7x + 3x + X Divided By X-2 Using Long Division (2024)

The purpose why these concepts are present in the pictures is to develop imagination power among students.

As you imagine more, your mind becomes stronger and you have greater mental control. Innovation requires a strong imagination. If you succeed in what you set out to do, the same individuals who now accuse you of daydreaming will begin to aspire to be like you. Keep your aspirations high and your imagination expanding.

Imagination is a potent brain stimulant because it forces you to think differently than most people do. Your imagination can help you come up with scenarios that most effectively handle difficulties, even though your brain might classify them as being unexpected.

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If two side lengths of a fence are 9 and 12 inches and the sum of the three lengths ranges from 31 to 40 inches, then the length of the third side, x, can be presented by the compound inequality 10 < x < 19.

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

Given that the sum of the three lengths of a fence ranges from 31 to 40 inches, the inequality can be written as:

31 < sum < 40

If two side lengths are 9 and 12 inches, and let x be the third length, the inequality becomes:

31 < 9 + 12 + x < 40

31 < 21 + x < 40

Subtracting 21 at all sides,

31 - 21 < 21 + x - 21 < 40 - 21

10 < x < 19

Hence, the compound inequality to show the length of the third side can be written as 10 < x < 19.

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The area and perimeter of the rectangle are 80 cm and 375 cm² respectively.

How to find area and perimeter of a rectangle?

The rectangle is 15 cm wide.

The width is 3 / 5 of its length

Therefore, the area and the perimeter of the rectangle can be found as follows:

area of a rectangle = lw

where

l = lengthw = width

Therefore,

w = 15 cm

15 = 3 / 5 × l

cross multiply

75 = 3l

l =75 / 3

l = 25 cm

Therefore,

area of the rectangle = 25 × 15 = 375 cm²

Perimeter of the rectangle = 2l + 2w

Perimeter of the rectangle = 2(l + w)

Perimeter of the rectangle = 2(25 + 15)

Perimeter of the rectangle = 2(40)

Perimeter of the rectangle = 80 cm

Therefore, the area and perimeter of the rectangle are 80 cm and 375 cm² respectively.

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Answer: 2000π mm^2

Step-by-step explanation:

A=area of entire circle. B=Area of Inside circle. C=Area of shaded region

A-B=C

π(120/2)^2 -π(80/2)^2=

π(60)^2 -π(40)^2=

3600π-1600π=2000π mm^2

Answer:

Hey!

Since we know that both expressions lay on a straight line, we know that when both lines add up it should be 180°

We can write the expression as (7x - 1) + (6x - 1) = 180

Simplify

→ (7x + −1) + (6x + −1) = 180

Combine Like Terms

→ (7x + 6x) + (-1 + -1) = 180 → 13 + -2 = 180

Add 2 To Both Sides

→ 13x - 2 + 2 = 180 + 2 → 13x = 182

Divide 13 To Both Sides

13x/13 = 182/13 → x = 14

Hence, the value of x is 14!

-------------------------------------------------

Hope This Helped! Good Luck!

The Constant of proportionality represented in equation is 4.75

The Constant of Proportionality defines the value which will remain constant in the whole system of equations. In the given equation, Liv earns $9.50 for selling every two bracelets. The equation represents the sale of Liv on the basis of its price and quantity and the Total amount that she gets. The equation is represented as y = 4.75x

Here, y is the total amount she gets, x is the number of pieces that she sold, and 4.75 is the constant of proportionality. In this case, the constant can be defined as the price of one bracelet that she sells.

This constant can be derived by simply dividing the total amount by the total number of pieces that she sells. It can be represented by :

=> y/x = c , where c is the constant

=> 9.5/2 = c => c = 4.75

Hence, the Constant of Proportionality is 4.75.

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The function g(x) is given as: g(x) = 3 ( x + 4 )^2 + 5

Given data

f(x)=x2

shifted 4 units left

stretched by a factor of 3

shifted 5 units up

How to find the function rule for g(x)

The function g(x) is formed from the function f(x) by the following moves:

Shifting 4 units to left

To shift the graph 4 units to the left is given by

f(x) = x^2

f(x) = ( x + 4 )^2

Stretching by a factor of 3

to stretch by a factor of 3 means multiplying by 3

f(x) = 3 * ( x + 4 )^2

f(x) = 3 ( x + 4 )^2

Shifting 5 units up

This movement is shows in the y axis and is represented as follows

f(x) = 3 ( x + 4 )^2 + 5

At this stage the function rule for g(x) is completed hence

f(x) = 3 ( x + 4 )^2 + 5 = g(x)

and

g(x) = 3 ( x + 4 )^2 + 5

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Answer:

D

Step-by-step explanation:

The number of questions is 20; it's the total points that are worth 50 and the question is asking for number of questions

Answer:

15

Step-by-step explanation:

225/15

2X-5=7

solved algebraically, X=6

Answer:

Step-by-step explanation: Step 1: Make a table of that equation suppose x = 7. You can consider it like x+y = 7 in which x = will be 7 only and y will become 0.
Step 2: To answer this on a graph.. make all four quadrants and mark the coordinates such a the value of x = 7 should lie on the x-axis and y = 0 lies on the y-axis.
Step 3: Draw a straight line at the coordinates you got which were (7,0)

Here you go :)

The function which represents how much money Janet makes each day according to the task content is; (8j/2) - 150.

Which function represents how much money Janet makes each day?

Given;

Booth rent = $150Cost of each honey jar = $8Number of jars sold = j

According to the given parameters; the total amount of money made from honey sale is; $8 × j = $8j.

Hence, since she splits the money with her mom, it follows that her personal income is; $8j/2.

Ultimately, after paying $150 a day for the booth rental, the amount made by Janet is; $8j/2 - $150.

The required function, f(j) is therefore;

f(j) = (8j/2) - 150.

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8x+y=31

perpendicular means the slopes are opposite reciprocals of each other. perpendicular to: y +5= 8(x +4) → m = 8 m⊥ = -8

Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)

y - (-1) = -8(x -4)

y + 1 = -8 x + 32 simplified

8x+y =31

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Answer:

sometimes

Step-by-step explanation:

There are several ways that dilation is used in real life. Here are several:

In graphic design. I actually do some graphic design, and I use dilation a lot. It is common to dilate photos to fit the space that you want it to fit.

In police work and crime investigation. Detectives and police dilate photos to see smaller details and evidence.

In architecture. It is normal for architects to make a prototype of their design or building. In order to make the building true to the prototype, they must dilate the scale and measurements.

In the doctor's office. Dilation is used in eye exams so that the eye doctor can view the patient's eye better. After a while it will slowly reduce in size and return back to normal.

Answer: D

Step-by-step explanation: 2,6

Answer:

[tex] \sf \large \: x=−1[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

4(x+3)−2=6

Step 1: Simplify both sides of the equation.

4(x+3)−2=6

(4)(x)+(4)(3)+−2=6(Distribute)

4x+12+−2=6

(4x)+(12+−2)=6(Combine Like Terms)

4x+10=6

4x+10=6

Step 2: Subtract 10 from both sides.

4x+10−10=6−10

4x=−4

Step 3: Divide both sides by 4.

4x/4 = −4/4

x=−1

Answer:

#9: B

#10: D

Step-by-step explanation:

#9 had biggest scientific notaiton

#10 had smallet scientific notaiton and numbeer

Answer:

9. B

10. D

Step-by-step explanation:

a. 5406000000

b. 56040000000

c. 550400000

d. 6503000000

a. 900000

b. 120000

c. 3010000000

d. 19010

A direct, consistent relationship between the independent variable and the dependent variable is called "dose-response relationship."

What is a dose-response relationship?

The effect on an organism and, more specifically, the risk of a defined outcome caused by a set quantity of an agent or level of exposure.

Some key features regarding the dose-response relationship are-

A dose-response relationship is considered the strongest proof for a causal relationship between exposure and outcome. Even in the absence of a dose-response relationship, the possibility of a causal relationship can not be discounted. Time can have a significant impact on dose-response relationships. For example, when examining the relationship between exposure and outcome, the time to response can be impacted by a latent period between outcome and exposure. If the effects have been measured too shortly after the exposed, no effect is seen, even if the exposure is the cause of the outcome.

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Answer:

f(7) = -113

Step-by-step explanation:

Hello!

Substitute 7 for x in the equation.

Evaluatef(x) = -4x² + 10x + 13f(7) = -4(7)² + 10(7) + 13f(7) = -4(49) + 70 + 13f(7) = -196 + 70 + 13f(7) = -113

f(7) is -113.

The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.

For Example , Derivative of [tex]3x^{2} =6x[/tex].

Product Rule of Differentiation

Let f(x) and g(x) be any two function. The derivative of their will be

F(x)=f(x)*g(x)

[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]

Given y=(sin(7x))ln(x)

[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]

[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]

[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]

Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

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Step-by-step explanation:

You want to demonstrate the identity ...

(1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

[tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]

__

Additional comment

The referenced identities are ...

tan = sin/cos

cos² = 1 -sin²

and the factorization of the difference of squares:

a² -b² = (a +b)(a -b).

The linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

Option (A) and (D) is correct.

What is inequality?

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

According to given question we have

a. y<-2x

To put the value of x any y (0,0) we get

=0<-2*0

=0<0

b. y<-3x+4

To put the value of x any y (0,0) we get

=0<-3*0+4

=0<0+4

=0<4

c. y>-2x+6

To put the value of x any y (0,0) we get

=0>-2*0+6

=0>0+6

=0>6

d. y>-3x

To put the value of x any y (0,0) we get

=0>-3*0

=0>0

Therefore, the linear inequality will have a solution of (0,0) is y<-2x and y>-3x.

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Answer:

12.5988 feet.

Step-by-step explanation:

Length of shadow = 15 feet.

Height of flagpole = A.

We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.

Hope this helps! :)

The equation which represents the relationship between 'h' the number of hours, and c, the total cost is y = 250x+850.

How to write equation of straight line?

A straight line equation is a mathematical equation that describes the relationship between the coordinate points on that straight line. It can be written in several ways and indicates the slope, x-intercept, & y-intercept of a line.

A straight line's general equation is y = mx + c, in which m is the gradient and y = c is the value at which the line intersects the y-axis. The above number c is known as the y-axis intercept. A straight line with gradient m as well as intercept c on the y-axis has the equation y = mx + c.

Now, as per the given question;

The attorney charges price for an initial meeting = $850.

And, the charges for each hour is = $250.

Thus, the equation which shows the given situation is-

y = 250x + 850.

In which, 250 is the value of the slope 'm'.

The y- intercept is shown by 850.

Thus, the total cost will be found out by equation y = 250x+850.

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Step-by-step explanation:

3.1.1 The base of the prism is a rectangle.we know this by checking the properties of the base,that is, opposite side are equal and it has all angles equal to 90°

3.1.2the area of a rectangle is calculated using the formula: A=LxB

where: A is the Area

L is the Length of the shape

B is the breadth

3.1.3 to calculate the volume of a prism we can use the formula V=A(base)xh

where:V is the volume

A is the area of the base

h is the height of the prism

3.1.4V=Axh

=(LxB)xh

=(140mm x 115mm)x 125mm

=2012500mm³

The equivalent expression to -1/3-(-5/12) is 1/12.

How to calculate the expression?

From the information, the expression given is -1/3-(-5/12).

Therefore, this will be computed thus:

= -1/3-(-5/12)

= - 1/3 + 5/12

= 5/12 - 1/3

= 5/12 - 4/12

= 1/12

Therefore, the equivalent expression to -1/3-(-5/12) is 1/12.

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Answer: It is the point where the line crosses the x axis of the cartesian coordinates. We can write an equation of the line that passes through the points y=0 as follows: Using the equation: y = 3x – 6, put y=0. To find the x-intercept. 0 = 3x – 6. 3x = 6. The x-intercept is 2 of the slope-intercept form of line

True, there are some undefined terms like line, point angle, distance between two points .

Which definition of angle is the best?

The figure in which two rays intersect at the vertex, or common point, is referred to as an angle. The symbol "∠" is used to represent the angle.

How does Euclid define angle?

A plane angle is the inclination toward one another of two intersecting, non-straight lines in the plane.

True, there are some undefined terms like line, point angle, distance between two points .

we intuitively know about the angle but can not give mathematical definition .

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Answer is 13.45 units

Step by step

We know the formula

d= √ (x2 - x1) ^2 + (y2 - y1) ^2

d = √ (10-1)^2 + (6- -4) ^2

d = √ 81 + 100

d = √ 181

d = 13.45

Problem solved