One year, the population of a city was 73,000. Several years later it was 85,410. Find the percentage decrease

The rectangular coordinates will be (x=7cot(θ), y=7).

A pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.

We have the standard conversion toolbox:

[tex]x=rcos(\theta)\\\\y=rsin(\theta)[/tex]

Here it is given that

[tex]r=7cosec(\theta)[/tex]

so

[tex]x=7cosec(\theta)\times cos(\theta)=\dfrac{7cos(\theta)}{sin(\theta )}=7cot(\theta)\\\\\\y=7cosec(\theta)\times sin(\theta)=\dfrac{7sin(\theta)}{sin(\theta)} = 7[/tex]

therefore the rectangular coordinates are (7cot(θ), 7)

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Answer:

the slope of parallel lines are - the same

i.e,m1=m2

the slope of perpendicular lines are- negative reciprocals

i.e,m1*m2= -1

where, m1 and m2 slopes of two lines

A. The slope of parallel lines are: the same/equal

B. The slope of perpendicular lines are negative reciprocals.

If two lines are parallel to each other, they will have the same slope. If the slope of one is 4, the slope of the other line that is parallel to it would also be 4.

On the other hand, the slope of perpendicular lines are negative reciprocal of each other. That is, if the slope of one is, -1, the slope of the other line would be 1.

Therefore, parallel lines have the same slope, while perpendicular lines have slope values that are negative reciprocal to each other.

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Answer:

x ≤ -4

Step-by-step explanation:

-7x + 13 ≥ 41

Rearrange the terms

-7x ≥ 41 - 13

Calculate

-7x ≥ 28

Divide both sides

x ≤ -28/7

Simplify

x ≤ -4

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

nation's leader

Step-by-step explanation:

As the nation's leader, President Reagan decided to address the country about the Challenger tragedy. Putting aside his scheduled State of the Union address before Congress, the President instead delivered an Oval Office address to comfort the people as the nation mourned.

Answer:

0.0005 and 100000

Step-by-step explanation:

solve them in the answer.

Answer:

11 over 20

Step-by-step explanation:

There are 20 altogether and 9 are green and red 20 - 9 = 11

The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

Let's suppose the equation that models the exponential decline is:

[tex]\rm y = a(b^x)[/tex]

From the data given, we can calculate the value of a and b:

a = 46348587109809610

b = 0.9861

y = 46348587109809610(0.9861)ˣ

Thus, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

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Answer:

30k + k²

Explanation:

First Step:

30 is added to k means : 30 + k

Second Step:

Resulting number multiplied by k means : (30 + k) × k

Results:

30k + k² ___prime number.

Check the picture below.

well, HIJK is a parallelogram only if its diagonals bisect each other, if that's so, the midpoint of HJ is the same as the midpoint of IK, let's check

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{0}~,~\stackrel{y_1}{5})\qquad J(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 + 0}{2}~~~ ,~~~ \cfrac{ -1 + 5}{2} \right)\implies \left( \cfrac{4}{2}~~,~~\cfrac{4}{2} \right)\implies \boxed{(2~~,~~2)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ I(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad K(\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \left(\cfrac{ 1 + 3}{2}~~~ ,~~~ \cfrac{ 1 + 3}{2} \right)\implies \boxed{(2~~,~~2)}[/tex]

Answer:

1. bisect each other 2. (2,2) 3. have the saem midpoint

Step-by-step explanation:

The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).

To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals

✔ bisect each other

, then the quadrilateral is a parallelogram.

The midpoint of HJ is

✔ (2, 2)

and the midpoint of IK is (2, 2).

Therefore, HIJK is a parallelogram because the diagonals

✔ have the same midpoint

, which means they bisect each other.

The probability that if you buy two dozen eggs, none of your eggs will be cracked is 94.09% if the 3 percent of the eggs supplied to a supermarket are cracked.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

3 percent of the eggs supplied to a supermarket are cracked.

The probability that no eggs are cracked = 1 - 0.03 = 0.97

The probability that if you buy two dozen eggs, none of your eggs will be cracked:

= 0.97×0.97

= 0.9409

= 94.09%

Thus, the probability that if you buy two dozen eggs, none of your eggs will be cracked is 94.09% if the 3 percent of the eggs supplied to a supermarket are cracked.

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Answer:

Step-by-step explanation:

Some qucik lil definitions of these words

Coefficient - A multiplicative factor in some term of a polynomial, a series, or any expression.

Constant - A value that is unchanging.

Term - A  single mathematical expression.

Variable - A letter used to represent an unknown.

Answer: which one ? ill edit this w/ the answer

Step-by-step explan

So

Interest

Amount

Answer:

120

Step-by-step explanation:

Because triangle is always 180.

180-30-30=120

Answer:

23

Step-by-step explanation:

AB and BC are tangent to circle P, which means that both lines are congruent. Set AB and CB equal to each other:
2x-7=5x-52
3x=45
x=15
Plug 15 into AB:
2(15)-7 = 23
Length of AB is 23.

Answer:

D

Step-by-step explanation:ik

Answer:

6 boxes

Step-by-step explanation:

2 boxes for each friend

:)

Answer:

So there's Artem and his 3 friends so thats 4 people and everyone wants 8 cookies each box has 4 cookies so he would buy 32 boxes.

Step-by-step explanation:

Step-by-step explanation:

sin = 15/17

cos = -8/17

tan = -15/8

csc = 17/15

sec = -17/8

cot = -8/15

Answer:

D. tanθ = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Trigonometric applied here :

tanθ = 1/cotθ

=============================================================

In Quadrant III, all values of tan and cot are positive.

⇒ tanθ = 1/(3/4)

⇒ tanθ = 4/3

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Let the present age of Meena be ' x ' years.

That means,

Present age of her mother

[tex]\sf{ = 4x \: years }[/tex]

Now,

After 5 years

The age of the Meena will be

[tex]\sf{ = x + 5 \: years }[/tex]

Therefore,

According to given condition,

The age of her mother will be

= [tex]\sf{ = 4x + 5 \: years ...eq(1)}[/tex]

But, It is given that,

That is,

After 5 years, Her mother age will be

[tex]\sf{ = 3(x + 5) \: years ...eq(2)}[/tex]

From eq(1) and (2) :-

[tex]\sf{ 4x + 5 = 3(x + 5) }[/tex]

[tex]\sf{ 4x + 5 = 3x + 15}[/tex]

[tex]\sf{ 4x - 3x = 15 - 5 }[/tex]

[tex]\sf{ x = 10 \: years }[/tex]

Thus, The present age of the Meena will be 10 years.

Therefore,

The present age of her mother will be

[tex]\sf{ 4x = 4 × 10 }[/tex]

[tex]\sf{ = 40 \: years }[/tex]

Hence, The present of Meena and her mother is 10 years and 40 years.

An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The simplification of the given expression can be done as,

[tex]\dfrac{5x}{x^2-1} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{x^2-1^2} \times \dfrac{x+1}{x^2}\\\\=\dfrac{5x}{(x+1)(x-1)} \times \dfrac{x+1}{x^2}\\\\= \dfrac{5}{(x-1)x}[/tex]

Hence, the simplification of the expression (5x/x^2-1 )×(x+1/x^2) is 5/x(x-1).

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Answer:

17 cm and 31 cm

12 cm and 36 cm

18 cm and 30 cm

Step-by-step explanation:

The midsegment of a trapezoid is equal to the average of the two bases. When taking an average of two numbers, you add them and divide by 2. So  the equation will be as follows:

[tex]\frac{PQ + SR}{2} = XY[/tex]

XY is given to be 24, so:

[tex]\frac{PQ + SR}{2} = 24[/tex]

Multiplying on both sides gets us:

[tex]PQ + SR = 48[/tex]

So any values of PQ and SR that add to 48 work. Therefore, we will sum the given options:

17 cm + 31 cm = 48 cm

18 m + 30 m = 48m (Did you mean meters?)

4 cm + 8 cm = 12cm

9 cm + 15 cm = 24cm

12 cm + 36 cm = 48cm

18 cm + 30 cm = 48 cm

Answer:

-7

Step-by-step explanation:

| anything inside these vertical lines becomes positive when the lines are removed. These lines are absolute value lines |

So |-2| becomes 2 when absolute bars are removed.

Using this logic, |-3| becomes 3 when bars removed. Thus 3 - 10 = -7

-> 3rd answer is correct

Answer:

y = 2x - 6

Step-by-step explanation:

For parallel lines, the mx (the slope) stays the same but the y-int changes.

Answer:

20 days of the 200 total days

Step-by-step explanation:

1.  200/100=2

2. 2x90=180

3. 200-180=20

Answer:

  £54,915

Step-by-step explanation:

The tax table is applied as follows:

  first 11,000 -- no tax

  11,000 to 43,000 -- tax is 0.20 × (43,000 -11,000) = 6,400

  43,000 to 150,000 -- tax is 0.40 × (150,000 -43,000) = 42,800

  150,000 to 162,700 -- tax is 0.45 × (162,700 -150,000) = 5,715

Then the total tax on earnings of £162,700 is ...

  £6,400 +42,800 +5,715 = £54,915

Nerys paid a tax of £54,915.

_____

Additional comment

The tax computation could be simplified to ...

  f(x) = max(0, 0.2x -2200, 0.4x -10800, 0.45x -18300)

In this instance, the value 0.45x -18300 is the highest, at £54,915. Not all the computations are required if you realize the lines cross at x = 11,000, 43,000, and 150,000.

Answer:

Step-by-step explanation:

31 × 29 + 14 = 913

Then

913 / 29 = 31 r 14

Answer:

[tex]l(\overline {AB})\approx9.22\: units[/tex]

Step-by-step explanation: