1. There are 2 floors in the initial building.
The workers can build 3 floors each week.
When will the building have 15 more floors
than the INITIAL building?
week #
2
5
0 1
8
2
?

Answer:

[tex]\sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

Explanation:

[tex]\sf \rightarrow x^2 + 2x +6 = 0[/tex]

[tex]\sf use\:quadratic\:formula: x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \: \: ax^2 + bx + c = 0[/tex]

comparing identify:

Substitute inside the formula:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{2^2 - 4(1)(6)}}{2(1)}[/tex]

evaluate:

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{4 - 24}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{- 20}}{2}[/tex]

[tex]\rightarrow \sf x = \dfrac{ -2 \pm 2\sqrt{5}\:i}{2}[/tex]

[tex]\rightarrow \sf x =-1 \pm \sqrt{5}\:i[/tex]

[tex]\rightarrow \sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]

The probability that the product of the two rolls is a multiple of 3 is 1/2.

Probability:

Probability mean the fraction of the possibility of the required event.

The formula for the probability is

P(E) = n(E)/n(S)

Where

P(E) = Probability of the event

n(E) = number of required event

n(S) = Total number of event

Given,

Juan rolls a fair regular octahedral die marked with the numbers 1 through 8.

Then Amal rolls a fair six-sided die.

Here we need to find the  probability that the product of the two rolls is a multiple of 3.

We know that,

On both dice, only the faces with the numbers 3,6 are divisible by 3.

Let

P(a) = 2/8

P(a) = 1/4

it is  the probability that Juan rolls a 3 or a 6,

and Similarly,

P(b) = 2/6

P(b) = 1/3

Is the probability of Amal does.

By the Principle of Inclusion-Exclusion,

[tex]\[P(a \cup b) = P(a) + P(b) - P(a \cap b) = \frac{1}{4} + \frac{1}{3} - \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{2} \Rightarrow \mathrm{(C)}\][/tex]

Thus the total probability is 1/2.

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The factors of the expression is 3x²(x+5)(x+5) .

Factors of a number are defined as the numbers which divide the given number completely.

For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.

Factors of algebraic expression can be  calculated by the following methods:

The given polynomial is of the form:

3x⁴ + 30x³ + 75x²

Taking 3x² common from all the terms we get:

3x² (x² + 10x + 25)

Now we use middle- term factorization method to factor (x² + 10x + 25)

3x² (x² + 5x + 5x + 25)

or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}

or, 3x² (x + 5) (x + 5)

or, 3x²  (x + 5)²

Hence the factors of the expressions are: 3x²  (x + 5)²

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Disclaimer: The complete question is :

Factor completely:  3x⁴ + 30x³ + 75x²

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Answer:

b=2/3

Step-by-step explanation:

Let's solve the equation step by step

( b ) = 2/3

Remove bracket

b=2/3

Answer: 24/54

Step-by-step explanation:

[tex]\displaystyle\\\frac{4}{9}=\\\\ \frac{4}{9}*1=\\\\ \frac{4}{9}*\frac{6}{6} =\\\\\frac{4*6}{9*6} =\\\\\frac{24}{54}[/tex]

The height of the building = 1026.328ft

Given the angle of elevation = 11°

The angle of elevation is the angle formed between the horizontal distance to the base of the building and the line of sight to the top of the building.

We know that tan x = opposite side/adjacent side.

Here the opposite side gives the height of the building and the adjacent side is the distance to the base of the building on the ground.

Distance to the base of the building on the ground = 1 mile = 5280 ft.

So tan 11° = h/5280

⇒ h= tan 11° x 5280 = 0.194 x 5280 = 1026.328 ft

So the height of the building = 1026.328 ft

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Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

Given the data in the question;

Since Q is a point between P and R.

PR = PQ + QR

Plug in the given values and solve for x.

5x - 3 = ( 2x + 8 ) + ( x + 11 )

5x - 3 = 2x + 8 + x + 11

5x - 3 = 3x + 19

5x - 3x = 19 + 3

2x = 22

x = 22/2

x = 11

Numerical value of segment PQ when x = 11 will be;

PQ = 2x + 8 = 2(11) + 8 = 30

Numerical value of segment QR when x = 11 will be;

QR = x + 11 = (11) + 11 = 22

Numerical value of segment PR when x = 11 will be;

PR = 5x - 3 = 5(11) - 3 = 52

Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

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Answer:

es equivalente al es 54x

Answer: 9x^2+6x

Step-by-step explanation:

(4x^2 - 2x) - (-5x^2 - 8x)=

4x^2 - 2x +5x^2 + 8x=

4x^2+5x^2 - 2x + 8x=9x^2+6x

Answer:

Option 1

Step-by-step explanation:

Perpendicular lines form right angles

Parallel lines never intersect.

The answer is most probably to round the the numbers to nearest 10 digits and multiply

697x82 =  56,154

700 x 80 = 56000

A rounded number is less precise but roughly equal to the original number in value.

To the closest hundred, 341 is equivalent to 300. This is due to the fact that 341 is more similar in value to 300 than to 400. Because $1.89 is closer to $2.00 than to $1.00, when rounded off to the nearest dollar, it becomes $2.00.

The standard rounding rule is as follows:

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Round to nearest 10 digits and multiply

697x82=________x________=________

Part a: The size of the game in standard form is 240000 kilobytes

Part b: The game was 5 times larger than the patch file

Part A:

Size of the game downloaded by Ryan on his computer = 2.4 * 10^5

Size of the patch file for the game = 48000 kilobytes

Therefore, converting the size of the game into the standard form:

Size of the game = 2.4 * 10^5

= 2.4 * 100000

= 240000 kilobytes

Therefore, the size of the game is 240000 kilobytes in standard form

Part B:

Size of the game = 240000 kilobytes

Size of the patch file = 48000 kilobytes

Computing the size of the game with respect to the patch file we get:

=240000/48000

= 5

Hence, the game was 5 times larger than the patch file

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The equation of the line in function notation is y.=-2x + 5

The standard equation of a line is expressed as y = mx + b

where

m is the slope

b is the y-intercept

Given the equation

2y=x-4

y = 1/2x - 2

The slope perpendicular will be -2

Substitute into y-y₁ = m(x-x₁)

y-(-7) = -2(x-6)

y+7 = -2x +12

y = -2x  + 5

Hence the equation of the line in function notation is y.=-2x + 5

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Answer:

The question states four less than twice its width so we first find twice the width. The width is 6 and twice that is 12. Note that it says four less than, so four less than 12 is 8. so the length of the triangle is 8.

Step-by-step explanation:

Hope it helps! =D

The location of point D on the number line is -5.15625

The given parameters are:

A = 5

B = -10

AC : CB = 1 : 3

This means that

C = AC/(AC + AB) * (A - B)

This gives

C = 1/4 * (5 + 10)

Evaluate

C = 3.75

Also, we have:

BD : DC = 3 : 5

So, we have:

D = BD/(BD + DC) * (B - C)

This gives

D = 3/8 * (-10 - 3.75)

Evaluate

D = -5.15625

Hence, the location of point D on the number line is -5.15625

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The given statement is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.

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The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)

How to partition a Line segment?

The formula to partition a line segment in the ratio a:b is;

(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]

We want to find point G on AB such that the ratio of AG to GB is 3:2.

From the graph, the coordinates of the points A and B are;

A(3, 5) and B(5, 0)

Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;

G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]

G(x, y) = (21/5, 10/5)

G(x, y) = (4.2, 2)

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Answer: 63.5

Step-by-step explanation:

90 - 26.5 = 63.5

Answer: Give me 11 min

Step-by-step explanation:

Answer:

x² + y² = z²

Step-by-step explanation:

(a)

Using the right triangle altitude theorem,

x/z = p/x

x² = pz

(b)

y/z = q/y

y² = qz

(c)

x² + y² = pz + qz

x² + y² = z(p + q)

z = p + q

x² + y² = z × z

x² + y² = z²

Answer:

a) A = 1, C = 0, and D > 0 --> Graph B

b) A = 1, C = 0, and D < 0 --> Graph C

c) A > 1, C > 0, and D > 0 --> Graph D

d) 0 < A < 1, C < 0, and D < 0 --> Graph A

The Absolute Difference and the Relative Difference is  mathematically given as

Absolute Difference = $40;

Relative Difference = 19%. Option B

This is further explained below.

Generally, Divide the difference in values by the value that was used initially, and you will get the relative difference between the two values: difference original value

Perform the conversion to get a percentage out of this amount. If there was a rise in value, we would say there was an increase of x %.

We state there was an x % decline in the value if there was a decrease in the value. x represents the number that was arrived at by us.

In conclusion, since we are comparing A from be we have

Absolute Difference = 250-210

Absolute Difference = $40;

and

Relative Difference =  (Original-ref)/ref

Therefore

Relative Difference 250-210/210

Relative Difference=19%

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Answer:

Interest = Rs. 1297.26

Step-by-step explanation:

To calculate the final amount, we can use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{100})^n}[/tex],

where:

A = final amount

P = principal (initial) amount

r = rate

n = time in years,

and then we can subtract the initial amount from the final amount to find the interest.

We have been told in the question that the principal, P = Rs. 10,000; and the time is [tex]2\frac{1}{2}[/tex] years, therefore n = 2.5. The rate is 5%, therefore r = 5.

Using this information, and the formula above, we can calculate the final amount:

[tex]A = 10000(1 + \frac{5}{100})^{2.5}[/tex]

⇒ [tex]A = 10000(1.05)^{2.5}[/tex]

⇒ [tex]A = \bf 11297.26[/tex]

Now that we know what the final amount was, we can calculate the interest by subtracting the initial amount from it:

Interest = 11297.26 - 10000

             = 1297.26

Therefore the interest was Rs. 1297.26.

Answer:

y = −2x + 8

Step-by-step explanation:

y = −2x + 8, the answer is this because, in order to find the slope, you must use the formula y2-y1/x2-x1, and the y-intercept is found by using the formula y=mx+b, in which b is the y-intercept which leads to the awnser,  y = −2x + 8.

Hi! Your answer is y = −2x + 8

Step-by-step explanation:

In order to find the slope, you have to use y2-y1/x2-x1 for the formula. The y-intercept can be found by using the formula y=mx+b. This means b is the y-intercept which makes the answer:  y = −2x + 8.

Hope this helps! Have a good day :)

The experimental research has two key advantages over correlational studies.

1. The possibility of random assignment

2. Causal connections can be assumed.

Correlational studies merely examine the data that already exists, whereas experimental studies give the researcher the opportunity to influence the study's factors. Researchers can make inferences about how changes in one variable affect changes in another through the use of experimental investigations.

The factors in a correlation study are out of the control of the researcher or research team. The researcher merely measures the information she discovers in the outside world. She can then determine whether changes in one are related to changes in the other, or if the two variables are correlated. In such a study, experimenters gather existing data and use statistical methods to examine it, such as economic statistics from governments. The findings of correlation studies can lead to hypotheses that can be verified through a more focused experimental one.

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By using the given pair of values we can see that the constant of proportionality is 8, and the proportional relation is:

y = 8*x

A proportional relation is a linear relation with an y-intercept of 0, so these are written as:

y = a*x

Where a is the constant of proportionality.

By knowing a pair of values x and y, we can find the value of a. In this case we can see that when x = 3, y = 24, replacing that in the general equation we get:

24 = a*3

24/3 = a = 8

Then the constant of proportionality is 8, and the proportional relation is:

y = 8*x

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I don't see why my answer got deleted from last time as nothing was wrong with it, but your answer is: x = 5/6.

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

Hope this helps!

Have a great day and God bless! :)

Answer:

6

12

1

2

Step-by-step explanation:

In 1, is 4. Okay, this a good answer.

to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]