Find, in gradient-intercept form, the equation of a line which has:

a gradient of -4/5 and which passes through (4,-2)

Answer:

256 ways

Step-by-step explanation:

Okay so n cannot be in the nth place, but there are 5 places available.

So thinking about it technically you can have 4 of each number in a different spot not their own, and 4x4x4x4 = 256

However, if that doesn't work, you could try 4! which is 4x3x2x1 = 24

Hope that helps :)

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer: 15,840 yards

Step-by-step explanation: First found out how many yards are in a mile: 1760. Then multiply by 1760 by 9. Which will give you 15,840.

The nth term of the pattern is (n²-1)

To find the nth term identify the patterns in a given sequence and use algebraic expressions to generalize the pattern and find the nth term.

By observing the given series we say that each number is one less than perfect Like 8 is one less than 9, 15 is one less than 16, etc. Use this condition to solve the problem.

Here we have

0, 3, 8, 15...    

To find the nth terms identify the patterns in a given sequence

Here each term can be written as follows

1st term => 0 = (1)² - 1 = 0

2nd term => 3 = (2)² - 1 = 3

3rd term => 8 = (3)² - 1 = 8

4th term => 15 = (4)² - 1 = 15

Similarly

nth term = (n)² - 1 = (n²-1)

Therefore,

The nth term of the pattern is (n²-1)

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Finding the maximum or minimum value of a function is a fundamental concept in calculus. It helps us determine the peak or bottom values of a given function, which can be essential in many real-life applications.

To find the maximum or minimum value of a function using a calculator, you first need to input the function into the calculator. The function must be written in the correct syntax and form for the calculator to understand it.

There are different methods to find the maximum or minimum value of a function on a calculator, depending on the model and software. However, the most common way is to use the "minimum" or "maximum" functions, depending on what value you are trying to find.

To use the "maximum" or "minimum" functions, you need to enter the function, followed by the variables or ranges of the function. The calculator would then display the maximum value of the function within that range.

In summary, finding the maximum or minimum value of a function using a calculator involves inputting the function, locating the "maximum" or "minimum" function tool, and specifying the range or variables of the function. This process allows you to quickly and accurately find the peak or bottom values of a given function, which can be useful in various mathematical and scientific applications.

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The factors of \(4p^2 - p = 0\) are p=0 and p = 1/4.

The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's factors have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF).

Given that \(4p^2 - p = 0\):

Solve the equation to find the value of p:

\(4p^2 - p =0\\\\p(4p -1 ) = 0\\\)

Here, the value of p = 0 or the value of (4p - 1) =0.

For (4p -1) = 0, the value of p is:

p = 1/4

Hence, the factors of \(4p^2 - p = 0\) are p=0 and p = 1/4.

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Answer: 14

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°

Answer:

Step-by-step explanation:

Basic Charge = $ 65

Rate per hour = $ 28

Number of hours = H

Rate for H hours = 28 *H = 28H

Equation:

65 + 28H ≤ 250

Anan consideration requires:

Requirements of the plumber

Thus, to determine the number of how many hours Anan can afford for his total amount of $250, we have the following:

The initial fee + hourly rate ≤ 250  

∴

   $65 + $28 H ≤ 250

Therefore, we can conclude that the perfect inequality that describes Anan Scenario is:    $65 + $28 H ≤ 250

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Answer:

$9.99

$12 99

$5.69

Step-by-step explanation:

the answer there is not any number in hundred place value

The statement "the interquartile range is least influenced by an outlying value in the data set" is true.

The range is simply the difference between the maximum and minimum values in a data set.

The variance is a measure of the spread of a data set, and is calculated by finding the average of the squared differences between each data point and the mean of the data set.

The interquartile range, on the other hand, is a measure of the spread of the middle 50% of the data set. It is calculated by finding the difference between the upper quartile and the lower quartile.

Because the interquartile range only takes into account the middle 50% of the data, it is less influenced by outliers than the range and variance. This is because outliers can greatly impact the range and variance, but have little effect on the interquartile range.

In conclusion, the interquartile range is a more robust measure of spread for a data set, as it is less influenced by outliers.

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We can identify a polynomial identity by applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity.

In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term. A sizable subset of algebraic expressions are polynomials. Polynomials are any expressions where the powers of the variables are all whole numbers. They frequently have a wide range of applications since they encompass such a sizable portion of all algebraic expressions.

Given,

We can identify a polynomial identity by,

Whatever the values given to the variables, the equation for the polynomial identity is always true. By applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity. When factorizing or extending a polynomial, we can employ polynomial identities to our advantage.

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The approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm is equal to the width (w) of the rectangle.

To determine the approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm, we need to calculate the change in area and divide it by the change in length.

Let's denote the length of the rectangle as L (in cm) and the corresponding area as A (in square cm).

Given that the initial length is 13 cm and the final length is 16 cm, we can calculate the change in length as follows:

Change in length = Final length - Initial length

= 16 cm - 13 cm

= 3 cm

Now, let's consider the formula for the area of a rectangle:

A = Length × Width

Since we are interested in the rate at which the area decreases, we can consider the width as a constant. Let's assume the width is w cm.

The initial area (A1) when the length is 13 cm is:

A1 = 13 cm × w

Similarly, the final area (A2) when the length is 16 cm is:

A2 = 16 cm × w

The change in area can be calculated as:

Change in area = A2 - A1

= (16 cm × w) - (13 cm × w)

= 3 cm × w

Finally, to find the approximate average rate at which the area decreases, we divide the change in area by the change in length:

Average rate of area decrease = Change in area / Change in length

= (3 cm × w) / 3 cm

= w

Therefore, the approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm is equal to the width (w) of the rectangle.

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Answer:

Answer is C

Step-by-step explanation:

There is one faulty light bulb in each box. 4 boxes 4 bad lightbulbs since there we two in the first to 2+2 is 4

Answer:

y = 1/4x + 1

Step-by-step explanation:

Rise/run = 1/4x

y-intercept: (0,1)

Equation: y = 1/4x + 1

Graph this equation or you can just put this equation in Desmos calculator and it'll graph for you.

Therefore , the solution of the given problem of quadrilateral comes out to be  3x - 4y = 2 is the equation of the line that contains the quadrilateral's lengthier diagonal.

A rectangular shape is a four-sided, four-cornered object in geometry. Latin terms were used to create the expression, both "quad" and "array of creative ideas." (meaning "side"). The three parts of a rectangle are four regions, four corners, and four corners. The two main types of concave and convex shapes are convex and concave. Subdivisions in trapezoids, geometric figures, angles, rhombuses, and cubes are also considered to be convex quadrilaterals.

Here,

With ends A(2, 2) and C(1, -1), Diagonal AC has the following length:

=> √[(1 - 2)² + (-1 - 2)²] = √[10]

Diagonal BD's length is given by its ends B(-2, -2) and D(6, 4).

=>  √[(6 - (-2))] + √[4 - (-2)] = √[100]

Inferring that diagonal BD is the longer diagonal from the fact that

=>  √[100] = 10 is larger than sqrt[10].

The inclination of the line containing diagonal BD can then be determined:

=>  slope = (4 - (-2)) / (6 - (-2)) = 6/8 = 3/4

Finally, we can determine the equation of the line containing the diagonal BD using the point-slope form of the equation of a line:

=> y - 4 = (3/4)(x - 6)

=>  4y - 16 = 3x - 18

=>  3x - 4y = 2

Consequently, 3x - 4y = 2 is the equation of the line that contains the quadrilateral's lengthier diagonal.

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55°

Step-by-step explanation:

110+15+x =180

x = 180 - 125

x = 55°

Answer:

Step-by-step explanation:

Answer:

56kmp

Step-by-step explanation:

That is all I know.

Answer:

1.6 kpm

Step-by-step explanation:

(32km)/(20min) = 1.6 km/min or kpm

Answer:

18750 miles in 3.75 hours

Step-by-step explanation:

5000 x 3.75 = 18,750

An isosceles right triangle has two congruent angles and a right angle

It is true that the base angle of an isosceles right triangle is 45 degrees

From the question, we understand that:

Triangle type = isosceles right triangle

The sum of angles in a triangle is:

x + y + z = 180

Assume the triangle is right-angled at z.

So, we have;

z = 90

The equation becomes

x + y + 90 = 180

Subtract 90 from both sides

x + y = 90

The triangle is an isosceles triangle.

So, we have: x = y

The equation becomes

x + x = 90

2x = 90

Divide by 2

x = 45

Hence, it is true that the base angle of an isosceles right triangle is 45 degrees

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Answer:

Add 2 to both sides.

1/4x=2x-7

Multiply both sides by 4

x=8x-28

-8x from each side.

-7x=-28

divide both sides by -7

X=4

Answer:  x=4

1. Multiply both sides by 4 to get rid of the denominator, which gives you x-8 = 8x-36
2. Subtract 8x from both sides, which gives you x - 8 - 8x= -36

3. Add 8 to both sides, which gives you x - 8x = -36 + 8

4. Simplify, -7x = -28

5. Divide both sides by -7, x = -28/-7

6. the negative signs cancel and you just get 4

Only possibility for the number written on the 21st card is 2.7.

In order to make a 4x5 rectangle, Ted needs to select 20 cards out of 21. Since the sums of numbers in all rows should be equal, we can find the sum of numbers in each row by dividing the sum of all selected numbers by 5.

For this problem, the sum of all selected numbers is: 41 + 22 + 73 + 84 = 4 + 4 + 21 + 32 = 61

So, the sum of numbers in each row should be 61/5 = 12.2

Now, we can find the sum of numbers in each column by adding the number of times each number appears on the cards.

For example, the sum of number 1's in each column should be 4/4 = 1.

The sum of number 2's in each column should be 2/4 = 0.5.

And so on.

The sum of numbers in each column should be: 1+2.5+3+3 = 9.5

So, to make all rows have the same sum, the 21st card should be a number that when added to 9.5 will give 12.2.

Therefore, the number written on the 21st card could be 2.7.

So the only possibility for the number written on the 21st card is 2.7.

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The solution for x in terms of a is x = -1 / (2a). This means that for any given value of a, x can be calculated using this equation.

To solve the equation 4a²x² + 8ax + 3 = 0 in terms of a, we can use the quadratic formula.

The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 4a², b = 8a, and c = 3. Plugging these values into the quadratic formula, we get:

x = (-8a ± √((8a)² - 4(4a²)(3))) / (2(4a²))

Simplifying the equation further:

x = (-8a ± √(64a² - 48a²)) / (8a²)

x = (-8a ± √(16a²)) / (8a²)

x = (-8a ± 4a) / (8a²)

Now we can simplify the equation by factoring out a common term from the numerator:

x = -4a (1 ± 1) / (8a²)

Simplifying further:

x = -4a (2 / 8a²)

Finally, we can simplify the fraction:

x = -1 / (2a)

Therefore, the solution for x in terms of a is x = -1 / (2a). This means that for any given value of a, x can be calculated using this equation.

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Answer: Answer in Photo

The statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.

To prove that Im(T) ker(T) - T.T=Z, we must first understand the terms "operator," "transformation," and "linear."

An "operator" is a function that maps one vector space to another. A "transformation" is a function that maps one set to another. A "linear" transformation is a transformation that satisfies the properties of linearity, meaning that it preserves addition and scalar multiplication.

Now, let's look at the equation Im(T) ker(T) - T.T=Z. The term "Im(T)" refers to the image of the linear operator T, which is the set of all vectors that can be obtained by applying T to any vector in V. The term "ker(T)" refers to the kernel of the linear operator T, which is the set of all vectors that are mapped to the zero vector by T.

To prove that Im(T) ker(T) - T.T=Z, we must show that the difference between the image of T applied to the kernel of T and the composition of T with itself is equal to the zero linear transformation.

First, let's consider the image of T applied to the kernel of T. Since the kernel of T is the set of all vectors that are mapped to the zero vector by T, applying T to any vector in the kernel of T will result in the zero vector. Therefore, Im(T) ker(T) = 0.

Next, let's consider the composition of T with itself, T.T. Since T is a linear operator, the composition of T with itself will also be a linear operator. However, there is no guarantee that T.T will equal the zero linear transformation.

Therefore, Im(T) ker(T) - T.T=Z can be simplified to 0 - T.T=Z. Since T.T is not necessarily equal to the zero linear transformation, the equation does not hold true for all linear operators T.

In conclusion, the statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.

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a+c = b+d , because angle c = angle b and a = d

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Angles on parallel lines can be alternate, corresponding or verically opposite to each other. And when they have these properties, the angles are equal to reach other.

b = c , since b+y = 360 and c+y = 360

and also a + x = 180

d + x = 180

therefore a = d

Therefore;

in b+d , we can substitute c for a and b for c

therefore b+d = a+c

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If A,B, and C are three collinear points such that AB=10 units and AC=15 units, the length of BC is  5 units.

This is because of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, AB + AC = 25, which is greater than the length of BC, which is 5.  

To calculate the length of BC, we can use the Pythagorean theorem. The formula is a² + b² = c², where a and b are the sides of the triangle and c is the hypotenuse. In this case, we have a = 10 and b = 15, so c² = 10² + 15² = 325. To find c, we take the square root of both sides, so c = √325 = 18.25. Since BC is the hypotenuse, its length is 18.25, but since its endpoints are collinear, the length of BC is 5 units.

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The possible volume of cylinder is  V= \(\frac{4\sqrt{3}\pi r^3 }{9}\)  .

What is Volume ?

A three-dimensional space's occupied volume is measured. It is frequently expressed numerically in terms of SI-derived units or different imperial units. Volume definition and length definition are connected.

There are several steps to this optimization problem.

1.) Find the equation for the volume of a cylinder inscribed in a sphere.

2.) Find the derivative of the volume equation.

3.) Set the derivative equal to zero and solve to identify the critical points.

4.) Plug the critical points into the volume equation to find the maximum volume.

Given the height, h , we can find the radius of the cylinder in terms of r

using the Pythagorean Theorem.

Note that h refers to half of the total height of the cylinder. I chose to use h instead of  \(\frac{h}{2}\) to simplify things later on.

To find the volume of our cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;

V= π \((radius of cylinder)^2 * (height of cylinder)\)

=> V = π (\((\sqrt{r^2-h^2} )^2\) (2h)

=> V = 2πh \((r^2-h^2)\)

This is our volume function. Next we take the derivative of the volume function and set it equal to zero. If we move the h inside the parenthesis, we only need to use the power rule to get the derivative.

=>V = 2π \((r^2h-h^3)\)

=> V= \(\frac{4\sqrt{3}\pi r^3 }{9}\)

This is the optimized volume for the cylinder. Its a good check to notice that V is in terms of \(r^3\) since volume should have cubic units. In other words, if our radius was given in term of meters, our volume units would be \(m^3\) .

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Answer:

Step-by-step explanation:

yeah you got it