find the solution of the system of equations 2x-4y=32 2x-8y=48

Answer:

The value of given expression is 49.

Step-by-step explanation:

The given expression is

[tex](3+4)^2[/tex]

On solving the parenthesis, we get

[tex](3+4)^2=7^2[/tex]

It can written as

[tex](3+4)^2=7\times 7[/tex]

On multiplication, we get

[tex](3+4)^2=49[/tex]

The simplified value of given expression is 49.

Therefore the required value is 49.

Answer:

50.24 square units

Step-by-step explanation:

Hope this helps.

Answer:

a) 8 : 11

b) 8:3

Step-by-step explanation:

Given: The total number of apples in the basket = 11

The number of green apples = 3

Then , the number of red apples = [tex]11-3=8[/tex]

a) The ratio of red apples to all apples in the basket will be :-

[tex]\dfrac{\text{Number of red apples}}{\text{Total apples}}=\dfrac{8}{11}=8 : 11[/tex]

b) The ratio of red apples to green apples will be :-

[tex]\dfrac{\text{Number of red apples}}{\text{Number of green apples}}=\dfrac{8}{3}=8 : 3[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is (5+3)×2-6.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is,

(5+3) × 2 - 6

= 8 × 2 - 6

= 16 - 6

= 10

Hence, The given expression 5+3×2-6 can be rewritten with parenthesis to equal it with 10 is (5+3)×2-6.

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[tex] \dfrac{y}{-6}+5=9\ \ \ \ |-5\\\\\dfrac{y}{-6}=4\ \ \ \ |\cdot(-6)\\\\y=-24 [/tex]

To find the number of students in the larger class, set up a system of equations using the given information. Solve the system to find the value of x, which represents the number of students in the larger class. The larger class has 28 students.

To find the number of students in the larger class, we can set up a system of equations. Let's call the number of students in the larger class x, and the number of students in the smaller class y. The problem states that one class has 6 more students than the other, so we can write the equation x = y + 6.

We also know that the two classes have a total of 50 students, so x + y = 50. We can solve this system of equations to find the value of x, which represents the number of students in the larger class.

Using the second equation, we can substitute the value of x from the first equation into the second equation: (y + 6) + y = 50. Simplifying this equation, we get 2y + 6 = 50. Next, subtract 6 from both sides to isolate the variable: 2y = 44. Finally, divide both sides by 2 to solve for y: y = 22. Now, we can substitute this value of y back into the first equation to find x: x = 22 + 6 = 28. Therefore, there are 28 students in the larger class.

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The mathematical rule (x,y) to (x-2, y-7) signifies a transformation in the coordinate plane shifting points 2 units to the left and 7 units down. To apply this rule to any point, subtract 2 from the x-coordinate and 7 from the y-coordinate.

The rule (x,y) to (x-2,y-7) in Mathematics signifies a specific transformation in a coordinate plane. This is essentially a rule used in graph transformations to shift a point in the coordinate plane. In this specific rule, every point (x, y) is shifted 2 units to the left and 7 units down to get the new point (x-2, y-7). For example, if we take a point, (5,10), applying this rule means we subtract 2 from the x-coordinate and 7 from the y-coordinate resulting in a new point (3,3). Therefore, simplifying this process, to apply the rule (x,y) to (x-2,y-7) to any point, all you need to do is subtract 2 from the x-coordinate and 7 from the y-coordinate of the point.

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Answer: There are 9 kennels containing 3 dogs per kennel.

Step-by-step explanation:

27 divided by 3 = 9

Answer:

The bus travels 15 miles more per hour than the train.

TTM ;)

Bus covers greater distance per hour as a form of transportation.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)        {Two point - slope form}

x/a + y/b = 1                                         {intercept form}

x cos(β) + y sin(β) = L                           {Normal form}

We have Jared wants a quick trip by bus or train to New York. The bus’s average speed is shown in the graph. The train’s average speed is shown in the table.

Distance covered per hour by the train = m[T] = (135 - 90)/(3 - 2) = 45 miles/hour.

Distance covered per hour by the bus = m[B] = (300 - 0)/(5 - 0) = 300/5 = 60 miles/hour

Therefore, Bus covers greater distance per hour as a form of transportation.

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To solve this problem, what we have to do is to divide the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 + x – 1. Whatever remainder we get must be the value that we have to subtract from the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible by 2 x^2 + x – 1.

By using any method, I used long division we get a remainder of -6.

Therefore we have to subtract -6 from the main equation which results in:

4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2 + x + 1

Answer:

$162.97 is the exact answer.

Step-by-step explanation:

110/5 = 22, that is the middle number

now use the 2 numbers below that and the 2 numbers above that

so you have 20 + 21 + 22+ 23+24 = 110

the 4th number is 23

This question deals with the physics of projectile motion and rocket trajectories. By analyzing the given equations for acceleration and position over time, we can determine the units of constants and describe the motion of the rockets, emphasizing their parabolic paths.

The question at hand involves understanding the motion of two rockets using principles of physics and applying mathematical functions to describe their trajectories. For rocket A, the given quadratic function A(t) = −(t − 8)2 + 535, describes its height as a function of time, indicating a parabolic trajectory, which is typical for projectiles under gravity's influence.

In rocket motion, the acceleration can sometimes be described by an equation of the form a(t) = A - Bt1/2. Here, A and B are constants that determine the rocket's changing acceleration over time. The units of A would be meters per second squared (m/s2), since it represents acceleration, and the units of B would have to be meters per second to the power of five halves (m/s5/2) to ensure the units of time (t) cancel out correctly. When a rocket starts from rest, its velocity changes over time, initially increasing but then possibly decreasing if the acceleration is negative due to the subtraction of the term involving Bt1/2.

If the initial position is set to zero, the rocket's position as a function of time can be found by integrating the velocity function, which is the integral of the acceleration function with respect to time. This integration process accounts for the initial conditions and gives a complete description of the rocket's motion.

In the context of projectile motion, the trajectory is indeed parabolic, represented by the equation y = ax + bx2. To prove this, we use the kinematic equations that separately describe the horizontal and vertical motions (x = Voxt for horizontal and y = Voyt - (1/2)gt2 for vertical motion) and eliminate the time variable to find y as a function of x.

Answer:38200000 Is the correct answer

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

on Edge

To find the exact solutions of the given equation 2sec^2x-tan^4x=-1, we can simplify the equation using trigonometric identities and solve for tanx. The solutions are x = pi/3 + n*pi for tanx = sqrt(3), and x = -pi/4 + n*pi for tanx = -1.

The given equation is 2sec^2x-tan^4x=-1. To solve this equation, we need to simplify the trigonometric terms using known identities. The identity sec^2x = 1 + tan^2x can be used here. Substituting this identity into the equation gives us 2(1 + tan^2x) - tan^4x = -1. Simplifying further, we have 2 + 2tan^2x - tan^4x = -1. Rearranging the terms, we get tan^4x - 2tan^2x - 3 = 0.

Now, let's substitute tan^2x with u, giving us the equation u^2 - 2u - 3 = 0. This is a quadratic equation that can be factored as (u - 3)(u + 1) = 0. Solving for u, we have u = 3 or u = -1. Substituting back tan^2x for u, we get tan^2x = 3 or tan^2x = -1. Taking the square root of both sides, we have tanx = sqrt(3) or tanx = -1.

Finally, to find the exact solutions of x, we need to consider the periodic nature of trigonometric functions. Since tanx repeats every pi radians, the solutions are x = pi/3 + n*pi, where n is an integer, for tanx = sqrt(3), and x = -pi/4 + n*pi, for tanx = -1.

Answer:

(5,32)

Step-by-step explanation:

Answer:

its option C

Step-by-step explanation: