(5x+1)(3x-5)-(x-3)(5x+1)

Since the rectangle's shorter side is half as long as its longer side, its top left vertex is (0,a).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

Here,

Let x be the length and y be the width,

y=x/2

x=2a

y=a

The top left vertex=(0,a)

The top left vertex is (0,a) as shorter side of the rectangle is half the length of the longer side.

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The y-intercepts of the functions are

The complete question is added at the end of this solution as an attachment

As a general rule, the y-intercept is the point in an equation or a function where x = 0

Using the above as a guide, we have the following:

For the function g(x), we have

g(x) = abˣ

Using the given points (1, -2) and the growth factor of 2, we have

g(x) = a(2)ˣ

This means that

a(2)¹ = -2

So, we have

2a = -2

a = -1

So, the equation is

g(x) = -1(2)ˣ

Set x = 0

g(0) = -1(2)⁰

g(0) = -1

So, the y-intercept of function g(x) = -1

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The number of miles that you ran on the treadmill on Monday will be 3 miles.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

On Monday you run on the treadmill for thirty minutes at x mph and on Tuesday you walk a similar distance on the treadmill at 2 mph increasingly slow takes you three-fourths 60 minutes.

Then the distance is the same in both cases. Then we have

x × (1/2) = (x - 2) × (3/4)

Simplify the equation, then we have

x × (1/2) = (x - 2) × (3/4)

4x = 6(x - 2)

4x = 6x - 12

2x = 12

x = 6 miles per hour

The number of miles is given as,

D = 6 × 1/2

D = 3 miles

The number of miles that you ran on the treadmill on Monday will be 3 miles.

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The values of the angles for the given figure are m  ∠M=76°,

m ∠N=76°.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.

Given,

In ΔLMN,

m ∠L=28°

As we know that,

Angle sum in a triangle=180°

m ∠L+ m ∠M+ m ∠N=180°

From the figure,

m ∠M= m ∠N

So, m ∠L+ m ∠M+ m  ∠M=180°

28°+ 2 m  ∠M=180°

2 m  ∠M=180°-28°

2 m  ∠M=152°

m  ∠M=76°

So, m  ∠N=76°

Therefore, the values of the angles for the given figure are m  ∠M=76°,

m  ∠N=76°.

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[tex]\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} X(\stackrel{x_1}{6},\stackrel{y_1}{0})\\ Y(\stackrel{x_2}{2},\stackrel{y_2}{8})\\ Z(\stackrel{x_3}{-2},\stackrel{y_3}{-2}) \end{cases} \\\\\\ \left( \cfrac{6+2-2}{3}~~,~~\cfrac{0+8-2}{3} \right)\implies \left(\cfrac{6}{3}~~,~~ \cfrac{6}{3} \right)\implies \text{\LARGE (2~~,~~2)}[/tex]

The value of x in the triangle is 26.1°

A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Acute triangle - all three angles are less than 90°

Right triangle - one angle is 90°

Obtuse triangle - one angle is greater than 90°

Equilateral triangle - all three sides are the same length

Isosceles triangle - two sides are the same length

Scalene triangle - all three sides are different lengths

Since the triangle is right-angled

tan x = opposite/adjacent

tan x = 26/53

tan x = 0.4905

x = arc(tan) 0.4905

x = 26.1°

In conclusion x = 26.1°

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The final cost is lie between the amount $46.00 and $92.00.

What is an equation?

When two expressions are connected with both the equals sign (=) in a mathematical formula, it expresses this same equality of the two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, an equation in French is defined as having one or maybe more variables, whereas in English, an equation is any properly formed formula that consists of two expressions linked by the equals sign.

The coupon is given = 15% off

New price = Cost of meal (1 - coupon)

Now Substitute the known values in the equation;

New price = between 55(1 - 15%) and 100.00 (1 - 15%)

Evaluate;

The final cost of the meal is between $40.00 and $80.00

Tip = 22%

Thus Final cost = New price (1 + tip)

Now Substitute the known values in the equation

Final cost = Between 40.00 (1 + 22%) and 80.00 (1 + 22%)

The Final cost is Between $46.00 and $92.00

Hence, the final cost is lie between the amount $46.00 and $92.00

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Answer:

D

Step-by-step explanation:

2 times 5x is 10x, and 2 x 1 is 2

Answer:

655

Step-by-step explanation:

20% is the percent decrease in the number of people who went to the pool over these four​ weeks

percentage, a relative value indicating hundredth parts of any quantity.

Given,

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

1020-100=920

In the third​ week,130 more people went to the pool than in the second week.

920+130=1050

In the fourth​ week, 234 fewer people went to the pool than in the third week.

1050-234=816

Now we need to find the percent decrease in the number of people who went to the pool over these four​ weeks

1020-816=204

204/1020=0.2×100=20

Hence, 20% is the percent decrease in the number of people who went to the pool over these four​ weeks

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Answer: x < -3

Step-by-step explanation: even tho if we solve you will get a big number number then you reduce the number to a smaller number

Answer:

c=-35/4

Step-by-step explanation:

For this, we would use Vieta's theorem, which states the roots of the equation added together would equal -b/a, x₁ + x₂ = -b/a

Lets create a system with this:
x₁ - x₂ = 6 (This is given from the problem)

x₁ + x₂ = -b/a  or -1/1, plugging in the values from your equation

next, we would add these systems together

x₁ + x₂ + (x₁ - x₂) = 6 + (-1)
x₁ + x₁ = 5
2x₁ = 5

x₁ = 2.5

If we plug x₁ back in, we get:

2.5 - x₂ = 6

-x₂ = 3.5

x₂ = -3.5

Now that we have the roots, we can use Vieta's theorem again to say

x₁ * x₂ = c/a

Plugging this in, we get:

2.5 * -3.5 = c/a

Lets change things to fractions to make things easier

5/2 * -7/2 = c/a

Plugging in a, we get

-35/4 = c/1

-35 = 4c

c = -35/4

Hope this helps!

By studying the graph of the function, it can be inferred that -

Domain = [-3, 3]

Range = ([tex]-\infty[/tex], 4]

Local maximum = 0, 4

Local minimum = -0.5

Increasing interval = [-3, -2) [tex]\cup[/tex] (-1, 2)

Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]

There is no constant interval.

What is graph of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of all points of the form (x, f(x)).

Suppose the size of each square of the graph is 1 unit

From the graph, it can be seen that the value on the horizontal axis ranges from -3 to 3

Domain = [-3, 3]

The value on the vertical axis ranges from [tex]-\infty[/tex] to 4

Range = ([tex]-\infty[/tex], 4]

The graph has a local maximum at (2, 4) and (-2, 0)

Local maximum = 0, 4

The graph has local minimum at (-1, -0.5)

Local minimum = -0.5

Increasing interval [-3, -2) [tex]\cup[/tex] (-1, 2)

Decreasing interval = (-2, -1) [tex]\cup[/tex] (2, 3]

There is no constant interval.

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m = 5 and m = -9/5 are the roots of the equation.

Factoring  4m²-11m-45

The first term is,  4m²  its coefficient is  4 .

The middle term is,  -11m  its coefficient is  -11 .

The last term, "the constant", is  -45

Step-1 : Multiply the coefficient of the first term by the constant   4 • -45 = -180

Step-2 : Find two factors of  -180  whose sum equals the coefficient of the middle term, which is   -11 .

     -180    +    1    =    -179

     -90    +    2    =    -88

     -60    +    3    =    -57

     -45    +    4    =    -41

     -36    +    5    =    -31

     -30    +    6    =    -24

     -20    +    9    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  9

                    4m² - 20m + 9m - 45

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4m • (m-5)

             Add up the last 2 terms, pulling out common factors :

                   9 • (m-5)

Step-5 : Add up the four terms of step 4 :

                   (4m+9)  •  (m-5)

            Which is the desired factorization

Theory - Roots of a product

Now ,

1.   Solve  :    m-5 = 0

    Add  5  to both sides of the equation :

                     m = 5

2. Solve  :    4m+9 = 0

   Subtract  9  from both sides of the equation :

                     4m = -9

   Divide both sides of the equation by 4:

                   m = -9/4

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Answer:

12.40mph

Step-by-step explanation:

The equations on the graph have no solution

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

y = -3(x - 1)

y = -3x - 1

Also, we have:

The lines are parallel to each other.

As a general rule:

Parallel lines are lines that do not intersect and they have the same slope

Because the lines do not intersect, it means that the system do not have any solution

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a sports team has 99 jerseys numbered 1, 2, 3, . . . , 99. show your work for each part, 49 pairs many ways are there to choose 2 different jerseys, without order, such that their numbers sum to 100, using the concept of combination formula.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The formula becomes: [tex]^nC_r[/tex]

Where, n = total number of objects

r = number of choosing objects.

Sports team has 99 jerseys. So, 49 pairs will be possible to have their sum is 100.

Example - (1+99), (2+98),......,(49+51)

Thus, there are 49 ways to choose two different jerseys.

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Answer: 3 years

Step-by-step explanation:

According to the given statement the answer of angle A is  [tex]\mathrm{m} \angle A=65^{\circ}[/tex].

A parallelogram with the opposing sides perpendicular is called a quadrilateral (and therefore opposite angles equal). A parallelogram among all right angles generally known as a rectangle, whereas a quadrilateral having equal angles is known as a rhombus.

[tex]\mathrm{m} \angle F G D=35^{\circ}\\\mathrm{m} \angle DFG=180^{\circ}-69^{\circ}\\\\[linear pair of angle]\\mathrm{m} \angle DFG=111^{\circ}\\\mathrm{m} \angle F DG=180^{\circ}-(35^{\circ}+111^{\circ})\\\\mathrm{m} \angle F DG=34^{\circ}[/tex]

because DC||AB, so  

[tex]\mathrm{m} \angle BDC={m} \angle ABD=Alternate angle[/tex]

[tex]so, \mathrm{m} \angle ABD=34^{\circ}[/tex]

because the sum of interior angle of a triangle = 180

[tex]so, \mathrm{m} \angle A=180^{\circ}-(81^{\circ}+34^{\circ})\\ \mathrm{m} \angle A=65^{\circ}[/tex]

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The solution to the problem expressed to the correct number of significant figures is, 2.13 + 1 = 3

Given that,

The solution to the problem expressed to the correct number of significant figures,

2.13 + 1 = ?

Unit is a quantity of constant magnitude which is used to measure the magnitudes of other quantities of the same manner.

Unit can be defined as the rightmost position in a number or the one's place. Here, 3 is the unit's number in the number 6713. A unit may also mean the standard units used for measurement.

You must round your answer to the same "place" when adding values as the measurement with the last significant figure that is farthest to the left.

= 2.13

= +1

= 3.13

The “1” has its last significant figure furthest to the left, so you round off the number to the “units" place. That's the last column that the measurements share.

3.13 → 3 (rounded to the "units" place)

Therefore,

The solution to the problem expressed to the correct number of significant figures is, 2.13 + 1 = 3

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The true mean of the data-set is given as follows:

46.35.

The mean of a data-set is calculated as the sum of all observations divided by the number of observations.

In this problem, the sum is given by the multiplication of the mid-values by the number of students with each value, as follows:

S = 37.5 x 30 + 42.5 x 20 + 47.5 x 15 + 52.5 x 13 + 57.5 x 22 = 4635.

The total number of students is given as follows:

30 + 20 + 15 + 13 + 22 = 100.

Hence the mean is calculated as follows:

Mean = 4635/100 = 46.35.

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Answer:

Step-by-step explanation:

-0.17301038

The triangles are then congruent according to the SAS congruence criteria for triangles.

Congruent triangles are those with the same size and form. This signifies that the respective sides are equal, as are the corresponding angles. We can determine if two triangles are congruent without evaluating all of their sides and angles. The phrase "congruent" refers to having exactly the same form and dimension. Even if we flip, turn, or rotate the forms, the shape and size should remain the same. In terms of shape and size, the adjective "congruent" implies "absolutely equal." The forms remain equal even when we spin, flip, or rotate them. Draw two circles with the same radius, then cut them out and stack them on top of each other.

Here,

If I understood correctly, then first let's call the angle BAC = CAD = α. From the statement we have angle ABC = 90° (AB ⊥ BC) and also angle ADC = 90° (AD ⊥ DC).

Then we have: angle BCA = ACD = 90 - α

We the have that:

AC = AC (the triangles share this size)

angle BCA = ACD

angle BAC = CAD

Then the triangles are congruent due to SAS criterion of congruence for triangle.

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By algebra properties we find the following relationships between each pair of algebraic expressions:

In this we must determine the equivalent algebraic expression related to given expressions, this can be done by applying algebra properties on equations from the second column until equivalent expression is found. Now we proceed to find for each case:

First equation

(7 - 2 · x) + (3 · x - 11)

(7 - 11) + (- 2 · x + 3 · x)

- 4 + (- 2 + 3) · x

- 4 + (1) · x

- 4 + (5 - 4) · x

- 4 - 4 · x + 5 · x

- 4 · (x + 1) + 5 · x → Case 4

Second equation

- 7 + 6 · x - 4 · x + 3

(6 · x - 4 · x) + (- 7 + 3)

(6 - 4) · x - 4

2 · x - 4

2 · (x - 2) → Case 1

Third equation

9 · x - 2 · (3 · x - 3)

9 · x - 6 · x + 6

3 · x + 6

(2 + 1) · x + (14 - 8)

[1 - (- 2)] · x + (14 - 8)

(x + 14) - (8 - 2 · x) → Case 2

Fourth equation

- 3 · x + 6 + 4 · x

x + 6

(5 - 4) · x + (7 - 1)

(7 + 5 · x) + (- 4 · x - 1) → Case 5

Fifth equation

- 2 · x + 9 + 5 · x  + 6

3 · x + 15

3 · (x + 5) → Case 3

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Answer:

$0.27875 or $0.28 1 cup = 2 ounces Number of cups in 1 jar = 4 ounce

Step-by-step explanation:

When a population is subjected to directional selection over time, the traits that are selected for will remain stable while the traits that are selected against will disappear.

Evolution is the study of how populations change over time. Most traits have multiple genes controlling their structure, function, appearance, and other characteristics. Single genes only very infrequently control a trait.

As a result, most traits have a tendency to be continuous in nature and to have a wide range of values. One side of these values will be picked against during directional selection, while the other side will be selected in favor of. Look at the illustration of a lemur's fur color below.

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Answer:

a) 5

b) -4/3

c) y = -4/3x - 11/3

Step-by-step explanation:

The length of the segment means the length in between two points. Use 2 dimensional distance formula.

[tex]d = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 }[/tex]

Plug in your points.

x value is the first point in the set, the horizontal measure in units.

y value is the second point in the set, the vertical measure in units.

x values of 2 points: -2, -5

y values of 2 points: -1, 3

[tex]d = \sqrt{(-5--2)^2 + (3--1)^2 }[/tex]

A negative value subtracted by another negative value is the first negative value plus the inverse of the second negative value.

For example,

-5 - -6 = -5 + 6 = 1

Simplify.

[tex]d = \sqrt{(-3)^2 + (4)^2 }[/tex]

[tex]d = \sqrt{9 + 16}[/tex]

[tex]d = \sqrt{25}[/tex]

5

Square root of 25 is 5 because 5^2, which is 5 x 5 is 25.

The slope is how much the y-value changes when the x-value increases by 1.

To calculate this, plug your points into the slope formula.

[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{3--1}{-5--2}[/tex]

[tex]\frac{4}{-3}[/tex]

-4/3

I'm going to assume that the problem is asking you to write it in the form of y=mx+b, or slope-intercept form, a way of easily graphing a line. If it  is asking you to express it in another way like Standard or Point-Slope Form, comment and I'll change it.

y = mx+b

m = slope

b = y-intercept, or the y-value of when the x-value is 0 on a line

y and x stays as variables if you want to graph it and for generally answering problems.

So, if x = 0, we can plug it into what we currently know.

We know the points: (-2,-1) or (-5,3)

Plug in either set of points into the slope-intercept equation.

I'll use -2,-1 but you can use either.

-1 = (-4/3) (-2) + b

Because we're solving for when x is 0, replace -2 for 0.

-1 = 8/3 + b

Subtract 8/3 on both sides.

-1 - 8/3 = 8/3 - 8/3 + b

-1 - 8/3 = b

b = -11/3

Now, the equation is:

y = -4/3x - 11/3

This is the beauty of the forms of linear equations. You can plug in any points to solve for the full set of points. You can convert any form of the linear equation to another form.

Bisector of the segment (3.5 , 5)

A line known as a bisector divides an angle or a line into two equally sized segments. A segment's midpoint is always contained in the segment's bisector.

A line segment's midpoint was crossed by the perpendicular bisector of the segment.

If C is the point on AB, through which its perpendicular bisector passes, then C = mid point of AB.

Mid x1 +x2/2 ,y1+y2/2

7+-2/2, 5+5/2

5/2,5

(3.5,5)

The angle bisector theorem states that PQ/PR = QS/RS or a/b = x/y. A line or ray that divides an angle in a triangle into two equal parts is known as an angle bisector.

Measuring the length of the line segment you need to bisect is an easy approach to discover a perpendicular bisector. Find the midpoint of the measured length by dividing it by two. From this midpoint, extend a line at a 90° angle.

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Given recursion function in options we have calculated values of f(1),f(2),f(3),f(4),f(5).

Find f(1), f(2), f(3), f(4), f(5) if f(0) = 3.

First recursive Function is given as

a) f(n+1) = -2*f(n)

f(1) = -2*f(0) = -2*3 = -6

f(2) = -2*f(1) = -2*(-6) =  12

f(3) = -2*f(2) = -2*12 = -24

f(4) = -2*f(1) = -2*(-24) = 48

f(5) = -2*f(4) = -2*(48) = -96

Second recursive Function is given as

b) f(n+1) = 3*f(n)+7

f(1) =  3*f(0)+7 = 3*3+7 = 16

f(2) = 3*f(1)+7 = 3*16+7=  55

f(3) = 3*f(2)+7 = 3*55+7 = 172

f(4) = 3*f(3)+7 = 3*172+7 = 523

f(5) = 3*f(4)+7 = 3*523+7 = 1576

Third recursive Function is given as

c) f(n+1) = [tex]f(n)^2-2*f(n)-2[/tex]

f(1) = f(0)*f(0)-2*f(0)-2 =3*3 - 2*3 - 2 = 1

f(2) = f(1)*f(1) - 2*f(1) - 2 = 1*1 - 2*1 - 2 =  -3

f(3) = f(2)*f(2) -2*f(2)- 2 =-3*(-3) - 2*(-3) - 2 = 13

f(4) = f(3)*f(3) -2*f(3)- 2 = 13*13 - 2*13 - 2 = 141

f(5) = f(4)*f(4) -2*f(4)-2 = 141*141 - 2*141 - 2 = 19597

Fourth recursive Function is given as

d) f(n+1) =  [tex]3^(f(n)/3)[/tex]

f(1) = 3^((f(0)/3) = 3^1 = 3

f(2) = 3^((f(1)/3) = 3^1 =  3

f(3) = 3^((f(2)/3) = 3^1 = 3

f(4) = 3^((f(3)/3) = 3^1 = 3

f(5) = 3^((f(4)/3) = 3^1 = 3  

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The probability of getting a number larger than 3 is P = 0.7

The probability is equal to the quotient between the number of outcomes that meet the condition, and the total number of outcomes.

The 10-sided die has the outcomes {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} so 10 outcomes.

The outcomes that are greater than 3 are {4, 5, 6, 7, 8, 9, 10} so there are 7 outcomes, then the probability is:

P = 7/10 = 0.7

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