By what will the product of 2 numbers decrease if one of the numbers is decreased by 25% and the other number is decreased by 50%

The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:

P = 2x + 2y

where x is the length of the rectangle in centimeters and y is the width of the rectangle in centimeters.

If the perimeter of the rectangle is z, then we can write the formula as:

z = 2x + 2y

Simplifying this equation, we get:

p = z

Therefore, the formula for p, the perimeter of the rectangle, is:

p = 2x + 2y

where x is the length of the rectangle in centimeters and y is the width of the rectangle in centimeters.

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The vector AC can be expressed in terms of vector AB and vector BC as follows:

In Euclidean geometry, a parallelogram is described as a simple quadrilateral with two pairs of parallel sides.

We have that  ABCD is a parallelogram, vector AC is equivalent to vector BD, which can be expressed in terms of vector AB and vector BC as follows:

Vector BD = Vector AB + Vector BC

We can substitute BD for AC in the above equation because  vector AC is equivalent to vector BD, we obtain the following:

Vector AC = Vector AB + Vector BC

In conclusion, vector AC can be expressed in terms of vector AB and vector BC as the sum of vector AB and vector BC.

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If f(x) is the parent function and g(x) is the transformation of f(x), then the required functions are as follows:

5. g(x) = -4ˣ and 6. g(x) = -(1/5)ˣ.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

5.

The given function is as follows:

f(x) = 4ˣ

When the function f(x) = 4ˣ is reflected about the x-axis, then we get the graph of function g(x).

So, g(x) = -4ˣ

6.

The given function is as follows:

f(x) = (1/5)ˣ

When the function f(x) = (1/5)ˣ is reflected about the x-axis, then we get the graph of function g(x).

So, g(x) = -(1/5)ˣ

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The graph of the quadratic equation has a minimum value, The extreme value is at the point (7,-3), and The graph of the quadratic equation has a maximum value are all true about the equation.

A quadratic equation is a mathematical expression made up of four terms which are arranged in the form of a polynomial. It is usually used to solve for the unknown values of two or more variables. It is also defined as a mathematical equation containing a second-order polynomial that can be written in the form of ax2 + bx + c = 0.

The graph of the quadratic equation has a minimum value, The extreme value is at the point (7,-3), and The graph of the quadratic equation has a maximum value are all true about the equation. The solutions for the equation are 3 and 7, which can be found by using the Quadratic Formula. The extreme value is at the point (7,-3) since this is the lowest value of the graph.

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The answer: no real solutions to this equation

To solve the equation, we need to find a common denominator for all of the fractions on the left side of the equation. The common denominator will be (y-2)(y-3), so we will multiply each fraction by the appropriate factor to get the common denominator.

[tex]y/y -2y+ 4/y-3 = 4/ y2-5y+6[/tex]

[tex]y(y-3)/(y-2)(y-3) - 2y(y-2)/(y-2)(y-3) + 4(y-2)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can combine the fractions on the left side of the equation:

[tex](y2-3y-2y2+4y+4y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Simplifying the numerator on the left side gives us:

[tex](-y2+5y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can cross-multiply and simplify:

[tex](-y2+5y-8) = 4[/tex]

[tex]-y2+5y-12 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]y=\left(-5\pm \sqrt{52-4\left(-1\right)\left(-12\right)}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{25-48}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{-23}\right)[/tex]

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is no solution.

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Answer:

110° and 215°

Step-by-step explanation:

the bearing of one point to another is the measure of the clockwise angle from the north line N at the point C to the point D , that is

(a)

bearing of D from C is 110° ( purple shaded angle )

(b)

the bearing of D from C is 215° ( blue shaded angle )

The cone is composed of a half sphere and a triangular cone, the total volume would be 301.59 cubic centimeters.

This cone is composed of two shapes, these shapes are:

The volume of the cone can be calculated using the following formula:

V=1/3hπr²

V= 1/3 10 π4²

V= 167.55 cm

The volume of the sphere can be calculated using the following formula:

V = 4/3 π r³ /

V = 4/3 π 4³/ 2  

V = 268.08 / 2 = 134.04 cm

Total volume : 134.04 + 167.55 = 301.59 cubic centimeters

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Answer:

14

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

9/5  X   4/1  X  1/6   =  ( 9 x 4 x 1)  / (5 x 1 x 6) = 36/30  = 1 6/30 = 1  1/5

Answer:

1 1/5

Step-by-step explanation:

The simplified trigonometric expression is sin(a).

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 trigonometric expression is,

=> [tex]\frac{sec(a)}{cot(a)+tan(a)}[/tex]

We know that [tex]cot(a)=\frac{cos(a)}{sin(a)}[/tex] and [tex]tan(a)=\frac{sin(a)}{cos(a)}[/tex] and [tex]sec(a)=\frac{1}{cos(a)}[/tex]

Then,

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos(a)}{sin(a)}+\frac{sin(a)}{cos(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos^2a+sin^2a}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{1}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{1}{cos(a)}\times\frac{sin(a)cos(a)}{1}[/tex]

=> sin a

Hence the simplified trigonometric expression is sin(a).

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The probability that the height of a randomly selected tree is as tall as mine or shorter is 0.1151. The probability that the full height of a randomly selected tree is at least as tall as hers is 0.0362.

To find the probability that the height of a randomly selected tree is as tall as yours or shorter, we need to find the z-score for your tree's height and use the standard normal table to find the corresponding probability. The z-score is calculated as follows:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For your tree, the z-score is:

z = (44.7 - 56.6) / 9.9 = -1.198

Using the standard normal table, the probability that the height of a randomly selected tree is as tall as yours or shorter is 0.1151.

For your neighbor's tree, the z-score is:

z = (74.4 - 56.6) / 9.9 = 1.798

Using the standard normal table, the probability that the height of a randomly selected tree is at least as tall as hers is 1 - 0.9638 = 0.0362.

So, the probability that the height of a randomly selected tree is as tall as yours or shorter is 0.1151, and the probability that the height of a randomly selected tree is at least as tall as your neighbor's is 0.0362.

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Answer:

answer is sus.

Step-by-step explanation:

sus is the correct answer to your problrm. hope this helps!

Answer:

Step-by-step explanation:

Im not sure I can't see the picture.

Answer: Hence, the width of the path is 4 meters.

First we should find the area of the pool. Our width is 14 and our length is 18. In order to find the area, we must multiply these two numbers. 14 times 18 is 252. This means that the area of the pool is 252.

Since we know that one side of the pool is 18 and one side is 14, we can write out the equation below.

572= (18+2x)(14+2x)

The first thing we should do is combine like-terms.Our equation would now be as below.

x^2+16-80=0

Next we would take our quadratic equation- x=-b+-√b2-4ac/2a and fill it in with the numbers that we had in the first equation, our equation would be like below.  A=1   B=16   C=-80

x=-16+-√16^2-4* 1 * -80 /2 * 1

When then simplify our equation leaving us with x=-16+-√16^2-4*1(-80)/2 * 1, which broken down is x=-16+-√+-24/2.

Lastly we must subtract and add to receive our two answers.

One side is 4 and the other is -20. Since the width of the walk cannot not be a negative number, we know that the width of the path is 4 meters.

Hence, the width of the path is 4 meters.

I hope this helped & Good Luck <3!!!

Answer:

103,92,81,70,59,48,37,36,15,4

Step-by-step explanation:

every number has difference of 11

Using the addition method the solution to the system is (x,y) = (14/3, 7/3) and using the substitution method the solution to the system is (x,y) = (7,7).

Using the addition method, we can rearrange the equations so that one of the variables cancels out:

y=2x-7  ->  -2x + y = -7
y=4x-21  ->  -4x + y = -21

Now, we can add the two equations together to eliminate the y variable:

-2x + y = -7
-4x + y = -21
______________
-6x = -28

Next, we can solve for x:

x = 28/6 = 14/3

Now, we can substitute this value of x back into one of the original equations to find y:

y = 2x - 7 = 2(14/3) - 7 = 28/3 - 21/3 = 7/3

So the solution to the system is (x,y) = (14/3, 7/3).

Using the substitution method, we can substitute one equation into the other to eliminate one of the variables. For example, we can substitute the first equation, y=2x-7, into the second equation, y=4x-21:

2x-7 = 4x-21

Next, we can rearrange the equation to solve for x:

2x = 14
x = 7

Now, we can substitute this value of x back into one of the original equations to find y:

y = 2x - 7 = 2(7) - 7 = 7

So the solution to the system is (x,y) = (7,7).

In conclusion, we can solve the system y=2x-7 and y=4x-21 using either the addition method or the substitution method to find the solution (x,y).

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Answer: (6x²+5) (6x²- 5)

Please give me brainliest :)

Step-by-step explanation:

The value of the expression is approximately -102.8571.

A set of guidelines known as the order of operations establishes the order in which mathematical operations should be carried out. Mathematical computations are carried out consistently and accurately by following the correct order of operations. Without a set order of operations, it would be possible for individuals to incorrectly and erroneously understand mathematical equations.

The given expression is:

6 x 7 - 3 x 96 / 2 + 86 / 7 x 354 / 21

= 42 - 288 / 2 + 86 / 49 x 354 / 21

= 42 - 144 + 4 x 354 / 21

= -102.8571

Hence, the value of the expression is approximately -102.8571.

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The linear system shown is "inconsistent" in nature.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The given figure is represented linear system represents two parallel lines.

Now, the solution set of the two system of equations could be find by finding their points of intersection.

And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.

Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.

And when the system of linear equation has no solution , then the system is said to be inconsistent.

Hence, The linear system shown is "inconsistent" in nature.

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The complete question is;

The linear system shown is _____.

independent

equivalent

inconsistent

Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sanghim twIan’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sango times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.

Answer:

Select the math statement that is true.

Step-by-step explanation:

You're welcome.

1 divided by 2/6 is equal to 3.

Division is a mathematical operation used to divide one number (the dividend) by another number (the divisor) to find out how many times the divisor is contained within the dividend

To divide 1 by 2/6, we need to find out how many times the denominator (2/6) fits into the numerator (1).

One way to approach this is to convert the fraction 2/6 to an equivalent fraction with a denominator of 1. To do this, we can multiply both the numerator and denominator of 2/6 by the same number, in this case 3:

2/6 = (23)/(63) = 6/18

Now, we can divide 1 by 6/18:

1 ÷ 6/18

= 1 x 18/6 (reciprocal of 6/18 is 18/6, which is equivalent to 3)

= 3

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By the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The given function is a polynomial of degree 4. Therefore, by the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

However, we do not know if these roots are all real or if some of them are complex. To determine this, we would need to use techniques such as factoring, synthetic division, or the quadratic formula to solve for the roots of the polynomial.

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The number of pounds of peaches sold is given as follows:

65 pounds, option 2.

The amount is obtained solving a system of equations, for which the variables are given as follows:

She sold a total of 165 pounds, hence:

x + y = 165

x = 165 - y.

She made $337.50, hence:

1.75x + 2.5y = 337.50.

Replacing the first equation into the second, the value of y is obtained as follows:

1.75(165 - y) + 2.5y = 337.50

0.75y = 48.75

y = 48.75/0.75

y = 65 pounds.

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I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.

If the ground already has an elevation of  15 degree. The degree that the ladder need to be set is 65.4 degrees.

Angle at which the ladder is set from the horizontal =  x.

Angle between the ladder and the ground =  (75 - 15 + x) degrees

Using trigonometry, we can write the equation:

tan(75 - 15 + x) = 10 / L

where:

L=  length of the ladder.

Simplifying the left-hand side using the trigonometric identity for the tangent of the difference of two angles, we get:

tan(60 + x) = 10 / L

Multiplying both sides by L, we get:

L * tan(60 + x) = 10

Dividing both sides by tan(60 + x), we get:

L = 10 / tan(60 + x)

Using a calculator, we can evaluate the right-hand side to be:

L = 10 / tan(60 + x) ≈ 5.768 / tan(x)

So, the equation we need to solve for x is:

5.768 / tan(x) = L

Substituting the value of L obtained from the previous problem, we get:

5.768 / tan(x) = 2.68

Multiplying both sides by tan(x), we get:

5.768 = 2.68 tan(x)

Dividing both sides by 2.68, we get:

tan(x) ≈ 2.153

Using a calculator, we can find the value of x that satisfies this equation by taking the inverse tangent (tan^-1) of both sides:

x ≈ 65.4 degrees

Therefore, the ladder needs to be set at an angle of approximately 65.4 degrees from the horizontal in order to reach a height of 10 feet when the ground already has an elevation of 15 degrees and the ladder is placed at a 75-degree angle with the ground.

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The complete question is:

Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75 degree  to the ground . The ground already has an elevation of  15 degree. What degree does the ladder need to be set?

The minimum value of f(x) over the interval [3,5] is -512 and the maximum value is 225.

To find the minimum and maximum values of the function f(x) = x^(4) - 32 x^(2) over the interval [3,5], we can use the following steps:

1. Find the first derivative of the function: f'(x) = 4x^(3) - 64x
2. Set the first derivative equal to zero to find the critical points: 4x^(3) - 64x = 0
3. Solve for x to find the critical points: x = 0, x = 4√2, x = -4√2
4. Check the value of the function at the critical points and at the endpoints of the interval to find the minimum and maximum values.
5. The minimum value occurs at x = 4√2, where f(4√2) = (4√2)^(4) - 32(4√2)^(2) = -512
6. The maximum value occurs at x = 5, where f(5) = 5^(4) - 32(5)^(2) = 225
7. Therefore, the minimum value is -512 and the maximum value is 225.

The least value of f(x) over the interval [3,5] is -512 and the largest value is 225.

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Answer:

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

-2x + -10 = 4

-2x = 4 + 10

-2x / -2 = 14/- 2

x = -7

All the best to you!

The answer of possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5

The Rational Zero Theorem states that if f(x) is a polynomial with integer coefficients, then any rational zero of f(x) must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

To find the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10, we need to list the factors of the constant term (10) and the factors of the leading coefficient (-5).

Factors of 10: ±1, ±2, ±5, ±10
Factors of -5: ±1, ±5

Now, we can list all possible rational zeros by taking each factor of the constant term and dividing it by each factor of the leading coefficient:

Possible rational zeros: ±1/1, ±2/1, ±5/1, ±10/1, ±1/5, ±2/5, ±5/5, ±10/5

Simplifying the fractions gives us the final list of possible rational zeros:

Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5, ±1, ±2

Removing duplicates, we get:

Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5

Therefore, the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5.

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Answer:

An exponential function in the form of y = a(m) x is of the form:

y = a * m^x

where "a" is a constant, "m" is a positive constant (the base of the exponential), and "x" is the independent variable.

To determine the exponential function in this form, you need to have some information about the function, such as its value at a particular point or its rate of growth.

Here are the general steps to determine the exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

Determine the value of "m" by solving for it using the given information.

For example, let's say you are given that the function passes through the point (2, 8) and has a growth rate of 3. To determine the exponential function in the form of y = a(m) x, you would follow these steps:

Plug in the values of x and y into the equation:

8 = a * m^2

Solve for "a" by isolating it on one side of the equation:

a = 8 / m^2

Use the given growth rate of 3 to find the value of "m":

m = 1 + r = 1 + 0.03 = 1.03

Plug in the value of "m" and the value of "a" you found in step 2 into the equation:

y = (8 / 1.03^2) * 1.03^x

Simplifying this equation gives:

y = 7.514 * 1.03^x

So the exponential function in the form of y = a(m) x that passes through the point (2, 8) and has a growth rate of 3 is y = 7.514 * 1.03^x.

Step-by-step explanation:

here is a more detailed explanation of the steps involved in determining an exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

In the equation y = a(m) x, "a" is a constant that represents the value of y when x is equal to 0. So to find the value of "a", we need to know the value of y for a specific value of x, other than 0.

Purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.

To calculate the break-even point on their mortgage, we need to determine how much Lenny and Lisa paid for the points and how much they save on their interest rate over the life of the loan.

First, we need to determine how much Lenny and Lisa paid for the points. One point is equal to 1% of the total loan amount, so 3 points is equal to 3% of 675,250:

3 points = 3% x 675,250 = 20,257.50

Next, we need to calculate how much Lenny and Lisa save on their interest rate by purchasing the points. Their original interest rate was 7.25%, but they were able to reduce it to 6.875% by purchasing 3 points. This means they save 0.375% on their interest rate.

To calculate how much they save over the life of the loan, we need to use an amortization schedule. An amortization schedule shows how much of each payment goes towards interest and how much goes towards principal, and it also shows the remaining balance on the loan after each payment.

Using an online mortgage calculator, we can generate an amortization schedule for Lenny and Lisa's loan. Based on this schedule, they will pay a total of 931,231.40 in interest over the life of the loan if they keep their original interest rate of 7.25%. If they reduce their interest rate to 6.875%, they will pay a total of 846,689.56 in interest over the life of the loan.

This means that by purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.

To determine the break-even point on their mortgage, we divide the cost of the points by the amount they save on their interest rate per year.

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