The figure below is painted on the street. It consists of a rectangle and an isosceles triangle.

The rational function that meets all the conditions is:

[tex]f(x) = \frac{-15}{(x - 3)*(x + 5)}[/tex]

A rational function is of the form:

[tex]f(x) = \frac{p(x)}{q(x)}[/tex]

As the horizontal asymptote is at y = 0, we know that the numerator can't depend on x, so it is just a constant.

p(x) = a

And we want to have two vertical asymptotes at x = 3 and x = -5, then q(x) becomes zero at these values, so we have:

q(x) = (x -3)*(x + 5)

At this point, the function is:

[tex]f(x) = \frac{a}{(x - 3)*(x + 5)}[/tex]

Finally, we know that the y-intercept is 1, then we need to solve:

[tex]f(0) = 1 = \frac{a}{(0 - 3)*(0 +5)} = \frac{a}{-15} \\\\-15 = a[/tex]

Then we conclude that our function is:

[tex]f(x) = \frac{-15}{(x - 3)*(x + 5)}[/tex]

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The solution to the equations 2x + 3y = 3, x – 2y = 5 using substitution method is y = -1 and x = 3 respectively.

2x + 3y = 3

x – 2y = 5

from equation (2)

x = 5 + 2y

Substitute x = 5 + 2y into equation (1)

2x + 3y = 3

2(5 + 2y) + 3y = 3

10 + 4y + 3y = 3

10 + 7y = 3

7y = 3 - 10

7y = -7

y = -7/7

y = -1

Substitute y = -1 into (2)

x – 2y = 5

x - 2(-1) = 5

x + 2 = 5

x = 5 - 2

x = 3

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Answer:

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = [tex]\frac{3}{5}[/tex] and (a, b ) = (4, - 6 ) , then

y - (- 6) = [tex]\frac{3}{5}[/tex] (x - 4) , that is

y + 6 = [tex]\frac{3}{5}[/tex] (x - 4)

The solution of the inequality is x ≥ -3 and the graph is shown below

From the question, we are to determine the graph that represents the given inequality

The given inequality is

−3x + 1 ≤ 10

First, we will solve the inequality

−3x + 1 ≤ 10

Subtract 1 from both sides

−3x +1 -1 ≤ 10 - 1

−3x ≤ 9

Divide both sides by -3 and flip the sign

x ≥ -3

The graph of the inequality is shown below

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Answer:

refer to the above attachment

Answer:

(0, 5)

(1, 6)

(4, 7)

(9, 8)

Step-by-step explanation:

y = √x + 5

y = √0 + 5

= 5

y = √1 + 5

= 6

y = √4 + 5

= 2 + 5

= 7

y = √9 + 5

= 3 + 5

= 8

After completing their trade, Store Owner A has 0 puzzles and 10 puppets, and Store Owner B has 30 puzzles and 0 puppets.

Here,

Let's assume the two toy store owners are Store Owner A and Store Owner B.

Before the trade, Store Owner A has 30 puzzles and 0 puppets, and Store Owner B has 0 puzzles and 10 puppets.

They agree to trade 30 puzzles for 10 puppets at a rate of 3 puzzles for each puppet.

So, for every 3 puzzles, Store Owner A will receive 1 puppet.

Store Owner A gives away 30 puzzles and receives 30 / 3 = 10 puppets.

After the trade, Store Owner A has 0 puzzles and 10 puppets.

Store Owner B gives away 10 puppets and receives 10 * 3 = 30 puzzles.

After the trade, Store Owner B has 30 puzzles and 0 puppets.

So, after completing their trade, Store Owner A has 0 puzzles and 10 puppets, and Store Owner B has 30 puzzles and 0 puppets.

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Answer:

the slope of a line is parallel to the line is (3,-2)

(0,2)

The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

The given parameters are:

Number of uniform = 8

Cost of each = $14

The cost of the uniforms and the shorts is then calculated as:

Cost = Number of uniforms * (Cost of uniform + Cost of short)

This gives

Cost= 8 * (14 + c)

Expand

Cost = 112 + 8c

Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

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Answer:

B. One

Step-by-step explanation:

Since the two angles are already given, the value of the third angle is already fixed. The third angle can be found by the sum of both angles subtracted from 180. Since 2 angles and lengths are already given, there can only be 1 triangle.

Hope this helps!

If not, I am sorry.

Diving the length AB into equal parts gives;

[tex]D→\left (4 \:,4.5\right) [/tex]

[tex]E→\left (5 \:,4.75\right) [/tex]

[tex]H→\left (8 \:,5.5\right) [/tex]

[tex]I →\left (9 \:,5.75\right) [/tex]

The number of equal parts obtained by counting are 8

Coordinates of point A is (2, 4)

Coordinates of point B is (10, 6)

Therefore;

Coordinates of point C is

[tex]\mathbf{ \left (2 + \frac{10 - 2}{8},\: 4 + \frac{6 - 4}{8}\right) }= \left (3 \:, 4.25\right) [/tex]

Coordinates of point D are;

[tex]\mathbf{\left (2 + \frac{10 - 2}{4} \: , 4 + \frac{6 - 4}{4}\right) }= \left (4 \:,4.5\right) [/tex]

Coordinates of point E are;

[tex]\mathbf{\left (2 + \frac{8 \times 3}{8} \: , 4 + \frac{2 \times 3}{8}\right)} = \left (5 \:,4.75\right) [/tex]

Coordinates of point F are;

[tex] \mathbf{\left (2 + \frac{8 \times 4}{8} \: , 4 + \frac{2 \times 4}{8}\right)} = \left (6 \:,5\right) [/tex]

Coordinates of point H are;

[tex]\mathbf{\left (2 + \frac{8 \times 6}{8} \: , 4 + \frac{2 \times 6}{8}\right)} = \left (8 \:,5.5\right) [/tex]

Coordinates of point I are;

[tex]\mathbf{\left (2 + \frac{8 \times 7}{8} \: , 4 + \frac{2 \times 7}{8}\right)} = \left (9 \:,5.75\right) [/tex]

Which gives;

[tex]D→\left (4 \:,4.5\right) [/tex]

[tex]E→\left (5 \:,4.75\right) [/tex]

[tex]H→\left (8 \:,5.5\right) [/tex]

[tex]I →\left (9 \:,5.75\right) [/tex]

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Answer:

$1265

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here length = 40 and  A = 2800 , then

2800 = 40 × width ( divide both sides by 40 )

70 = width

the perimeter (P) is calculated as

P = 2(length + width) = 2(40 + 70) = 2 × 110 = 220 ft

cost = 220 × $5.75 = $1265

Answer:

$1265

Step-by-step explanation:

area = length × width

area = 2800

length = 40

2800 / 40 = 70

So, the width of the lot is 70ft , and the length is 40

when building a fence, it would surround the entire property's perimeter (which is the length of the outside edges/sides of the shape added together)

so, it would need to cover 70 + 40 + 70 + 40

(the perimeter = 70 + 40 + 70 + 40)

= 220

so, if each foot costs 5.75, we can multiply 220 × 5.75 to find the cost:

220 × 5.75 = 1265

So, this will cost him $1265

hope this helps! have a lovely day :)

14  triangles with exactly two equal sides can be formed

The triangles will be isosceles as there have to be 2 equal sides.

The possible triangles are :

2 2 3      3 3 2        5 5 2       7 7 2         11  11  2

             3 3 5        5 5 3       7 7 3         11  11  3

                             5 5 7       7 7 5         11  11  5

                                            7 7 11       11  11  7

So 14   triangles are possible

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Answer:

30 degrees

Step-by-step explanation:

180-56-90=34

34 rounded off to nearest tenth is 30

Answer:

62.9643082106 degrees

Step-by-step explanation:

First, notice that triangle ABC is a right triangle. This allows us to use SIN, COS, and TAN to find the measure of angle A. Recall SOH CAH TOA, so SIN = OPPOSITE / HYPOTENUSE, COS = ADJACENT / HYPOTENUSE, and TAN = OPPOSITE / ADJACENT.

Looking at angle A, sides c and b correspond to hypotenuse and adjacent respectively. Therefore, we can use COS to set up an equation.

cos(A) = b/c

cos(A) = 5/11

A = arccos(5/11)

A = 62.9643082106 deg

Answer:

21.1

Step-by-step explanation:

sin 49 = x / 28

0.75470958 = x/28

x = 21.1

Answer:

x=18.4

y=35

Step-by-step explanation:

So to solve for x, you're going to use one of the six trigonometric functions (you really only need to use the three main ones, sin, cos, and tan, to solve these problems). In this case you know the adjacent of the angle 49 degrees, and the hypotenuse. There is a trigonometric function which is defined as: [tex]\frac{adjacent}{hypotenuse}=cos(\theta)[/tex]. So let's plug in the known values:

[tex]cos(49) = \frac{x}{28}[/tex]

Multiply both sides by 28

[tex]cos(49) * 28 = x\\[/tex]

Calculate cos(49) using a calculator (make sure it's in degree mode):

[tex]0.656 * 28 \approx x[/tex]

[tex]18.4 \approx x[/tex]

So the second problem, you need to use the inverse of one of the trigonometric function, which essentially takes what f(x) is, and returns x. So in this case we're looking for a trigonometric function that is defined using the opposite and adjacent side, which tan is. [tex]tan(\theta)=\frac{opposite}{adajcent}[/tex]. In this case opposite=19, and adjacent=27. So plug in the known values:

[tex]tan(y)=\frac{19}{27}[/tex]

Apply the inverse of tan to both sides

[tex]y=tan^{-1}(\frac{19}{27})[/tex]

Calculate inverse of tan of 19/27 using a calculator:

[tex]y\approx35[/tex]

Answer:

Step-by-step explanation:

In the give diagram, the value of f is 6.0

From the question, we are to determine the value of f

Using the law of sines, we can write that

[tex]\frac{f}{sinF} =\frac{e}{sinE}[/tex]

From the given information,

F = 27°

e = 13

E = 98°

Putting the parameters into the equation, we get

[tex]\frac{f}{sin(27)} =\frac{13}{sin(98)}[/tex]

[tex]\frac{f}{0.4540} =\frac{13}{0.9903}[/tex]

[tex]f=\frac{13 \times 0.4540}{0.9903}[/tex]

f = 5.9598

f ≅ 6.0

Hence, the value of f is 6.0

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Part A

If the number is n, then the expression is 7n+6.

Part B

Three times the sum of a number and 8.

Answer:

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

Step-by-step explanation:

the formula of a circle is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

knowing the values of h, k, and r we can substitute them into the formula

knowing the

The profit percent of supplier is 17.972 %

The given parameters are:

Start by calculating the selling price without VAT

Selling price = Rs 47460 * (1 - 13%)

Evaluate

Selling price = Rs 41290.2

The percentage profit is then calculated as:

Percentage profit = (Selling price - Cost price)/Cost price * 100%

This gives

Percentage profit = (41290.2 - 35000)/35000 * 100%

Evaluate

Percentage profit = 17.972 %

Hence, the profit percent of supplier is 17.972 %

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Answer:

if x=0 then they have same value

1st and 2nd options are out

for x=-1

g(-1)=1

h(-1)=-1

3rd is true

4th

false

for all values except zero, g(x)>h(x)

correct ones are

ANSWER: g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.

To gauge the strength of the linear link between two variables, correlation coefficients are used.

For a value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.

Zero correlation coefficient means there is no correlation between the two variables under comparison.

A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.

Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.

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Answer:

k = - 3 1/6

Step-by-step explanation:

-8-3k(2)=11

-8-6k = 11

8 - 8 - 6k = 11 + 8

-6k = 19

-6k/-6 = 19/-6

k = -3.16667

k = -3 1/6

The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

According to statement

In location A the chance that two people have four repeats is  1 in 100.

In location B the chance that two people have eight repeats is  1 in 50.

In location C the chance that two people have three repeats is  1 in 200.

So, to find the probability that two people would have matching DNA fingerprints for these three locations

Multiply the all chances in these locations:

1/100 x 1/50 x 1/200 = 1/1,000,000    

So, The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

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The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

Given the expression: 2x² - x - 6

First, we factor -1 out of -x

2x² - x - 6

2x² -1(x) - 6

Not that, -1 can also be written as 3-4

2x² + (3-4)x - 6

2x² + 3x - 4x - 6

Next, we group the first two terms and the last two terms and factor out the GCF

(2x² + 3x) - 4x - 6

x(2x + 3) - 2( 2x + 3)

Factor out the GFC which is ( 2x+3 )

We have; ( 2x + 3 )( x - 2 )

The factorized form of the expression ( 2x² - x - 6 ) is ( 2x + 3 )( x - 2 ).

Hence, the missing values are 3 and 2 respectively.

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The sample space neeeded for the experiment to find the face cards is 52.

Given there is a standard deck of cards.

We have to finf the sample space needed for the experiment of finding the probability of face cards.

Probability is the chance  of happening an event among all the events that are possible. It lies between 0 and 1. The probability is the number of items divided by the total items.

Sample is a part of population. It is studied when the study of whole population is difficult to do.

Cards in a deck=52

Number of face cards is 12.

When we  draw a card from the deck then it might be a face card or not. So we have to draw all the cards of a standard deck because it might possible that face card is present at the end of deck.

Hence the sample size needed in the experiment is 52.

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Answer:

a= 79° because they are in the position of co interior and b°is 101 it's self because of VOA