Gigi makes a scale drawing of a patio the drawing below shows the two scales she used to plan two patios of different sizes

Answer:

w=3units  l=6 units

Step-by-step explanation:

The required length and width of the rectangle are 6 and 3 units

Given that,
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Here,
Let the length of the rectangle be l and the width of the rectangle is l -3
Now,
area of the rectangle,
18 = l [l - 3]
18 = l² - 3l
l² - 3l - 18 = 0
l² - 6l + 3l  - 18 = 0
(l - 6) + 3 (l - 6) = 0
(l - 6)(l + 3) = 0
l = 6   {negative value of the l can be neglected.}
now,
width = 6 - 3 = 3

Thus, the required length and width of the rectangle are 6 and 3 units.

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There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.

we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2

we will find the values by partial derivative with respect to x,y,xy

f ₓ= -2 -2x

[tex]f_{y}[/tex] = 4 -8y

to find the saddle point we should first find the critical points so equate

-2 -2x=0 and   4 -8y=0

we get x= 1  and y =1/2 so, critical points are (1,1/2)

to find local maximum or minimum we have to find  [tex]f_{xx}[/tex]  , [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]

formula is  [tex]f_{xx}[/tex]* [tex]f_{yy}[/tex] - [tex]f_{2xy}[/tex] =0

[tex]f_{xx}[/tex] = -2

[tex]f_{yy}[/tex] = -8

[tex]f_{2xy}[/tex]=0

putting values in formula

(-2)*(-8) -0 =16 > 0, and [tex]f_{xx}[/tex] < 0  and [tex]f_{yy}[/tex] <0

so, here we have local maximum

we have no saddle point for this function by using the same formula we used to find extrema.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the lines above

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{-3 +2}{2}\implies \boxed{-\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{13}-\underset{x_1}{15}}} \implies \cfrac{-1}{-2}\implies \boxed{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \textit{different slopes, \underline{not parallel}}~\hfill[/tex]

Considering a rectangular plot measuring 16 by 25 feet in a community garden the equation that models the the number of tomato plant and the number of pepper plant is 8x + 5y = 400

given data

a rectangular plot measuring 16 by 25 feet

area to grow tomato plants = 8 square feet

area to grow pepper plants = 5 square feet

From the  given data the total area is

Area = 16 * 25

Area = 400 square feet

let the number of area required by tomato plant be x and the area required by pepper plant be y

The equation that models how many tomato plants and how many pepper plants you can grow can be written as

8x + 5y = 400

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Answer:

Trisha should save for 18 weeks.

Step-by-step explanation:

1 week = $25

Total = $350

Also wants over $100

350+100 = 450

450 ÷ 25 = 18

Answer:

d, e, a, b, h, c, f, g

Step-by-step explanation:

if you convert them all to decimals you get

a = 0.57

b = 0.64

c = 1.6

d = 0

e = 0.4

f = 2.5

g = 4.3

h = 1.2

in order it goes 0, 0.4, 0.57, 0.64, 1.2, 1.6, 2.5, 4.3

Answer:

0.95

Step-by-step explanation:

19/20

19÷2/20÷2

9.5/10

0.95

Answer:

13/4 or 3.25

Step-by-step explanation:

Since they are vertical angles, they are equal to each other. Thus, set the two equations together:

8x + 32 = 12x + 19

Isolate x

32 = 12x + 19 - 8x = 4x + 19

32 - 19 = 4x

4x = 13

4x/4 = 13/4 = 3.25

In this problem bout segment has the same distance so we can write an equation like:

So the answer is 14.8

The cost of 6 bottles of juice is $2.34 if the each bottle costs the same.

According to the question,

We have the following information:

Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.

Cost of 20 bottles of juice = $7.80

Now, from here we can find the cost of 1 bottle of juice by dividing the total cost by the number of bottles purchased.

Cost of 1 bottle of juice = $(7.80/20)

Cost of 1 bottle of juice = $0.39

Now, we can easily find the cost of 6 bottles of juice by multiplying the cost of 1 bottle of juice by 6.

Cost of 6 bottles of juice = $(0.39*6)

Cost of 6 bottles of juice = $2.24

Hence, the cost of 6 bottles of juice is $2.24.

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y=10-2x..(3)

[tex]3x+4(10-2x)=12\\\\3x+40-8x=12\\3x-8x=12-40\\-5x=-28\\\frac{-5x}{-5} =\frac{-28}{-5} \\x=\frac{28}{5}[/tex]

[tex]y=10-2(\frac{28}{5} )\\y=10-\frac{56}{5} \\y=-\frac{6}{5}[/tex]

Answer: 100 = 4x + 6y

Step-by-step explanation:

We have a total of 100 guests, small tables seat 4, and large tables seat 6. So for each small table used, 4 guests are subtracted from the total.

x = small tables

y = large tables

The value obtained for f(3) after substituting x = 3 in the function f(x) is 0.0067.

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

The list of function formulas is divided into two categories: formulas for performing numerous arithmetic operations across functions and formulas for performing combined operations involving two or more functions.

The given function is f(x) = (1/7)/(7x)

We need to find the value of f(3) so we will substitute x = 3 in the given function as follows:

f(3) = (1/7)/(7×3)

∴ f(3) = (1/7)/21

∴ f(3) = 0.142/21

∴ f(3) = 0.0067

Therefore, after substituting x = 3 in the function f(x), the value obtained for f(3) is 0.0067.

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[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 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}{(-4)}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}[/tex]

The value of x is determined by solving the equation  14 + 5/7x - 20 = 4/7x - 4, which is: x = 14.

When given an equation, to solve the equation means to find the value of the variable in the equation.

Given the equation:

14 + 5/7x - 20 = 4/7x - 4

Combine like terms

5/7x - 6 = 4/7x - 4

Add 6 to both sides

5/7x - 6 + 6 = 4/7x - 4 + 6

5/7x = 4/7x + 2

Subtract both sides of the equation by 4/7x:

5/7x - 4/7x = 4/7x + 2 - 4/7x [subtraction property of equality]

x/7 = 2

Multiply both sides by 7

x/7(7) = 2(7) [multiplication property of equality]

x = 14

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The line e is parallel to f by converse alternate interior angles theorem.

What is converse alternate interior angle theorem?

Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

What is parallel lines?

Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.

Given,

angle 1 is congruent to angle 2 and g is parallel to h.

similarly, angle 2 is congruent to angle 3,

by transitive property angle 1 is congruent to angle 3.

By converse alternate interior angle theorem, e is parallel to f.

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Answer:

168

Step-by-step explanation:

= 2[3-{3(-9)(3)}]

= 2[3-{-81}]

= 2(84)

= 168

Hope it helps!!
BTW it was very easy...

If one student is chosen at random, the probability that the student was a female and got 'A' is 0.38

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.

The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will learn the likelihood of various outcomes in a random experiment.

The total number of outcomes that can occur should be known before calculating the likelihood that a specific event will occur.

Total numbers of students = 53

Total numbers of females = 34

Total numbers of females of A grades = 20

So probability = 20/53

                        = 0.38

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Answer:

Step-by-step explanation:

Answer:

Domain: All real numbers

Range:  f(x) ≥ 5 or f(x) < 2

Step-by-step explanation:

The given graph is a graph of a piecewise function.

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

When graphing piecewise functions:

Domain

The domain of a function is the set of all possible input values (x-values).

From inspection of the graph, the arrows show that the function continues indefinitely in both the positive and negative directions.

The value of x = 1 is not included in the left part of the graph, but it is included in the right part of the graph.

Therefore, the domain of the function is all real values of x:  

Range

The range of a function is the set of all possible output values (y-values).

From inspection of the graph, there is an open circle at y = 2 and a closed circle at y = 5.  Therefore, there are no y-values in the interval:
2 ≤ y < 5.

Therefore, the range of the function is f(x) < 2 or f(x) ≥ 5:

Using proportions with mixed numbers, the inequality to determine the minimum number of hours she needs to practice on each of the 3 days is: m ≥ 3/4.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example is the mean of a data-set, as the mean is given by the sum of all observations in the data-set divided by the number of values.

For this problem, we have that:

Hence the minimum number of hours that she still needs to practice is:

5 - 2.75 = 2.25 hours.

The amount is split evenly amount the 3 days, hence the lower bound of the inequality is:

2.25/3 = 0.75 = 3/4.

Hence the amount is given by:

m ≥ 3/4.

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Answer:

6

Step-by-step explanation:

If f(n) is f(-6), that means you need to input -6 in any places that have n in them.

f(-6) = --6

Two negatives make a positive.

f(-6) = 6

Hope this helps! :)

Hello!

To find the value of f(-6)

 ==> must plug '-6' into n's position in the equation

    f(-6) = -(-6) = 6

Hope that helps!

Answer:

If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Step-by-step explanation:

Answer:If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Step-by-step explanation:

Step-by-step explanation:

730 teens voted.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

Given Data

Teens to adult ratio 10:9

Total people votes = 1387

Ratio of teen vote:

= 1387 × [tex]\frac{10}{19}[/tex]

= 73(10)

= 730

730 teens votes.

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Answer:

you can buy 5 cans

Step-by-step explanation:

$2 per can

have $10

10 divided by 2

5

The fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

A bird of species A, when diving, can travel four times as fast as a bird of species B at top speed which is given in the question.

Let b = the speed of bird species B.

So the speed of bird species A is 4b.

If the total speed for these birds is 170, then there is an equation :

⇒ 4b + b = 170.

⇒ 5b = 170

⇒ b = 170/5 = 34 mi/hr.

So the speed of bird species A will be 4×34 ⇒ 136 mi/hr.

Therefore, the fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.

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