please solve:
3(d+12)=8-4d

Answer: x = 5

Step-by-step explanation:

3( x - 3 ) = 6

Divide 3 on both sides

x - 3 = 2

Add 3 on both sides

x = 5

Answer:

n = 5.5

Step-by-step explanation:

Let the number be n. The quotient of a number divided by 11 is 0.5.

ATQ,

\(\dfrac{n}{11}=0.5\)

Multiply both sides by 11.

\(\dfrac{n}{11}\times 11=0.5\times 11\\\\n=5.5\)

Hence, the required number is 5.5.

Answer:

b. - = 0.5 = 5.5

Step-by-step explanation:

Answer:

18 units

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

To find zx and zy, we need to take partial derivatives of z with respect to x and y. Taking z with respect to x, we get zx = 3x2 + 12xy and zy = 6x + 16y. Taking z with respect to y, we get zy = 6x + 16y and g(x, y) = 3xy - 7x. Therefore, gx = 3y - 7 and gy = 3x.

A derivative is a measure of how much a function changes as its input changes. More specifically, the derivative of a function at a particular point is the slope of the function at that point, which describes how quickly the function is changing at that point.

Geometrically, the derivative of a function at a given point can be thought of as the slope of the tangent line to the function at that point.

To find zx and zy, we need to take partial derivatives of z with respect to x and y, respectively.

Given z = \(x^3 + 6x^2y + 8y^2\),

Taking partial derivative of z with respect to x, we get:

zx = \(3x^2 + 12xy\)

Taking partial derivative of z with respect to y, we get:

zy = 6x + 16y

Therefore, zx = 3x^2 + 12xy and zy = 6x + 16y.

Given g(x, y) = 3xy - 7x,

Taking partial derivative of g with respect to x, we get:

gx = 3y - 7

Taking partial derivative of g with respect to y, we get:

gy = 3x

Therefore, gx = 3y - 7 and gy = 3x.

To know more about derivatives visit:

brainly.com/question/25324584

#SPJ1

Answer + Step-by-step explanation:

• is it a function?  

No , because f(2) = 1 and f(2) = -1

• Domain :

[1 , 5]

• Range :

[-4 , 4]

• y-intercept :

It doesn’t have y-intercepts ,because the graph doesn’t cross the y-axis.

• Zero :

x = 1 ,because f(1) = 0

• f(3) = ± 2

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Here, for some values of x, we have more than one value of y. so we can conclude that it's not a function.

or

Draw vertical lines all over the graph, if the vertical lines cut the curve once then it is a function, and if more than once then it isn't a function.

Since the lines cut the curve more than once, it isn't a function

\(\qquad \sf  \dashrightarrow \: ( 1 , 5 )\)

\(\qquad \sf  \dashrightarrow \: (-4 , 4)\)

It doesn't cut y - axis, so it doesn't have y - intercept

The values of x at which the curve cuts the x - axis are the zeros.

If we plug the x - coordinate as 3, it has two y - coordinates : -2 and 2

So, F (3) = - 2 and 2

The population mean income of the five families is their average income

The population mean income of the five families is #15.2

The income of the five families in a thousand dollars is given as:

A 12 B 23 C 18 D 7 E 16

The population mean is then calculated as:

\(\mu = \frac{\sum x}n\)

So, we have:

\(\mu = \frac{12 + 23 + 18 + 7 + 16}5\)

Evaluate the sum

\(\mu = \frac{76}5\)

Evaluate the quotient

\(\mu = 15.2\)

Hence, the population mean income of the five families is #15.2 thousand

Read more about mean at:

https://brainly.com/question/15858152

The differentiation of the given function f(x) = eˣ+6 is eˣ

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function f(x) = eˣ+6, we need to find the derivative of this function,

f(x) = eˣ+6

f'(x) = d / dx (eˣ+6)

= d(eˣ)/dx + d(6)/dx

Since, 6 is a constant and derivative of a constant is zero,

d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0

Now, when we differentiate eˣ, we get eˣ itself,

Therefore,

d(eˣ)/dx = eˣ

Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ

Learn more about differentiation, click;

https://brainly.com/question/14496325

#SPJ9

Answer:

33

Step-by-step explanation:

396/x - 10 = -22

add 10 to each side

396/x = -12

multiply both sides by x

396 = 12x

divide both sides by 12

33 = x

The value of the function f(x) = 3x^2 - 2x + 1 at x = -1, will be 6

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Algebraic expressions are expressions that are made up of variables and constants. Any value can be assigned to a variable. The value of an expression changes depending on the values assigned to the variables it includes. There are an unlimited number of points on a number line.

To evaluate the function f(x) = 3x^2 - 2x + 1 at x = -1,

we simply substitute -1 for x in the expression:

f(-1) = 3(-1)^2 - 2(-1) + 1

= 3(1) + 2 + 1

= 6

Therefore, f(-1) = 6.

For more questions on Value of the Expressions

https://brainly.com/question/28993394

#SPJ4

Answer:

6

Step-by-step explanation:

20 41 6

20 6 41

6 41 20

6 20 41

41 20 6

41 6 20

After 1 year, the book value of the computer is $2,000.

To calculate the book value of the $2,500 computer after 1 year using the given MACRS rates, we need to apply the depreciation percentages for each year.

Given the MACRS rates:

Year 1: 20.0%

Year 2: 32.0%

Year 3: 19.2%

Year 4: 11.52%

Year 5: 11.52%

Let's calculate the depreciation for each year:

Year 1: 20.0% of $2,500 = $500

The computer's value after Year 1 is $2,500 - $500 = $2,000.

Therefore, after 1 year, the book value of the computer is $2,000.

for such more question on book value

https://brainly.com/question/28256489

#SPJ8

Answer:fafafafafaf

Step-by-step explanation:

Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are     y = (-4/3)x + 11 and y = (-4/3)x + 9.

First, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:

Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.

Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):

r = √((7-3)^2 + (9-4)^2) = √(85)

So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.

To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.

To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.

To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).

The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:

At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.

At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.

Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.

Learn more on equation of circle here;

https://brainly.com/question/24810873

#SPJ1

Answer: ⇒V=π×32×53=45×π3≈47.124 cubic cm

Hope this helps!!

Therefore, the equation that represents the relationship between C and F is c = 7/3 F

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

Clare must use 9 containers, each of which has a 1/3 portion filled with flour to make 4 pastries.

So, Andre's recipe will have the same ratio of cups of flour per cake:

We can set up the proportion as follows:

F cups / c cakes = (9 ×1/3 cups) / 4 cakes

To solve for C, we can multiply both sides by c:

9× 1/3 cups / 4 cakes * c cakes = F cups

Multiplying the left side gives:

(28/3) * (c/4) = F

Simplifying:

7c/3 = F

Therefore, the equation that represents the relationship between C and F is c = 7/3 F

To know more about Equation visit:

https://brainly.com/question/22688504

#SPJ1

We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

Given the equation of the surface is xy + 15x + z^2 = 209.

Let's determine the shortest distance from the surface to the origin.

The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:

Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.

For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).

The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.

Here, the normal vector is ∇f = (y + 15, x, 2z).

Now, let's consider a point A on the surface which is closest to the origin.

Let the coordinates of A be (a, b, c).

Therefore, the position vector of A is given by: OA = ai + bj + ck.

The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.

Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.

Since A lies on the surface, we have: a*b + 15a + c^2 = 209.

We also know that OA passes through the origin.

Therefore, the position vector of A is perpendicular to the direction vector OA.

This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0

Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0

Also, we know that OA passes through the origin.

Therefore, the magnitude of OA is equal to the distance of A from the origin.

Hence, we can write: |OA| = √(a^2 + b^2 + c^2)

The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))

Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k

Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|

The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.

Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.

Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

For more such questions on shortest distance, click on:

https://brainly.com/question/28935294

#SPJ

Answer:

a. Peaches cost more by pound because the line it forms is steeper

b. draw a line that is less steep than the plums and under the plums line

Answer:

33

Step-by-step explanation:

x(14 - x)

Step One: Substitute

3(14 - 3)

Step Two: Brackets/Parenthesis

3(11)

Step Three: Multiply

33

Answer:

33

Step-by-step explanation:

1. Subtract the numbers

(14-3)

2. Multiply the numbers

3*11= 33

Answer:

can yoy show modl

Step-by-step explanation:

Answer:

£16:£144

Step-by-step explanation:

1+9=10

160/10=16

1×16=16

9×16=£144

Answer:

16£ and 114£

Step-by-step explanation:

add the ratios

1 + 9 = 10

for the first ratio

(1/10) × 160

= 16£

for the second ratio

(9/10) × 160

= 114£

Answer:

0.00084

Step-by-step explanation:

We are given that

Mean,\(\mu=2400\) square feet

Standard deviation, \(\sigma=450\)square feet

n=50

We have to find the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet.

\(P(x<2200)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}<P(\frac{2200-2400}{\frac{450}{\sqrt{50}}})\)

\(P(x<2200)=P(Z<\frac{-200}{\frac{450}{\sqrt{50}}})\)

Using the formula

\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)

\(P(x<2200)=P(Z<-3.14)\)

\(P(X<2200)=0.00084\)

Hence, the probability that a random sample of 50 homes in Anytown, USA has mean square footage less than 2200 square feet=0.00084

Answer:

100% = 65 Gallons; 70% = 45.5 Gallons

Step-by-step explanation:

The important piece of information here is that 13 gallons of water makes the container 1/5 of the way full, aka 20%.  If the question is simply, how many gallons will it hold, then we multiply 13 by 5 to get 100% at 65 gallons.  To get the amount held at 7/10, or 70%, we simply multiply 65 with 7/10 to get 45.5 gallons.

Cheers.

Answer:

y=-2 or y=3

Step-by-step explanation:

Y^2-y-6=0

y^2-3y+2y-6=0

y(y-3)+2(y-3)=0

(y+2)(y-3)=0

y=-2 or y=3

hope it helps

Answer:

Step-by-step explanation:

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

The statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

In the case of testing about test scores, teacher can't use random or controlled experiment as the teacher would more likely work with real data of test scores instead of students faking it.

The sample survey is not needed as getting test scores doesn't destroy them, nor the population of students is too high(assuming math class has small number of students (usually under some hundreds) ).

Observational study is best choice here, and this is done on all students by observing how much students achieved in scored in test and relate it with them completing the review worksheets or not.

Thus, the statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

Learn more about observational study here:

https://brainly.com/question/14410103

Answer: Okay, well first lets find the quotient 345 ÷ 8:

It is 43. 125, but we're going to simplify it to 43

Now this is the really easy part, so lets find a number greater than 43, which would be 44.

Now that we have that, we need to find a decimal that's lower than 43, which would be 42.

So our numbers would be 44 and 42.

Step-by-step explanation: