X^2+2xy-2y^2+x=2 find gradient at point (-4,1)

Answer: This is a linear equation problem. The farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer. We can create two equations to represent this information:

Let x be the number of old packages

x(60) + y(65) = 1550 (long-term-growth supplement)

x(50) + y(45) = 1200 (weed killer)

Now we can use the system of equation to find the number of old and new packages:

x(60) + y(65) = 1550

x(50) + y(45) = 1200

We can use any method of solving system of equations like substitution, elimination or graphing to find the solution.

Example using substitution method:

x(50) + y(45) = 1200

x = (1200 - y(45)) / 50

x(60) + y(65) = 1550

(1200 - y(45)) / 50 * 60 + y(65) = 1550

We can then solve for y and then x by substituting the value of y back into the first equation

y = (1550- (1200 - y(45)) / 50 * 60 ) / 65

Finally, the number of old packages is x and the number of new packages is y.

Step-by-step explanation:

The number of old packages and the number of new packages is 15 and 10 respectively.

Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true.

Given that, the farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer.

We can create two equations to represent this information:

Let,

x = the number of old packages

y = the number of new packages

The system of equations that describes the situation is:

60x + 65y = 1550

12x+13y = 310......(i)

50x + 45y = 1200

10x+9y = 240......(ii)

Solving the equations,

Multiply the eq(i) by 10 and the eq(ii) by 12, and then subtract,

22y = 220

y = 10

Put y = 10 in eq(ii)

10x+90 = 240

10x = 150

x = 15

Hence, the number of old packages and the number of new packages is 15 and 10 respectively.

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Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Using the concept of ratio and proportions, the number of employees in A and B restaurant are 0.72 and 0.28

The relationship between two amounts of the same kind or that are linked is known as a proportion. It is used to compare the magnitude of one quantity to another and is typically expressed as a ratio or fraction. A percentage in mathematics is an equation proving the equality of two ratios.

In this problem, we have a total of 25 employees.

18 out of the 25 employees what to go to restaurant A.

The proportion of this is calculated as

18 / 25 = 0.72

Also, we have 7 employees that want to go to restaurant B

This is calculated as;

7 / 25 = 0.28

The proportion of employees that want to go to restaurant A and B are 0.72 and 0.28 respectively

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Complete Question:

A group of 25 employees want to go out for a group dinner.

18 employees want to go to Restaurant A.

7 employees want to go to Restaurant B.

Use this information to answer the questions below.

What is the proportion of employees who want to Restaurant A and B

c.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

A diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair is known as graph.

Here,

Given :

Suppose that F(x) = x² and G(x)

compares the graph of G(x) with the graph of F(x)

-(x+4)².

Thus , the solution by observing the given information is:

So, it is

C.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

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Area of given polygon is 39 unit².

As seen above, a polygon is a geometric shape that is described as "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, as well as the line segments joining the points."

A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. We can quickly determine the geometry of a polygon based on how many sides it has.

For the given polygon,

Below is the given image of partition,

We will calculate the area by dividing the figure in different portions,

triangle and rectangle,

Area of triangle = 1/2 × Base × Height

Base = 6 units

Height = 3 units

= 1/2 × 6 × 3 = 9 unit²

Area of rectangle = length × breadth

length = 5 units

breadth = 6 units

Area = 5 × 6 = 30 unit²

Total area = area of triangle + area of rectangle = 9 + 30 = 39 unit²

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the slope is -4

hope this helps!!

Answer:

the slope is -4

Step-by-step explanation:

If the APR on your credit card is current 31.2%. your monthly periodic rate is: 2.6%.

Using this formula to determine the monthly periodic rate

Monthly periodic rate = APR / 12 months

Where:

APR = Annual percentage rate = 31.2% or 0.312

Let plug in the formula

Monthly periodic rate = 0.312/12

Monthly periodic rate = 0.026 or 2.6%

Therefore we can conclude that the monthly periodic rate is 2.6%.

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Quadrilateral  ABCD is a Parallelogram can be proved by many postulates. The most important three Postulates are:-

1. The two opposite side pairs are parallel.

2. The two opposing side pairs are both congruent.

3. One set of opposite sides is parallel and congruent.

In geometry, you'll frequently be required to provide evidence that a particular shape actually exists. For instance, you can be asked to demonstrate that a quadrilateral is a parallelogram after being shown it. Do not forget that a quadrilateral is a flat, four-sided shape. A quadrilateral with two sets of opposing, parallel sides is referred to as a parallelogram.

A quadrilateral ABCD is a Parallelogram

The five approaches to demonstrate that a quadrilateral is a parallelogram will be discussed first, though. You'll employ one of these five methods, depending on the data you've got to work with.

1. Establish the parallelism of the two pairs of opposite sides.

This one is just the opposite of what a parallelogram is. If you can demonstrate that the quadrilateral satisfies the requirements for a parallelogram, then it is one.

2. Establish the congruence of both pairs of opposite sides.

There will always be two opposite pairs of parallel sides in a quadrilateral if both pairs of opposite sides are congruent. They measure similarly when objects are congruent.

3. Establish that one pair of opposing sides is parallel and congruent.

The previous procedure and this one are quite comparable. It simply presents the evidence in a different manner. Actually, four toothpicks will work for this experiment. Try it by aligning two toothpicks in a parallel but opposing direction. Now join these two toothpicks to the other two toothpicks at both ends. You'll see that your second pair of toothpicks will always be parallel, regardless of how you arrange your first set.

Hence, Quadrilateral establish parallelogram.

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By taking the quotient between the total amount that she makes and the time of work, we will see that the rate of payment is $45 per hour.

The rate of payment is equal to the quotient between the amount she is paid and the time in which she works.

We know that Theresa wins $0.03 per word, and she can write 3000 words in 2 hours.

Then the amount that she wins is:

$0.03*3000 = $90

Then the rate of payment is:

$90/2 hours = $45 per hour.

Theresa wins 45 dollars per hour.

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The two factors of the first number 28 that their sum is will be equal to the second number 16 are 2 and 14.

Factor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.

The first number 28 have the following factors:

1, 2, 4, 7, 14, and 28.

the factors 2 and 14 are the factors we need because;

2 × 14 = 28

2 + 14 = 16

Therefore, 2 and 14 are the two factors of 28 that their product is the first number 28 and their sum is the second number 16.

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Answer:

13.389 = 13.4

The number of sides that the polygon has is given as follows:

24 sides.

A regular polygon is a polygon in which all side lengths have the same measure, hence all the internal angles of the polygon will also have the same measure.

The sum of the internal angle measures of a polygon of n sides is given as follows:

S(n) = (n - 2) x 180º.

For a regular polygon of n sides, with n angles of equal measure, the measure of each interior angle is given as follows:

I = (n - 2) x 180/n.

In the case of the center of the polygon, the sum of the internal angles is of 360º, hence the number of sides n can be obtained as follows:

n  = 360/I.

For this problem, the internal angle measure is given as follows:

I = 15º.

Hence the number of sides is calculated as follows:

n = 360/15

n = 24 sides.

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Answer: 23,760 feet

Step-by-step explanation:

1 mile = 5280 feet

4.5 * 5280 = 23,760

There is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

At the null hypothesis, it is tested if the means are the same, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if the means are different, hence:

[tex]H_0: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = -7/3.5119

z = -1.99.

We have a two-tailed test, as we are testing if the mean is different of a value.

Using a z-distribution calculator, with z = -1.99, and a two-tailed test, the p-value is given as follows:

0.0466.

As the p-value is less than the standard significance level of 0.05, there is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

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The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

X is N(5, 16)

means that, Z=(x-mean)/√variance = (x-5)/√4

=(x-5)/2

that is, Z is standard normal.

Then, by symmetry of the standard normal curve,

P(X>4)=P(X−5>4−5)

=P(X−54>4−54)

= P(Z>−14)

=P(Z>−.25)

=P(Z<.25)

= 0.5987.

Similarly

P(6.72<X<10.16)

= P(6.72−5<X−5<10.16−5)

=P(6.72−54<10.16−54)

=P(0.43<Z<1.29)

=P(Z<1.29)−P(Z<.43)

=.9015−.6664

= 0.2351.

Therefore, The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

Complete question - X is a normal random variable with mean=5 and variance=4 What are the possibilities for P(X>4) and P(6.72<X<10.16)?

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Answer: -1/2

Step-by-step explanation:

The measure of all the angles are given as follows;

<XVR = 125°  [Sum of angle on a straight line]

<RVS = 55° [Angle on a straight line or Opposite Angles]

< WVS = 125° [Opposite Angles]

< RST = 125° [Angle on a straight line] Note that ΔRVS is an equilateral

< RSV = 55° [Equilateral Triangle]

<VSU = 125° [VSU and RST are Opposite angles]

<UST = 55° [Opposite Angles]

<TUS = 54° [Sum of angles in a Triangle.

A straight line's angles add up to 180°. Angles may also be calculated using this information.

Opposite angles are non-adjacent angles created by two intersecting lines, which is also a mathematical truth.

Angles that are opposite each other are congruent (equal in measure). They are also known as vertically opposing angles and are occasionally referred to as vertical ones. Because they are vertically opposing' at the same vertex, the two angles labeled 'a' are equal.

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The value of m from the given equation is 37.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The given equation is m+6=43

We need to find the value of m from the given equation.

The group of values used to replace the unknowns in an equation to make it true is known as the solution.

To solve given equation:

Transpose 6 to RHS of the equation, we get

m=43-6

Subtract 43 and 6 we get 37

So, m=37

Therefore, the value of m from the given equation is 37.

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The correct statement based on the number line is,

⇒ √68 is to the right of Point Q because it is greater than 8.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The number line showing numbers from -8 to 8 in increments of 2, has point P at 0, and point Q is at 8.

Now, We know that;

⇒ √68 = 8.24

And,

⇒ 8.24 > 8

Hence, √68 is to the right of Point Q because it is greater than 8.

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The distance travelled by larger circular wheel is 2π(R-r) more than the distance travelled by old tires.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now

let radius of old tires =r

radius of new tires =R

distance travelled by new tire in one rotation= 2πR

distance travelled by old tire=2πr

Hence,

            The distance travelled by larger circular wheel is 2π(R-r)  more than the distance travelled by old tires.

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Answer:

3/20.

Step-by-step explanation:

Answer: it’s 25

Step-by-step explanation:

15 +10

Answer: 0.06 + 0.004

The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

Linearity is a property of equations with highest degree of 1. There isn't a single variable in it with an exponent greater than 1. The name "linear equation" comes from the fact that a linear equation always results in a straight line on a graph.

Linear equations in one variable and two variables are common in mathematics.

Two of lines' points on the plane are (1, 0)and (0, 9)

Lets put the value in the slope formula

y₂ - y₁ = m(x₂ - x₁)

9 - 0 = m(0 - 1)

9 = -m

m = -9

As we have the slope of the line lets put one of the values to get slope intercept form

y - y₁ = m(x - x₁)

y - 9 = -9(x - 0)

y = -9x + 9

Thus, The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

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Answer:

B

Step-by-step explanation:

Each floor, the rent is 3% more than the previous floor, so we multiply by 1.03.

Since we do this 17 times, the answer is [tex]1420 \cdot 1.03^{17}[/tex].

Answer: B

Step-by-step explanation:

You just need to find the formula, replace 17 with variable x and $2347.04 with y and graph. It will give you the right answer.

The values of u and v in the table are directly proportional to each other with a constant k is 3.

When x increases, y increases; when x decreases, y decreases.

The opposite of direct is indirect. When x rises, y falls; when x falls, y rises.

If you said y is directly proportional to x,

it would be y/x=k or y=kx.

Here given that,

u = 0.25, 0.3, 0.1

v = 0.75, 0.9, 0.3

So here v = 3u

That is v = 3 x 0.25

v = 0.75

Hence u and v are directly proportional with a constant k = 3

When v = 2/5

To find u,

v = 3u

2/5 = 3u

u = 2/15

When u = 3/7

Then v = 3 x 3/7

v = 9/7

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The value of p and w in the triangle are 6 units and 13√3 units respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In the triangle, we have angles of 30° and 90°

Using trigonometric ratios:

sin 30° = (2p+1)/(6p-10)     [sin = opp/hyp]

1/2 = (2p+1)/(6p-10)

1/2(6p-10) = (2p+1)

3p -5 = 2p + 1

3p -2p = 1+5

p = 6 units

cos 30° = w/(6p-10)       [cos = adj/hyp]

(√3)/2 = w/(6p-10)

(√3)/2 = w/((6×6) -10)

(√3)/2 = w/(36 -10)

(√3)/2 = w/26

w = (√3)/2 × 26

w = 13√3 units

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The greatest number of friends Gary can give shells and coins to is 8

friends. Each friend will receive 9 shells and 5 coins.

We have to find the factors of 72

72/ 2 = 36 / 2 = 18/ 2 = 9/ 3 = 3

72 = 2 * 2* 2 * 3

We would find the factors of 40

40 / 2 = 20 / 2 = 10 / 2 = 5

40 = 2 * 2 * 2 * 5

Then we would find the common factors they have

2 * 2 * 2 = 8

This is the number of friends that Gary can have

Then 72 / 8 = 9

40 / 8 = 5

The greatest number of friends Gary can give shells and coins to is 8

friends. Each friend will receive 9 shells and 5 coins.

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