³, then we can replace these two in the equation to get:

600cm³ = 3.14*(76cm)*R^2

Solving for R, we will get:

R = √( 600cm³/3.14*(76cm)) = 1.59 cm

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The radius of the cylinder is r=50.129

The radius of the cylinder is the radius of a base. The altitude of the cylinder is a perpendicular segment from the plane of one base to the plane of the other and the height of the cylinder is the length of the altitude. The axis of a cylinder is the segment containing the centers of the two bases

The volume of a cylinder is 600,000.

The height is 76cm and the radius is unknown. How do you solve it?

The volume of a right cylinder can be determined by πr²h,

where

r is the radius,

h is the height, and

pi is a constant.

So:

76πr²=600000

πr²=600000/76=7894.736

r²=2512.972

r=50.129 cm^2

Hence, the radius is 50.129 cm^2

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Answer:

Not sure what you meant and could of used some specifics but I got this with my experience in algebra and geometry.

9906513923.77

98765 times triangle A 32598765÷325

Customers who purchase items with discount of  credit has 30 days to repay the balance. However, if clients pay for their products within 10 days,

A trade discount, often referred to as a functional reduction, can be applied as a fixed percentage or flat rate deduction from the a seller's initial catalogues list price, in which case the trading discount amount is calculated by multiplying the list price by the percentage difference. Calculating the trade discount requires knowledge of both the item's original list price and the trade discount percentage. The list price is multiplied with the trade discount % in decimal form to arrive at the trade discount.

Here,

they will receive a 2% discount. Customers need only pay $9,800

if they buy $10,000 from Group A underneath the terms 2/10 gross 30 and pay within ten days ($10,000 x 0.98 = $9,800).

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Answer: To find the perimeter of a triangle, we need to add the length of all three sides of the triangle.

To find the length of each side, we can use the distance formula which is the square root of (x2-x1)^2 + (y2-y1)^2.

The distance between point A (9,-2) and point B (5,1) is: √((9-5)^2 + (-2-1)^2) = √16 + 9 = √25 = 5.

The distance between point B (5,1) and point C (9,-3) is: √((9-5)^2 + (-3-1)^2) = √16 + 16 = √32 = 5.66.

The distance between point C (9,-3) and point A (9,-2) is: √((9-9)^2 + (-3- -2)^2) = √1 + 1 = √2 = 1.41

The perimeter is the sum of the length of all three sides:

Perimeter = 5 + 5.66 + 1.41 = 12.07

Round the answer to two decimal places, the perimeter of the triangle is 12.07.

Step-by-step explanation: