which matrix equation represents the system of equations?

The rational expression [tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2}[/tex] using the least common denominator is [tex]\dfrac{5 + 5x}{4x^2}[/tex]

How to express the rational expression using the least common denominator?

From the question, we have the following parameters that can be used in our computation:

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2}[/tex]

Take the LCM of the expression

So, we have

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{x + 1 + 4(x + 1)}{4x^2}[/tex]

Expand the bracket

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{x + 1 + 4x + 4}{4x^2}[/tex]

So, we have

[tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{5 + 5x}{4x^2}[/tex]

Hence, the rational expression using the least common denominator is [tex]\dfrac{x + 1}{4x^2} + \dfrac{x + 1}{x^2} = \dfrac{5 + 5x}{4x^2}[/tex]

Answer:

f(x) = (x + 3) - 7

Step-by-step explanation:

the original function f(x) = x - 9 is the parent function f(x) = x shifted down 9 units

from f(x) = x - 9, we are told that the function is shifted 2 units up, this is a vertical shift. so we add 2 to -9

-9 + 2 = -7

we now have f(x) = x - 7

next we are told that the function is shifted 3 units to the left. this is a horizontal shift. a horizontal shift looks similar to this:

f(x) = (x ± b)

if a function is shifted to the left, we would use an addition sign. if it was going to the right, we would use a subtraction sign

the function looks like the following when we apply the above knowledge

f(x) = (x + 3) - 7 this would be our new function

The new function will be f(x) = (x + 3) - 9 + 2.

The function given is f(x) = x - 9. When this function is shifted 2 units up and 3 units to the left, the new function is obtained by transforming the original function accordingly.

Shifting up by 2 units means adding 2 to the function, and shifting 3 units to the left means substituting x+3  for x.

Thus, the new function, after applying the transformations, is:

f(x) = (x + 3) - 9 + 2

Simplifying the above transformation, we get:

f(x) = x - 4

Answer:

slope   3/5

Step-by-step explanation:

3x − 5y − 6 = 0

To find the slope, we want to solve for y

(y = mx+b   slope intercept form of the equation(

Add 5y to each side

3x − 5y+5y − 6 = 0+5y

3x-6 = 5y

Divide by 5

3/5x -6/5 = 5y/5

3/5 x -6/5 = y

The slope is 3/5 and the y intercept is -6/5

In tandem with general linear equation, the slope of the equation is 3/5

Another name for slope is gradient. From the general linear equation,

Y = mx + c

To determine the slope of the line 3x − 5y − 6 = 0,

Make y the subject of formula and make the equation in line with general linear equation.

5y = 3x - 6

y = 3x/5 - 6/5

Therefore, from the equation above, the slope is 3/5

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Answer:

56

Step-by-step explanation:

Let's say that D is the point where AB is split, so AD = x-6 and DB = x.

And let's say that E is the point where AC is split, so AE = x+6 and EC = x+20.

Triangle ADE is similar to triangle ABC.  Therefore:

(x-6) / (x-6 + x) = (x+6) / (x+6 + x+20)

Solving:

(x-6) / (2x-6) = (x+6) / (2x+26)

(x-6) (2x+26) = (x+6) (2x-6)

2x² + 26x - 12x - 156 = 2x² - 6x + 12x - 36

2x² + 14x - 156 = 2x² + 6x - 36

14x - 156 = 6x - 36

8x = 120

x = 15

So the length of AC is:

AC = x+6 + x+20

AC = 2x + 26

AC = 2(15) + 26

AC = 56

Still don't know what the given line is, so I'm just going to attach images of the graphs of each equation.

Graph 1: y = -2x

Graph 2: x = 4

Graph 3: y = x

Graph 4: y = 3

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\boxed{1gal.=4qt.=8pt.=16c}\\\\1pt.=2c.\Rightarrow 2c.=1pt.\\\\1qt.=8pt.\to1pt.=\dfrac{1}{8}qt.\Rightarrow2pt.=2\cdot\dfrac{1}{8}qt.=\dfrac{1}{4}qt.\\\\1gal=4qt.\Rightarrow4qt.=1gal.[/tex]

Answer:

30.5

0<h<10 =5

10<h<20 =15

20<h<30 =25

30<h<40 =35

40<h<50 =45

50<h<60 =55

multiply by frequency

5*1=5

15*4=60

25*7=175

35*2=70

45*3=135

55*3=165

add

=610

610 divided by 20 =30.5

The question is best categorized under Computers and Technology for a high school-level student, focusing on SEO and HTML formatting skills, which are crucial in the field of digital communication.

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In constructing a detailed response to such a question, it is important to always provide more than 100 words and to ensure that all information provided is accurate, informative, and includes relevant details and examples. When approaching tasks like these, the exercise in SEO and HTML formatting provides practical skills that can be applied in many areas of digital communication and content creation.

Answer:

The Answer is C. 35 in

Step-by-step explanation:

This is easy 5 x 7 = 35

I'll help you!

The y intercept is simple where the line touches the Y-Axis (the one going up and down  ↑↓)

In this case the y intercept is (+3)

Answer:

(-8+i )

Step-by-step explanation:

We'll multiply these 2 binomials like any other pair of binomials: using the FOIL method.

(-3+2i)•(2+i) after being FOILed is:

(-3•2)+(-3•i)+(2i•2)+(2i•i)

this equation simplified equals

-6-3i+4i+2i²

Whenever we see i², we should know that is equals -1, so our equation rewritten again is

-6-3i+4i+(2•-1)

Simplifying that, we get

-6-3i+4i+-2

From here, we just continue to simplify by subtracting  2 from −

6.

−8−3i+4i

Finally, add −3i and 4i to get our answer of

−8+i

Answer: Your slope would be 0

Step-by-step explanation: Why? Because the X coordinate does not change only the Y coordinate if the X or Y coordinate does not change but the other does your slope is always 0.

Answer:

there is no slope

Step-by-step explanation:

There is no slope because the line would be vertical and a vertical line can not have  a slope

ANSWER

The circumcenter is (2,1)

EXPLANATION

The midpoint of BC is (-3,2)

The equation of the perpendicular bisector of BC is x=2

The midpoint of AB is (-1,1)

The midpoint of AB is (-1,1)

The perpendicular bisector of AB is y=1.

These two lines intersect at (2,1).

The point of intersection of the perpendicular bisectors of a triangle is called the circumcenter of the triangle.

Based on the graph, the coordinates of the circumcenter of this triangle are (2, 1).

In Mathematics and Euclidean Geometry, a circumcenter is the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect.

This ultimately implies that, the circumcenter of any triangle is always equidistant from all the rays (vertices) of that triangle.

By critically observing the graph of triangle ABC, we can logically deduce the following parameters;

Based on the equation of the perpendicular bisector of BC and AB, the coordinates of the circumcenter are (2, 1).

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it might be wrong but i am pretty sure it’s right but 537.15

Answer:

The estimated volume would be 594 feet.

Step-by-step explanation:

Well, since this is an estimate you should round all your numbers and multiply them together.

5.6 is rounded to 6

8.8 is rounded to 9

and 10.9 is rounded to 11

Multiply 6 and 9 and you get 54. Then multiply 54 by 11 and that gives you 594.

- Your freshman friend :)

Taken together, these three facts imply that triangles AOB and COB are congruent (side-side-side congruence postulate).

Now, it's not exactly clear whether A and C lie on the same line (it's possible that the figure is not drawn to scale). If they do, then both angles AOB and COB are right angles, so angle BOK has measure 45º, and so [tex]m\angle AOK=135^\circ[/tex].

By applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

Recall the Theorem of Isosceles Triangle:

We would apply the above stated to solve the problem given.

We know the following:

We can deduce that:

m<AOK = m<AOB + m<BOK

m<AOK = 90 + 45

m<AOK = 135 degrees.

Therefore, by applying the theorems of an isosceles triangle and an angle bisector, m<AOK = 135 degrees.

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Answer:

P(-2,7)

P'(-2,-7), ANSWER

reflection across the x-axis rule:

(×,y) ===> (x,-y)

Easy way to do this is draw the point on graph paper and count the same units above/below the x-axis. This example you are 7 units above the x-axis so you would count 7 units below the x-axis giving you the point.

Reflection of a point across an axis involves flipping the sign of the coordinate for that axis. So the reflection of point P(-2,7) on the x-axis is P'(-2,-7).

The concept described in your question refers to the reflection of a point across the x-axis. Given a point P(-2,7), the reflection of this point across the x-axis, denoted as Rx-axis(P), reverses the sign of the y-coordinate. This happens because a reflection is a transformation that flips a figure across an axis of reflection.

So, if we consider P(-2,7) to reflect about the x-axis, we just switch the sign of y-coordinate. Therefore reflection of point P(-2,7) about x-axis will be P'(-2,-7).

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The base is 11 cm and the height is 8 cm.

Step-by-step explanation:

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First, rearrange the equations:

[tex]x + y = 0[/tex]

[tex] - x + y = - 1[/tex]

Then, do equation 1 minus equation 2 to cancel y:

[tex]x - - x = 2x[/tex]

[tex]0 - - 1 = 1[/tex]

[tex]2x = 1[/tex]

[tex]x = \frac{1}{2} [/tex]

Substitute x to find y:

[tex]y = - x = - \frac{1}{2} [/tex]

So the point of intersection is (1/2, -1/2), which is represented by graph 1.

Answer:

Given system of equations,

y = - x   ------(1)

y = x - 1 ------(2),

From equation (1) and (2),

-x = x - 1

-x - x = -1

-2x = -1

[tex]\implies x = \frac{1}{2}[/tex]

Again from equation (1),

[tex]y = -\frac{1}{2}[/tex]

Thus, the intersection point of the lines (1) and (2), is [tex](\frac{1}{2}, -\frac{1}{2})[/tex]

Hence, the below graph represents the solution to the system of equations.

Answer:

Option C. AB/BC=CD/DE

Step-by-step explanation:

we know that

In the triangle ABC the slope is equal to

m=AB/BC -----> equation A

In the triangle CDE the slope is equal to

m=CD/DE -----> equation B

Remember that the slope of a line is a constant

so

equate equation A and equation B

AB/BC=CD/DE

Answer:

C is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

√2= 1.414 because ; (1.414)² =1.999396≃2

Answer:

b

Step-by-step explanation:

Look at the pattern

Answer: A and B are independent events if P(A∩B)=P(A).P(B)=0.15.

Step-by-step explanation:

Let A be the event that a shopper buys bread.

Let B be the event that a shopper buys cheese.

So, P(A∪B)=100

Probability that a shopper buys bread during a visit to the grocery store =n 0.60

P(A) = 0.60

Similarly, Probability that a shopper buys bread = 0.25

P(B) = 0.25

Since A and B are independent then,

[tex]P(A\cap B)=P(A).P(B)=0.60\times 0.25=0.15[/tex]

So, A and B are independent events if P(A∩B)=P(A).P(B)=0.15.

When using the formula for the volume of a pyramid, substituting the given values of base area and volume results in a candy box height calculation of 20 inches.

The question asks about the height of a box of candy shaped like a triangular pyramid, given the volume and the area of the base. The volume of a pyramid is given by the formula V = 1/3 * Base Area * height. In this case, the box volume equals 120 in³, and the base area equals 18 in². We can use these values to solve for the height.

By rearrangement of the formula, height = V / (1/3 * Base Area). If we plug in the values, height = 120 in³ / (1/3 * 18 in²) = 20in. Therefore, the height of the candy box is 20 inches.

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The height of the candy box is 20 inches.

To find the height of the candy box, we need to use the formula for the volume of a triangular pyramid, which is V = (1/3) * A * h, where V is the volume, A is the area of the base, and h is the height.

We are given that the volume is 120 in³ and the area of the base is 18 in², so we can plug these values into the formula and solve for h.

120 = (1/3) * 18 * h

Simplifying the equation, we get:

360 = 18h

Dividing both sides by 18, we find that h = 20.

Therefore, the height of the candy box is 20 inches.

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Answer:

[tex]\left[\begin{array}{cc}7&1\\3&-3\end{array}\right][/tex]

Step-by-step explanation:

We simply add entry of each column of matrix 1 with its corresponding column entry of second matrix.

[tex]= \left[\begin{array}{cc}3&1\\0&-2\end{array}\right] + \left[\begin{array}{cc}4&0\\3&-1\end{array}\right]\\= \left[\begin{array}{cc}3+4&1+0\\0+3&-2+(-1)\end{array}\right]\\=\left[\begin{array}{cc}7&1\\3&-3\end{array}\right][/tex]

For this case we must add the following matrices:

[tex]\left[\begin{array}{ccc}3&1\\0&-2\end{array}\right][/tex]

And

[tex]\left[\begin{array}{ccc}4&0\\3&-1\end{array}\right][/tex]

Adding up:

[tex]\left[\begin{array}{ccc}3+4&1+0\\0+3&-2+(-1)\end{array}\right]=\\\left[\begin{array}{ccc}3+4&1+0\\0+3&-2-1\end{array}\right]=\\\left[\begin{array}{ccc}7&1\\3&-3\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}7&1\\3&-3\end{array}\right][/tex]

X^4 because it has 4 zeroes ( the graph crosses the x axis 4 times

The parent function of the given graph is:

                    Option: C

                   [tex]F(x)=x^4[/tex]

Since, the graph of the function has four real zeros this means that the parent function must be a function of degree four.

Also, we know that if the degree of the parent function would be odd then the end behavior of the graph ( i.e. the behavior of the graph when x tends to infinity and when x tends to minus infinity ) must be in opposite direction.

But here the graph is in the same direction.

Hence, the degree of the function is four i.e. even.

From the given choice the choice that best matches the condition is:

     [tex]F(x)=x^4[/tex]

Answer:

x = 2√7, y = √21

Step-by-step explanation:

The textbook has right angles, so we can use Pythagorean theorem to find the missing lengths.

For the triangle on top of the textbook:

c² = a² + b²

8² = 6² + x²

64 = 36 + x²

28 = x²

x = √28

x = 2√7

For the triangle on the side of the textbook:

c² = a² + b²

7² = x² + y²

49 = 28 + y²

21 = y²

y = √21

Answer:

314.25

Step-by-step explanation:

To find the total of all three checks, we add them together, lining up the decimals

 36.98

  17.27

260.00

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

314.25

The total is 314.25

Answer:

A. left parenthesis 3 comma 2 right parenthesis

Step-by-step explanation:

The point A is at (-2, 2)  which is 2 units to the left and 2 units up from zero

We want 5 horizontal units from A.  Horizontal means left and right

If we go 5 units to the right

(-2 +5 , 2) = (3,2)

If we go 5 units to the left

(-2 -5 , 2) = (-7,2)

Answer:

Because it is

Step-by-step explanation:

You don't need to. You can explain yourself using words but it takes ages that way. You use equations to solve problems, equations, and later on with functions and methods as you develop your math career. All I can say is, don't ignore it.

Answer:

An equation is the mathematical representation of those two things which are equal, one on each side of an 'equals' sign. Equations are useful to solve math problems in which multiple numbers are in the need of being solved.. Most of the times we take pre-algebra help to resolve real life problems.

Step-by-step explanation:

PLZZ MARK BRAINLIST!!!!!

The answer is B (6x-5)(x+2)

Answer:

B) (6x-5)(x+2)

Step-by-step explanation:

Distribute each until you find the answer:

A) 6x^2+17x+10

B) 6x^2+7x-10