Consider the following graph:

What is the slope/rate of change between the inputs of 0 and 4? _______.

What is the slope/rate of change between the domain values of 4 and 8? ______.

Is the slope/rate of change constant (not changing/the same)? ______.

Is the function linear? _______.

Answer: 4 x 4 = 16

Step-by-step explanation: If you want a number one less that 5, subtract 1 from 5, then find a number that you can multiply by the answer to 1-5 to get less than 24. In this case, we used 4, to get 16. 16<24.

The angle θ is changing is 36.9 degrees per second.

The distance between the dog and its owner when the dog is 46 meters at the northernmost point of the track.

As per the question, the circumference of the circular track is

⇒ 2 × 3.14 × 14 = 87.92 meters.

Since the dog is running at a constant speed of 9 meters per second, it will take the dog 87.92 / 9 = 9.77 seconds to complete one lap of the track.

The angle θ is defined as the angle between the position of the dog and the position of the owner, measured from the center of the track.

Since the track is circular, the angle theta will change at a constant rate of 360 degrees per lap. Since it takes the dog 9.77 seconds to complete one lap, the rate at which the angle θ is changing is 360 / 9.77 = 36.9 degrees per second.

To answer the second question, we must first calculate the distance between the dog and its owner when the dog is at the northernmost point of the track.

The owner is standing a distance of 48 meters from the center of the track, and the radius of the track is 14 meters, the distance between the dog and its owner is given by the Pythagorean theorem: d = √(48² - 14²) = 46 meters.

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Answer:

Step-by-step explanation:

use equation [tex]\frac{y2-y1}{x2-x1}[/tex] to calculate the slope, in this case the slope would be [tex]\frac{11-11}{3-(-2)}=\frac{0}{6} =0[/tex]

The slope would be 0 for the line,

another way we can tell the slope is 0 is that we can see the two sets of coordinates are on the y=11, they just have different x coordinates.

But the equation above shows the complete work and supported the answer.

Answer:

Slope (m) = 0

Step-by-step explanation:

Given coordinates,

→ T(-2, 11)

→ U(3, 11)

Formula we use,

→ Slope = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (11 - 11)/(3 -(-2))

→ m = (0)/(3 + 2)

→ m = 0/6

→ [ m = 0 ]

Therefore, the slope is 0.

A variation on Lagrange polynomial interpolation is called barycentric interpolation. Second, just use Newton interpolation formula to assess p(x) for each x.

The Lagrange interpolation theorem can be used to create a polynomial that traverses a specified set of points and takes particular values at random locations. This theorem provides the approximate formula for the nth degree polynomials to the function f if a variable f (x) is available at discrete places xi, I = 0, 1, 2,... (x).

The Lagrange theorem extrapolates well-known mathematical principles like the statement that a line is uniquely specified by two points, the knowledge that the quadratic function polynomial is completely determined by three points, and so forth.

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a. The orthocenter for the coordinates (0,0), (6,3), and (3,24) is (24, 2).

b. The orthocenter for the coordinates (5,3), (8,6), and (4,10) is (8, 6).

The orthocenter is the point where the altitudes of the triangle coincide. An obtuse triangle, will be outside the triangle. For a right triangle, it will be the right angle vertex. Of course, each altitude is a line through a vertex and perpendicular to the opposite side.

The equation can be written as,

y -y₃= -(x₂ -x₁)/(y₂ -y₁)(x -x₃)

This can be rearranged to something resembling standard form:

(x₂ -1x₁)(x -x₃) +(y₂-y₁)(y -y₃) = 0

(x₂ -x₁)x +(y₂ -y₁)y = (x₂ -x1)x₃ +(y₂ -y1)y₃ . . . . line through P3, ⊥ to P1P2

Part(a).

For the first altitude, we choose P1 = (0, 0), P2 = (7, 3), and P3 = (3, 51). This gives,

(x₂-x₁) = 7 -0 = 7

(y₂ -y₁) = 3 -0 = 3

altitude equation = 7x +3y = 7·3 +3·51 = 174

For the second altitude, we choose P1 = (0, 0), P2 = (3, 51), and P3 = (7, 3). This gives,

(x₂ -x₁) = 3 -0 = 3

(y₂ -y₁) = 51 -0 = 51

altitude equation = 3x +51y = 3·7 +51·3 = 174

Finding the point of intersection of these two equations can be done in a number of ways. Cramer's Rule provides a quick solution:

x = ((3)(-174) -(51)(-174))/(7·51 -3·3) = 8352/348 = 24

y = ((-174)(3) -(-174)(7))/348 = 696/348 = 2

The orthocenter for the triangle is (24, 2).

Part(b).

We can use the method just described, or we can verify the triangle is a right triangle, as it appears to be when the points are plotted.

The slope of P1P2 is (6 -3)/(8 -5) = 3/3/ = 1.

The slope of P2P3 is (10 -6)/(4 -8) = 4/-4 = -1

These slopes have a product of -1, so the segments are perpendicular. The vertex P2 has the right angle, hence the orthocenter.

The orthocenter for the triangle is (8, 6).

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On solving the problem of expression we can say that , the answer is 5x + 9.A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions.

[tex]3x + 2 - 3x + 7 + 5x = 5x + 9[/tex]

Group the like terms

[tex]3x - 3x + 5x + 2 + 7[/tex]

now adding similar elements: 3x - 3x + 5x = 5x

[tex]5x + 2 + 7[/tex]

and add the numbers: 2+7=9

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Technically none of them because "quotient" means the answer to a division problem. But the only positive answer is B

Answer:

196

Step-by-step explanation:

(18-4)^2

14^2 or 14x14

14x14=196

By using the provided formula of inflation, the answer is $35.35.

The rate at which consumer prices for a variety of products and services are increasing is known as inflation.

The common ways followed are:

[tex]C(t) = P(1.04)^{t}[/tex]

P= $23.95

t=10

The estimated price is [tex]23.95*(1.04)^{10}[/tex]

=$35.35

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The area of the quadrilateral is equal to √901 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the quadrilateral in a two-dimensional plane is called the area of the quadrilateral.

Given that quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Calculate the sides of the quadrilateral by the distance formula,

AB = √[(2+2)² + (-3+4)²]

AB = √(16+1)

AB = √17

CD = √[(4-2)² + ( 4 + 3)²]

CD = √ (4+49)

CD = √53

The area will be calculated as,

Area = AB x CD

Area = √17 x √53

Area = √901 Square units

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The range of h of the given function table is; A)All real numbers greater than or equal to -7

The range of a function is defined as the set of all possible output values for which the function is valid.

From the given function table, we can see the following coordinates;

(-3, 18)

(-1, 8)

(2, -7)

(3, -12)

(4, 17)

(6, -27)

Now, from the above coordinates, we can see that the maximum value of h(x) is 17 while the minimum value is -27.

Looking at the options, the only one that  fits the available range of the function is option A.                                    

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Answer: Commutative Property

Answer:

False

Step-by-step explanation:

2/3 - 1/6 = 3/6

Answer:

Jacks Rate: 3 miles per hour

Jills Rate: 4.5 miles per hour

Time: 40 minutes or 2/3 of an hour

Step-by-step explanation:

This problem in it self isn't necessarily too complex, but a crucial part of it is taking the context given and somehow making that into a algebraic expression which we can then use to solve the equation.

So let's first assign two unknowns to the rates at which Jack and Jill walk. Since both of there names start with J, I'll use a subscript to differentiate between the two.

[tex]\text{let }J_a=\text{Jack's walking rate}\\\text{let }J_i = \text{Jill's walking rate}[/tex]

Notice that both have a J, but there is a little letter to the right and below, which is a subscript. This way we can easily tell which person we are referring to while not having to write out their entire name as a variable.

Now let's assign two variables. First let's assign distance: [tex]D=\text{distance from top of hill}[/tex]

and let's also assign time to a variable: [tex]t = \text{time in hours}[/tex]

Now let's start making some equations! If jack is two miles away from the top of the hill, in general, the distance from the hill can be calculated using the following equation: [tex]D=2-t*j_a[/tex]

Essentially, Jack starts off with a distance of two miles away, and after one hour, Jack will walk [tex]j_a[/tex] miles, this is his rate, what Jake travels in one hour. After another hour passes, he will do the same thing, but twice. So this is why we're multiplying by time. Since for each hour that passes, he will walk a further: [tex]j_a[/tex] miles, meaning he will be that much closer, so we subtract it from 2, the initial distance.

The same logic can be applied to Jill, except with an initial distance of 3 miles and using the unknown: [tex]j_i[/tex] which is Jill's rate. So we get the following equation: [tex]D=3-t*j_i[/tex]

If we're looking for when they reach the top of the hill, that means that the distance from the hill is zero. So let's set both equations to zero.

[tex]0=3-t*j_i\\0=2-t*j_a[/tex]

From here let's solve for time for both equations. So let's start with the first equation.

[tex]0=3-t*j_i[/tex]

From here let's subtract 3 from both sides to get rid of the 3 on the right side.

[tex]0-3=(3-3)-t*j_i\implies-3=-t*j_i[/tex]

from here let's divide both sides by Jill's rate.

[tex]\frac{-3}{j_i} = \frac{-t*j_i}{j_i} \implies \frac{-3}{j_i}=-t[/tex]

From here let's divide both sides by -1 to get t isolated.

[tex]\frac{\frac{-3}{j_i}}{-1} = \frac{-t}{-1} \implies \frac{3}{j_i}=t[/tex]

We can essentially apply the same steps to the equation we derived from Jack's rate.

[tex]0=2-t*j_a\\\\(0-2)=(2-2)-t*j_a \implies -2 = -t*j_a\\\\ \frac{-2}{j_a} = \frac{-t}{j_a} \implies \frac{-2}{j_a} = -t\\\\\frac{\frac{-2}{j_a}}{-1} = \frac{-t}{-1} \implies \frac{2}{j_a} = t[/tex]

Now we have the equations:

[tex]\frac{2}{j_a} = t\\\\\frac{3}{j_i} = t[/tex]

and this represents the time needed to reach the top of the hill (since we set both equations equal to zero)

From here we need to look once more at the question, specifically where it says: "It takes them the same amount of time to get there". So we set the equations equal to each other.

[tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex]

Now we use our last piece of needed context: "Jill walks 1.5 miles per hour faster than Jack".  We can set up one more equation: [tex]J_i = J_a+1.5[/tex].

This is super useful to have, since we can now make a substitution give this equation, converting our two-variable equation into a one-variable equation, allowing us to solve for one numerical value.

We have: [tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex] and we know that: [tex]J_i = J_a+1.5[/tex], so let's simply plug in [tex]J_a+1.5[/tex] for [tex]j_i[/tex].

This gives us the equation:

[tex]\frac{2}{J_a}= \frac{3}{J_a + 1.5}[/tex].

Cross Multiply:

[tex]2(J_a+1.5) = 3(J_a) \implies 2J_a + 3 = 3J_a[/tex].

Subtract [tex]2J_a[/tex]:

[tex]3=J_a[/tex].  

We can solve for Jills value, since Jill's value is just 1.5 miles per hour more than this, so [tex]J_i = 3+1.5=4.5[/tex]

Now let's take Jacks value and substitute it into his time equation

[tex]t = \frac{2}{3}[/tex]

we can keep this in hours, or we can convert this into minutes. We can convert this in to minutes by multiplying the amount of minutes in an hour by 2/3, so: [tex]60 * \frac{2}{3} = \frac{120}{3} = 40\text{ minutes}[/tex]

The value of expression 9 1/2k - [7 + 3 1/4k] without parentheses is 25 / 4 k - 7.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

9 1/2k - [7 + 3 1/4k]

Simplify the above expression and convert mixed fractions into improper fractions,

19 / 2 k - [7 + 13 / 4k]

19 / 2 k -[(28 + 13 k) / 4]

(38k - 28 -13k) / 4

(25k - 28) / 4

25 / 4 k - 7

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There are 896 trips will it take him to haul all of the dirt away.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.

Now,

Since, The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.

And, His pickup truck can haul one cubic meter.

Hence, Number of trips will it take him to haul all of the dirt away will be;

⇒ 16 × 7 × 8 / 1

⇒ 896

Thus,  Number of trips = 896

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Answer: n=30

Step-by-step explanation:

first, you subtract 3, as 'and' refers to addition and the opposite is subtraction. this gives you 60.

then you divide by 2, which gives you 30.

if you want, you can input 30 into the equation the situation creates, which is 63 = 2n + 3. input 20 makes 2(30) + 3, which is 60 + 3, which is 63.

The equation that satisfies the given pattern is y = -2x

Given,

x ; 1, 2, 3, 4, 5

y ; -2, -4, -6, -8, -10

The pattern; y = -2x + ?

We have to find an equation that satisfies the given pattern;

Here,

Take k as ?

Then,

y = -2x + k

Where,

x = 1 and y = -2

Now,

-2 = -2 × 1 + k

-2 = -2 + k

k = -2 + 2 = 0

k = 0

That is,

The equation will  be like, y = -2x

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Answer:

z=10.5. give me brainly

Answer: there is nothing

Step-by-step explanation: there is nothing to see so if there is no photo nobody can help you. Sorry

The weight of 45 gallons of fuel is 2412 pounds.

What is weight ?

The force exerted on an object by gravity is known as the weight of the object in science and engineering. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

Weight is a gauge of how strongly gravity is pulling something down. It relies on the mass of the item and the acceleration brought on by gravity, which on Earth is 9.8 m/s2. F = m 9.8 m/s2 is the formula for computing weight, where m is the object's mass in kilograms and N is the object's weight in Newtons (N).

The weight of one gallon is

w = (2296 - 2122) / (35 - 20)

   =  174 / 17

   = 11.6 pounds

Now, to answer the question, we need to add the weight of (45-35) = 10 gallons of fuel to the weight of the plane

carrying 35 gallons of fuel, 2296 pounds.

So, the answer is 2296 + 10*11.6

                           = 2412 pounds.

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Answer:

[tex]2 x 3^{2} x 7[/tex]

Step-by-step explanation:

The answer is 2 × 3 × 3 × 7 which is 2 x 3^2 x 7

The missing length and the missing angle are approximately 40.447 and 20.034°.

In this question we have a geometric system formed by a equilateral triangle divided into two triangles by a line segment. The missing sides and angles can be found by means of algebra properties, Euclidean geometry and trigonometry.

First, obtain the missing side by taking approach of properties for equilateral triangles:

y = 46 - 16

y = 30

Second, find the length of line segment by law of cosine:

l = √(46² + 16² - 2 · 46 · 16 · cos 60°)

l ≈ 40.447

The missing length is approximately 40.447.

Third, the measure of the missing angle by law of sine:

16 / sin x = 40.447 / sin 60°

sin x = (16 / 40.447) · sin 60°

sin x = 0.343

x ≈ 20.034°

The missing angle is approximately 20.034°.

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The graph of the line y = (-2/3)x + 8 with appropriate labels and scale has been plotted

The equation of the line is given that

y = (-2/3)x +  8

The given equation is in slope intercept form of the line

y = mx + b

Where m is the slope of the line

b is the y intercept

y is the y coordinate value

x is the x coordinate value

The slope of the line = -2/3

The slope of the line is the change in y coordinates with respect to the change is x coordinates of the line

y intercept is 8

Substitute the value of x in the equation and find the value of y

Plot the graph using the equation

Therefore the graph of the line has been plotted

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Answer: 50

Step-by-step explanation:

Assuming your expression is 2x^2+yz, just plug the numbers in: 2*4*4+6*3 = 32 +18 = 50

Plugging in just means looking at the values the probme give syou for variables (x=4 for example) and replacing the variable with that number in the expression you want to find the value of.

The equations representing the situations are P + S = 384 and 2.5P + 1.25S = 696.25. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the cost of pizza is $2.5 and the soda is $1.25 and the total cost is $696.25. The total number of the Pizza and the Soda is 384.

The equations can be written as,

P +S = 384

2.5P + 1.25S = 696.25

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Answer:

To maximize profit, the Banana Apple company should determine the number of each kind of apple box that they should make. To do this, they need to know the number of each type of apple that they have, as well as the price of each box.

Based on the information provided, the company has 2800 Golden apples, 2200 Macintosh apples, and 2300 Red Ida apples. This means that they can make 700 Box A's (2800 / 4 = 700), 1100 Box B's (2200 / 2 = 1100), and 575 Box C's (2300 / 4 = 575).

The price of each box is also given: Box A costs 3€, Box B costs 3€, and Box C costs 4€. This means that if the company makes 700 Box A's, they will earn 2100€ (700 x 3 = 2100€), if they make 1100 Box B's, they will earn 3300€ (1100 x 3 = 3300€), and if they make 575 Box C's, they will earn 2300€ (575 x 4 = 2300€).

To maximize profit, the company should make as many of the most profitable box as possible. In this case, the most profitable box is Box B, which earns 3€ per box. The company should make 1100 Box B's, which will earn them a total of 3300€.

Answer:

To solve this problem, we need to determine how many boxes of each type the company should make to maximize their profit. We can set up a system of equations to represent the number of apples in each box and the total number of apples the company has.

Let's call the number of boxes of type A x, the number of boxes of type B y, and the number of boxes of type C z. We can represent the number of apples in each box using the following equations:

x + y + z = 2800

4x + 6y + 0z = 2200

2x + 2y + 6z = 2300

To maximize the profit, the company should make as many boxes as possible while still having enough apples to fill all the boxes. We can solve this system of equations using substitution to find the values of x, y, and z that maximize the profit.

First, we can solve the first equation for z in terms of x and y:

z = 2800 - x - y

Next, we can substitute this expression for z into the second and third equations to eliminate z:

4x + 6y + 0(2800 - x - y) = 2200

4x + 6y = 2200

2x + 2y + 6(2800 - x - y) = 2300

2x + 2y + 17600 - 6x - 6y = 2300

2x + 2y = -15300

We can then solve this system of equations using substitution. From the second equation, we have:

4x + 6y = 2200

2x + 2y = -15300

We can solve the second equation for y in terms of x:

y = -15300/2 - x/2

We can substitute this expression for y into the first equation to solve for x:

4x + 6(-15300/2 - x/2) = 2200

4x - 45300 - 3x = 2200

x = (2200 + 45300) / (4 - 3)

x = 13600/1

x = 13600

We can then use this value of x to find the value of y:

y = -15300/2 - 13600/2

y = -13650

Finally, we can use these values of x and y to find the value of z:

z = 2800 - 13600 - (-13650)

z = 1650

Therefore, the company should make 13600 boxes of type A, -13650 boxes of type B, and 1650 boxes of type C to maximize their profit.

Step-by-step explanation:

The probability of selecting at least one marble that is not red is given as follows:

1.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Considering a success as selecting non-red marbles, the values of these parameters are given as follows:

N = 4, n = 2, k = 3.

The probability of at least one not red is given as follows:

P(X > 0) = 1 - P(X = 0).

In which:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,4,3,2) = \frac{C_{3,0}C_{1,2}}{C_{4,2}} = 0[/tex]

Hence the probability is of:

P(X > 0) = 1 - P(X = 0) = 1 - 0 = 100%.

The problem is given by the image shown at the end of the answer.

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