Find the values of a and b such that
x²-x+ 5 = (x-a)² + b

Please, the person that explains it explain it with the part of
(x+b/2)^2 - (b/2)^2 + c

-because if not I won’t understand :)

Answer: 3

Step-by-step explanation:

You would need to use the Pythagorean theorem to solve this equation. 6 is the hypotenuse and 3[tex]\sqrt{3}[/tex] is the longer leg.  

a^2+b^2=c^2

c= hypotenuse

6^2=3[tex]\sqrt{3}[/tex]^2 + a^2

36=27+a^2

36-27=9

[tex]\sqrt{9}[/tex] = 3

The equation of exponential function of following table is represented by the table below is y = A(Bˣ).

An exponential function is a mathematical function denoted by f(x) = eˣ (where the argument x is written as an exponent). Unless otherwise stated, the term usually refers to positive-valued functions of real variables, but can be extended to complex numbers and generalized to other mathematical objects such as matrices and Lie algebras. Although the exponential function arose from the notion of exponentiation (iterative multiplication), its modern definition (which has several equivalent characterizations) allows it to be extended exactly to any real argument, including irrational numbers. Its ubiquitous appearance in pure and applied mathematics has led mathematician Walter Rudin to believe that the exponential function is "the most important function in mathematics."

To find the equation of exponential form:

For case 1,

Exponential form: y = A(Bˣ)

y = 0.1, x = 0

[tex]0.1 = A(B^{0})[/tex]

0.1 = A(1)

A = 0.1

For case 2,

Exponential form: y = A(Bˣ)

y = 0.05, x = 1

[tex]0.05 = 0.1(B^{1})[/tex]

B = 0.5

For case 3,

y = 0.025, x = 2

[tex]A = 0.1(B^{2})[/tex]

[tex]0.025 = 0.1(0.5^{2})[/tex]

0.025 = 0.025

For case 4,

y = 0.0125, x = 3

0.0125 = 0.1(0.5³)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

We calculated the value of A and B, and proved it in case 3 and case 4.

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The complete question is as follows:

Find the equation of the exponential function represented by the table below:

The percentage of Kira's free throws is 68%.

We have,

From the grid,

We can see that,

There are 25 boxes.

Now,

The number of shaded boxes = 17

Now,

The percentage of the shaded boxes.

= 17/25 x 100

= 17 x 4

= 68%

Thus,

The percentage of Kira's free throws is 68%.

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The complete question.

The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.

Find the percentage of Kira's free throws.

Applying the intersecting secants theorem, the value of x is calculated as: x = 5.

According to the intersecting secants theorem, if two secant lines intersect outside of a circle, then the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

Using the theorem, the equation below is created to find the value of x:

4(4 + 5) = (x - 2)(x - 2 + x + 4)

4(9) = (x - 2)(2x + 2)

36 = 2x² - 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

Factorize:

(x + 4)(x - 5) = 0

x = -4 or x = 5

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The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Answer:  the longest poster that could fit in the box is approximately 22.56 inches long.

Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:

diagonal^2 = 11^2 + 18^2 + 8^2

diagonal^2 = 121 + 324 + 64

diagonal^2 = 509

inclining = sqrt(509)

corner to corner ≈ 22.56 inches

Keara has climbed up to 41 feet in the tree.

Rounding off a value to the nearest tenth means finding the closest multiple of 0.1 to the given value. To do this, you need to look at the digit in the hundredths place. If the digit is 5 or greater, you round the tenths place up by 1. If the digit is less than 5, you leave the tenths place unchanged. For example, to round the value 3.874 to the nearest tenth, you would look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, you round up the tenths place to 8, and the rounded value is 3.9. Rounding to the nearest tenth is often used when working with measurements or values that require a certain level of precision.

According to the range finders, the distance from Keara to her friend is 55 feet and the angle of depression from Keara to her friend is 40°.

From this the following diagram can be drawn.

Now, we need to find the length of AB which will denote how high Keara climbed.

We can use the trigonometric sine function to find the length of AB,

Sin 40° = opposite side / hypotenuse = AB/ BC = AB/ 55

Hence AB = 55 × Sin 40° ≈ 40.981

That is she would have climbed approximately 41 feet.

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The quadratic equation written in vertex form is:

y = (x + 1)^2 - 9

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

On the graph we can see that the vertex is at (-1, -9), then we have:

y = a*(x + 1)^2 - 9

Now we also can see that the y-intercept is y = -8, then evaluating in zero we should get:

-8 = a*(0 + 1)^2 - 9

-8 = a - 9

-8 + 9 = a = 1

The quadratic equation is:

y = (x + 1)^2 - 9

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Answer:

5)

$332.19

6)

$16,857.36

7)

$248.91

Step-by-step explanation:

monthly premium = Base Rate * [tex]\frac{Monthly Payroll}{100}[/tex]

5)

given:

Base rate = $2.24
Monthly payroll = $14,830.00

unknown = monthly premium

 [tex]2.24 * \frac{14,830.00}{100}[/tex] = $332.192≈$332.19

6)

given:

Base rate = $19.89
Monthly payroll = $84,752.96

unknown = monthly premium

[tex]19.89 * \frac{84,752.96}{100}[/tex] = $16,857.364≈$16,857.36

7)

given:

Base rate = $2.90
Monthly payroll = $8,582.94

unknown = monthly premium

[tex]2.90 * \frac{8,582.94}{100}[/tex]=$248.90526≈$248.91

Proof that cos²(x) + sin²(x) = 1 using the unit circle shows that this equation represents a circle with radius 1

The equation of the unit circle is given by:

x² + y² = 1

where x and y are the coordinates of any point on the circle. Let us assume that the point P on the circle makes an angle of x with the positive x-axis. Then, the coordinates of P are given by:

x = cos(x)

y = sin(x)

Substituting these values in the equation of the circlet:

cos²(x) + sin²(x) = 1

Therefore, we have shown that sin²(x) + cos²(x) = 1 using the unit circle.

Graphically, this equation represents a circle with radius 1 centered at the origin, and any point (cos(x), sin(x)) on the circle will satisfy this equation.

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The solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

4x + 6y - 2z = 2 (multiply first equation by 2)

x + 2y - 3z = -5 (third equation)

Add the two equations, we get:

5x + 8y = -3 (eliminated z)

-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)

3x + y + 2z = 12 (second equation)

Add these two equations, we have:

-4x + 8y = -21 (eliminated z)

5x + 8y = -3

5x = -8y - 3

x = (-8y - 3)/5

Substituting this expression for x into the second equation, we get:

3((-8y - 3)/5) + y + 2z = 12

z = (39/10) - (19/10)y

Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:

2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1

Simplifying and solving for y, we get:

y = 2

x = (-8(2) - 3)/5 = -19/5

z = (39/10) - (19/10)(2) = 1/10

In conclusion, the solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

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The solution to the given system of linear equations is

x = 3, y = -1 and z = 2

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

2x + 3y − z = 1

3x + y + 2z = 12

x + 2y − 3z = −5

Multiply the third equation by 2

x + 2y − 3z = −5 ) ×2

2x + 4y - 6z = -10

Subtract the first equation from the resulting equation

  2x + 4y - 6z = -10

- (2x + 3y − z = 1

----------------------------------------

y - 5z = -11     ---------- (1)

Now,

Multiply the third equation by 3

x + 2y − 3z = −5 ) ×3

3x + 6y -9z = -15

Subtract the second equation from the resulting equation

 3x + 6y -9z = -15

- (3x + y + 2z = 12

-----------------------------------------

5y - 11z = -27     ----------- (2)

Solve equations (1) and (2) simultaneously

y - 5z = -11         ------------ (1)

5y - 11z = -27     ------------ (2)

Multiply equation (1) by 5

y - 5z = -11  ) ×5

5y - 25z = -55

Subtract the resulting equation from equation (2)

  5y - 11z = -27

-( 5y - 25z = -55

-----------------------------

14z = 28

Divide both sides by 14

14z/14 = 28/14

z = 2

Substitute the value of z into equation (1)

y - 5z = -11

y - 5(2) = -11

y - 10 = -11

Add 10 to both sides of the equation

y - 10 + 10 = -11 + 10

y = -1

Substitute the value of y and z into the third equation

x + 2y − 3z = −5

x + 2(-1) − 3(2) = −5

x - 2 - 6 = -5

x - 8 = -5

Add 8 to both sides of the equation

x - 8 + 8 = -5 + 8

x = 3

Hence,

The solution is

x = 3, y = -1 and z = 2

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The equations that will make a linear function are

A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.

This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.

It takes on the standardized form:

y = mx + b

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Answer: To calculate the cost of the triangular lot, we need to first find the area of the triangle using the given dimensions. To do this, we can use Heron's formula, which states that the area of a triangle with sides of lengths a, b, and c is given by:

area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, we have a = 188, b = 145, and c = 158. Substituting these values into the formula, we get:

s = (188 + 145 + 158)/2 = 245.5

area = √(245.5(245.5-188)(245.5-145)(245.5-158)) ≈ 12463.15 square feet

Now that we have the area of the lot, we can multiply it by the price per square foot to get the total cost:

cost = 12463.15 × $3 = $37,389.45

Therefore, the lot would cost approximately $37,389.45.

Step-by-step explanation:

The solution of the system of equations given y = -6x + 5 and 4x - y = 5,  is (1, -1).

To solve this system of equations, we can use the substitution method. We can rearrange the first equation to solve for y in terms of x:

y = -6x + 5

Next, we can substitute this expression for y in the second equation:

4x - (-6x + 5) = 5

Simplifying this equation, we get:

4x + 6x - 5 = 5

Combining like terms, we get:

10x = 10

Dividing both sides by 10, we get:

x = 1

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Using the first equation, we get:

y = -6(1) + 5 = -1

Therefore, the solution of the system of equations is (1, -1). This means that the two equations intersect at the point (1, -1) on the coordinate plane, and this is the only point that satisfies both equations simultaneously.

In summary, to solve the system of equations y = -6x + 5 and 4x - y = 5, we used the substitution method to find that the solution is (1, -1).

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Answer:

d)367

Step-by-step explanation:

Given, Tn = 5n² - 4

To find the 5th term, substitute n = 5 in the equation Tn = 5n² - 4

T5 = 5(5)² - 4

T5 = 121

To find the 7th term, substitute n = 7 in the equation Tn = 5n² - 4

T7 = 5(7)² - 4

T7 = 241

Therefore, the sum of the 5th and 7th terms = T5 + T7 = 121 + 241 = 362.

Hence, the correct option is (d) 367.

The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.

Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.

The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:

ME = 1.96 × √[(p × q) / n]

where:

1.96 is the z-score associated with a 95% confidence level

p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)

q is 1 - p

n is the sample size

Assuming a conservative estimate of p = 0.5, we have:

ME = 1.96 × √[(0.5 × 0.5) / 6400]

≈ 0.016 or 1.6%

Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.

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Answer:

Once a person has identified the ways they are wasting money, there are several steps they can take to stop wasting money and start saving it:

By taking these steps, a person can stop wasting money and start building a solid financial foundation for the future.

Answer:

Volume = (1/2)(7)(24)(22) =

1,848 cubic meters

Surface area = 2(1/2)(7)(24) + 7(22) + 22(24) + 22(25) = 1,400 square meters

The amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, it's the interest earned on the principal amount plus any interest earned previously.

To calculate the amount after 5 years, we need to use the formula for compound interest:

A = P × {1 + r ÷ (n × 100)} ∧ (n × t)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 2.25% , n = 4 (since interest is compounded quarterly), and t = 5.

After applying these values, we get:

A = $5000 x (1 + 2.25/400) ⁴ ˣ ⁵

A = $5000 x (1.005625) ²⁰

A = $5000 x 1.1871955

A = $5593.60 (rounded off to 2 decimals)

Therefore, the amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

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A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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Answer:

The mean of the numbers 5, 3, 6, x, 9, and 10 is given as 7.

To find the value of x, we can use the formula for the mean:

mean = (sum of all the numbers) / (number of numbers)

In this case, we have:

7 = (5 + 3 + 6 + x + 9 + 10) / 6

Multiplying both sides of the equation by 6, we get:

42 = 33 + x

Subtracting 33 from both sides of the equation, we get:

x = 9

Therefore, the value of x that makes the mean of 5, 3, 6, x, 9, and 10 equal to 7 is 9.

The total amount that Meihua pays for the 36 pencils is  9M - 36n

We know that a set of 4 pencils has a price M, then the price of each single pencil is:

P = M/4

And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:

P = M/4 - n

Now we know that she buys 36 of these, so the amount that she pays is given by the product:

amount  = 36*(M/4 - n)

amount = 9M - 36n

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Answer:

(-2)

Step-by-step explanation:

just do -2 x-3 x than + 13 and than you will get - 2

Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).

Answer:

D. 263 degrees

Step-by-step explanation:

We know that central angles are congruent to the arcs they encompass or intercept. So, if the minor arc is 97 degrees, and the total measure of a circle's arcs are 360 degrees, then the major arc is 263 degrees.

Therefore, the answer is D.

The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.

A rectangular prism's volume V is determined by:

V = l × w × h

where l denotes the prism's length, w its width, and h its height. Here are the facts:

l = 2 3 ft

w = 1 1/2 ft

h = 1 1/4 ft

When we enter these values into the formula, we obtain:

V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)

= (7/3 ft) × (3/2 ft) × (5/4 ft)

= 35/8 ft³

Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.

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Answer:

Okay, let's think through this step-by-step:

• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.

• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest

• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back

•Monthly payments = $3,797.50 / 12 months = $285.55

• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)

The choices do not match this:

A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.

B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.

C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.

D. $35.00 - This is also too low and does not make sense based on the loan details provided.

In summary, to find the interest in just the first payment, we calculate:

Interest over full loan ($297.50) / Number of payments (12) = $24.79

So the interest amount in just the first monthly payment is $24.79.

But the total interest paid over the life of the loan (1 year) is $297.50.

Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.

Let me know if you have any other questions!

Step-by-step explanation:

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

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