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If we use the method of completing the square to solve the quadratic equation x² + 5x - 1 = 0, we have to add (-25/4) to convert it to (x + 5/2)²  - 29/4 = 0

The standard form of a quadratic equation is:

ax² + bc + c = 0

In this case, the quadratic function is:

x² + 5x - 1 = 0

To solve it using the "complete the square" method, write the equation as:

(x + 5/2)² - 1 + .... = 0

The blank part in the above equation means we need to add a number to make the equality still holds.

Note that:

(x + 5/2)² = x² + 5x + 25/4

Hence,

(x + 5/2)²  - 1  =  x² + 5x + 25/4 - 1

Hence, we need to add (-25/4) to make the original equality holds:

(x + 5/2)² - 1 + (-25/4) = 0

(x + 5/2)²  - 29/4 = 0

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if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that a triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length

We have to find the measure of the third angle.

By angle sum property the sum of three angles is equal to 180 degrees.

43+94+x=180

137+x=180

Subtract 137 from both the sides

x=43 degrees.

Hence, if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

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The sum of the interior angles for a Polygon of 5 angles is 540°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

The sum of the interior angles of a Polygon is calculating by the formulation:

Sum of Interior Angles = (n-2) x 180°

Replacing the number of angles (n = 5) in the equation we get:

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (5-2) x 180°

Sum of Interior Angles = 3 x 180°

Sum of Interior Angles = 540°

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By applying the distributive property to open the parentheses and then combining like terms, the answers above are gotten when each expressions are simplified.

To simplify an expression that as parentheses, we can apply the distributive property to get the answer.

Given the expression, 2(4 + 3(x - 5)), to get the answer in simple form. apply the distributive property to open the parentheses:

2(4 + 3x - 15)

Combine like terms:

2(3x - 11)

Apply the distributive property:

6x - 22

Also, follow the same process to simplify -3(9 - 2(k + 3) + 5k):

-3(9 - 2(k + 3) + 5k)

Apply the distributive property:

-3(9 - 2k - 6 + 5k)

Combine like terms:

-3(3k + 3)

Apply the distributive property:

-9k - 9

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The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔSTW and ΔUVW, we have

∠T = ∠V      (Given)

∠W = ∠W    (Common angle)

Then the triangles ΔSTW and ΔUVW will be similar to each other. Then the ratio of the corresponding sides will be constant. Then the equation is given as,

ST / UV = VW / TW

ST / UV = VW / (TV + VW)

5 / x = 6 / (9 + 6)

x = 5 (9 + 6) / 6

x = 5(15) / 6

x = 75 / 6

x = 12.5

The triangle ΔSTW is similar to the triangle ΔUVW. Then the value of the variable 'x' is 12.5 meters.

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The correct way to write greater than 3 is A > 3 where it tells that A having greater value than 3.

In mathematics,

→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.

→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.

→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.

→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.

These symbols are commonly used in mathematical expressions, equations, and inequalities.

To write "greater than 3" in mathematical notation, you would use the greater than symbol (>) followed by the letter 3. For example:

A > 3

This means that A is greater than 3.

Therefore, the correct way to write greater than 3 is A > 3 where it tells that A having greater value than 3.

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The standard deviation is 6.

What a standard deviation means?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Standard deviation in statistics is a measure of dispersion of a set of data relative to the mean of the data set.

The square root of the variance of the data set gives the standard deviation of the data set.

In this case, the variance,

s²=36 ( as given, variance of the set of values is 36 )

The standard deviation,

s=√36 =6

Therefore, the standard deviation is 6.

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Coupon 1 is the better deal, as it offers a 40percentage discount on one of the two items.

Coupon 1:

Cost of 1 item: 18

Discount of 1 item: 40% (7.2)

Total cost with coupon 1: 10.8

Coupon 2:

Cost of 2 items: 36

Discount of 2 items: 25% (9)

Total cost with coupon 2: 27

Coupon 1 is the better deal for Brittni's purchase. It offers her a 40% discount on one of the two items, which means she would save 7.2 on the item. The total cost with coupon 1 would be 10.8. On the other hand, coupon 2 offers a 25% discount on the entire purchase, which would amount to 9 in savings. However, the total cost with coupon 2 would still be higher at 27. Thus, coupon 1 is the better deal for Brittni's purchase.

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The two lines in the system of equations will be parallel when the value of k is 15/4.

Let 2 equations of the line be,

ax+by=c1

dx+ey=c2

for lines to be parallel it is necessary that their slopes are equal

we can easily find the slopes of these equations by re-arranging them in the standard equation of a line i.e, y=mx+c

after rearranging we'll get the following equations,

y=(-a/b)x+c1/b

y=(-d/e)x+c2/e

and it should satisfy the given condition,

-a/b=-d/e≠c1/c2

as, if the ratio of the slope is the same as the constants it will become the same line. So, according to the given question

-3/2k must be equal to -2/5

k must be 15/4.

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Answer:

p = t - a - b

Step-by-step explanation:

T = a + p + b

- p + T = a + b

- p = - T + a + b

p = T - a - b

Answer:

The variable that belongs in the green box is T

(p=T-a-b)

Step-by-step explanation:

The total amount of fruit (T) minus the apples (a) and minus the bananas (b) would leave us with just the pears (p).

Writing this out mathematically, we have : T - a - b = p

Answer:

0.80g

Step-by-step explanation:

8/10 = 0.80

Add the variable(g)

0.80g

With a $250 original cost and a 30% discount, The cost after discount is $175.00. $75.00 was saved by you.

Think about the pre-sale price. Multiply the initial cost by 30, then divide it by 100. Subtract the old number from this new one. Your discounted value is the new figure. With a $250 original cost and a 30% discount, The cost after discount is $175.00. $75.00 was saved by you.

The simplest method for figuring out a discount is to multiply the original cost by the percentage rate in decimal notation. Any item's selling price is determined by deducting the discount from the purchase price. Value-based rebates or discounts are described by Discount Rules at the product (SKU) or order level. They can be described in terms of proportions or absolute values (net price). A discount rule only applies to the product to which it refers.

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Answer:

B and E

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.

Answer:

B and E.

Step-by-step explanation:

A translation is a slide.  If your only moves was a slide, y would slide right over B and E.  The others would you have to flip or rotate or expand.

In the trigonometric functions angles are,

1) 53.13°

2) 48.19°

3) 36.87°

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given ,

1) sin x = [tex]\frac{4}{5}[/tex]

=> x= [tex]sin^{-1}\frac{4}{5}[/tex]

=> x = 53.13°

2) cos x = [tex]\frac{2}{3}[/tex]

=> x = [tex]cos^{-1}\frac{2}{3}[/tex]

=> x = 48.19°

3) tan x = [tex]\frac{3}{4}[/tex]

=> x = [tex]tan^{-1}\frac{3}{4}[/tex]

=> x = 36.87°

Hence the angles are,

1) 53.13°

2) 48.19°

3) 36.87°

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If two numbers A and B are given, then the formula of the commutative property of numbers for addition is given as: A + B = B + A

The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.

For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of two numbers being added does not affect the sum.

As a result, the commutative property is concerned with moving the numbers about. So, if altering the order of the operands has no effect on the result of the arithmetic operation, that arithmetic operation is commutative.

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If you are given a graph, you may perform the vertical line test; if a vertical line crosses the graph more than once, the relation represented by the graph is not a function.

Determine the input values. Determine the output values. If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.

The connection is a function if each ordered pair has a unique x x x-coordinate. If the relation is specified as a mapping, check to determine if each domain value is present. Has only one arrow pointing to a range value. If the relation is given as a graph, use the Vertical Line Test.

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Addition symbols are called plus signs. They are used to indicate a mathematical operation or expression that adds two numbers or values together. They are represented by a cross or a plus sign (+) and are usually placed between the two values being added.

The plus sign is often used in algebra and other mathematical equations to indicate that two numbers should be added together. It is also used in programming languages to indicate the addition of two values. Additionally, the plus sign is used to indicate the inclusion of something, such as a plus sign in front of a movie title to indicate that it is an extended edition.

The plus sign is an important part of mathematics and programming and is used in many different contexts. It is a versatile symbol that is used to indicate the addition of two values. Knowing how to use the plus sign correctly is an important part of understanding basic mathematics and programming.

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The average speed of Keddy based on time of travel and distance covered is 160 km/hr.

The time taken to reach the destination = 13:51 - 12:36

Performing subtraction

Time taken to reach the destination = 1:15 or 1 hour and 15 minutes

As we know, 1 hour has 60 minutes.

So, total time in hour = 1 + 15/60

Total time in hour = 1.25 hours

The speed, distance and time are related as -

Average speed = total distance travelled ÷ total time taken

Keep the values in formula -

Average speed = 200/1.25

Performing division

Average speed = 160 km/hr

Thus, the average speed of Keddy is 160 km/hr.

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The value of 'n' in the equation 3n + 7 = 25 is equal to 6.

In the equation 3n + 7 = 25, 'n' is a variable representing an unknown value. To find the value of 'n', we need to isolate it on one side of the equation.

The first step is to remove the constant term 7 from the equation. This can be done by subtracting 7 from both sides of the equation, which gives:

3n = 18

The next step is to get 'n' alone on one side of the equation. This can be done by dividing both sides of the equation by 3, which gives:

n = 18/3

n = 6

So the value of 'n' in this equation is 6.

--The question is not readable, answering to the question below--

"What is the value of an in 3n + 7 is equal to 25?"

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The ratio between of the two legs of a 30-60-90 triangle:

√3 : 2.

The correct option is D.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Given:

A triangle is a 30-60-90 triangle.

So, the sides of a 30-60-90 triangle are always in the ratio of 1:√3: 2.

The side opposite is 60° is √3.

And The side opposite to 90° is 2.

So, the ratio,

= s/h

= √3 : 2.

Therefore, the ratio is √3 : 2.

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The formula of distributive property is the following, a(b+c) = ab + ac , where a,b,c are real numbers.

The distribution property of multiplication over addition applies when values are multiplied by sums. The expression for the distribution characteristic is expressed as: a × (b + c) = (a × b) + (a × c); where a, b, and c are the operands. The numbers outside the brackets are multiplied by each term inside the brackets and the products are added. For example, you want to multiply the sum of 20 + 3 by 9. Since we have similar terms, we usually add numbers first and then multiply by 5. But according to the property, we can first multiply each summand by 5, so 5( 20 + 3)

= 5 × 20 + 5 × 3

= 100 + 15 = 115.

Hence, distributive property is one of basic property follows by addition and multiplcation operations.

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[tex] = \frac{3}{5} - \frac{1}{10} \\ [/tex]

[tex] = \frac{3}{5} \times \frac{2}{2} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6}{10} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6 - 1}{10} \\ [/tex]

[tex] = \frac{5}{10} \\ [/tex]

Change in lowest term

answer [tex] = \frac{1}{2} \\ [/tex]

The cosine of a right-angled triangle is defined by the trigonometric word “cos” meaning.The neighboring base-to-hypotenuse ratio is known as the cos function in a right-angled triangle.

It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right triangle, the ratio between an angle's adjacent side and the hypotenuse is known as the cosine of the angle. It is written as:

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

The cosine function takes up different values depending upon the value of

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Answer:

  False

Step-by-step explanation:

You want to know if it is true or false that "the number 0.3333... repeats forever; therefore it is irrational."

Any repeating decimal is a form of rational number. A number will only be irrational if it has an infinite number of decimal digits and never repeats.

The number 0.3333... is rational.

The offered statement is false.

__

Additional comment

There are enough typos in your statement that we cannot be certain what the statement is. We can be certain that 0.3333... is rational.

Check to make sure the question being answered here is the one you want the answer for.

The theoretical probability of getting a blue color is 1/4.

The experimental probability of landing a blue color is 35%.

Option A is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of times the blue color is recorded = 7

The total number of times each color is recorded = 20

Now,

Number of sections = 4

Number of blue sections = 1

So,

The theoretical probability of getting a blue color.

= 1/4

Now,

Experimental probability of landing a blue color.

= 7/20

= 7/20 x 100

= 35%

Thus,

Theoretical probability of getting a blue color is 1/4.

Experimental probability of landing a blue color is 35%.

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a) The ratio of the number of white tiles to the number of blue tiles = 3:1

b) The ratio of the total cost of the white tiles to the total cost of the blue tiles = 3:2.

a)Since they are 48 white tiles and 16 blue tiles, the ratio of the number of white tiles to the number of blue tiles is the number of white tiles divided by the number of blue tiles. Therefore-

The ratio of white tiles to the blue tiles = number of white tiles/number of blue tiles = [tex]\frac{48}{16}[/tex] = 3

b)Total cost of the white tiles = number of white tiles × cost of each white tile = 48 tiles × £2 per tile = £96

Total cost of the blue tiles = number of blue tiles × cost of each blue tile = 16 tiles × £4 per tile = £64

The ratio of the total cost of the white tiles to the total cost of the blue tiles = total cost of the white tiles/total cost of the blue tiles = [tex]\frac{96}{64} = \frac{3}{2}[/tex]

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The complete question is:

Ewen has 48 white tiles and 16 blue tiles.

(a) Write down the ratio of the number of white tiles to the number of blue tiles.

Give your ratio in its simplest form.

The cost of each white tile was £2

The cost of each blue tile was £4

(b) Work out the ratio of the total cost of the white tiles to the total cost

of the blue tiles

By evaluating the system of inequalities we will see that the point (0, 1) is not a solution.

Here we know that a student says that (0, 1) is a solution to the system of inequalities below:

y > x

y > 2x + 1

A point (x, y) is a solution of the system of eqations if, when we replace both values, both inequalties are true.

Replacing the values of the point (0, 1) we will get:

1 > 0

1 > 2*0 + 1  → 1 > 1

The second inequality is false, then the point (0, 1) is not a solution of the system.

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For a specific distance between two places, a grid scale factor is determined and referred to as a "line scale factor."

The ratio of the two equivalent side lengths of comparable figures is known as the scale factor, sometimes known as the linear scale factor. The shapes of similar figurines are the same, yet they come in various sizes. Geometrical problems are solved using the scale factor. To determine a figure's missing side lengths, apply the scale factor.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

A figure's size may enlarge or contract by dilation.

The diagram shows:

scaling factor of BA = AC/CA' = 4/(4 + 16)=1/5

Line segment BA's elongation is scaled by a factor of 1/5.

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The 29th term in the given arithmetic sequence is −170.

An arithmetic sequence can be defined in one of two ways. In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term," or "each term is obtained where the differences between every two successive terms are the same." The arithmetic sequence that comes next is created by adding 4 to the term that comes before it.

Given that 89th term in an arithmetic sequence is -590

And 8th term is -23

-590 = a₁ + (89 - 1)d

-590 = a₁ + 88d

a₁ = -590 - 88d

and

-23 = a₁ + (8 - 1)d

-23 = a₁ + 7d

a₁ = -23 - 7d

Factor out a₁ in both equations

-590 - 88d =  -23 - 7d

-88d + 7d = 590 - 23

-81d = 567

d = -567.81

d = −7

As we have the d lets find fist term

a₁ = -23 - 7(-7)

a₁ = -23 + 49

a₁ = 26

Now, find  29th term

a₂₉ = 26 + (29 - 1)(−7)

a₂₉ = −170

Thus, the 29th term in the given arithmetic sequence is −170.

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C)The greatest number is 8.2 × 10-3. It is 2,000 times greater than the smallest number.

In scientific notation, a number is written as the product of a number between 1 and 10 and a power of 10. The power of 10 tells us how many places to move the decimal point to the right (if the exponent is positive) or to the left (if the exponent is negative).

In this case, 8.2 × 10-3 means 8.2 × (10^-3) = 0.0082, 5.2 × 10-6 means 5.2 × (10^-6) = 0.0000052 and 4.1 × 10-6 means 4.1 × (10^-6) = 0.0000041.

To compare the numbers, we can compare the coefficient or the number in front of the 10 power. We can see that 8.2 is greater than 5.2 and 4.1. To check how many times greater the smallest number is, we can use the following formula: (greatest number / smallest number) = (8.2 / 0.0000041) = 2,000

Therefore, the greatest number is 8.2 × 10-3 and it is 2,000 times greater than the smallest number.

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