An architect drew the blueprint for a new office building. He used a scale in which 1 inch represents 7.5 feet. The floor of an office in the building will have actual dimensions of 14 feet by 24 feet. What will the dimensions on the blueprint be?
A.
105 inches by 180 inches
B.
21.5 inches by 31.5 inches
C.
6.5 inches by 16.5 inches
D.
1.87 inches by 3.2 inches

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

because it is a triangle we square the lenght and equate to the other side,and square all the other side

X²=20²+10²

X=√20²+10²

=22.36m

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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Note that the phrases that best describe the graph of f(x) = |x| are:

1) Note that the function given above is an Absolute Function, and as given in the attached graph, you'd notice that the graph of an absolute function is always V-shaped. Thus, option A is true.

2) One must also note that where the sign before the modulus is positive, then the graph opens up (as in the case above) otherwise it opens down. Thus, option C is correct.

3) If (x,-y) lies on the function, then f(x) is in proportion with respect to the x-axis. If (-x,y) lies on the function, then f(x) is in proportion with respect to the y-axis.

Put (x,-y) in the given function.

-y = |x| ⇒ -y ≠ y

Thus,  f(x) is not symmetric with regard to the x-axis.

Placing (-x,y) in the given function, we have

y = |x| ⇒ y = y

Because the point (-x,y) lies on the function, therefore (fx) is symmetric with regard to the y-axis. Hence, Option F is correct.

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Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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Answer:

all real numbers

only the range value is with a minimum of -1 and a maximum of 1 unless there's a vertical shift.

The domain of the sine and cosine functions are all real numbers

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the domain of the function be represented as D

Now , the functions are

f ( x ) = sin x

g ( x ) = cos x

where the trigonometric functions have the range as [ -1 , 1 ]

And , sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle

Therefore , the value of D is all real numbers

Hence , the domain is all real numbers

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Answer:

$8

Step-by-step explanation:

if 6 balls= $42

what about 1 ball

you cross multiply

Answer:

D 6,9

Step-by-step explanation:

Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Answer:

8

Step-by-step explanation:

The given monomial is :

The degree of the monomial is the highest power to which a variable is raised to in the monomial. The greatest power in this case belongs to b⁸, which has a power of 8.

Hence, the degree of the monomial is 8

Answer:

15x^4+2x^3-8x^2+2x-15

Step-by-step explanation:

The probability of the customer wants to take snack B is 144/320 as they have already taken snack A

and the probability of the customer who has not taken snack A before

wants to take snack A =108/252

It is the ratio of favorable outcome to total possible outcome of an event.

based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.

hence, probability to take snack B = 144/320

probability to take A =108/252

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a) The probability a person who has eaten snack A before is 59/143.

b) The probability a person who has eaten snack A before is 84/143

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the total number of people that are taken for the event is 572.

The number of people who have eaten snack A before is 236.

The number of people who have not eaten snack A before is 336.

Probability = The number of outcomes of favorable event/ Total number of outcomes

The probability getting a person who has eaten snack A before is

= 236/ 572

= 59/143 [Divide denominator and numerator by 4]

The probability getting a person who has not eaten snack A before is

= 336/ 572

= 84/143 [Divide denominator and numerator by 4]

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Answer:

1) 11

2) 4

Step-by-step explanation:

1) It is 11 because in the first row we ignore the 0 since it is referring to the first digit, so the first row has 7. In the second row, we ignore the one so it would be 4 because the 9, or would be 19, is above 18.

2) It is 4 because there is one person over 65. In the second row we ignore the 7 and there are 3 people in the 7 row.

a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, in item a, the minimum height is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

Item b:

The roots of the function, in item b, are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver, in item c, is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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Both h ≥ –5 and h < 2 represent the area more than or equal to negative 5 and less than 2.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality equation is given below.

h ≥ –5 and h < 2

Then h ≥ –5 represents the area more than or equal to negative 5.

And h < 2 represents the area less than 2.

Then both h ≥ –5 and h < 2 represent the area more than or equal to negative 5 and less than 2.

The graph is given below.

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Answer:

THe Answer is A

Step-by-step explanation:

Answer:

La forma en que relaciono lo que escucho o leo en mi vida es a través de la interpretación de la información, es decir, todo aquello que leo o escucho es procesado, evaluado e interpretado conforme a mi experiencia, vivencias, estudios e ideología, lo que me permite obtener una conclusión de la información que percibo.

Así, no considero todo lo que leo y escucho como hechos comprobados, sino que lo someto a un análisis exhaustivo y completo respecto de su validez y sus implicancias respecto de mi persona.

The equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

A line is the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;

y = mx + b

m is the slope

b is the y-intercept

Given that m=1, b=-3, the required equation will be y = x - 3 or x - y = 3

For the parameter m=1, (-1,2)

y - 2 =1(x+1)

y - 2 = x+1

y =x + 3

Hence the equation of the line for the parameters m=1, (-1,2)  is y = x + 3

For the coordinates (-2,3),(-3,4)

Slope = 4-3/-3+2
Slope = -1

For the intercept;

4 =-1(-3) + b

b = 4 - 3

b = 1

Hence the equation of the line passing the points (-2,3),(-3,4) is y = -x + 1 or x+y = 1

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Answer:

Butter per portion equals 60 cents .

Step-by-step explanation:

A pound of butter is worth $ 5.60.

5.60 dollars are converted to cents, 1 dollar equals 100 cents, then:

- One pound of butter equals 560 cents.

A portion of onion compote requires 1.7 oz of butter.

Convert 1.7 oz to pounds, so:

- 1.7 oz of butter equals 0.10625 pounds.

If a pound of butter is worth 560 cents, how much will 0.10625 pounds of butter be worth.

- Rule of 3 is used:

- 560 cents        1 pound butter

  X cents            0.10625 pounds of butters

X = 560 * 0.10625

X = 59.5 cents

X = 60 cents per portion

Answer:

All you have to do is divide 1 by 26 and that should be the value of x.

Step-by-step explanation:

Can I just say that is a very strange math equation XD

Answer:

a) 341

b) 7243

c) 11018

d) 33000

Megan's walking speed is calculated to be 3¾ miles per hour using proportions.

What exactly is a proportion?

We can apply the relationship between velocity, distance, and time to this issue, where velocity is defined as distance divided by time, as follows:

The following parameters are listed in the text for this issue:

The velocity is thus determined as follows:

Therefore, Megan's walking speed is calculated to be 3¾ miles per hour using proportions.

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Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Answer:

6

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer: please 2.9

Step-by-step explanation:

I think

Answer:

1/36

Step-by-step explanation:

The probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6). The probability of rolling any number twice in a row is 1/6, because there are six ways to roll a specific number twice in a row (6 x 1/36).

Hope this helps

Answer:

(6 x 2) /3  

Step-by-step explanation:

(6 x 2) / 3

(Six times two) divided by three

Use Pemdas.

Parenthesis-Exponents-Multiplication-Division-Addition-Subtraction

6 multiplied by 2 equals 12

12 divided by 3 equals 4.

There are 4 shirts on each shelf.

____________________________________________________________

On the other hand though, if this question is looking for the total amount of shirts in general, it would be 12.

Answer:

its the last one

Step-by-step explanation:

because the percent you have to turn it in to a decimal.

Answer:

0.19444444444

Step-by-step explanation:

Answer:

7/36

Step-by-step explanation:

(7/9)/4

7/36

Answer:

15÷17

Step-by-step explanation:

C A/H....adjacent over hypotenuse

Answer:

Well, I got B. Because it seems the most reasonable answer to this question.

Step-by-step explanation: