Question 2(Multiple Choice Worth 2 points)
(02.05 MC)
Solve x2 + 12x+6=0 using the completing-the-square method.

In given inequalities the value of x is x <-3 and x >4

Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.

Given that :4x-3<-15 or 2x+4> 12

4x -3 <-15

4x < -12

x <-3

2x + 4 > 12

2x > 8

x >4

x <-3 and x >4

In given inequalities the value of x is x <-3 and x >4

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Find the zeros of the polynomial 15x + 5.

Equating to 0:

Subtracting 5:

Dividing by 15 and simplifying by 5:

To determine whether the third figure is a translation image of the first figure, we say that; B: No; it is a reflection followed by a translation

Transformation could be reflection, translation, rotation or even dilation.

Reflection can be thought of as the mirror image of a shape across a line.

Rotation is when one turns an object around a point

Translation is simply moving an object from one point to another without any change of dimension.

If we look at the given three figures in the attached image, we can see that the second image is the reflection or mirror image of the first figure.

After reflection, we can see that it is undergoes translation, which means it is moved apart from the first figure.

Thus, the third figure is a reflection of the first figure, and then it is translated.

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The volume of prism A and B are 27 cm³ and 25 cm³ respectively and the Surface area of prism A and B are 54 cm² and 70 cm² respectively.

No, the prism with a greater volume doesn't always have the greatest surface area.

Given:

Prism B is a rectangular prism, whereas prism A is a cube.

The prism's volume is determined by

Volume = length × width × height

So, the Volume of prism A whose each side 3 cm is,

Volume of prism A = 3 × 3 × 3 = 27 cm³

Volume of prism B with sides 5 cm,5 cm, and 1 cm is

Volume of prism B = 5 × 5 × 1 = 25 cm³

The cube's surface area is 6a², where a is one of the cube's sides. So

Surface Area of prism A = 6 × (3)² = 6 × 9 = 54 cm²

Surface area of the rectangular prism is given by,

2(length × width + length × height + width × height)

Surface Area of prism B =  2(5×5 + 5×1 + 5×1)

                                        = 2(25 + 5 + 5)

                                        = 2 × 35 = 70 cm²

From the above calculations, it is clear that the prism with a greater volume doesn't always have the greatest surface area.

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The written and solved equation to determine the cost of the desserts, d is  5(9.75 + d) = 63.75; d = 3.00

Five friends ate lunch and spent a total of $63.75.

They each bought the same meal for $9.75, and they each bought the same dessert.

The equation to determine the cost of the dessert, d can be represented as follows:

Hence,

5 (9.75 + d) = 63.75

48.75 + 5d = 63.75

Therefore, let's use the equation to solve for d.

48.75 + 5d = 63.75

subtract 48.75 from both sides of the equation

63.75 - 48.75 = 5d

15 = 5d

divide both sides of the equation by 5

15 / 5 = 5d / 5

d = 3

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The reason why the square root of 15 to the nearest tenth is 3.9 is because the square root was rounded off to the tenth digit.

When rounding off to the tenth digit, the decimal will need to be rounded off to number that comes immediately after the decimal.

This means that if the number that is two places after the decimal is 5 or more, the number in the tenth place (one digit after decimal) will be rounded up.

The square root of 15 is:

= √15

= 3.87298

The second number after the digit is 7 which is higher than 5 so the number 8 will need to be rounded up to 9 to get:

= 3.9

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Its A, A is congruent to B and B is congrument to c

The translation equation, often known as the vertical translation equation, is g(x) = f(x+k) + C.Because the triangles are not congruent, Figure B is not an exact replica of Figure A.

In what direction does a figure move on a coordinate grid?

An example of one of these is a translation. A geometric figure moves in the coordinate plane when it slides up, down, left, or right. The figure shifts its position but maintains its original orientation. Additionally, it maintains its size and shape.

The vertical translation equation, or the formula for translation, is g(x) = f(x+k) + C.

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Solution

The diagram given is a right angle triangle

To find the value of x; we consider the relationship between the three sides.

Pythagoras theorem actually gave the relationship between the three sides of a right angle triangle.

By Pythagoras theorem;

x = 10.25

Answers:  1)  " 2ab ".
                2) "  2xz ".

________________________

Step-by-step explanation:

ab + ba = ab + ab = 1ab + 1ab = (1+1)*ab = 2ab .

xz +  zx = xz  + xz = 1xz  + 1xz = (1+1)*xz  = 2xz.

________________________

A. Mean and range for each set of data is given by:

Data 1:

Mean is equal to 58.59375

Range is equal to 3.2s

Data2:

Mean is equal to 47.87125

Range is equal to 0.92

B. Two inference based on results from part A is :

Mean of data1 is better than data2.

Range of data2 is less spread as compare to data1.

As given,

From the given values of data1 :

Note: 1:00.5s is 60.5s

57.3s, 57.8s, 58.1s , 58.3s, 58.3s, 59.3s, 59.6s, 60.5s

Mean = (Sum of all values)/ (Total number of values)

         = (57.3+ 57.8+ 58.1+ 58.3+ 58.3+ 59.3+ 59.6+ 60.5)/8

         = 468.75/8

         = 58.59375

Range = Highest value -lowest value

           =60.5 -57.3

           = 3.2s

From the given values of data2 :

47.52s,47.53s, 47.80s, 47.84s, 47.88s, 47.92s, 48.04s, 48.44s

Mean =(47.52+47.53+ 47.80+ 47.84+ 47.88+ 47.92+ 48.04+ 48.44)/8

          =382.97/8

          = 47.87125

Range = 48.44 -47.52

           = 0.92

Therefore,

A. Mean and range for each set of data is given by:

Data 1:

Mean is equal to 58.59375

Range is equal to 3.2s

Data2:

Mean is equal to 47.87125

Range is equal to 0.92

B. Two inference based on results from part A is :

Mean of data1 is better than data2.

Range of data2 is less spread as compare to data1.

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We know that

Square roots can be expressed as a fraction on the exponent:

The magnitude and direction of the vectors are

11.  <0,4> :

Magnitude = 4

Direction =  90°

12.  <-3,0>:

Magnitude = 3

Direction = 0°

13. <6,5>:

Magnitude = √(61)

Direction =  39.8°

14. <3,7>:

Magnitude = √58

Direction =  66.8°

15. <-2,1>:

Magnitude = √5

Direction =  -26.57°

16. <-10,13>:

Magnitude =  √(269)

Direction =  -37.57°

17. <2,-5>:

Magnitude = √(29)

Direction = -68.2°

18. <8,-4>:

Magnitude =  √(80)

Direction =  -26.57°

19. <-4.-6>:

Magnitude =  √(52)

Direction =  56.3°

20.  <-1,9>:

Magnitude = √(82)

Direction =  -83.66°

We are asked to find the magnitude and direction of the vectors given as <x, y>. We have the formulas for magnitude and direction of the vectors.

Magnitude = √(x²+y²)

and direction, θ = tan⁻¹(y/x)

11. The vector is <0,4>

Magnitude = √(0²+4²) = 4

Direction = tan⁻¹(4/0) = tan⁻¹∞ = 90°

12. The vector is <-3,0>.

Magnitude = √(-3²+0²) = 3

Direction = tan⁻¹(0/-3) = tan⁻¹0 = 0°

13.The vector is <6,5>

Magnitude = √(6²+5²) = √(61)

Direction = tan⁻¹(5/6) = 39.8°

14. The vector is <3,7>

Magnitude = √(3²+7²) = √58

Direction = tan⁻¹(7/3) = 66.8°

15.The vector is <-2,1>

Magnitude = √(-2²+1²) = √5

Direction = tan⁻¹(1/-2) = -26.57°

16.The vector is <-10,13>

Magnitude = √(13²+-10²) = √(269)

Direction = tan⁻¹(-10/13) = -37.57°

17.The vector is <2,-5>

Magnitude = √(2²+-5²) = √(29)

Direction = tan⁻¹(-5/2) = -68.2°

18.The vector is <8,-4>

Magnitude = √(8²+-4²) = √(80)

Direction = tan⁻¹(-4/8) = -26.57°

19.The vector is <-4.-6>

Magnitude = √(-4²+-6²) = √(52)

Direction = tan⁻¹(-6/-4) = 56.3°

20. The vector is <-1,9>

Magnitude = √(-1²+9²) = √(82)

Direction = tan⁻¹(9/-1) = -83.66°

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The equation, in slope-intercept form to represent the monthly price

as a function of the number of MB used is  y = mx + c.

It is given in the question that the cell phone provider charges you

$35 a month for a phone plan and charges $0.12 per MB of data used.

Hence,

Total monthly charges = MB used*Charge per MB+ Fixed charge  

Let y represents total monthly charges

x represents the charge per MB

m represents the MB used and,

c represents the fixed charge

Therefore, we can write the above equation as:-

y = mx + c

Hence the equation is written in the slope-intercept form.

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Kylie has 5 pears and she divide each pear into 3.

So 1 pear will become 3 slices.

Then 5 pears will be 5 x 3 = 15 slices.

The answer is 15 slices

he equation you can use is :

umber of slices = 5 x 3

Answer:

The answer is 15

Answer:

solution: [tex]Sn= \frac{a_{1} (1-q^{n} )}{(1-q)} = \frac{1(1-4^{n}) }{1-4} = \frac{4^{n}-1 }{3}[/tex]

Step-by-step explanation:

Based on the definition of the functions, the value of x if f(x) = g(x) is 3

The equations of the functions are given as

f(x) = -2x + 4

g(x) = 2x - 8

It should be noted that the above equations are linear equations

From the question, we understand that the functions are equal

This means that, we have the following equation

f(x) = g(x)

Substitute the known values in the above equation

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms in the above equation

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides by 4

x = 3

Hence, the value of x such that the equations are equal is 3

See attachment for the graph of the functions

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If JK || MN, then angle JKM is equal 61;

Also, angle JLK = 39 degrees as it is opposite angle to MLN.

Thus;

Thus x= 25 proves that JK || MN

Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.

This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

How to Apply the Unitary Method

Let's first list the data that we currently have. The number of ice creams is 5. It costs $125 for 5 ice creams.

step 1:Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.

Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.

Given:

Cots of 1 liter jar of Mayonnaise (I) = 2.45

Cost of 2 liter jar of Mayonnaise (II)=4.75

Cots of 1 liter jar of Mayonnaise (II)= 4.75/2= 2.375

If she eats half liter Mayonnaise in a day

So, she eat in 14 days = 0.5 x 14 = 7 liter

Hence, Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.

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Answer

Triangle B is not a rotation of triangle A because on careful observation of this two triangles, one would see that they are mirror images of each other; reflections of each other.

A mental rotation of triangle A all through the 360° shows that at no point is it seeming exactly like triangle B.

This is why it is evident that triangle B is not a rotation of triangle A, rather, they are reflections of each other.

Hope this Helps!!!

Answer:

<U = 54

<T = 72

Step-by-step explanation:

Find the angle measures

The marks on the sides means the sides are the same length

That means the base angles have the same measurement

<S = <U = 54

The sum of the angles of a triangle equals 180

<S + <U + < T = 180

54 + 54 + < T =180

108 + < T =180

<T =180-108

<T = 72

Answer:

m<U = 54°

m<T = 72°

Step-by-step explanation:

According to the isosceles triangle theorem ( If two sides of a triangle are equal , then the angles opposite to these sides are also equal. ),

ST = UT

So,

m<S = m<U.

Given that,

m<S = 54°

So,

m<U = 54°

Also, we know that the sum of the interior angles of a triangle is added up to 180 degrees.

So,

m<S + m<U + m<T = 180°

54° + 54° + m<T = 180°

108° + m<T = 180°

m<T = 180° - 108°

m<T = 72°

Answer:

A) 60 that's i know !!!

Step-by-step explanation:

A) 60

55 mph

if we assume it takes an hour for the last 30 miles then the rest of the time the trucker could go 55

A three-person jury can be selected from a pool of eleven people in 165 ways.

For the given question;

The total number of person in the pool = 11.

The number of jury selected = 3.

Thus, the combination will be ⁿCₓ.

Where, n = 11 and x = 3.

¹¹C₃ = 11!/3!(11 - 3)!

Simplifying;

¹¹C₃ = 165

Thus, the number of ways in which three jury can be selected from 11 pool of members is 165.

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The only effective methods for determining the number of points are 5a and 5c.

Solving algebraic word problems involves breaking down sentences into equations and then figuring out how to solve those equations.

To construct the equations we need, we will only need to employ one variable and basic arithmetic operations. The variable often represents an uncertain number in a real-world scenario.

Given that Josiah scores six three-pointers during his basketball game, 6*3 = 18, which is general multiplication; or adding three times six times, would be a workable choice for determining the number of points.

Therefore, the two viable alternatives for determining Josiah's point total are 5a and 5c.

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To solve this question we will compute the magnitude of each vector.

Recall that the magnitude of a vector

is:

Therefore, the speed of the first car is:

Simplifying the above equation we get:

The speed of the second car is:

Simplifying the above equation we get:

Answer:

The first car is the faster car.

Speed= 40.46.

Answer: My new music player has a capacity of 3 * 10^11 bytes.

Step-by-step explanation: giga=billion=10^9. 300 in scientific notation is 3*10^2. Since 3 is between 1 and 10. So 10^2 * 10^9=10^11.