may someone help me ASAP? I am solving polynomial equations and I don't know how to do it, here is the equation... x^4+11x^2=3x^2+128

Answer:

a=49/

a7 is 25/7

Step-by-step explanation:

The first term of the geometric sequence is 49/5 and the common ratio is 1/7.

So, the seventh term is:

a7 = a * r^(7-1) = (49/5) * (1/7)^6 = 25/7

the seventh term (a7) of the geometric sequence is 5.

To find the common ratio (a) of the given geometric sequence, we can divide any term by its preceding term. Let's take the second term (7) and divide it by the first term (49/5):

a = 7 / (49/5)

a = 7 * (5/49)

a = 35/49

a = 5/7

So, the common ratio (a) of the geometric sequence is 5/7.

To find the seventh term (a7) of the sequence, we can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

Given a1 = 49/5 and r = 5/7, we can substitute these values into the formula:

a7 = (49/5) * (5/7)^(7-1)

a7 = (49/5) * (5/7)^6

a7 = (49/5) * (25/49)

a7 = 25/5

a7 = 5

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The Number of ways that four people can be seated on the bench so that john is not next to paul is 12

In mathematics, An arrangement of things or items in a specific sequence is known as a permutation. One should think about both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important.

The arrangement of n items in r ways is given by

Here we have

4 people (John, Paul, George, and Ringo) are seated in a row on a bench

Here total No of ways that 4 can be seated = 4 × 3 × 2 × 1 = 24

The number of ways of seating the four people so that john is next to paul is 12

Then the number of ways the four people on the bench so that john is not next to paul can find as given below

= Total No of ways, 4 can be seated - No of ways that john next to paul  

= 24 - 12 = 12        

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Answer: The square root of 96 in simplified form is 4√6.

Have a great day !

Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

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An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.

In a case whereby letters in the word bubble are arranged in a row the number of unique arrangements that are there  in the letters is 120.

From the question we were given the word, bubble  which can be recognized as 6! arrangements  however we know that the  3 B’s are interchangeable, from the word which is to be arranged, and we can see that there are 6 letters all together in the word and can be arranged as;

6!/3!

= 720/6

= 120

Hence, we can conclude the arangement here is 120 unique wayas.

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Step-by-step explanation:

Total number of students taking Geometry

74 + 47 + 112 + 51 = 284

12th grade students taking Geometry = 51

Answer : 51/284 = 0.18

The original number x is decreased y% = 25% to get 3N/4(the final number).

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A positive number a or the same number a decreased by 50% and then increased by 50% of the result.

Here, A number 'x' is reduced by 50% and the result increased by 50% decrease.

Hence, We get;

x + 50% of x

x + 50x/100

x + x/2

3x/2

Thus, Increased number is, 3x/2

Now this result is decreased by 50%

Decreased number = result - 50% of  result

Since 50% of result is:

3x/2 × 50/100

3x/4

Thus, Decreased number = 3N/2 - 3N/4 = 3N/4

Let us suppose that the original number N is decreased y% to get 3N/4(the final number)

Then, we get;

3N/4 = N - y% of N

y = 25

Thus, the original number x is decreased y% = 25% to get 3N/4(the final number).

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

C. 4

Step-by-step explanation:

The necessary preprocessor directive to enable the use of functions like sqrt and sin

#include <math.h>

Generally, A preprocessor directive is a command that is processed by the preprocessor in a programming language before the actual compilation of the source code begins.

Preprocessor directives are used to give instructions to the preprocessor, which is a program that performs text substitution on

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Step-by-step explanation:

The equation |a| = 5 represents the set of all real numbers whose absolute value is equal to 5. Geometrically, this corresponds to two points in the number line located 5 units away from the origin in opposite directions.

To plot these numbers, we can mark the two points on a number line. One point would be located at -5, and the other at +5. These points are equidistant from the origin, and represent the two solutions to the equation |a|=5.

Here is a sketch of the number line with the two points plotted:

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

| | | | | | |

* *

The "*" symbols represent the two points that satisfy the equation |a| = 5.

A real-world situation consistent with the data provided would be (a) the height of a balloon as it ascends in the air at a constant rate, (b) the speed of a car as it accelerates from a standstill to a constant speed, (c) the height of a soccer ball as it is kicked into the air (d) the velocity of a skydiver as they fall to the ground.

a. A real-world situation consistent with the data provided would be the height of a balloon as it ascends in the air at a constant rate. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The balloon's height will not change with time (f'(x) = 0), meaning the balloon is not accelerating, and the height remains constant as it moves from 0 to 3 seconds.

b. A real-world situation consistent with the data provided would be the speed of a car as it accelerates from a standstill to a constant speed. In this case, x can be the time elapsed in seconds, and y can be the speed in meters per second.

The speed of the car will increase at a constant rate (f'(x) = 50), meaning the car is accelerating, and the speed increases as it moves from 0 to 3 seconds.

c. A real-world situation consistent with the data provided would be the height of a soccer ball as it is kicked into the air. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The height of the ball will increase as time goes by (f'(x) is increasing as x increases), meaning the ball is moving upwards, and the height increases as it moves from 0 to 3 seconds.

d. A real-world situation consistent with the data provided would be the velocity of a skydiver as they fall to the ground. In this case, x can be the time elapsed in seconds, and y can be the velocity in meters per second.

The velocity of the skydiver will decrease as time goes by (f'(x) is decreasing as x increases), meaning the skydiver is falling faster and faster, and the velocity decreases as it moves from 0 to 3 seconds.

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--The given question is incomplete; the complete question is

"Describe different real-world situations (include the units of x and y) that would be consistent with the data provided:

a. f'(x)=0, 0 ≤ x ≤ 3

b. f'(x) = 50, 0 ≤ x ≤ 3

C. f'(x) is increasing as x increases, 0 ≤ x ≤ 3

d. f'(x) is decreasing as x increases, 0 ≤ x ≤ 3"--

Answer:

222 cm²

Step-by-step explanation:

For the rectangle's area you do 15×12= 180

And the the triangle is 12×7÷2= 42 (you divide by 2 because the triangle is half of a rectangle)

So then you just add them together and you get 222 cm²

The surface area of the triangular prism is 152 sq, ft.

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

The surface area of the triangular prism is given as:

SA = bh + (b1 + b2 + b3)l

Here, b = 6, h = 4, b1 = b2 = 5, b3 = 6 and l = 8.

Substituting the values we have:

SA = (6)(4) + (5 + 5 + 6) (8)

SA = 24 + (16)(8)

SA = 152 sq. ft.

Hence, the surface area of the triangular prism is 152 sq, ft.

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Answer:

Step-by-step explanation: umm i'm a middle schooler so i tried i'm sorry.

Answer:

h( x ) = ( x + 1 )^2 - 4 x(h)×(÷×1)^2-4

Answer:

Step-by-step explanation:

Recognize from examining this function h( x ) = ( x + 1 )^2 - 4 that it is a quadratic function whose graph is a parabola that opens up.  The vertex is at (h, k):  (-1, -4).  The axis of symmetry is the vertical line passing through the vertex:  x = -1.

To find the y-intercept, let x = 0 and solve for y:  h(0) = (0 + 1)^2 - 4 = -3.  Thus, the y-intercept is (-3, 0).

To find the x-intercepts, set y = 0 and solve for x:  0 = h(x) = (x + 1)^2 - 4, or

(x + 1)^2 = 4.  Taking the square root of both sides, we get x + 1 = ±2, whose roots are x = 1 and x = -3:  (1, 0) and (-3, 0).

Graph all of these points and the axis of symmetry.  Sketch the parabola that goes through these points.

Answer:

2 step because they changed 1/4 into 1/8

Step-by-step explanation:

To improve your concentration and memorization, you can implement in your study routine some simple techniques, such as analytical reading, capable of improving your performance in the educational environment.

It is essential that the student seeks to understand and actually learn the subjects studied in the classroom instead of just memorizing them, for that, some study techniques can be useful, such as:

Therefore, study techniques can understand writing, speaking, reading and conversation skills, and it is essential for the student to identify the most aligned with their needs and characteristics.

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Answer:

to improve your memorizing you need to focus on your study and try reading harder it will make you memorize alot more then you can already

Answer:

r= -1.2

Step-by-step explanation:

first use distributive property

- 3(4r - 8) = 36 - 2r

-12r +24 = 36-2r

+2r.           +2r

-10r +24= 36

-24.           -24

-10r = 12

/-10.     /-10

r= -1.2

Answer:

Step-by-step explanation:

Equation: -3(4r - 8) = 36 - 2r

Step 1:

-12r + 24 = 36 - 2r       Multiply (4r - 8) by -3 using the Distributive Property.

Step 2:

-10r + 24 = 36        Add -12r and -2r by 2r.

Step 3:

-10r = 12        Subtract 24 and 36 by 24.

Step 4:

r = -12/10          Divide both sides by -10

Step 5:

r = -6/5           Simplify the fraction.

After using mental math to find how much he spent in all, we have come to find that total cost of notebook, pencils and eraser is $7.79

A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math facts, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities.

It is the process of performing mathematical calculations and problem-solving without the need for a lengthy physical process or a formal written process. Children will learn to perform mental addition, subtraction, and other calculations that call for the use of all four operations as well as particular methods.

Students will be able to solve a variety of problems without having to memorize equation solutions, pull out a calculator, or use a pen and paper for their calculations thanks to these mental techniques.

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Answer: $7.79

Step-by-step explanation:

Answer:

its 252500

Step-by-step explanation:

Answer:

252500

Step-by-step explanation:

Let's solve the problems and provide the answers with the correct number of significant figures:

(4.307 × 10^4) × (6.2 × 10^-3)

Multiplying the numbers:

(4.307 × 6.2) × (10^4 × 10^-3) = 26.6974 × 10^1

Since the result is in scientific notation, we multiply the decimal part by the power of 10:

26.6974 × 10^1 = 266.974

To express the answer with the correct number of significant figures, we consider the least number of significant figures in the original values, which is three significant figures in this case.

Therefore, the answer is 267 with three significant figures.

26.127 + 3.9 + 0.0324

Adding the numbers:

26.127 + 3.9 + 0.0324 = 30.0594

To express the answer with the correct number of significant figures, we consider the least number of decimal places in the original values, which is one decimal place in this case.

Therefore, the answer is 30.1 with one decimal place.

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The length of side LJ is 12.41.

Since triangle XYZ is similar to triangle JKL, we know that the corresponding sides are proportional. This means that the ratio of the lengths of the sides in triangle XYZ to the corresponding sides in triangle JKL is constant. We can use this fact to solve for the length of side LJ.

Let k be the constant of proportionality. Then we have:

XY / JK = YZ / KL = ZX / LJ = k

Substituting the given values, we have:

8.7 / 13.05 = 7.8 / KL = 8.2 / LJ

Solving for KL and LJ, we get:

KL = (7.8 x 13.05) / 8.7 = 11.70

LJ = (8.2 x 13.05) / 7.8 = 12.41

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Step-by-step explanation:

Find how many data are there that in between 60-64.99

The solution to the given initial value problem is \(y = \frac{2 \sin x}{x²} - \frac{3 \cos x}{x²}\). This is a linear first-order ordinary differential equation, where \(x\) is the independent variable and \(y\) is the unknown function to be determined. The general solution is obtained using an integrating factor and solving the resulting linear equation. The initial condition \(y\left(\frac{\pi}{2}\right) = -3\) is then applied to find the specific solution.


To solve the given initial value problem, we start by rearranging the equation into the standard form for a linear first-order ordinary differential equation: \(y' + \frac{4}{x}y = \frac{6 \sin x}{x³}\).

This equation can be solved using an integrating factor. The integrating factor is defined as the exponential of the integral of the coefficient of \(y\) with respect to \(x\), which in this case is \(\int \frac{4}{x} \, dx = 4 \ln|x|\). Therefore, the integrating factor is \(e^{4 \ln|x|} = x⁴\).

Multiplying both sides of the equation by the integrating factor, we obtain \(x⁴ y' + 4x³ y = \frac{6 \sin x}{x}\).

Now, notice that the left-hand side of the equation can be rewritten using the product rule of differentiation: \((x⁴ y)' = \frac{d}{dx}(x⁴ y) = x⁴ y' + 4x³ y\).

Therefore, the equation becomes \((x⁴ y)' = \frac{6 \sin x}{x}\).

Integrating both sides with respect to \(x\), we have \(x⁴ y = 6 \int \frac{\sin x}{x} \, dx\).

The integral on the right-hand side is a well-known function called the sine integral, denoted as Si(x). Therefore, the equation becomes \(x⁴ y = 6 \, \text{Si}(x) + C\), where \(C\) is the constant of integration.

Solving for \(y\), we find \(y = \frac{6 \, \text{Si}(x)}{x⁴} + \frac{C}{x⁴}\).

To determine the value of the constant \(C\), we apply the initial condition \(y\left(\frac{\pi}{2}\right) = -3\).

Substituting \(x = \frac{\pi}{2}\) and \(y = -3\) into the equation, we get \(-3 = \frac{6 \text{Si}(\frac{\pi}{2})}{(\frac{\pi}{2})⁴} + \frac{C}{(\frac{\pi}{2})⁴}\).

Simplifying this equation, we can solve for \(C\) and find the specific solution to the initial value problem.

After evaluating the value of \(C\), the final solution to the initial value problem is \(y = \frac{2 \sin x}{x²} - \frac{3 \cos x}{x²}\).

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The area of the parallelogram shown in this problem is of:

A = 432 units squared.

The area of a parallelogram of base b and height h is given by the multiplication of these two dimensions, as presented as follows:

A = b x h.

In this problem, these dimensions are given as follows:

(the height is perpendicular to the sides of the parallelogram, forming an angle of 90º, as is the case in this problem).

Hence the area of the parallelogram, applying the multiplication of the obtained base and height, is calculated by the multiplication of the base and of the height given as follows:

A = 27 x 16 = 432 units squared.

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Answer:

432

Step-by-step explanation:

The area of a parallelogram is the product of a side length (the base) and the perpendicular distance between that side and the opposite side (the height). In this case, we can use (line)DC as a base and (line)EG as the matching height, so the area is equal to

(DC) ∙ (EG) = 27 ∙ 16 = 432.