Let f(x)=(x-1)^2


Find a domain on which f is one-to-one and non-decreasing.

Find the inverse of f restricted to this domain

Answer:

Second inequality is
12x + 16y ≥ 460

We also have implied inequalities x ≥ 0, y ≥ 0 meaning hours cannot be negative

Step-by-step explanation:

The other equality refers to the earnings

Let x be the hours worked in the first job
Earnings at $12 per hour = 12x

Let y be the hours worked in the second job
Earnings at $16 per hour = 16y

Total earnings = 12x + 16y
This must be at least $460
"at least" means ≥

So second inequality is
12x + 16y ≥ 460

The midpoint M of the given line segment with end points (−8,−11) and (2,5) is (-3,-3).

What is meant by the midpoint of a line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. The centre of a line segment is known as the midpoint. It is the centroid of the segment and of the endpoints, and it is equally distant from both of them. It cuts the section in half.

Given a line segment with endpoints A and B.

   A = (−8,−11) = (x₁ , y₁)

  B = (2,5) = (x₂, y₂)

W asked to find the midpoint. Let the midpoint be M.

M = ( (x₁ + x₂) /2  , (y₁ + y₂) / 2)

(x₁ + x₂) /2  =  (-8 + 2) /2 =  -  6/2 = -3

(y₁ + y₂) / 2 =  (-11 + 5) /2  = -6/2 = -3

Therefore the midpoint M of the given line segment with end points (−8,−11) and (2,5) is (-3,-3).

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The number of students in mrs. Smith's class in exponent form is 3⁷.

Given that, Mrs. Smith has 3¹⁰ pencils in her classroom. Each student gets 3³ pencils.

Let the number of students in the class be represented by n.

To get the number of students in the class, divide the total number of pencils by the number of pencils each student got.

n = Total number of pencils ÷ Number of pencils each student gets

n = 3¹⁰ ÷ 3³

Since they both have the same base, we subtract the exponents

n = 3¹⁰ ⁻ ³

n = 3⁷

Therefore, the number of students is 3⁷.

Option D) 3⁷ is the correct answer.

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(-7, 4).

[tex]x=-2y+1\\ \\3x+8y=11[/tex]

Most of the times you solve a systems of equations, you'll have to solve one of the equations for one of the variables (x or y), since the first equation is already solved for "x", we may use that and skip this first solving step.

[tex]x=-2y+1[/tex]

[tex]3(-2y+1)+8y=11[/tex]

Chech attached image 1.

[tex](3)(-2y)+(3)(1)+8y=11\\ \\(-6y)+(3)+8y=11\\ \\-6y+3+8y=11[/tex]

[tex]-6y+3+8y-3=11-3\\ \\-6y+8y=8[/tex]

[tex]2y=8[/tex]

[tex]\frac{2y}{2} =\frac{8}{2} \\ \\y=4[/tex]

[tex]x=-2(4)+1\\ \\x=-8+1\\ \\x=-7[/tex]

Now that weëve found a value for both "x" and "y", write the solution as an ordered pair:

(x, y)

(-7, 4).

To algebraically verify your answer, you must use the value of either "x" or "y" on both of the equations and it should return the other value of the missing variable.

Since we already checked with the first equation, go ahead and plug in any of the values on the second equation and check if it returns the correct value.

For example, if we use y=4 in equation 2, it should return an "x" value of -7. Let's test it!

[tex]3x+8(4)=11\\ \\3x+32=11\\ \\3x=11-32\\ \\3x=-21\\ \\\frac{3x}{3} =\frac{-21}{3} \\ \\x=-7[/tex]

That's correct! Answer is (-7, 4).

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The expression 25^(2x-3)=125^(x+1) has its solution to be x = 15

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

25^(2x-3)=125^(x+1)

Express 25 and 125 as exponent with a base of 5

So, we have the following representation

5^2(2x-3)=5^3(x+1)

By comparison, we have

2(2x - 3) = 3(x + 1)

Open the brackets

4x - 12 = 3x + 3

Evaluate the like terms

x = 15

HEnce, the value of x is 15

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The measure of angle 1 and the measure of angle 2 are 45° and 90°.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other.

Given is a square,

We are asked to find the missing angles,

We know that, The diagonals of the square bisect each other at 90°,

The diagonal of a square bisects its internal angle,

Therefore, the measure of angle 1 = 45°

And,

The measure of angle 2 = 90°

Hence, the measure of angle 1 and the measure of angle 2 are 45° and 90°.

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The value of x is given as follows:

x = 3.

Applying the secant-tangent theorem, we have that the following equation holds true:

4x² = 6².

Hence we can solve the equation for x to obtain the value of x, as follows:

4x² = 36

x² = 36/4

x² = 9

x = sqrt(9)

x = 3.

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The side length of the cube can be written as:

S = 3*∛5  centimeters.

We know that the cube has a volume of V = 135cm³.

Now, remember that for a cube of side length S, the volume is:

V = S³

Here we can replace the volume in the equation above, we will get:

135cm³ = S³

If we apply the cube root in both sides, we will get:

∛(135 cm³) = S

∛135 cm = S

Now we can rewrite that as:

135 = 9*5

Then we can rewrite the expression:

∛135  = ∛(27*5) = ∛27*∛5 = 3*∛5

That is the sidelength of the cube.

So we have A = 3 and B = 5.

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Answer:

Where is the question??

Answer:

Step-by-step explanation:

The probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.

This is a binomial distribution problem, where each toss is a Bernoulli trial with a probability of success of 0.4 (i.e., catching the ball mid-air) and a probability of failure of 0.6 (i.e., not catching the ball mid-air).

The number of successes (mid-air catches) in four tosses follows a binomial distribution with parameters n = 4 and p = 0.4.

The probability of getting exactly three mid-air catches in four tosses is:

P(X = 3) = (4 choose 3) * 0.4^3 * 0.6^1 = 4 * 0.064 * 0.6 = 0.154

where (4 choose 3) is the number of ways to choose 3 out of 4 tosses, and 0.4^3 and 0.6^1 are the probabilities of getting 3 mid-air catches and 1 miss, respectively, in any order.

Therefore, the probability that Winston makes exactly three mid-air catches in four tosses is 0.154, rounded to three decimal places.

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Answer:

meidien 39 and the mean 37.2

Step-by-step explanation:

23 32 39 40 52 see 32 is the mediem

add them than dived than u get 37.2

The area of the picture frame is 72 cm². Thus, option C is correct.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm²), square metres (m²) or square kilometres (km²).

Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The area of the picture frame will be given by:

Area = (area of picture and frame)-(area of pictures)

area of picture and frame is given by:

A1=Length × width

A1 = 10 × 12

= 120cm²

area of the picture will be:

A2=8 × 6 = 48 cm²

thus the area of the frame will be:

A = A1 - A2

A = 120 - 48

A = 72cm²

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Complete question:

Select the correct answer.

Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame?

A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm.

A. 120 square centimeters

B. 88 square centimeters

C. 72 square centimeters

D. 64 square centimeters

I think the radius would be 2

Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:

Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is

[tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex]

Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
[tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex]

Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:

[tex]A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]

Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:

det(A+B) = (1)(1) - (1)(1) = 0

Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.

Therefore, the matrices [tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex] are non-invertible matrices that can be added together to form an invertible matrix [tex]A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex].

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The true statement about the figure is not represented in the options

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

The triangle

The value of y can be calculated using the following Pythagoras theorem

y^2 = (3x)^2 + (4x)^2

Evaluate

y^2 = 25x^2

So, we have

y = 5x

The height is given as

Height = 100

This means that

4x = 100

So, we have

x = 25

For y, we have

y = 5x

y = 5 * 25

y = 125

For the area, we have

Area = 1/2 * 4x * 3x

Area = 1/2 * 4 * 25 * 3 * 25

Evaluate

Area = 3750

Hence, none of the options are true

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Answer:

$2700

Step-by-step explanation:

The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -6 and b = 360, so we have:

x = -360/(2*(-6)) = 30

Therefore, the company will maximize its profit by selling 30 units of the product.

p(x) = -6x^2 + 360x - 2500

(x = 30 )

p(30) = -6(30)^2 + 360(30) - 2500 = 2700

So, the maximum profit for the company is $2700.

Answer:

if Hassan got 48/50 and scored an overall 5.7/6.0, and Emily got 32/40, her overall score would be approximately 5.6/6.0 (rounded to one decimal place).

Step-by-step explanation:

If Hassan got 48/50 and scored an overall 5.7/6.0, what would Emily's overall score be is she got 32/40?​

To determine Emily's overall score, we can use a proportion:

Hassan's score / Hassan's total = Emily's score / Emily's total

Substituting the given values, we get:

48/50 = 32/Emily's total

To solve for Emily's total, we can cross-multiply:

48/50 * Emily's total = 32

Simplifying the left-hand side, we get:

0.96 * Emily's total = 32

Dividing both sides by 0.96, we get:

Emily's total = 33.33 (rounded to two decimal places)

Now, we can use another proportion to find Emily's overall score:

Emily's score / Emily's total = 5.7/6.0

Substituting the value of Emily's total that we just found, we get:

Emily's score / 33.33 = 5.7/6.0

Solving for Emily's score, we get:

Emily's score = 31.4 (rounded to one decimal place)

Therefore, if Hassan got 48/50 and scored an overall 5.7/6.0, and Emily got 32/40, her overall score would be approximately 5.6/6.0 (rounded to one decimal place).

The equation of the graphed function is y = x + 4, x ≥ 4 and y = x² + 3, x < 4

A similar question is added as an attachment

From the attached, we can see that the function types are:

Based on the list of options, we have:

Next, we look at the intervals (domain)

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The constant of proportionality (k) for the graph is 11.7.

The proportional equation for the graph is y = 11.7x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for money earned per hour as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 35.1/3 = 81.9/7

Constant of proportionality, k = 11.7.

Therefore, the required equation is given by:

y = kx

y = 11.7x

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The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

What is a linear factor?

A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.

We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:

b² - 4ac = k² - 4(2)(-5) = k² + 40

For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.

One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:

k² + 40 = m²

where m is an integer. Rearranging, we get:

k² - m² = -40

This is a difference of squares, so we can factor it:

(k + m)(k - m) = -40

We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.

The pairs of factors of -40 are:

(-1, 40), (-2, 20), (-4, 10), (-5, 8)

For each pair, we can solve the system of equations:

k + m = a

k - m = b

where a and b are the two factors in the pair. Adding these equations, we get:

2k = a + b

Subtracting them, we get:

2m = a - b

Solving for k and m, we obtain:

k = (a + b)/2

m = (a - b)/2

We can now check if the values of k and m are integers and if they satisfy the original equation.

For example, if we take the pair (-1, 40), we get:

k + m = -1

k - m = 40

Adding these equations, we get:

2k = 39

This implies that k = 39/2, which is not an integer, so this pair does not work.

Trying the other pairs, we find that:

(-2, 20) gives k = 9 and m = 11, which works

(-4, 10) gives k = 3 and m = 7, which works

(-5, 8) gives k = 1 and m = 3, which works

Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

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If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.

The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).

The monthly cost of the 4-yard dumpster = $95.00

1 year = 12 months

The total annual cost = $1,140 ($95 x 12)

Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.

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The proof is incorrect and step number 3 is the first unjustified step due to missing prior step.

A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

The step 3 in the given explanation is unjustified step. The step needs to be place at the last in order to take in consideration all the steps and properties of a rectangle.

Hence, the proof is incorrect and step number 3 is the first unjustified step due to missing prior step.

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Answer:

Brian hiked 6 1/2 more miles than Christine.

Step-by-step explanation:

Ok. 5.25+4.75+6-2*4.75=6.5 or 6 1/2 more miles.

The Account receivable turnover for Year 1 is 21.04.

The Account receivable turnover for Year 2 is 20.86.

The average number of the times a company collects its accounts receivable balance is measured by the accounts receivables turnover ratio. It is a measurement of how well a business manages its line of credit process and collects unpaid balances from customers. A company's accounts receivable turnover ratio is higher for an efficient business and lower for an inefficient one.

For year 1:

Account receivable turnover:

= Net sales / Average account receivable

= 13,612 / ((654 + 640)/2)

= 13,612 / 647

= 21.0386398764

= 21.04

For year 2:

Account receivable turnover:

= Net sales / Average account receivable

= 12,808 / ((640+588)/2))

= 12,808 / 614

= 20.8599348534

= 20.86

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Shyam would need S$250 to send NRs 20,000 to Nepal.

To determine how many Singapore dollars Shyam needs to send NRs 20,000 to Nepal, we need to first use the exchange rate provided to convert NRs to Singapore dollars.

The exchange rate given is S$1.00 = NRs 80.00. This means that for every Singapore dollar, Shyam can get 80 Nepalese rupees.

To find out how many Singapore dollars Shyam needs to send NRs 20,000, we need to divide NRs 20,000 by 80, which gives:

NRs 20,000 / 80 = S$250

Therefore, Shyam would need S$250 to send NRs 20,000 to Nepal.

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Answer:

Step-by-step explanation:

If (x + a) is a factor of x³ + 8x² + 4ax - 3a, then we know that dividing x³ + 8x² + 4ax - 3a by x + a will give a quotient of x² + (8 - a)x + (4a - 3), and a remainder of 0.

We can write this as:

x³ + 8x² + 4ax - 3a = (x + a)(x² + (8 - a)x + (4a - 3))

Expanding the right-hand side, we get:

x³ + 8x² + 4ax - 3a = x³ + (8-a)x² + (4a-3)x + ax² + (8-a)ax + (4a-3)a

Collecting like terms, we get:

x³ + 8x² + 4ax - 3a = x³ + (a+8)x² + (5a-3) x + a(4a-3)

Comparing the coefficients of x², x and the constant term, we get the following equations:

a + 8 = 8   --> a = 0

5a - 3 = 0   --> a = 3/5

4a^2 - 3a = 0 --> a(4a-3) = 0

Therefore, we have:

a³ - 4a² + 3a = a(a² - 4a + 3) = a(a-1)(a-3) = 0

So, a can be 0, 1, or 3

Therefore, the possible values of a are 0, 1, and 3.

Answer:

Step-by-step explanation:

We can use the law of sines to find the length of side a. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

We are given that A = 80°, B = 60°, and b = 15 cm. We can substitute these values into the law of sines and solve for a as follows:

a/sin 80° = 15/sin 60°

Multiplying both sides by sin 80°, we get:

a = 15*sin 80°/sin 60°

Using a calculator, we can evaluate sin 80° and sin 60° as follows:

sin 80° ≈ 0.9848

sin 60° = √3/2 ≈ 0.8660

Substituting these values, we get:

a ≈ 15*0.9848/0.8660

a ≈ 17.06

Rounding this to the nearest whole number, we get:

a ≈ 17

Therefore, the length of side a is approximately 17 cm.

Answer:

Step-by-step explanation:

no because they don't have the same dominator