assume a pool measuring 26 meters by 12 meters is surrounded by a path of uniform width as shown in the figure Express the area in the past A in Square meters as a function of its width X in meters

To answer this question we will use the following diagram as a reference:

Notice that the perimeter of the given figure is the sum of 2 times the perimeter of the semicircles and 48m, the perimeter of each semicircle is:

Therefore the perimeter of the given figure is:

Answer: 85.68m.

A temperature drop of 7 degrees Fahrenheit in 3.5 hours is represented by 2 f/hour.

Fahrenheit temperature scale, based on the freezing point of water at 32° and the boiling point of water at 212°, with the interval between the two divided into 180 equal parts.

Given: The outside temperature drops by 7 degrees Fahrenheit in 3 1/2 hours.

We need to represent the temperature as a unit.

To do so, we must represent the temperature change per hour.

7f/3.5 hours = 2 f/hour

Therefore, the temperature that decreases by 7 degrees Fahrenheit in 3.5 hours can be represented as 2 f/hour.

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Multiply the coordinates by the scale factor (5)

T'= (-1 x 5 , 5x5) = (-5,25)

T' = (-5,25)

Answer: -6/5=2/9

Step-by-step explanation:

Answer:

(-1,-6) --> (1,-6) --> (1,6)

(1,6) is E''

The three methods that are generally used to solve f(x) =g(x) are Graphing technology, Tables of values, and Successive approximation.

Determine the exact value of x by replacing the values of x with f(x) and g(x).

The hit-and-trial technique is used in f(x) = g(x) to compute the exact value of x by selecting an interval and then substituting the value of x in that interval.

This is a bit longer and takes more time.

Graph Technique: Create a graph that contains both f(x) and g(x). The values of x given by these two functions are the same.  Some features are difficult to plot, but once plotting is done, the right solution is obtained. The graphics technique is prioritised in determining f(x) = g(x) and x.

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Answer:99cm.l

Step-by-step explanation:100-1

100-1=99

So then the answer is 99, because 99+1 is also equal to 100.

And if you subtract 1 from 100, you get 99.

Answer: 99cm

Step-by-step explanation:

1cm + x = 100cm

100cm - 1cm = x
Which means,

99cm is the correct answer.

Given:

Find: fill in the blanks.

Explanation:

Answer:

43

Step-by-step explanation:

The value of y varies directly with x. When y = 21, x = 3. What is the value of y when x is 14.

when y = 21 and x = 3 the ratio of y to x is 21 to 3 or (reduced) 3 y to 1 x

This means y is three times the size of x.

When x = 14 then y = 14 × 3 = 42

From the figure given in the question, we are asked to find the area and perimeter.

(a) Area:

Since the figure is a trapezoid, the formula for the area of a trapezoid is:

Area = (a + b)h

2

Where:

a = 2

b = 5

h = 4

Area = (2 + 5)4

2

Area = 7/2 * 4

Area = 3.5 * 4

Area = 14 cm²

(b) Perimeter:

To get the perimeter, we will have to add all the side length.

But we will have to find the missin side length first.

Using pythagoras:

a² + b² = c²

Where:

a = 4

b = 3

c² = 4² + 3²

c² = 16 + 9

c² = 25

Taking square of both sides:

c = √25

c = 5

Since we have gotten the missing side length as 5cm, we can now add all the given side length to get the perimeter.

Perimeter = 4 + 2 + 5 + 5

Perimeter = 16 cm

Let x = volume of 20% solution=0.2

Let y = volume of 30% solution=0.3

Equation of total volume:

x + y = 90

Equation of amount of acid:

Substitute into the second equation

Therefore 45 liters of 20% solution and 45 liters of 30% solution

Hence the volume of 20% acid = 45 litres

the volume of 30% acid = 45 litres

Let's use a rule of three to solve this:

This way,

The crew will take 36 hours to repave the road

[tex]\cos \theta=\frac{x}{16} \implies x=16 \cos \theta \\ \\ \sin \theta=\frac{y}{16} \implies y=16 \sin \theta[/tex]

A hypothesis can be seen as an assumption about something, If the hypothesis is wrong, you have information about that something, and you can be sure that the behavior you assumed is never going to happen. In conclusion, you also learn from the mistakes made

Given:

Area of base of the prism, B = 96 square centimeters

Height of prism, H = 9 centimeters

Let's find the volume of the prism.

To find the volume of the prism, apply the formula below:

Where:

V is the volume in cubic units

B is the area of the base = 96 square centimeters

H is the height = 9 centimeters

Hence, we have:

Therefore, the volume of the prism is 864 cubic centimeters

ANSWER:

t - the number of years the money is invested for
P = $16,000
m =2
t = 12 yr
r = 8% or .08
FV = 16,000* ( 1+ .08/2) 2*12 = 16000 (1.04) 24 = 16000* (2.5633041) = $41012.8656
FV - the future value of the investment = $41012.87 is answer

The refrigerator is to be set at 5 degrees celsius for the cheese to keep for 5 days.

Since we are given the relation for the exponential function

H(T) = 130 (1/2) ^(T/43.3), where H(T) is the  number of hours

since we are asked for a cheese to keep for  5 days, so

H(T)=  5 * 24 = 120 hours

so the equation we will have

=>120 =130 (1/2) ^(T/43.3)

we multiply both sides by 120

=> 12/13=  (1/2) ^(T/43.3)

taking logarithms on both sides, we get

=> ln (12/13) = (T/43.3) ln(1/2)

=>43.3 ln (12/13) = T ln (1/2)

dividing both sides by ln (1/2), we get

=> T = 43.3  ln (12/13) / ln (1/2)

=> T=  5.0016

=> T = 5.0 celsius  

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The length of time that a particular type of blue cheese will keep in the refrigerator can be modeled by the exponential function H(T) = 130 (1/2) ^(T/43.3) where H(T) represents the number of hours after the cheese is put in the refrigerator and T represents the temperature of the refrigerator in degrees Celsius. If you want the cheese to keep for 5 days, at what temperature should the refrigerator be set ; round your answer to the nearest tenth of a degree.

Answer: Slope of 1.

Step-by-step explanation:

    First, we will put the equation into slope-intercept form.

x - y = 4

x = y + 4

y = x - 4

    Our slope, when the line is written as y = mx + b, is the m value. Our m value here is one, so the slope of a line parallel to the line whose equation is x - y = 4 is 1.

Answer: √195 or 13.96424004

Step-by-step explanation:

Answer:

[tex]\sqrt{195}[/tex]

Step-by-step explanation:

Given:

[tex]\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{13}[/tex]

[tex]\textsf{Apply the radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\implies \sqrt{3 \cdot 5 \cdot 13}[/tex]

[tex]\implies \sqrt{15 \cdot 13}[/tex]

[tex]\implies \sqrt{195}[/tex]

This cannot be simplified any further.

a)

The slope intercept equation of a line is expressed as

y = mx + c

where

m is the slope

c is the y intercept

The given equation is

x + y = 3

y = - x + 3

By comparing both equations,

m = - 1

If two equations are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 3, 2) is - 1

We would find the y intercept by substituting x = - 3, y = 2 and m = - 1 into the slope intercept equation. It becomes

2 = - 1 * - 3 + c

2 = 3 + c

c = 2 - 3

c = - 1

By substituting m = - 1 and c = - 1 into the slope intercept equation, the equation of the line is

y = - x - 1

b) If two equations are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line Thus, the slope of the perpendicular line passing through the point (- 3, 2) is - - 1/1 = 1

We would find the y intercept by substituting x = - 3, y = 2 and m = 1 into the slope intercept equation. It becomes

2 = 1 * - 3 + c

2 = - 3 + c

c = 2 + 5

c = 5

By substituting m = 1 and c = 5 into the slope intercept equation, the equation of the line is

y = x + 5

a) y = - x - 1

b) y = x + 5

Answer:

This statement is True.

Step-by-step explanation:

5/8 is equal to 0.625 in decimal form. Use our fraction to decimal calculator to convert any fraction to a decimal and to know if it is a terminating or a recurring (repeating) decimal. It is, a so called, 'terminating' decimal. To convert this fraction to a decimal, just divide the numerator (5) by the denominator (8).

Given the triangle DEF.

Angle E = 71.2˚

e = 29.5 cm

f = 30.3 cm

We are to solve for each triangle.

Using laws of sine:

a = b = c

sinA SinB SinC

In this case we will have:

e = f

SinE SinF

29.5 = 30.3

sin 71.2˚ sinF

cross multiply

sinF(29.5) = sin 71.2˚(30.3)

sinF = sin 71.2˚(30.3)

sin 29.5

sinF = 0.9466 * 30.3

0.4924

sinF = 58.2524

Answer:

So,

let the amount of each transaction be x.

3x= 115.25+77.73

x= 192.98÷

x= 64.327

each transaction was of 64.327

Step-by-step explanation:

since the amount left is -77.73 then three equal transaction will also include 115.25+77.73= 1 92.98

192.98 was the total amount used

Given:

The equation above is written in slope intercept form:

y = mx + b

To rewrite in standard form, use the standard form of linear equations below:

Ax + By = C

Thus, we have:

Multiply through by 9 to eliminate the fraction:

Add 2x to both sides:

Therefore, the equation in standard form is:

2x + 9y = 27

ANSWER:

D. 2x + 9y = 27

The value is x≤1 or x>2

Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

2x +6≤8 or 2x + 8 > 12

2x +6≤8

2x ≤2

x≤1

2x +8>12

2x>4

x>2

The value is x≤1 or x>2

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Data:

• Cumulative probability of -2.18 ,: 0.0146

• Cumulative probability of 3.74 ,:, ,0.9999

Procedure:

0. Using the following formula we can get our probability.

The value of m is -6/5.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

2m -3 = 3/10 (5m - 12)

Now, cross multiplying

10( 2m -3)= 3( 5m -12)

20m -30 = 15m - 36

20m- 15m= -36 + 30

5m = -6

Divide both side by 5

m= -6/5

Verification:

LHS = 2m-3

=2(-6/5)-3

=-12/5-3

=-27/5

and, RHS

= 3/10( 5m -12)

=3/10(5 x (-6/5) -12)

=3/10 (-6 - 12)

=3/10 x -18

= -54/10

= -27/5

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