In the first week of​ July, a record
1,020 people went to the local swimming pool. In the second​ week,
100 fewer people went to the pool than in the first week. In the third​ week,
130 more people went to the pool than in the second week. In the fourth​ week,
234 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four​ weeks?

The depth of the water is 5.3 meters

The dolphin jumps to a height of 4.5 over the water's surface, and her companion swims 9.8 straight beneath her, according to the story.

We will take the position of the dolphin's friend and subtract it from the dolphin's position to determine the location of the dolphin's friend with respect to the water's surface.

-5.3 denotes the depth of the water.

As a result, the friend of the dolphin is located 5.3 meters below the water's surface.

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A graph of the given system of equations f(x) = 2x² - 8x + 3 and g(x) = -2x + 3 is shown in the image attached below.

The points that make both equations true is (0, 3)

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

In Mathematics, the graph of every quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic equation (function) would always form a parabolic curve.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each, which is the ordered pair (0, 3);

f(x) = 2x² - 8x + 3

3 = 2(0)² - 8(0) + 3

3 = 3 (True).

g(x) = -2x + 3

3 = -2(0) + 3

3 = 3 (True).

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The ordered pair that describes the location of Q' is (-3, -1)

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

Point Q = (3, -1)

This point can be represented as

(x, y) = (3, -1)

Also, from the question, we have the transformation to be:

Point Q is reflected over the y-axis

Mathematically, this can be expressed as

(x, y) = (-x, y)

So, we have the following representation

Point Q' = (-3, -1)

Hence, the image is (-3, -1)

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Answer: 325 adult tickets

Step-by-step explanation:

721 = (a+71) + a

721 = 2a + 71

2a = 650

a = 325

Answer:

[tex]7\sqrt5[/tex]

Step-by-step explanation:

245 ÷ 5 = 49

49 is a square number (7)

So you put 7 on the outside and 5 on the inside.

Answer: B

Step-by-step explanation:

Range will always be Y

Domain will always be X

6️⃣9️⃣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

After solving the given equation for c, we know that the value of c is (A) -56.

Equivalent systems refer to sets of equations with the same solution.

We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

So, we have the equation:

-5 = 9+(c/4)

Now, solve for the subject c as follows:

-5 = 9+(c/4)

-5 -9 = (c/4)

-14 = c/4

c = -14*4

c = -56

Therefore, after solving the given equation for c, we know that the value of c is (A) -56.

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Answer:

x=102/25 y=9/5

Step-by-step explanation:

Answer:

[tex]117.8cm ^{2} [/tex]

Step-by-step explanation:

[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]

The relation represents y as a function of x as for each value of x there is a unique value of y.

A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).

The given data is as follows,

A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).

Here x is the element of domain and y is of the range of the given relation.

Here, the values of y are distinct for different values of x.

Hence, the given relation represents y as a function of x  because for each value of x there is a single value of y.

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Answer: I = $ 200.00

Step-by-step explanation:

I = Prt

Convert R (percent) to r (decimal)

r = R/100 = 1%/100 = 0.01 per year

I = 2000 × 0.01 × 10 = 200

I = $ 200.00

hope this helps!

The time t = 3.4209 will it take for the concentration to reach 350,000 material per millimeter.

In an hour, there are 60 minutes. Divide the number of minutes by 60 to convert it to hours. For instance, 120/60=2 means that 2 hours are equal to 120 minutes.

The millimeter, abbreviated mm in the International System of Units (SI), or millimeter, abbreviated mm in the American spelling, is a unit of length that is one thousandth of a metre long, the SI base unit of length. As a result, a metre is made up of 1000 millimeters.

We are going to use formula

y = a * e ^ (b * t)

a and b are constants and t is for time.

Initially there are 100,000 bacteria, so;

100000 = a * e ^ (b * 0)

100000 = a * 1

a = 100000

given condition is that the concentration doubles every 3 hours so

300000 = a * e ^ (b * 3)

As a equals to 100,000

e ^ (b * 3) = 3

b * 3 = ln 3

b = (ln 3) / 3

b = 0.3662

now we have to find value of the time when concentration of bacteria reaches to 350,000:

350000 = 100000 * (e ^ 0.3662 * t)

3.5 = e ^ 0.3662* t

ln 3.5 = 0.3662* t

t = 1.2527 / 0.3662

t = 3.4209

That is the required value of time

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Answer:

x = 4

Step-by-step explanation:

5 x .8 = 4

Answer: the value of x is 4

Step-by-step explanation:

x=5*0.8=4

Answer:

1. no solution

2. one solution

3. infinitely many solutions

4. one solution

Step-by-step explanation:

1. same slope, different intercepts, parallel lines, no solution

2. different slopes, lines intersect at 1 point, one solution

3. same equation, infinitely many solutions

4. different slopes, lines intersect at 1 point, one solution

Answer:

It is y = 3/5x - 19/5

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. Thus, the slope is 3/5x. Plug in -2 as x and solve for the intercept. It ii -19/5.

The amount of simple interest is (a) $341.60

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

Principal, P = $800

Rate, r = 6.1 %

Time = 7 years

The simple interest on the investment is calculated as

I = PRT

Substitute the known values in the above equation, so, we have the following representation

I = 800 * 6.1% * 7

Express 6.1% as decimal

So, we have the following representation

I = 800 * 0.061 * 7

Evaluate the products

I = 341.6

Hence, the amount is (a) $341.6

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Out of the 14 coins she has, she will have 4 dimes, totaling $2.5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Here,

Let n be the nickels, d be the dimes, q be the quarters.

Total coins=14

Total amount=$2.5

n=2d

d=2q

q=d/2

d+q+n=14

d+2d+d/2=14

2d+4d+d=28

7d=28

d=4

She will have 4 dimes out of 14 coins that she owns with an amount of $2.5.

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Answer:

y = -8x + 23

Step-by-step explanation:

8y=x-16

we need to turn this into slope-intercept form by dividing 8 on both sides

y = x/8 - 2

to make a line perpendicular from another, we must make sure the slope is the negative reciprocal of the original line.

Right now, it's the same as the original. To make it a negative reciprocal, switch the places of the denominator and numerator and flip the signs

-8x is the negative reciprocal of x/8

Does it go through (4,-9)? No.

To make sure it goes through 4,-9, we change it's y-intercept.

Plug in the coordinate given (4,-9) in the y = -8x + b ( we removed -2 since it's not the right answer.

y = -8x + b

(-9) = -8(4) + b

-9 = -32 + b

-9 +32= -32 + b +32

23 = b

plug in b and we get our answer

y = -8x + 23

Answer:

Step-by-step explanation:

(0, 2) (4, 0)

(0 - 2)/(4 - 0) = -2/4 = -1/2

y - 2 = -1/2(x - 0)

y - 2 = -1/2x + 0

y = -1/2x + 2

Min needs to gain 80 marks to raise her average to 75.

Average number is got from sum of all numbers divided by the number of values.

Average value is used to compare among different quantities of same terms.

given, Min receives an average score 70 from 5 math test.

let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.

she gained average 70 from 5 test

if average is 75 then

75 = (X+ 70)/2

X=80

hence, in the 6th test she needs to gain 80 marks.

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The equation of the lines is,

1. (4, -1); m = 3 : - y = 3x - 13

2. (-8, 0); m = -4 :- y = -4x - 24

3. (-6, -10); m = 1/6 :- y = -1/6x - 9

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The equation of the lines will be,

y = mx + c

y = 3x + c

-1 = 4 x 3 + c

c = -13

y = 3x - 13

y = mx + c

y = -4x + c

0 = -4 x -8 + c

c = -24

y = -x -24

y = mx + c

y = 1/6x + c

-10 = -1 + c

c = -9

y = -1/6x - 9

Therefore, the equation of the lines is,y = 3x - 13 y = -4x - 24 and y = -1/6x - 9.

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Answer:

0.004

Step-by-step explanation:

Hope it helps!

Answer:

It A

Step-by-step explanation:

Answer:

in 40 minutes ... travelled 50km

Step-by-step explanation:

Answer:

Step-by-step explanation: One denominator in the question is 4/5 and another is 1/2. A common denominator would be /10 because it applies to /5 and /2.