What is the LCM of the expressions?

b. x² + 3x - 4, x² + 2x - 8 , and x² - 4x + 4

The equation of the line in point-slope form, which passes through the pair of points located at (3/2 , -1/2) and (-2/3 , 1/3), is y + 1/2 = -5/13(x - 3/2).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (3/2 , -1/2) and (-2/3 , 1/3).

m = (y2 - y1)/(x2 - x1)

m = (1/3 - -1/2)/(-2/3 - 3/2)

m = (5/6)/(-13/6)

m = -5/13

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -5/13 and (x1 , y1) = (3/2 , -1/2)

(y - -1/2) = -5/13(x - 3/2)

y + 1/2 = -5/13(x - 3/2)

To learn more about equation of line in point slope form: brainly.com/question/24907633

#SPJ4

Answer:Lowering rates makes borrowing money cheaper. This encourages consumer and business spending and investment and can boost asset prices. Lowering rates, however, can also lead to problems such as inflation and liquidity traps, which undermine the effectiveness of low rates.

Step-by-step explanation:

Answer:

1. A sole proprietorship is distinguished by the fact that it has

Answer - only one owner.

2. James would like to create a sole proprietorship operating under the name Super Lawn Care. Which of the following is true?

Answer - James will need to register the business with his local state as the name of his business differs from his own.

3. A recent high school graduate would like to establish an online tutoring service as a sole proprietorship operating under her own name. Having never worked before and having no current income, which of the following hurdles is she likely to face?

Answer - It will be difficult to cover start-up costs since banks will be unlikely to loan her money.

4. What is a subsidy?

Answer - a government payment to a business to generate employment and economic growth

5. Explain whether the Federal Reserve reducing interest rates helps to expand economic growth.  

Answer - Reducing interest rates helps the economy expand because it lowers the cost of borrowing for business to expand, leading to more jobs and economic growth.

Step-by-step explanation: I just took the test and got it right

Answer: [tex]a=110^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem,

[tex]a+15^{\circ}=125^{\circ}\\\\a=110^{\circ}[/tex]

  The algebraic expression or sigma (summation) notation is given by:

∑ = 22(105 - 71)/2

And its value is ∑ = 374

 The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

  The equation for this type of problem is:

∑ = n(a1 + an)/2

  Our values are:

105+97+89+ . . . . . . +(-71)

∑ = 22(105 - 71)/2

∑ = 22(34)/2 = 11(34)

∑ = 374

Learn more about arithmetic series in:

https://brainly.com/question/24295771

#SPJ4

Answer:

x(x+8)=84

x² + 8x = 84

x² + 8x - 84 = 0

(x+14) (x-6) = 0

x= -14 or 6

Perimeter = 40 in.

The total area of given polyhedron is 68.75 sq. units

The given polyhedron is made up of 1 square, 2 triangles, and 2 rectangles.

Firstly. the dimensions of triangle are -

base = 2.5 units,

height = 3.5 units

area of the triangle = 1/2 × B × H

= 1/2 × 2.5 × 3.5

= 4.375 sq. units

The area of 2 triangles will be - 2 (area of 1 triangle)

⇒ 2× 4.375

= 8.75 sq. units

Area of Rectangle 1 = L × B

Length = 5 units

Breadth = 3 units

Area = 5×3 = 15 sq. units

Area of Rectangle 2 = L × B

Length = 5 units

Breadth = 4 units

Area = 20 sq. units

Area of square = Side²

⇒ 5 × 5

= 25 sq. units

Total area of polyhedron = Area of 2 triangles + Area of 2 Rectangles + Area of square

⇒ 8.75 + 15 + 20 + 25

= 68.75 sq. units

To learn more about area from given link

https://brainly.com/question/25292087

#SPJ9

Answer:No

Step-by-step explanation:

It does not

Answer:

No

Step-by-step explanation:

given 3 sides of a triangle

using the converse of Pythagoras' identity

if the square of the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.

longest side = 35 and 35² = 1225 , then

15² + 15² = 225 + 225 = 450

since 1225 ≠ 450 then the 3 sides do not form a right triangle.

We have proved that all circles are similar.

It is given that there are some circles.

We have to prove that all circles are similar.

What is the locus of a circle ?

The locus of a circle is the set of points on a plane at the same distance from the center point.

As per the question ;

We have to prove that all circles are similar.

We know that ;

A circle is a geometric shape in which the outside points are all equidistant from a center point.

Let's assume there are two circles and the radius of circle A is a and circle B is b .

If we center the circles on the same point, we found that by multiplying the radius of Circle B which is b by an unknown value x will give the radius of Circle A which is a.

and

The scale factor will be ;

bx = a

or

x = a / b

We know that dilation makes the shape bigger or smaller.

So , we have satisfied the definition of similarity and we can conclude Circle A is similar to Circle B.

and

This can also be considered for all circles and thus it states that all circles are similar.

Thus , we have proved that all circles are similar.

To learn more about similarity of circle click here ;

https://brainly.com/question/1395091

#SPJ4

Energy and mass are related by the formula, E = mc², where m is the mass of the object and c is the speed of light. The equation that finds m, given e and c, is:   m = E/c²

The equation, E = mc² was coined from Albert Einstein's theory of relativity, which shows the relationship between mass and energy. It shows that energy and mass can be interchanged into each other. The equation tells us that if we multiply the mass of a body (m) with the square of the speed of light (c²), we will get the total amount of energy (E) contained in that body, which can potentially be converted to other forms of energy.

However, if are given the energy contained in a body and the speed of light, then told to find the mass of the body, we will divide the equation by the coefficient of m. The coefficient of m in the equation is c², thus:

                          E = mc²

                          E/c² = mc²/c²

   c² divided by c² is 1, therefore, the new equation is:

                               m = E/c²

 Thus, the equation that finds m, given e and c is m = E/c².

Learn more about energy and mass here:

https://brainly.com/question/15219830

#SPJ4                    

Step-by-step explanation:

You only need to change the x for a 3

Answer:

$85

Step-by-step explanation:

y=5x+40

x=weeks

y=total money

y=5(9)+40

y=45+40

y= 85

The probability will:

a) Increase.

b) decrease.

c) increase.

We know that as larger is the size (or the diameter at least) of the hole, the easier will be to lading the skee ball on that hole.

So "If the size of the 40-point hole is enlarged, the probability... "

If you increase the size, then it will be easier to land the ball, thus we can conclude that the probability will increase.

" If the 40-point hole is made smaller, the probability..."

Opposite as the case above, this time will be harder to land the ball, thus the probability will decrease.

"If the 40-point hole stays the same size, but the scoring zone is made smaller, the probability..."

If the ball is thrown in a random way, such that the probability of landing in any region of the scoring zone is the same, then the probability of landing on the 40-point hole is equal to the quotient between the area of the hole and the total area of the scoring zone.

Thus, is you decrease the area of the scoring zone, then the probability increases.

If you want to learn more about probability.

https://brainly.com/question/25870256

#SPJ1

Answer: The probability will:

a) Increase.

b) decrease.

c) increase.

Answer:

12 meters below sea level?

Step-by-step explanation:

Not entirely sure if that is what the question is asking...

Answer: -12 meters

Step-by-step explanation:

umm lol

Answer:

Myrna's Farms

Step-by-step explanation:

Fouster's Farms has 5^3 = 5 x 5 x 5 = 125 fruit trees

Myrna's Farms has 5x times this many trees = 5 x 125 = 625

commercial farm has 500 fruit trees

So Myrna's Farms has the most trees = 625

Use the kinematic formula

[tex]{v_2}^2 - {v_1}^2 = 2a\Delta x[/tex]

where [tex]v_1,v_2[/tex] are initial/final velocities, [tex]a[/tex] is acceleration, and [tex]\Delta x[/tex] is displacement. We're given [tex]a=-5.00\frac{\rm m}{\rm s^2}[/tex] and [tex]\Delta x=15.0\,\rm m[/tex], and the car comes to a stop so [tex]v_2=0[/tex]. Solve for [tex]v_1[/tex].

[tex]-{v_1}^2 = 2\left(-5.00\dfrac{\rm m}{\rm s^2}\right) (15.0\,\mathrm m) \\\\ ~~~~ \implies {v_1}^2 = 150.\dfrac{\rm m^2}{\rm s^2} \\\\ ~~~~ \implies v_1 = \sqrt{150.\dfrac{\rm m^2}{\rm s^2}} \approx \boxed{12.2 \dfrac{\rm m}{\rm s}}[/tex]

According to the question, the given data are as follows:

Zoe’s distance = ZZ(miles); Stadium time = tt (hours); Mackenzie’s distance = MM(miles)

Distance between Zoe and stadium = 249 miles

Distance between Mackenzie and stadium = 237 miles

Zoe speed = 58 miles per hour

Mackenzie speed = 55 miles per hour

Time = 2 hours

Using standard distance formula:

Distance = (speed)(time)

As per relative speed, distance gets added and speed gets subtracted when objects are away or parallel from each other.

ZZ = 249 -58tt

MM = 237 -55tt

When both are at the same distance, the time will be t = 4 hours

249 -58tt = 237 -55tt

tt = 4 hours

What is distance?

Distance can be defined as the resultant displacement between two points. It can be calculated in different units like kilometers, meters, miles etc. Based on direction, the distance formulas change.

To learn more about time, speed and distance from the given link:

https://brainly.com/question/26046491

#SPJ1

x = 107.1 is the value of x.

To find the value of x:

So,

Then rounding to the nearest tenths gives x = 107.1.

Therefore, x = 107.1 is the value of x.

Know more about the values here:
https://brainly.com/question/27944341

#SPJ4

YES ,The condition can result in more than one triangle.

We may comprehend the characteristics of this shape by using triangle laws and theorems. Triangles have a variety of geometric principles because they are one of the fundamental components of trigonometry. These assist us in separating right triangles from isosceles and equilateral triangles, among other things.

According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side. See the acute triangle's side lengths below. The two shortest sides, 6 and 7, add up to a total length of 13. That measurement exceeds the longest side's length of eight.

YES ,The condition can result in more than one triangle because as rule of side of triangle largest side is more than other to sides would if two sides a given from multiple triangle by changing their angles

learn more about triangles here :

brainly.com/question/25813512

#SPJ1

Answer:

Point (0, 0) satisfies the inequalities

Step-by-step explanation:

Sometimes graphing is the best way to determine where the region is that satisfies both inequalities. Then you can choose a point accordingly

The graph of both inequalities is attached. The heavily shaded region in blue represents the region that satisfies both inequalities

If you look at the graph, you can see that (0, 0) falls in the heavily shaded region and therefore it satisfies both constraints

Indeed at (0, 0)

7(0) + 2(0) = 0 which is > -4 since 0 is greater than all negative numbers

Also
-5(0) + 6(0) = 0 which is indeed ≤ 6

So one point is (0, 0)

Answer:

11.8

Step-by-step explanation:

I simply just did multiplication

I multiplied the whole numbers alone and did the same with the fraction

Example: -2*-4=8

2/3*3/7

then you add the two products and get your answer

Answer:

3

Step-by-step explanation:

The two terms of each arithmetic sequence an=a1+(n-1)d are  2,7,12,17,..., 52.

an=a1+(n-1)d

a1=2

a2=2+5=7

a3=7+5=12

a4=12+5=17

a11=2+(11-1)*5=2+10*5=2+50=52

so terms are 2,7,12,17,..., 52

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

To learn more about arithmetic sequence from the given link:

brainly.com/question/15412619

#SPJ4

The distance round a polygon, which include a rectangular or a rectangle, is referred to as the perimeter (P). On the alternative hand, the space round a circle is called the circumference (C). Therefore, the circumference of a circle is the linear distance of an fringe of the circle.

What is the formula here we use to calculate the equation:

[tex]c^{2} =a^{2} +b^{2}[/tex]

Find the solution:

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]x^{2} =7^{2} +3^{2}[/tex]

[tex]\sqrt{x} ^{2} =49+9[/tex]

[tex]x=\sqrt58[/tex]

To learn more about the equation refer:

https://brainly.com/question/28565833

#SPJ4

An equation that could represent a linear combination of the system with  no solution is: B) 0 = 26.

In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.

From the information provided above, we have this system of equations:

2x/3 + 5y/2 = 15     ........equation 1

4x + 15y = 12           ........equation 2

Multiplying equation 1 by 6, we have:

6 × (2x/3 + 5y/2 = 15)

4x + 15y = 90      ......equation 3

Subtracting the equation 3 from equation 2, we have:

(4x - 4x) + (15y - 15y) = (12 - 90)

0 + 0 = -78

0 = -78  ≡ 0 = 26.

Read more on equation here: https://brainly.com/question/28148072

#SPJ1

Complete question:

The system of equations below has no solution.

2x/3 + 5y/2 = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

A) 4/3x=42

B) 0 = 26

C) 15/2y=33

D) 0=0

Answer:

Based on the information given the rate of return is 10.8%.

First step is to find the shares of stock price:

Shares of stock price=25 shares×$30/share

Shares of stock price= $750

Second step is to calculate the total sold price:

Total sold price= $825+$6

Total sold price= $831

Third step is to calculate the Rate of return:

Rate of return=$831-750/$750×100

Rate of return=$81/$750×100

Rate of return=10.8%

Inconclusion the rate of return is 10.8%.

The line q passes through (2, 0) and (-7, -4)

If line Q does not intersect the line LM, then these lines are parallel, thus, have the same slope.

The slope of line LM is given by:

s = (3 + 4)/(2 + 4) = 7/6

Now we know that the line Q contains point N (2, 0) ( i will assume is this because in the image the points don't have the correspondent names).

Then the line also passes through another point (a, b) such that:

s = (0 - b)/(2 - a) = 7/6

Then:

b = -7

a = -4

The line q passes through (2, 0) and (-7, -4)

learn more about parallel lines.

https://brainly.com/question/24607467

#SPJ1

The required value of constant of variation, k for which x and y vary directly is 6.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is y - 6x = 0

y = 6x

On comparing it with equation 1, we get,

k = 6

Hence, the required value of constant of variation is 6.

To learn more about the constant of proportion, visit the link:

https://brainly.com/question/24868934

#SPJ4

Under unitary method -  168Minutes did it take her to paint one room

If it took 14 hours to paint 5 rooms and we need to find  how many

Minutes did it take her to paint  one room, we need to know  how much time taken to paint a room

this can be obtained using unitary method

so time taken to paint one room is time taken to paint 5 rooms divided by  number of rooms

                       = 14 hours /5

                      =2.8 hours

As we need answer in  unitary method minutes we are required to convert hours into minutes which can be done  by multiplying with the number of minutes in an hour that is 60

Minutes did it take her to paint one room = 2.8 hours × 60

                                                                   =168 minutes

To know more about  unitary method- https://brainly.com/question/28276953

#SPJ9