7x + 5 = 3(2x + 3) + x - 4​

Answer:

(x-2)(x-11)

Step-by-step explanation:

Answer:

(x - 2)(x - 11)

Step-by-step explanation:

We have a polynomial and are asked to factor it.

Polynomial : x^2 - 13x + 22

Usually a trick I follow when factoring is that for c (in this case 22). You need to find two numbers that will multiply to it. And for b (in this case -13) you will need to find two numbers that will add to it, the same numbers you multipled for c.

So

x * y = 22

x + y = -13

These two numbers are -11 and -2.

The volume of the solid the region defined by the given curves must be rotated about the x-axis is V = \(\frac{384\pi }{5}\).

Given that,

The region defined by the given curves must be rotated about the x-axis to determine the solid's volume, which is y =6 -x², y =2.

We know that,

Take the equation of the curves about the x- axis

y =6 -x², y =2.

Substitute y = 2 in equation y = 6 - x²

2 = 6 - x²

-x² = 2-6

x² = 4

Taking square root on both sides

x = ±2

Now, volume formula is define by using washer method

V =  \(\pi \int\limits^a_b {[f(x)]^2 - [g(x)]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {[6-x^2]^2 - [2]^2} \, dx\)

V = \(\pi \int\limits^2_{-2} {(36 + x^4 - 12x^2 - 4}) \, dx\)

V = \(\pi \int\limits^2_{-2} {(x^4 - 12x^2 - 32)} \, dx\)

V = \(\pi( [\frac{x^5}{5}] - 12\times\frac{x^3}{3} -32x)^2_{-2}\)

V = \(\pi[( [\frac{2^5}{5}] - 12\times\frac{2^3}{3} -32(2))-([\frac{-2^5}{5}] - 12\times\frac{-2^3}{3} -32(-2))]\)

V = \(\pi[( [\frac{32}{5}] - 4 \times 8 -64)-( [\frac{-32}{5}] - 4\times(-8) +64)]\)

V = \(\pi[( [\frac{32}{5}] - 32 -64)-( [\frac{-32}{5}] +32 +64)]\)

V = \(\pi( [\frac{384}{5}] )\)

V = \(\frac{384\pi }{5}\)

Therefore, The volume of the solid is V = \(\frac{384\pi }{5}\)

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Answer:

  3 °C

Step-by-step explanation:

You want the temperature that, when added to four others, changes the mean from 8°C to 7°C.

The mean is the sum of the values in a data set, divided by the number of values. For the purpose here, we can assume that all of the first four temperatures were their mean. Then the mean after 5 days is ...

  (8 +8 +8 +8 +x)/5 = 7

  32 +x = 35 . . . . . . . . . . multiply by 5 and simplify

  x = 3 . . . . . . . . . . . . subtract 32

The temperature on Jan 5 was 3°C.

The mass of the solid is 7π/2 units.

The task is to calculate the mass of the solid.

Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.

The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.

Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.

The density is equal to the distance from the origin, i.e. ρ = r.

The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr

The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀  π dθ= 14π/4= 7π/2 units.

The mass of the solid is 7π/2 units.

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By using scientific notation we calculated (2.3\(\times\)10⁵)(1.5 \(\times\)10⁴) we got 345 \(\times\)10⁷.

Given that,

(2.3\(\times\)10⁵)(1.5 \(\times\)10⁴)

By using scientific notation

The scientific notation allows us to express extremely large or extremely small numbers by multiplying them by single-digit integers and by 10 raised to the power of the corresponding exponent. The exponent is either positive or negative depending on how big or little the number is.

Now, we calculate

(2.3\(\times\)10⁵)=2.5\(\times\)100000=230000

(1.5 \(\times\)10⁴)=1.5\(\times\)10000=15000

Now,

=230000\(\times\)15000

=3450000000

=345 \(\times\)10⁷

Therefore, By using scientific notation we calculated (2.3\(\times\)10⁵)(1.5 \(\times\)10⁴) we got 345 \(\times\)10⁷.

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Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

Answer:

Step-by-step explanation:

First turn the mixed fractions into improper fractions

--> (\(\frac{2*5+4}{5}\)) × (\(\frac{-5*5+4}{3}\))

      \(\frac{14}{5}\)×\(\frac{-17}{3}\)

Then multiply. the answer becomes −15 13/15

The partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned.

The given water wave function is graphed as z = 1 + sin(x - y) using Mathematica. The crests and troughs of the wave are aligned in the direction of zero change in the height function, which can be determined by analyzing the partial derivatives. The steepest descent from a crest to a trough corresponds to the direction perpendicular to the alignment of crests and troughs. These conclusions are consistent with the graph of the wave.

The water wave function z = 1 + sin(x - y) represents a snapshot of a frozen water wave. To graph this function using Mathematica, the x and y coordinates are assigned appropriate ranges, and the resulting z-values are plotted.

To determine the alignment of the crests and troughs, we examine the rate of change of the height function. Taking the partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned. Setting dz/dx = 0 gives cos(x - y) = 0, which implies x - y = (2n + 1)π/2, where n is an integer. This equation represents lines in the xy-plane along which the crests and troughs are aligned.  

For the steepest descent from a crest to a trough, we need to find the direction of maximum decrease in the height function. This direction corresponds to the negative gradient of the height function, which can be obtained by taking the partial derivatives dz/dx and dz/dy and forming the vector (-dz/dx, -dz/dy). Simplifying this vector, we get (-cos(x - y), cos(x - y)), which represents the direction perpendicular to the alignment of crests and troughs.    

Upon examining the graph of the wave, we can observe that the lines of alignment for the crests and troughs match the lines where the height function has zero change, confirming our conclusion from part (b). Similarly, the direction of steepest descent from a crest to a trough, indicated by the negative gradient, aligns with the steepest downward slopes on the graph.

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Prediction problems where the variables have numeric values are most accurately defined as regressions.

Regression analysis is a set of statistical processes used in statistical modeling to estimate the relationships between a dependent variable and one or more independent variables.

Researchers can use regression to predict or explain variation in one variable based on another variable. Definitions include: The response variable is the variable that researchers are attempting to explain or predict. It is also known as the dependent variable because it is dependent on another variable.

Understanding linear regression is critical because it provides a scientific method for identifying and forecasting future outcomes. The ability to find and evaluate predictions can help many businesses and individuals by providing benefits such as optimized operations and detailed research materials.

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(a)The optimal order quantity is  4609 units.

(b)The time between orders is  1.98 months.

To determine the optimal order quantity and the approximate time between orders, the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of inventory by balancing ordering costs and carrying costs.

Optimal Order Quantity:

The formula for the EOQ is given by:

EOQ = √[(2DS) / H]

Where:

D = Annual demand

S = Cost per order

H = Holding cost per unit per year

calculate the annual demand (D) using the 2020

sales numbers provided:

D = 651 + 808 + 514 + 174 + 435 + 426 + 687 + 582 + 662 + 1551 + 1295 + 1774

= 9559 units

To calculate the cost per order (S) and the holding cost per unit per year (H).

The cost per order (S) is given as $500.

The holding cost per unit per year (H)  calculated as follows:

H = Carrying cost percentage × Unit value

= 0.30 × $3

= $0.90

substitute these values into the EOQ formula:

EOQ = √[(2 × 9559 × $500) / $0.90]

= √[19118000 / $0.90]

≈ √21242222.22

≈ 4608.71

Approximate Time Between Orders:

To calculate the approximate time between orders, we'll divide the total number of working days in a year by the number of orders per year.

Assuming 360 days in a year and a lead time of 1 week (7 days) for shipping, we have:

Working days in a year = 360 - 7 = 353 days

Approximate time between orders = Working days in a year / Number of orders per year

= 353 / (9559 / 4609)

= 0.165 years

Converting this time to months:

Approximate time between orders (months) = 0.165 × 12

= 1.98 months

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Answer:

D. 3

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Answer is Option A

Step-by-step explanation:

the things people do for points smh :/

The rectangular equation which represents the parametric equations; x = t^(¹/2) and y = 4t is; y = 4x2, for x ≥ 0.

From the task content, it follows that the parametric equations given are;

Hence, it follows that; t = x² and y= 4t

Ultimately, upon substitution of x² for t; the resulting rectangular equation is; y = 4t².

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The best approximation for the solution of the system of equations is (0.88,0.65).

Given a system of equations is y=-(2/5)x+1 and y=3x-2.

A system of linear equations consists of two or more equations, and one attempts to solve the equations together.

To find the best approximation solution solve the system of equations.

The given system of equations are

y=-(2/5)x+1     .......(1)

y=3x-2           .......(2)

Firstly, substitute the value of y into equation (1) to find the value of x, we get

3x-2=-(2/5)x+1

Now, we will add (2/5)x in both sides, we get

3x-2+(2/5)x=-(2/5)x+1+(2/5)x

3x-2+(2/5)x=1

Further, we will add 2 on both sides, we get

3x-2+(2/5)x+2=1+2

3x+(2/5)x=3

17x/5=3

Furthermore, we will multiply both sides with 5, we get

5×(17x/5)=3×5

17x=15

Now, divide both sides with 17, we get

17x/17=15/17

x=0.88

Further, we will find the value of y by substituting the value of x in equation (2), we get

y=3(0.88)-2

y=2.65-2

y=0.65

Hence, the best approximation for the solution of the system of equations y=-(2/5)x+1 and y=3x-2 is (0.88,0.65).

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Step-by-step explanation:

(1) 4mn × 6mp × 3mnp

= 4 × 6 × 3 ( mn × mp × mnp)

= 72 × (m³n²p²)

72m³n²p²

sorry, I'm busy, won't be able to complete it

The equation based on the information is:

34 = x - 18

In mathematics, an equation is an expression that states that two expressions are equal by joining them with the equal sign =. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation. To solve an equation involving variables, it is necessary to determine which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values ​​of the variable. A constraint expression applies only to specific values ​​of a variable.

Given that :

Bella is baking 34 cookie for the holiday party tonight. She baked 18 before leaving for school and will bake the ret when he return home.

Therefore, the equation is:

34 = x - 18

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Answer:

Step-by-step explanation:

sinS = 9/41 ≅ 0.22°

Answer: The answer is 2

Step-by-step explanation:

Rewrite in simplest terms: -4(-8w-4x)-7x-10(-10x+8w)

Answer: -48w + 109x

Answer:

−48w + 109x

Step-by-step explanation:

a) Distribute:

(−4)(−8w) + (−4)(−4x) + −7x + (−10)(−10x) + (−10)(8w)

32w + 16x + −7x + 100x + −80w

b) Combine Like Terms:

32w + 16x + −7x + 100x + −80w

(32w + −80w) + (16x + −7x + 100x)

−48w + 109x

The variable in the study is "miles walked per week", which represents the estimated distance that 150 people living in coastal regions of California walk each week.

The study aimed to understand the walking habits of people living in coastal regions of California by measuring the number of steps they take using pedometers. These steps were then converted into an estimate of distance traveled, and this estimate was used as the dependent variable in the study, referred to as "miles walked per week".

The goal of the study was to better understand the physical activity patterns of the participants and how it might relate to other factors, such as their health, lifestyle, and environment. The data collected could be analyzed to identify trends and make recommendations for promoting healthy physical activity.

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Answer:

-18

Step-by-step explanation:

-3*5=-15

-15-3=-18

Answer: -18

Step-by-step explanation:

Substitute x for -3

5(-3)-3

-15-3

-18

Answer:Is an estimate of the average grams of salt used in 2012

Step-by-step explanation: Let

x ---> the number of years since 2012

f(x) ---> is the total amount of salt ingested in grams

we have

This is a linear equation in slope intercept form

where

The slope is equal to

The y-intercept or initial value is equal to

The y-intercept is the value of the function f(x) when the value of x is equal to zero

In this context, the y-intercept is the average amount of grams of salt ingested  in the year 2012

The exact value of the average amount of grams of salt ingested  in the year 2012 is 3,554 grams (see the data in the table)

Compare the exact value with the y-intercept

therefore

3,548 grams Is an estimate of the average grams of salt used in 2012

Answer:

its a

Step-by-step explanation:

The derivative of the function y = x sinh(x/3) - (9 + x²) is ln((x + √(x² + 9))/3) + (x/(3√(x² + 9))) - 2x.

To find the derivative of y = x sinh⁻¹(x/3) - (9 + x²), we will use the chain rule and the power rule of differentiation.

First, we can simplify the expression by using the identity sinh⁻¹(x) = ln(x + √(x² + 1)), so we have:

y = x ln(x/3 + √((x/3)² + 1)) - (9 + x²)

Now we can differentiate term by term, using the chain rule for the first term:

y' = ln(x/3 + √((x/3)² + 1)) + x(1/(x/3 + √((x/3)² + 1))) (1/3) - 2x

Simplifying the first term and combining like terms in the second term, we get:

y' = ln((x + √(x² + 9))/3) + (x/(3√(x² + 9))) - 2x

This is the final answer for the derivative of y.

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The question is -

Find the derivative of the function y = x sinh(x/3) - (9 + x²).

Answer:

Step-by-step explanation:

M being midpoint of AB means:

\(x_B-x_M=x_M-x_A\qquad\quad\ \wedge\qquad y_B-y_M=y_M-y_A\\\\x_B-3=3-8\qquad\quad\wedge\qquad\quad y_B-(-2)=-2-4\\\\x_B-3=-5\qquad\quad\ \wedge\qquad\quad y_B+2=-6\\\\x_B=-5+3\qquad\quad\ \wedge\qquad\quad y_B=-6-2\\\\x_B=-2\qquad\qquad\ \wedge\qquad\qquad y_B=-8\)

Answer:

\(4x\left(x-3\right)\)

Step-by-step explanation:

\(x^{y+z}=x^yx^z\\x^2=xx\\=4xx-12x\\=4xx-4\cdot \:3x\\=4x\left(x-3\right)\)

Answer:

4 foot

Step-by-step explanation:

divide by 12

Answer:

78.5

Step-by-step explanation:

Radius: 12.5

Circumference: 2 π r

Circumference: 2 π 12.5 = 78.54

Hope this helps!

Answer:  C ≈78.54

Step-by-step explanation:

C=2πr

C=2 π (12.5)

C=25π

C≈78.54

Answer:

It can be represented by the expression 2r, or “two times the radius.” So if you know a circle's radius, you can multiply it by 2 to find the diameter; this also means that if you know a circle's diameter, you can divide by 2 to find the radius. Find the diameter of the circle.

Step-by-step explanation:

you'r welcome :)