Solve the equation by completing the square

a^2+14a-51=0

Answer:

4 or t = -8

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are solving for the variable, t. Note the equal sign, what you do to one side, you do to the other.

To isolate t, add 7 to both sides of the equation:

21 = t - 7

21 (+7) = t - 7 (+7)

21 + 7 = t

t = 28

t = 28 is your answer.

Check: Plug in 28 for t in the given equation:

21 = t - 7

21 = (28) - 7

21 = 21 (True).

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If rectangle is similarity to rectangle, to find the value of x we use proportion (c) 5/12 = 2/x.

When applying a scale factor, similar shapes are enlarged versions of one another.

All of the matching angles and lengths in related shapes are equal and in the same ratio.

If two figures share the same shape, congruent corresponding angles (which means the angles in the same places of each shape are the same), and identical scale factors, they are said to be "similar figures."

Given that rectangle EFGH is similar to rectangle JKLM, it means the corresponding sides of both rectangles are similar, and as such the ratios if the corresponding sides of rectangle EFGH and rectangle JKLM would be equal.

Thus, EF/JK = FG/KL

Since, EF = 5; JK = 12; FG = 2; and KL= x, therefore, the proportion to use in finding x would be:

5/12= 2/x

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Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

On solving the question, unit rate by using the given graph could be 2.4 potatoes/pound

Graph can be defined as the visual representation which is used to represent the data.

The unit rate is the slope of the line.

The slope of the line =  (change in y-value)/(change in x-value)

= (36 potatoes - 12 potatoes)/(15 pounds - 5 pounds)

= (24potatoes)/(10 pounds)

= 2.4 potatoes/pound

The relationship here is proportional, so the line goes through the point (0, 0) and the unit rate can be figured from any point:

(12 potates)/(5 pounds)

= (24 potatoes)/(10 pounds)

= (36 potatoes)/(15 pounds) = 2.4 potatoes/pound

Hence, The unit rate by using the given graph could be 2.4 potatoes/pound .

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The correct question is -

Identify the unit rate in the graph.

A. 40mph

B. 75mph

C. 50mph

D. 25mph

The amount invested in each mutual fund is $400 and $1200 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 10 and 8x − 4y = 2

Let represent the amount the first fund get by x and the amount the second fund get by y.

Therefore x+y = 1600 equation 1

and 9/100 × x + 4/100 × y = 84

9x/100 + 4x/100 = 84

multiply through by 100

9x + 4x = 8400 equation 2

using elimination method

9x+ 9y = 14400 equation 3

9x + 4y = 8400 equation 4

subtract equation 4 from 3

5y = 6000

divide both sides by 5

y = 6000/5

y = $1200

substitute 1200 for y in equation 1

1200+x = 1600

x = 1600-1200

x = 400

Therefore the first fund will get $400 and the second fund will get $1200

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The equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14. The solution has been obtained by using the concept of arithmetic progression.  

What is arithmetic progression?

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

We are given that the third term is 10.

This means that [tex]a_{3} =10[/tex]

So, n=3

Substituting this value in the given equations, we get

1)  [tex]a_{n}[/tex] = 8*3+10 = 34

2)  [tex]a_{n}[/tex] = 8*3 - 14 = 10  

3)  [tex]a_{n}[/tex] = 16*3+10 = 58

4)  [tex]a_{n}[/tex] = 16*3 - 38 = 10

So, the second and the fourth equation satisfy the condition.

We are also given that the fifth term is 26.

This means that [tex]a_{5} =26[/tex]

So, n=5

Substituting this value in the given equations, we get

2)  [tex]a_{n}[/tex] = 8*5-14 = 26  

4)  [tex]a_{n}[/tex] = 16*5 - 38 = 42

So, the second equation satisfies the condition.

Hence,the equation for the nth term of this sequence is  [tex]a_{n}[/tex] = 8n - 14.

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To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values.

A group of numbers, often known as "terms," such as 2, 5, or 8, make up a sequence. Some sequences can be made infinitely long by utilizing a specific pattern that they follow. Add 3 and use the example of 2,5,8 to continue the series. There, you can find formulas that outline where to hunt for terms in a series. A collection of elements in some order is what is referred to as a sequence informally in mathematics (or events). Like a set, it is made up of parts (also called elements or terms). The entire, perhaps indefinite number of arranged objects is referred to as the length of the sequence. the process of logically ordering two or more objects. Chronological.

given

To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values. Researchers and scientists record their data using tables of numbers, then examine the data to look for patterns.

This pattern can then be applied to generate forecasts.

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The 8 quadratic formulas are essential for solving quadratic equations. They are derived from the quadratic equation, which is expressed as ax² + bx + c = 0. The 8 quadratic formulas are:

1. Standard Quadratic Formula: x = [-b ± √(b² - 4ac)]/2a

2. Quadratic Formula for Negative Discriminant: x = [-b/2a] ± i√(-b² - 4ac)/2a

3. Quadratic Formula for Zero Discriminant: x = -b/2a

4. Quadratic Formula for One Real Root: x = -2c/b

5. Quadratic Formula for Two Real Roots: x = [-b ± √(b² + 4ac)]/2a

6. Quadratic Formula for Two Identical Real Roots: x = -b/a

7. Quadratic Formula for Two Imaginary Roots: x = [-b/2a] ± √(-b² + 4ac)/2a

8. Quadratic Formula for One Imaginary Root: x = [-b/2a] ± i√(b² + 4ac)/2a

By understanding these formulas, it's possible to solve for any unknowns in a quadratic equation.

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The rider has 141 laps left to finish the race.

If a rider has already cycled 4.75 km, and each lap measures 0.25 km, we can determine how many laps the rider has completed by dividing the distance already cycled by the distance per lap.

To find out how many laps the rider has left to finish the race, we will use the information on the total number of laps to complete the race: 160 laps.

The rider has completed:

4.75 km / 0.25 km = 19 laps

The rider has yet to finish:

160 laps - 19 laps = 141 laps

So the rider has 141 laps left to finish the race.

Therefore, the rider has 141 laps left to finish the race.

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The system of equations that represents this situation is D + Q  =24 and 10D + 25Q = 465 with 15 and 9 quarters and dimes respectively.

Given that

let the quarter be represented by Q and dimes with D

D + Q  =24 (multiply this by 10)

10D  + 10Q = 240

10D + 25Q = 465

Subtracting both the equations:

15Q  =225

Q = 225/15 = 15 quarters

Now putting this value in equation 1st we get

D = 24-15 = 9 dimes

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Exponent 2 means the number of times one number is multiplied. The number of time the base is multiplied.

The Exponents refers to the repeated multiplication of the same thing by itself.

For example, [tex]x^{2}[/tex] . here 2 is the exponent and x is the base. Then we can write it as x . x . The base is multiplied by 2 time by itself.

Exponents are  also called powers or orders. This is the shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power" where the exponent is the "power". The expression [tex]4^{3}[/tex] is pronounced as four raised to the third power", "four, raised to the power three", or "four to the third". It stands for many times the value is being multiplied.

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Answer: To find the capacity of the tin can, we can use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length is 5 cm, the width is 4 cm, and the height is 15 cm. So the volume of the tin can is 5 x 4 x 15 = 300 cubic cm.

To find the capacity of the plastic cylinder, we can use the formula for the volume of a cylinder, which is pi x radius squared x height. The diameter of the circular base is 7 cm, so the radius is half of that, or 3.5 cm. So the volume of the plastic cylinder is pi x (3.5 cm)^2 x 10 cm = 385.4 cubic cm.

So the plastic cylinder has a greater capacity by 385.4 - 300 = 85.4 cubic cm.

Step-by-step explanation:

An equation that has one solution for y for each value of x is referred to be a function. A function pairs each input of a particular type with exactly one output.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function.  Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

An equation that has one solution for y for each value of x is referred to be a function.

A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

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Answer: The perimeter of a rectangle is the sum of the lengths of its four sides which is given by the expression: P = 2l + 2w (where l is the length and w is the width)

The expression that does not show this relationship is P = l + w

It doesn't show the relationship because it doesn't take into account the two sides that are equal to the width and the two sides that are equal to the length.

P = 2l + 2w shows the relationship as it considers both length and width of the rectangle twice, once for each pair of sides.

Step-by-step explanation:

Answer:

It seems that your question is missing something, it looks like a question to a previous question. Please add all info when making a question. Also you can comment underneath my reply with that additional info.

The perimeters of the two composite figures are listed below:

Case C: 50.913π mm

Case D: 20.310 cm

In this problem we find two composite figures, whose perimeter have to be found. Perimeter is the length of all borders of the figure. The first figure is formed two semicircles and the second figure is formed by two semicircles and two right triangles, whose perimeter formulas are:

Semicircle

s = π · r

Triangle

s = b + h + p

Where:

Case c - The perimeter of the shape is:

s = π · (28 mm) + π · (14 mm) + 28 mm

s = 50.913π mm

Case d - The perimeter of the shape is:

s = 2π · (1.8 cm) + 2 · (4.5 cm)

s = 20.310 cm

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The inequality can be written as g * 37.5 >= 120.

What is linear inequality?

A linear inequality is a mathematical statement that describes a relationship between two or more variables that form a half-plane when graphed. The equation of a linear inequality is in the form of "ax + by < c" or "ax + by > c" or "ax + by <= c" or "ax + by >= c", where x and y are variables, and a, b and c are constants.

An inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother's house is:

g >= 120/37.5

This inequality states that the number of gallons, g, must be greater than or equal to the number of miles Darla needs to drive, 120, divided by the number of miles per gallon her car gets, 37.5. This is because Darla wants to ensure that she has enough gasoline to make the trip, and she may not want to risk running out of gas on the way.

Another way to write this inequality is

g * 37.5 >= 120

This inequality represents the same meaning as before, we multiply g by the number of miles per gallon the car gets, 37.5 and it should be greater than or equal to the distance she needs to travel which is 120 miles.

Hence, the inequality can be written as g * 37.5 >= 120.

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The distance between the points E(3, 7) and F(6, 5) is 3.605 units.

Algebraic expression that gives the distances between pairs of points in terms of their coordinates.

The distance between two points having coordinates P(a, b) and Q(c, d) is,

D= √(c-a)² + (b-d)².

Given:

Points E(3, 7) and F(6, 5).

Now, using Distance Formula

D= √(6-3)² + (5-7)²

D = √(3)² + (2)²

D= √9+4

D= √13 units

D= 3.605 unit

Hence, the distance is 3.605.

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The polynomial h(x)=x^4+2x^3-13x^2-14x+24 in the factored form is (x−1)(x+2)(x−3)(x+4). The real roots of the polynomial is x= 1, x = 3, x = -2, x  = -4.

What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

The polynomial function is -

h(x)=x^4+2x^3-13x^2-14x+24

Divide the polynomial h(x) by (x-1) -

(x^4+2x^3−13x^2−14^x+24)=(x−1)(x3+3x2−10x−24)

Divide (x^3+3x^2−10x−24) by (x+2) -

(x−1)(x^3+3x^2−10x−24)=(x−1)(x+2)(x^2+x−12)

Solve the quadratic equation x^2+x−12=0.

x^2+x−12=0

x^2+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

So, (x−1)(x+2)(x^2+x−12)=(x−1)(x+2)(x−3)(x+4)

Therefore, x^4+2x^3−13x^2−14x+24=(x−3)(x−1)(x+2)(x+4) .

The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction q/p, where p is a factor of the constant term and q is a factor of the leading coefficient.

We can see that p(1)=0 so x=1 is a root of a polynomial h(x).

Divide the polynomial by (x-1) -

(x^4+2x^3−13x^2−14x+24)/(x-1)=(x^3+3x^2−10x−24)

Divide (x^3+3x^2−10x−24) by (x-3) -

(x^3+3x^2−10x−24)/(x-3) = (x^2+6x+8)

To find the last zero, solve equation x+4=0

x=-4

Therefore, the real roots are - x = 1, 3, -2, -4.

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The sum of: (-14.2b - 97.35) + (6.76d - 118.7 - 3.4d ) is -14.2b + 3.36d -216.05

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

(-14.2b - 97.35) + (6.76d - 118.7 - 3.4d )

Remove the brackets

So, we have

-14.2b - 97.35 + 6.76d - 118.7 - 3.4d

Evaluate the like terms

-14.2b + 3.36d -216.05

Hence, the sum is -14.2b + 3.36d -216.05

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No, the set of 2nd coordinates is not a set. It is a pair of numbers that identifies a particular point on a coordinate plane.

1. It is not a collection of items.

2. It is not an ordered list.

3. It is not a group of elements.

4. It is not a set of elements.

5. It is not a collection of points.

6. It is not a grouping of numbers.

7. It is not a sequence of numbers.

8. It is not a selection of numbers.

9. It is not a combination of numbers.

10. It is not a union of numbers.

11. It is not a cluster of numbers.

12. It is not a set of components.

13. It is not a combination of values.

14. It is not a sequence of values.

15. It is not a selection of values.

16. It is not a union of values.

17. It is not a set of points.

18. It is not a set of data points.

19. It is not a selection of coordinates.

20. It is not a set of ordered pairs.

21. It is not a set of numbers.

22. It is not a set of measurements.

23. It is not a set of data.

24. It is not a set of variables.

25. It is not a set of parameters.

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Answer:

yes

Step-by-step explanation:

a^2 + b^2 = c^2

so

32^2 + 60^2 = 68^2

1024 + 3600 = 4624

The correct answer is -60

When you look at -70 it looks like it would be higher then -60 but -60 is actually higher then -70 because it has a negative line.

Therefore, the correct answer is -60

Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

Since a triangle has three sides or three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one of a triangle that has endpoints A, B, and C. When the points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where its three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

Here,

Using the ABC/XYZ technique, planned units (characteristic product combinations, SKUs) are grouped according to their value (income or product sales) and consumption or sales dynamics.

The planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.

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Answer:  32

Step-by-step explanation: because the line has to add up to 180 degrease

Answer

-17

Step-by-step explanation:

5 times -17= -85 and then add 5 = -80

340 feet deep was well dug relative to ground level

Two or more expressions with an Equal sign is called as Equation.

Given that Mr. Jakarta is having a well built in his backyard.

On Monday 175 feet of the well was drug

Another 165 feet was dug tuesday.

We need to find the how many feet deep was well dug relative to ground level

To find the number of feet, we simply make an addition of the number of feet dug on both days

The total will be 175 feet + 165 feet = 340 feet

Hence, 340 feet deep was well dug relative to ground level

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Answer:

Function A

Step-by-step explanation:

doesn't have vertical points

Answer:

Let x be the cost of the phone.

we know that the cost of the phone case is 10 times cheaper than the phone so the cost of the case is x/10

We also know that the total cost of the phone and the case is 660.

so we can write an equation:

x + (x/10) = 660

We can solve this equation for x by multiplying both sides by 10:

10x + x = 6600

11x = 6600

x = 600

So the cost of the phone is 600 and the cost of the phone case is 600/10 = 60