Four thousand runners began the marathon. Eighty-nine percent of them completed the run. What percentage of the runner finished the marathon?

The solution to the original equation will be -2 and -6

Given the function [tex](x + 3)^2 + (x + 3) - 2 = 0.[/tex]

If u = x + 3, the function in terms of "u" will be;

[tex]u^2+u-2=0[/tex]

Factorize the resulting equation as shown:

[tex]u^2+u-2=0\\u^2+2u-u-2=0\\u(u+2)-1(u+2)=0\\(u-1)(u+3) = 0\\u=1 \ and \ -3[/tex]

Since x + 3 = u

x = u - 3

If u  = 1

x = 1 - 3  = -2

If u  = -3

x = -3 - 3  = -6

Hence the solution to the original equation will be -2 and -6

Correct question:

Solve (x + 3)^2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?

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Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

[tex]\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}[/tex]

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

[tex]\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}[/tex]

Another identity is:

[tex]\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}[/tex]

Therefore:

[tex]\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}[/tex]

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

[tex]\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}[/tex]

Another identity:

[tex]\displaystyle \large{\sin^2x+\cos^2x=1}[/tex]

Therefore:

[tex]\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}[/tex]

Hence proved, this is proof by using identity helping to find the specific identity.

Answer:

50% increase

Step-by-step explanation:

half of 6 is 3 thus 50%, and vise versa.

Answer:

D) Zero solutions

Step-by-step explanation:

9 - 5x = 8 - 3x - 1 - 2x

9 - 5x = 7 - 5x

9 = 7

Zero solutions

i took the quiz its D. Zero

Hi,

if it's 11:24, it wil be 12:13

✅(◠‿◕)

Answer:

2.05

Step-by-step explanation:

To find the Median value, we begin by sorting Or arranging our numbers In ascending Or descending order.

-8.8,-5.7,-2.6,0.5,3.6,6.7,9.8,11.9

Having an even (8) number of values, the median is the midway point between the two middle numbers.

In our case the two middle numbers are 0.5 and 3.6

(0.5+3.6)/2

Median=2.05 (In words: two && 5/100)

Answer:

x=8

Step-by-step explanation:

open the brackets to be

6x-6=42

then collect like tems

6x=48

x=8

Answer:

The range is y≥0

Step-by-step explanation:

The shape of this graph is a parabola

You may see this by using the Desmos calculator and typing y=x^2 if you would like to visualize.

(a) The function y = x^2 simply takes whatever number you feed it (x) and outputs x squared.

For example

y = (2)^2=4

y = (3)^2 = 9

(b) To graph x^2 simply make a table of values and plug in 0 -> however high you would like to go ( usually to 5 or so is fine but you could go to infinity).

Example

      y = x^2

                 Y    |     X

                ________

                 2      |   4  

                 3     |   9

                 4    |    16

In this case the function's range is y≥0 because all y values will be greater than or equal to 0.

If you are wanting to learn how to specifically graph this you can look up (Graphing y = x²) if my quick graphing explanation back at mark (b) does not help.

Answer:

(i) 4000

(ii) $5.00

Step-by-step explanation:

Let no. of shares of Company A be X

Let share price of Company B on Day 7 be $y

Share price of Company B on Day 12 = $(y-0.50)

(i)

Consider Day 7:

4.60x - 2000y = 7400................ (1)

Consider Day 12:

4.80x - 5000(y-0.50) = -5800

4.80x - 5000y + 2500 = -5800

4.80x - 5000y = -8300............... (2)

(1)*2.5:

11.5x - 5000y = 18500................. (3)

(3)-(2):

11.5x - 4.80x - 5000y + 5000y = 18500 + 8300

6.70x = 26800

x = 4000

(ii)

Sub. x = 4000 into (1):

4.60(4000) - 2000y = 7400

-2000y = 7400 - 18400

-2000y = -11000

y = 5.5

Share price of Company B on Day 12

= 5.50 - 0.50

= $5.00

Answer: Great U?

Have a great Day/Night

Answer:

15km

Step-by-step explanation:

45mins = 25km

1 min =25/45

=5/9

27mins=5/9×27

=15km

The Matching of the inequality is

x ≤ 7.8 -> (-∞,7.8]

x < 7.8 -> (-∞,7.8).

x > 7.8 -> (7.8,∞)

x ≥ 7.8 -> [7.8,∞).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

1. x ≤ 7.8

Here the value of is less than equal to 7.8 which means starting from -∞ to 7.8

Thus, the interval is (-∞,7.8]

2. x < 7.8

Here the value of is less than 7.8 which means starting from -∞ to less than 7.8.

Thus, the interval is (-∞,7.8).

3. x > 7.8

Here the value of is greater than 7.8 which means starting from 7.9 to ∞.

Thus, the interval is (7.8,∞)

4. x ≥ 7.8

Here the value of is greater than equal to 7.8 which means starting from 7.8 to ∞.

Thus, the interval is  [7.8,∞).

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Answer:

god help you

Step-by-step explanation:

i think we should add all the ratio together.......

Answer:

{- 3, - 2, 0, 2 }

Step-by-step explanation:

The range is the y- coordinates of the points

(- 4, - 3 ) , (- 1, - 2 ) , (- 2, 0 ) , (0, 2 )

The y- coordinates are - 3, - 2, 0, 2

Then the range is { - 3, - 2, 0, 2 }

Answer:

30

Step-by-step explanation:

4(3)^2 +(3*-2)

4*9-6=36-6=30

Answer:

30

Step-by-step explanation:

Substitute x = 3 and y = - 2 into the expression

4x² + xy

= 4(3)² + 3(- 2)

= 4(9) - 6

= 36 - 6

= 30

The value of x is [tex]\mathbf{8\dfrac{1}{3}}[/tex]

The objective of this question is to evaluate and determine the value of x. The fraction given in the question consists of algebraic expressions and, we need to solve it through following process;

∴

[tex]\mathbf{\dfrac{x-1}{3-x} + \dfrac{3}{4}=-1 }[/tex]

Collect like terms

[tex]\mathbf{(\dfrac{x-1}{3-x})=-1 -\dfrac{3}{4}}}[/tex]

[tex]\mathbf{(\dfrac{x-1}{3-x})=-(\dfrac{7}{4}})}[/tex]

-4(x - 1) = -7(3 -x)

-4x + 4 = -21 + 7x

4x -7x = -21 - 4

-3x = - 25

[tex]\mathbf{x= \dfrac{25}{3}}[/tex]

[tex]\mathbf{x= 8\dfrac{1}{3}}[/tex]

Learn more about evaluating fractions here:

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Answer:

15 in

Step-by-step explanation:

d^2 = w^2 + l^2

25^2 = 20^2 + l^2

l^2 = 225

l = 15

Answer:

12, 63 and 21 sum to 96

.....

Half the perimeter is the length + the width

62/2 = 31

Area = length x width

16 + 15 = 31, 15 x 16 = 240

17 + 14 = 31, 17 x 14 = 238

20 + 11 = 31,  20 x 11 = 220

Answer: 20 meters x 11 meters

Answer: The answer is D, the first ten amendments to the constitution.

Answer:

x = (−2 ± √−12)/2

Step-by-step explanation:

Using the quadratic formula (search it up if you don't know what it is, but it's basically the first thing in the pic):

Answer:

92

Step-by-step explanation:

- ( 2 - 6 )

= - ( - 4 )

= 4

- ( 2 - 6 ) ( 23 )

= 4 x 23

= 92

The evaluation of  - (2- 6) ( 23) is 92

In mathematics, evaluation is a systematic method used in solving expressions. From the given information, we need to first solve the expressions in the brackets before multiplying them together.

From the given information:

= - ( 2 - 6) (23)

= - ( -4) (23)

= 4 × 23

= 92

Learn more about how to evaluate in mathematics here:

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Answer:

  40.5°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

In this triangle, that means ...

  tan(x°) = 4.7/5.5

The angle is found using the inverse function:

  x° = arctan(4.7/5.5) ≈ 40.5°

Answer:  y ≤ (1/2)x + 3

Step-by-step explanation:

The slope is 1/2 and the y-intercept is 3.

The linear inequality represented by the graph is [tex]y \le \frac 12x + 3[/tex]

From the graph, we have the following highlights:

The first highlight implies that the inequality sign to use is ≤

The slope (m) is calculated as:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{3 -4}{0-2}[/tex]

[tex]m = \frac{-1}{-2}[/tex]

[tex]m = \frac{1}{2}[/tex]

The y-intercept (b) is where the line crosses the y-axis:

b = 3

The linear inequality is represented as:

[tex]y \le mx + b[/tex]

So, we have:

[tex]y \le \frac 12x + 3[/tex]

Hence, the linear inequality is [tex]y \le \frac 12x + 3[/tex]

Read more about linear inequality at:

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Answer:

83/100

Step-by-step explanation:

10/11x11/12 is 0.8333333....