Solve 3[-x + (2 x +1)]=x-1

The expression which shows the earning of Mrs. Fresneda is 4x and the money that she will earn by selling 26 bars of soap is $144.

Given that price of soap is $4.00 per bar.

We have to find the expression which shows the earning of Mrs. Fresneda after selling soap bars and the money that she will earn by selling 26 bars of soap.

let the number of soap bars be x.

We know that the revenue is the product of price and quantity.

Money that Mrs.Fresneda earns is 4*x

=4x

Expression is 4x which shows that money that Mrs. Freneda will earn by selling soap bars.

We have to just put x=26 in the expression to calculate the money after selling 26 bars of soap.

Money=4*26

=$144

Hence the expression is 4x and the money that Mrs.Freneda will earnby selling 26 bars of soap is $144.

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Another name for AXW is <X

The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point

Hence, another name for XW is WX

A ray with an endpoint X is a ray that ends at point X

An example of such ray is XY

The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point

Hence, another name for WX is XW

The name AXW represents an angle

An angle can be named after its middle point

Hence, another name for AXW is <X

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The solution to the equation using the completing the square are 2 and -3

These are equation that has a leading degree of 2. Given the equation below

-x^2 +x+6=0

This can also be written as

x^2-x-6 = 0

Complete the square

x^2-x = 6

x^2-x+ (1/2)^2 = 6 + (1/2)^2

(x-1/2)^2 = 6 + 1/4

(x+1/2)^2 = 25/4

x+1/2 = ±√25/4

x = 5/2 -1/2  or -5/2-1/2

x = 4/2  or -6/2

x = 2 and -3

Hence the solution to the equation using the completing the square are 2 and -3

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Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

Answer:

925.5

Step-by-step explanation:

Hope it helps!

<3

Mark and Don have 18  and 92 marbles respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

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Answer:

Step-by-step explanation:

To solve this equation log both sides and apply log rules.

Substitute the values of logs:

Solve it as linear equation:

Answer:

x = 34

Step-by-step explanation:

The three angles form a straight line and are thus supplementary angles.  The sum of a supplementary angles is always 180, so we can use the equation 180 = x + 12 + 100 + x to find x:

180 = 2x + 112

68 = 2x

x = 34

The package has a surface area of 4520cm². The area of the package is less than the area of the wrapping paper. So, dayson  can cover the package with the wrapping paper.

According to the question,

The first step is to determine the surface area of the package.

Total surface area of a cuboid = 2 (l w + w h + l h)

where:

• l = length

• w = width

• h = height

2[(50 x 20) + (50 x 18) + (20 x 18)] = 4520cm²

The second step is to convert 1 square meter to cm

1m² = 100 cm²

100 x 100 = 10,000

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v = 1.21 m/s is the answer

Kinetic energy of object = 25 J

Mass of object = 34 kg

The formula for the kinetic energy of an object is given by

K.E. = 1/2 m v2.

25 =  1/2 *34* v2.

v2= 25/17

v2 = 1.47

v = 1.21 m/s

In physics, the kinetic energy of an object is the energy that the object has due to its motion. This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, it retains this kinetic energy unless the velocity changes

Everything that moves at home is an example of kinetic energy. This could be a cue ball rolling on a pool table, a fan that circulates air on warm days, or a glass that shatters on the floor after falling off the counter. Electrical equipment that is turned on uses kinetic energy, much like people move around the house.

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The solution to the equation is 2

Given the equation

4 + 4(x-2) = 2(x+1) - x

First, we expand the bracket

4 + 4x - 8 = 2x + 2 - x

collect like terms

4x - 2x + x = 2 - 4 + 8

Add like terms

3x = 6

Make 'x' the subject

x = 6/3

x = 2

Thus, the solution to the equation is 2

The complete question is

What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work

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Answer:

Step-by-step explanation:

This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is

[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get

12.8CD = 16 and divide both sides by 12.8 to get that

CD = 1.25

That means that the length of the whole thing, BD, is

12.8 + 1.25 = 14.05

A binomial probability density function should be used to represent the probability

The given parameters are:

The proportion that plays sport indicates that

68% of the students do not play sport

So, we have two events, which are

When there are two possible events, then the binomial probability density function should be used

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Answer:

ASA

Step-by-step explanation:

The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

The formula for calculating the slope of a line is expressed as

slope = y2-y1/x2-x1

Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:

Slope = 1-0/-2-0

Slope = 1/-2

Slope = -1/2

Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

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The slope of the line m is - 1 / 2.

The slope a line can be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (0, 0)(2, -1)

hence,

slope = - 1 - 0 / 2 - 0

slope = - 1 / 2

hence,

slope = - 1 / 2

Therefore, the slope of the line m is - 1 / 2.

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Answer:

x^3-4x^2+25x-100

Step-by-step explanation:

We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root

Combining the roots into a polynomial gives us:

(x+5i)(x-5i)(x-4)

Expand:

(x^2 + 25)(x-4)

x^3-4x^2+25x-100

Answer:

The possible length of the third side is greater that 4ft and less that 20 ft

4<x<20

Answer:

five number summary is a specially useful in the scriptive analysing what during the premier league investigation of a large data set a summary consists of 5 values of the most extreme values in data set the maximum and minimum values of the lower and upper quality and the meridian

Answer:

B) 16

Step-by-step explanation:

12/3 = x/4

48 = 3x  Divide both sides by 3

16 = x

Answer:

========================

We have a diagram and need to find the number of routes without repeat paths:

We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.

This gives us the number of routes:

Total number is:

The matching answer choice is B

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

From the given we can observe that:

ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.

From similarity we get same ratio of corresponding sides:

We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:

As per ratio of corresponding sides:

As per segment addition:

From the two equations above we get:

Now, the required area is:

This is matching the answer choice D

Answer:

9)  B. 8

10)   D. 4.5

Step-by-step explanation:

Question 9

For ease of visualization, label the different legs of the journey on the diagram (see attachment).

The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.

The different routes are:

Therefore, there are 8 different routes.

Question 10

Triangles EDC and EAB are similar since they have congruent angles:

Therefore, their corresponding sides are in proportion.

⇒ CD : BA = ED : EA

⇒ 9 : 3 = ED : EA

⇒ 3 : 1 = ED : EA

Since we know that AD = 4:

⇒ ED = 3

⇒ EA = 1

Area of a triangle

[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]

To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.

[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]

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The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]

[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]

[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]

Similarly, we have;

[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;

Therefore;

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The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.

It follows that the equation given is;

(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)

Hence, by multiplying both sides by (x²+5x+6); we have;

3 + x² +2x -3 = 7x + 14.

x²-5x -14 = 0

On this note, the solutions of the quadratic equation are; x =7 and x=-2.

It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.

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Answer:

x=7  

x=-2

Step-by-step explanation:

Answer:

x = 20 units

Step-by-step explanation:

See attached.

Answer:

[tex]x = 94[/tex]

Step-by-step explanation:

To find the value of [tex]x[/tex], we have to first find the lengths of the sides of the squares and add them.

The formula for area of a square is as follows:

[tex]{area = (length \space\ of \space\ side)^2}[/tex]

This means the length of a side of a square can be found by:

[tex]\boxed {length \space\ of \space\ side = \sqrt{area}}[/tex]

Now we can find the lengths of sides of each of the squares:
• Length of side of larger square = [tex]\sqrt{8100}[/tex]

                                                       = 90

• Length of side of smaller square = [tex]\sqrt{16}[/tex]

                                                          = 4

Next we can just add the lengths of the sides to get the value of [tex]x[/tex] :

[tex]x = 90 + 4[/tex]

⇒ [tex]x \bf = 94[/tex]

Answer:

180 - 92 - 41 = 47

There are not two similar congruent angle in the triangles.

Hope this helps!

The point estimate of the proportion of students who prefer the new schedule is 0.22.

Definition of Point Estimate

Point estimation is a technique used in statistics to determine a single value that will serve as the "best guess" or "best estimate" of an unidentified population characteristic, known as the point estimate. More precisely, in order to produce a point estimate, we apply a point estimator to the data.

For the confidence interval (0.195, 0.245), point estimate is calculated as follows,

p = (0.195 + 0.245) / 2

p = 0.44 / 2

p = 0.22

Hence, the point estimate of the proportion of students who prefer the new schedule comes out to be 2.2.

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The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.

It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.

Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.

The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.

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Answer:

[tex]x^2+8x+8+\frac{-9}{x+4}[/tex]

Step-by-step explanation:

it would be simpler to do synthetic division by removing the variables and using the coefficients:

i hope this helped!

The equation in slope intercept form is y = -4x/3 + 10

The representations are given as:

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

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