if this same population size wants to start decreasing over time, the population growth rate needs to be

The possible values of k are -11 and 11.

Given that equation is: x²-kx+28

Roots are: [tex]\alpha ,\alpha +3[/tex]

To find: the value of x:

The general quadratic equation is:

ax²+bx+c

Product of roots=c/a

sum of roots=-b/a

From given,

x²-kx+28=0

a = 1

b = -k

c = 28

Therefore,

Product of roots=28/1=28

sum of roots=-k/1=-k

Given roots are:

[tex]\alpha ,\alpha +3[/tex]

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, the sum of roots is:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11.

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The measure of the side length CL is equal to 9m using trigonometric ratio of cosine 60° for thy right triangle ACL

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Angle m∠BAC = 180° - (m∠C + m∠ABC)

m∠BAC = 180° - (90° + 30°)

m∠BAC = 60°

line AL is an angle bisector so;

m∠CAL = 30° and m∠BAL = 30°

which implies triangle ∆ALB is an isosceles with line LB = AL = 18m

considering the right triangle ∆ACL;

angle m∠L = 180° - (90° + 30°)

m∠L = 60°

cos 60° = CL/18 {adjacent/hypotenuse}

1/2 = CL/18m {cos 60° = 1/2}

CL = 18m/2 {cross multiplication}

CL = 9m

Therefore, the side length CL is equal to 9m using trigonometric ratio of cosine 60° for the right triangle ACL.

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Answer: So 2(b+5) would be the answer to your question.

Step-by-step explanation:

The amount of glass needed to cover a table measuring 0.8m long and 0.65m wide is (d) 0.52m²

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

Length = 0.8 m

Width = 0.65 m

The area of a rectangle can be calculated using tge following equation

Area = Length * Width

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

Area = 0.8 * 0.65

Evaluate

Area = 0.52

Hence, the amount is 0.52 square meters

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Answer: 1/6

Step-by-step explanation:

2/6 - 1/6 = 1/6

Hi There!

Your Answer must be The Realation is a function or A...

Why did i get this answer?

To Find if a Graph is a Function, We must use the concept called vertical line test.

If the vertical line drawn across at anywhere of the graph intersects the graph at most once, we decide the given graph represents the function.

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Tasha has the highest batting average because 0.9(27/30) is greater than 0.8( 24/30 ) ( optionD)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The batting average for Jana is 12/15 = 0.8

The battling average for Tasha is 9/10 = 0.9

The battling average of Tasha is higher than that of Jana

0.6 can also be in form of 6/10

0.9 can also be in form of 9/10

therefore 8/10 = 24/30 and

9/10 = 27/30

Therefore Tasha has the highest batting average because 27/30 is greater than 24/30

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Answer:

27/30

Step-by-step explanation:

Answer: 1 1/2

Step-by-step explanation:

You have to do the keep change flip method where you keep the first fraction the same change the sign to a multiplication sign and flip the other fraction, it would then look like this: 1/2 x 3. after just multiply across and you get 1.5

The translations, reflections, and rotations are types of transformations that change an original object to form a new image, each with its own specific rule and properties. They are used in a variety of real-world applications to change the position or orientation of objects.

There are 3 types of Transformations :

(i) Translation: A translation involves moving an object from one place to another without changing its size or orientation.  

The algebraic rule for a translation is to add the same constant to each coordinate of each point

The Translations preserve congruence, meaning that corresponding parts of congruent figures will still be congruent after a translation.

An example of a real-world application of translation is moving a store to a new location.

(ii) Reflection: A reflection involves flipping an object over a line or point, creating a mirror image.

The algebraic rule for a reflection is to negate the value of one of the coordinates.

Reflections preserve orientation, meaning that the orientation of the reflected image is opposite that of the original object.

An example of a real-world application of reflection is looking at your reflection in a mirror.

(iii) Rotation: A rotation involves turning an object about a fixed point, called the center of rotation, through a certain angle.

The algebraic rule for a rotation is to multiply each coordinate by a rotation matrix.

Rotations preserve distance and angle measures, meaning that the lengths of corresponding parts and the angles between them are equal in the original and rotated images.

An example of a real-world application of rotation is turning a steering wheel to change the direction of a car.

The given question is incomplete , the complete question is

Compare and contrast the three types of transformations: translations, reflections, and rotations.

Include the algebraic rules, whether each transformation preserves congruence and any examples of real-world application.

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The solution of the equations using elimination method is x = 2.5, y = 5.25

The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.

8x+4y = 49 --- (1)

3x+2y = 21  ----(2)

To eliminate x, multiply (1) by 3 and multiply (2) by 8. Then subtract the result. That is:

3 × (8x+4y = 49)   = 24x + 12y = 147

8 ×(3x+2y = 21)    = 24x + 16y = 168

.......................................................................

                                          4y = 21

.........................................................................

4y = 21

y = 21/4

y = 5.25

Put y = 5.25 into (1):

8x+4y = 49

8x + 4(5.25) = 49

8x + 21 = 49

8x = 49 -21

8x = 28

x = 28/8

x = 3.5

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Answer: 9 points

Step-by-step explanation: 8 rounds=8 points; If Harriet has 19 points and they have played 8 rounds which equal 8 points, 19-8=9 points

1. A softball player can have six (6) possible outcomes

2. Six (6) combinations can be made.

Since the player bats six times, it means that there is possibility of having six outs, or six on base, or six homerun or even a mixture of the three outcomes in six times. The constant touch is six times

Since the sandwiches are just three types and can be ordered with either white bread or multi-grain bread, it means that there is possibility of having two different pairs each making six possible combinations of the available toppings.

Therefore, there will be six possible outcomes and six possible combinations of the sandwiches.

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The complete question goes thus:

1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun. How many possible outcomes can the player have?

2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings. How many combinations can be made?

The midpoint between the two given points is given by M(-4,-11)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates

Given here: The coordinates of the two points as  K(–20, 3) and L(12, –2).

We know that the midpoint of the line between the two points is given by

x=a+b /2

and y= c+d/ 2

Where the end points of the line is given by (a,b) and (c,d)

Thus x=-20+12 /2

         =-4

y= -20-2 /2

 =-11

Thus the midpoint has the co-ordinates M(-4,-11)

Hence, The midpoint between the two given points is given by M(-4,-11)

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Answer: A - (-4,1/2)

Step-by-step explanation: trust me bro...

Answer:

[tex]\displaystyle \frac{1}{10}(x+9)[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{10}x+\frac{9}{10}=\frac{1}{10}(x+9)[/tex] because [tex]\displaystyle \frac{1}{10}(x+9)=\frac{1}{10}(x)+\frac{1}{10}(9)[/tex] by the Distributive Property

In a case whereby  walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 0.41 the distance from the monument at this point is 5.63km

The concept that will be use is bearing. A bearing is the angle, measured in degrees clockwise from north, in mathematics. In most cases, bearings are specified as three-figure bearings. For instance, the standard notation for 30° clockwise from north is 030°.

From the diagram we can see that the interpretation gave us a triangle and from trigonometry,

Cos θ= adjacent / hypothenus

Then  Cos 41 = XY/XM

Cos 41 = XY/7.5

0.75 = XY/7.5

0.75 *7.5 =5.63km

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Answer:

22%

Step-by-step explanation:

[tex]\frac{11}{50}[/tex]  times 100% = 22%

Answer:

The answer is 4

answer mine

The three lowest values of x are 30, 31 and 32.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

The statement "x is a whole number if three quarters of x is subtracted from 62. the result is less than 40" can be written as:

62 - (3/4)x < 40

- (3/4)x < 40 - 62

-3x/4 < -22

-3x < -22 × 4

-3x < -88

x > -88/-3

x > 29.33

Since x > 29.33 and x is a whole number, the three lowest values of x are 30, 31 and 32.

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To determine the submarine's depth, you would need to use trigonometry. The angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) form a right triangle.

You can use the tangent function (tan) to find the opposite side (depth) of the triangle, given the adjacent side (distance) and the angle.

Depth = distance * tan(angle of depression)

Depth = 500 meters * tan(40 degrees)

You can use a calculator or table to find the value of tan(40 degrees), which is approximately 0.8391.

Depth = 500 meters * 0.8391

Depth = 419.55 meters

So the submarine's depth is 419.55 meters deep.

Right triangles can be used to represent word problems involving angles of elevation and depression. When working right triangles, the trigonometric rates are used to break for the right triangle's sides and angles representing the problem.

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For the angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) the submarine's depth will be 419.55 meters

Right triangles can be used to express word problems with elevation and depression angles. When working with right triangles, trigonometric rates are employed to break for the sides and angles of the right triangle that represent the problem.

Trigonometry would be required to estimate the depth of the submarine.

Given the neighbouring side (distance) and the angle, you can use the tangent function (tan) to get the opposite side (depth) of the triangle.

Depth = distance multiplied by tan (angle of depression)

500 metre depth * tan (40 degrees)

You may determine the value of tan(40 degrees) using a calculator or a table, which is about 0.8391.

So, the value of the depth = 500 meters * 0.8391

Depth = 419.55 meters

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Answer:

3/8

Step-by-step explanation:

In these type of problems, I like making all of my denominators the same.

1/8 is good.

1/2 is half. 4/8 is also half. I'll use 4/8 because 1/8 also has the 8

A whole circle is 100%, which is 1/1. It's also 8/8

To find the shaded area, we'll first add 1/8 and 4/8. That equals 5/8. We just have to add nominators/top now because the denominator/bottom is the same

Now we'll subtract 8/8 from 5/8. Again denominator is the same, so we only need to subtract the top

8-5=3

Also known as 3/8

The solution set for the given graph is (4, 1)

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

The graph

On the graph, we have two straight lines of inequalites

The point that represent the solution set is any point in the shaded region

This is so because the lines are inequality lines

An instance of these points is (4, 1)

Hence, the point is (4, 1)

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Answer: D

Sorry if it is not.

Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that  B C ‾ ∥ D E ‾ BC ∥ DE .

Assume that points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y)

( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 )

∴PA=PB

With the aid of the distance formula

= (x 2 −x 1  )

2  +(y 2  −y 1  )

2

There are

⇒ (x+2) 2  +(y+2) 2

= (x-5) 2  +(y−2)2

(x-2) 2  +(y+6)2

⇒(x+2) 2  +(y+2)

2  =(x+2) 2 +(y+2) 2

⇒ x2−4x+4+y 2

−7y+10=  x2 +4x+4+y 2  −7y+14

⇒−4x−4x−10y+7y+14−16=0

⇒−8x−3y+2=0

⇒3x+y−5=0

ΔAD

Eare Similar triangles

∴( CB / DE )=( AB / AD )

B C ‾ ∥ D E ‾ BC ∥ DE .

Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that  B C ‾ ∥ D E ‾ BC ∥ DE .

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Residuals measure the vertical distance between two observations of the response variable - False.

An individual data point's residual is a measurement of how well a line fits it. Take a look at this straightforward data set with a line of fit through it.

The discrepancy between expected values of y (the dependent variable) and actual values of y is the residual for each observation. Relative to projected and actual y values, residual is equal to yi. Actual y value minus expected y value equals residual; therefore, r I = y I y i.

A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement.

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Answer:

Have a Nice Day :  ) if Incorrect sorry .

The town and PSA are (a) 10 units apart

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

Points = (2, 3) and (-4, -5)

The distance between the two towns can then be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

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

distance = √[(2 + 4)² + (3 + 5)²]

Evaluate

distance = 10

Hence, the distance apart is 10 units

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Step-by-step explanation:

8 + (22 + 15) = 8 + 37 = 45

To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 22 + 15 = 37. Then we can add 8 to that result, which gives us 8 + 37 = 45. So the final value of the expression is 45.

Answer:

Using BODMAS, you are to solve the one in the bracket

22+15 which=37

then you add it to 8

37+8=45

A recipe for hot chocolate requires 4 cups of milk , 1/4 cup of chocolate powder , 1/3 cup of honey and for which Simplified  Ratio is 16 : 1 : 3.

This can be calculated by following steps:

Find the ratio of milk to chocolate powder.

 Ratio of Milk to Chocolate Powder = 4 : 1/4

Find the ratio of chocolate powder to honey.

 Ratio of Chocolate Powder to Honey = 1/4 : 1/3

Find the ratio of milk to chocolate powder to honey.

 Ratio of Milk to Chocolate Powder to Honey = 4 : 1/4 : 1/3

Simplify the ratio in its simplest form.

 Simplified Ratio = 16 : 1 : 3

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Answer: A. The distance across the lake is 626.6 m.

              B. The lake is not long enough Additional 123.4m distance will need to be set off.

Step-by-step explanation:

1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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