Please simplify these equations

The expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .

In the question ,

two expressions are given as

8x²+3(x²+y) and 7x²+7y+4x²-4y .

Simplifying the first expression

we get ,

= 8x²+3(x²+y)

= 8x² + 3x² + 3y

adding the like terms , we get

= 11x² + 3y

Simplifying the second expression

we get ,

= 7x²+7y+4x²-4y

adding and subtracting the like terms ,

we get

= 11x² + 3y

We can see that both the expressions are giving the final answer  as 11x² + 3y  .

hence , both the expressions are equivalent .

Therefore , the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .

The given question is incomplete , the complete question is

Are the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y equivalent ? Explain your reasoning .

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As a result, the cone's volume is equal to three times its radius √343/π .

The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.

So with respect to the information provided to us :

Height of a cone =3* radius of the base

let height be h and radius be r

h=3r

The Formula for volume of cone is:

V=1/3hπr²

Putting the value we get:

343=1/3*π*r²*3r:

r= √343/π

Therefore ,

the volume of the cone whose height is three times its radius is:

√343/π

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The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.

The variance's positive square root is the standard deviation. One of the foundational strategies in statistical analysis is standard deviation. The term "standard deviation," often shortened as "SD," tells us how far a value deviates from the mean value. It is represented by the symbol "."

Given that : The mean birth weights of infants born at an area hospital in the month of April is 128 oz. with a standard deviation of 10.2 oz.

So let's look at this and see what the correct interpretation of a standard deviation is, which is the distance between each person's actual way of being born and a braille and the main way it was, which is typically about 10 points two oh. From this, we can deduce what the question Act is. The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.

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The coordinates of the image of polygon A'B'C'D' after a translation of 4 units down and 5 units right would be A' (-1, 1), B' (-1, -2), C' (3, -2), D' (3, 2).

In Geometry, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of polygon ABCD vertically down 4 units and horizontally right 5 units, the coordinates of the image of polygon A'B'C'D' include the following:

(x, y)                               →                  (x + 5, y - 4)

Coordinate A = (-6, 5)   →    Coordinate A' (-6 + 5, 5 - 4) = (-1, 1)

Coordinate B = (-6, 2)   →    Coordinate B' = (-6 + 5, 2 - 4) = (-1, -2)

Coordinate C = (-2, 2)   →     Coordinate C' = (-2 + 5, 2 - 4) = (3, -2)

Coordinate D = (-2, 6)   →     Coordinate D' = (-2 + 5, 6 - 4) = (3, 2)

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The smallest possible number of students in the algebra class is 13.

Let n≥5 be the number of students.

The sum of their scores must be at least 5×100 + (n - 5).

Simultaneously, we must achieve the mean 76, which is equivalent to achieving the mean sum 76n.

As a result, we have a sufficient precondition on n: we should have 5×100 + (n - 5) ≤ 76n.

This can be reduced to 200 ≤ 16n. This is true for the smallest integer n = 13.

To complete our solution, we must now determine how 13 students might have scored just on test.

We have 13×76 = 988 points to distribute to them. Because five 100s equal 500, we must distribute the remaining 488 points as among remaining eight students.

This can be accomplished, for example, by awarding each of them 61 points.

Thus, the smallest possible number of students in the class is 13.

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Answer:

k = 1

Step-by-step explanation:

since the graph contains the point (2, 12 ) then the coordinates of the point make the equation true.

substitute x = 2 and f(x) = 12 into the equation and solve for k

12 = k(2)³ + 2² - k(2) + 2 , that is

12 = 8k + 4 - 2k + 2

12 = 6k + 6 ( subtract 6 from both sides )

6 = 6k ( divide both sides by 6 )

1 = k

Answer:

Step-by-step explanation:

The attached graph is NOT a function, since it doesn't pass the vertical line test.

If a vertical line cuts the graph more than once, then this relation is not a function.

The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]

The inverse of a matrix is given by

[tex]A^{-1} = \frac{1}{|A|} adjA[/tex]                   ...(1)

Now, determinant of matrix A is

|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]

= (3)(2) - (2)(1)

= 6 - 2

= 4

Now, adjoint A will be

[tex]A_{11}[/tex] = 3

[tex]A_{12}[/tex] = -1

[tex]A_{21}[/tex] = -2

[tex]A_{22}[/tex] = 2

AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]

Now, substituting the values of |A| and AdjA in equation (1), we get

[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]        

Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]      

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The equation that represents the miles of the car's odometer after 2020 is y = 14000x

Odometer:

Basically Odometer is the instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car.

Given,

An odometer shows that a car has traveled 56,000 miles by January 1, 2020. The car travels 14,000 miles each year.

Here we need to write an equation that represents the number y of miles on the car's odometer x years after 2020

Through the given question we know that,

x represents the year

y represents the miles

We know that, for one year it will travels 14,000 miles.

Then the equation is written as,

miles = number of years x 14000

Therefore, the equation is,

y = 14000x

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Answer:

11

Step-by-step explanation:

If you input the number and then solve, you should get that #=#

2(11)+9=4(11)-13

22+9=44-13

31=31

Answer: 11

Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31

Answer:

Step-by-step explanation:

x = 39

C. 39 Cars

To divide two fractions, simply cross-multiply as following:

The temperature in the evening is 79.5 degrees Fahrenheit.

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

Jesse recorded a temperature in the morning of 75 degrees Fahrenheit

The temperature increased by [tex]4\frac{1}{2}[/tex] degrees Fahrenheit in the afternoon

75 +  [tex]4\frac{1}{2}[/tex] =[tex]\frac{159}{2}[/tex]

=79.5 degrees Fahrenheit

Before decreasing by 2.6 degrees Fahrenheit in the evening. The temperature in the evening is 79.5 degrees Fahrenheit.

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Answer:

y = 12x + 18

Step-by-step explanation:

Equation of line in slope-intercept form: y =mx +b

Here, m is the slope and b is the y-intercept.

  m = 12

Substitute m =12 in the above equation,

        y = 12x + b

This line passes through (-2,-6). So, plugin the point in the above equation.

       -6 = 12*(-2) + b

      -6 = -24 + b

-6 + 24 = b

         b = 18

Equation of the line:

         [tex]\sf \boxed{\bf y = 12x + 18}[/tex]

a) The x-intercepts of y=f(x) is (-3,0) (4,0)

b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.

Here to determine the x-intercept put y=0,

Given f(x)=(x-4) (x+3)

a) y=(x-4) (x+3)

Replacing y by 0 we get,

(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)

b) y = -2(x-4) (x+3)

Replacing y by 0 we get,

-2(x-4) (x+3) =0

x=-3, 4

Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)

c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)

Replacing y by 0 we get,

(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0

By solving the above equation

(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0

-1/2x=4 and -1/2x=-3

x=-1/8 and x=1/6

Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)

d) y=(-(x+1)-4) (-(x+1) +3)

Replacing y by 0 we get,

(-(x+1)-4) (-(x+1) +3) =0

By solving the above equation

(-(x+1)-4) =0 and (-(x+1) +3) =0

-(x+1) =4 and -(x+1) =-3

x=-5, 2

Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)

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The likelihood or probability that she will give the first student a blue calculator and the second student a yellow calculator is 6.6%.

The math teacher Mrs. Piatt has six black, nine yellow, and two blue calculators.

Therefore, the total number of calculators is 17.

The probability that she hands out a blue calculator to the first student is:

P₁ = Number of blue calculators/ Total number of calculator

P₁ = 2/17

Now, as a calculator is handed out to a student. Then the remaining number of calculators is 16.

Therefore, the probability that the second student gets a yellow calculator will:

P₂ = Number of yellow calculators/ Total number of calculators.

P₂ = 9/16

Therefore, the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second will be:

P = P₁ × P₂

P = 2/17 × 9/16

P = 18/272

P = 0.06617647058

P = 6.6%

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     The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

     Then, add or subtract 50% from the first total and then, I believe, add (or it might be the other way around) to get your actual total. We would want it because it shouldn't affect the cost of the first machine. I'm sorry, but I haven't done any math in a long. use a calculator if necessary

    Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price + profit margin = selling price.

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The probability that the experiment results in exactly successes is; [tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there be x successes is given as;

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are given as:

[tex]E(X) = np\\Var(X) = np(1-p)[/tex]

Hence, the probability that the experiment results in exact success are;

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

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GOOD LUCK! ????????????????????????????????????????????????????????????????????????????????////

Answer:

the  next year population is 122,689      

Step-by-step explanation:

The computation of the next year population is as follows:

= This year population × increase percentage

= 119,000 × (1 + 0.031)

= 119,000 × 1.031

= 122,689

Hence, the  next year population is 122,689

The above formula is applied so that the correct value of the population could come

and the same is relevant

Answer:

50

Step-by-step explanation:

25x2=50

300-50=250

250/5=50

50 ribbons needed :) hope this helped

The parallel street to that one lines on the equation y = 2x -1

To find the parallel street to the one we have the points given, we have to first of all, find the slope of the given point and then pick a coordinate.

Using the value above, let's find the slope of the line.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]

Let's substitute the values into the equation and solve.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{9 - (-5)}{5 - (-2)} \\m = \frac{14}{7} \\m = 2[/tex]

The slope of the line is equal to 2.

Let's use this to find the equation of the line

[tex]y = mx + c[/tex]

Using one of the points,

[tex]y = mx + c\\9 = 2(5) + c\\9 = 10 + c\\c = - 1\\[/tex]

The equation of the line is

[tex]y = 2x - 1[/tex]

From the calculation above, the equation of the line is y = 2x - 1

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Step-by-step explanation:

2x+(-8x) +5-5

-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know

The length of AG=8.5 cm that is diagonal. There are four body diagonals of cuboid and twelve face diagonals. A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is √(l² + b² + h²) units.

A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid means "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces.

A diagonal in geometry is a line segment that connects two polygonal vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.

A, B, C, D, E, F, G & H form a cuboid. AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm. That is l=3.2 cm, b=1.6 cm, h=7.7 cm.

√(l² + b² + h²) units.

=√(3.2²+1.6²+7.7²)

=8.49 cm

≈8.5 cm

A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is √(l² + b² + h²) units. The length of AG=8.5 cm that is diagonal. There are four body diagonals of cuboid and twelve face diagonals.

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bring the fractions to a common denominator

The nearest degree of the measure of the angle having trigonometric ratios are answered below.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

Given Data

Trigonometry  Ratios:

1) cosine x = 0.8988

cos⁻¹ = 26.103°

2) sine x = 0.6691

sine⁻¹ x = 41.99°

3) tangent x = 2.50

tan⁻¹ x = 68.2°

4) tan x = 20

tan⁻¹ x = 87.14°

5) sin x = [tex]\frac{6}{11}[/tex]

sin⁻¹ x = 0.518

6) cos x =[tex]\frac{7}{9}[/tex]

cos⁻¹ = 0.7

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Answer: 5,723.19

Step-by-step explanation:

to find the answer you subtract 57.81 from 5781 to get 5,723.19

Is that what you were asking? I hope so.

22) 68

24) 90

26) 158

Coordinates of PQRSTU

P = (-2, -6)

Q = (-4, -6)

R = ((-4, -2)

S = (2, -4)

T = (2, -8)

U = (0, -10)

They changed to ABCDEF

A = (4, 4)

B = (2, 4)

C = (2, 8)

D = (8, 6)

E = (8, 2)

F = (6, 0)

Transformations used = (x + 6, y + 10)

Considering the age of Amy and sum of their ages, Jamie is 12 years old.

Let the age of Amy be x years. Thus, the age of Jamie be (x + 5) years. Forming equation as per the age -

x + x + 5 = 19

Performing addition on Left Hand Side of the equation

2x + 5 = 19

Shifting 5 to Right Hand Side of the equation

2x = 19 - 5

Performing subtraction on Right Hand Side of the equation

2x = 14

Shifting 2 to Right Hand Side of the equation

x = 14 ÷ 2

Performing division to Right Hand Side of the equation

x = 7

The age of Amy = 7 years

The age of Jamie = 7 + 5

Performing addition

The age of Jamie = 12 years

Thus, the age of Jamie is 12 years old.

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