Four Representations: Equations, Tables, Words,
WARM-UP and Graphs
Select the words that best describe the given
equation Y = X-1
DONE
w the following questions, look at different ways to
represent the relation given by the
equation y = x2 - 1.
Which graph represents the relationship?
The table below shows some values for the given
equation. Find the values of a and b.
a =
Nyt
Intro

If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).

Note: (f•g)(x) means f(x) times g(x).

(f•g)(x) = (5x^3)(x + 1)

(f•g)(x) = 5x^4 + 5x^3

Answer: Choice C

Answer:

slope rise 3 run 2 1/2

Step-by-step explanation:

if you start from the bottom and if you start from the top it's -3 and -2 1/2

Answer: The slope is 3 and the y-intercept is 3/2

Step-by-step explanation:

The slope of a linear function can be calculated as:

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

Where y2 = f(x2) and y1 = f(x1) and f(x) is the linear function.

So here we can use any two pairs of the set of data, for example, the first two.

(-1 , -3/2) and (-1/2,0)

s = (0 -(-3/2))/(-1/2 - (-1)) = (3/2)/(1/2) =(3/2)*(2/1) = 3

So the slope is equal to 3.

the y-intercept is the value of y when x = 0, in the table we can see that when x = 0. the value of y = 3/2

So the function is: y = 3*x + 3/2

and the correct option is the fourth one.

Answer:

[tex]y = \frac{1}{2}x+10[/tex]

Step-by-step explanation:

The given path is:

y = -2x+5

Comparing with the standard form of equation:

y = mx+b

So,

m = -2

We know that product of slopes of two perpendicular lines is -1

Let m1 be the slope of the perpendicular line

m*m1=-1

-2*m1 = -1

m1 = -1/-2

m1 = 1/2

So the slope of perpendicular path is 1/2.

Since the new path passes through (-2,9)

[tex]9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10[/tex]

Putting the values of m and b in standard form

[tex]y = \frac{1}{2}x+10[/tex]

Hence the equation of new path is:

[tex]y = \frac{1}{2}x+10[/tex] ..

bearing in mind that the average rate of change = slope, and for that we can simply use two points off the table.

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -2&12\\ 0&3\\ 3&-10.5\\ 7&-28.5\\ \cline{1-2} \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-10.5}) \\\\\\ slope \implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10.5-12}{3-(-2)} \\\\\\ \cfrac{-10.5-12}{3+2}\implies \cfrac{-22.5}{5}\implies -\cfrac{4.5}{1}\implies -4.5 \end{array}[/tex]

The rate of change of y with respect to x for the given function with coordinates expressed in the table is; dy/dx = -9/2

The rate of change of y with respect to x for a given linear function is simply the slope expressed as;

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates which are;

(-2, 12) and (0, 3)

Thus;

dy/dx = (3 - 12)/(0 - (-2))

dy/dx = -9/2

Or dy/dx = -4.5

Read more at; https://brainly.com/question/19378449

Answer:

y+3 = -7/5(x+2)

Step-by-step explanation:

First we need to find the slope

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

   = (4--3)/(-7--2)

  = (4+3)/(-7+2)

  =7/-5

  = -7/5

The point slope form is y-y1 = m(x-x1)

y--3 = -7/5(x--2)

y+3 = -7/5(x+2)

We could use the second set of points

y-4 = -7/5(x--7)

y-4 =-7/5(x+7)

Answer:

5, 11,17,23,29

Step-by-step explanation:

To obtain the term in the sequence add the common difference to the previous term, that is

a(1) = 5

a(2) = 5 + 6 = 11

a(3) = 11 + 6 = 17

a(4) = 17 + 6 = 23

a(5) = 23 + 6 = 29

The first five terms of an arithmetic sequence starting with 5 and a common difference of 6 are 5, 11, 17, 23, and 29.

The first five terms of the arithmetic sequence with the first term 5 and a common difference of 6 can be found by successively adding the common difference to the previous term.

Third term (a3) = a2 + 6 = 11 + 6 = 17

Fifth term (a5) = a4 + 6 = 23 + 6 = 29

Therefore, the first five terms of the arithmetic sequence are 5, 11, 17, 23, and 29.

Answer:

x = -8  &  x = 3

Step-by-step explanation:

Vertical asymptote occur when denominator is 0.

So to find the x-values, we need to middle term factor the denominator. Shown below:

[tex]x^2+5x-24\\=(x+8)(x-3)\\x=3, -8[/tex]

Thus, at x = 3 and at x = -8  --  there is vertical asymptote.

Answer:

The value of x is 55 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- It has 4 equal sides

- Every two opposite sides are parallel

- Every two opposite angles are equal

- Every two adjacent angles are supplementary (their sum is 180°)

* Now lets solve the problem

- A square divided into two rectangles

- Each rectangle contains a shaded rhombus

- The shaded rhombus has two adjacent angles their measures are

 (2x + 20)° and 50°

∵ Every two adjacent angles in the rhombus are supplementary

∵ The sum of the supplementary angles = 180°

∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°

- lets put the equation and solve it to find x

∴ (2x + 20)° + 50° = 180° ⇒ add the like terms

∴ 2x + 70° = 180° ⇒ subtract 70° from both sides

∴ 2x = 110° ⇒ divide both sides by 2

∴ x = 55°

* The value of x is 55

Answer: b,c,e or 2,3,5

Step-by-step explanation:

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]

We replace:

[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]

Thus, the distance between the two points is 25 units.

Answer:

25

Answer:

The distance is 25 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)

Distance = √[(x2 - x1)² + (y2 - y1)²]

= √[(21 - -3)² + (11 - 4)²]

= √[(21 +3)² + (11 - 4)²]

= √[24² + 7²]

 = √(576 + 49)

 = √625

 =25

Therefore the distance is 25 units

Answer:

True options:

[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]

Side Q'S' lies on a line with a slope of -1.

The distance from Q' to the origin is twice the distance from Q to the origin.

Step-by-step explanation:

Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule

[tex](x,y)\rightarrow (2x,2y)[/tex]

So,

[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]

True options:

[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]

Side Q'S' lies on a line with a slope of -1.

The distance from Q' to the origin is twice the distance from Q to the origin.

False options:

QR is longer than Q'R', because QR is twice shorter than Q'R'.

The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).

Answer:

1, 2, 5 on Ed

Step-by-step explanation:

Answer:

5.6b + 3.4a

Step-by-step explanation:

Simply evaluate be match each term with its corresponding variable, and watch out for where you have to distribute negatives, meaning that you have a couple of double negatives in there.

Double Negative = Positive

Answer:

it’s C and E

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]

[tex]\text{Percentages (\%) usually run out of 100}[/tex]

[tex]\text{First, put the numbers set to multiply from each other.}[/tex]

[tex]\text{7\%}\times\text{14.50}[/tex]

[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]

[tex]\dfrac{7\%}{100}[/tex]

[tex]\dfrac{7\%}{100}=0.07[/tex]

[tex]\text{Next, solve for your answer.}[/tex]

[tex]\text{0.07}\times\text{14.50 = ?}[/tex]

[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]

[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

The expression can be simplified to [tex]625 \times (uv)^4.[/tex]

To rewrite the expression (-5uv)(-5uv)(-5uv)(-5uv) using the properties of exponents, you can consolidate it using the exponent rule that states when you multiply numbers with the same base, you add the exponents. In this case, the base is -5uv, and you are multiplying it four times, so the exponent is 4:

[tex](-5uv)(-5uv)(-5uv)(-5uv) = (-5uv)^4[/tex]

Now, you can simplify further by applying the rule for raising a power to a power, which states that when you raise an exponentiated term to another exponent, you multiply the exponents:

[tex](-5uv)^4 = -5^4 \times (uv)^4[/tex]

-5^4 means -5 multiplied by itself four times:

[tex]-5^4 = -5 \times -5 \times -5 \times -5 = 625[/tex]

So, the expression can be simplified to:

[tex]625 \times (uv)^4[/tex]

This is the expression rewritten using the properties of exponents.

for such more question on expression

https://brainly.com/question/1859113

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Answer:

The correct answer is R(2, 4)

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

ok, so, the line below says HJ is (x+1) units long. therefore:

2x-16+8 = x+1

now, let's isolate the variable.

2x-x = 1+16-8

x = 9

since we now defined variable x, we can add it to the equation that determines the length of HI.

2x-16

2(9)-16

18-16

2

the length of line segment HI is 2 units

hope this helped!

HI + IJ = HJ

With this knowledge you can from an equation like so...

2x - 16 + 8 = x + 1

Now combine like terms and solve for x

2x + (- 8 + 8) = x + 1 + 8

2x = x + 9

2x - x = x - x + 9

x = 9

To find HI plug 9 in for x and simplify

2(9) - 16

18 - 16

2

The length of HI is 2!!!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The scale factor is equal to 1/2

The dimensions of each channel when splits the screen is 46 in x 38 in

Step-by-step explanation:

we know that

The dimensions of the new television is 92 in x 76 in

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

A1 -----> the area of the new television

A2 ----> the area of each channel when splits the screen

z-----> the scale factor

[tex]z^{2} =\frac{A2}{A1}[/tex]

we have that

The area of the new television is 4 times the area of each channel

[tex]A1=4A2[/tex]

[tex](A2/A1)=1/4[/tex]

[tex]z^{2} =\frac{1}{4}[/tex]

[tex]z=\frac{1}{2}[/tex] -----> the scale factor

so

When splits the screen, the dimension of each channel is equal to

92/2 in x 76/2 in

so

46 in x 38 in

Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides

Verify the value of the scale factor

92/46=1/2

or

76/38=1/2

Answer: ≈ 1.414

Step-by-step explanation:

You can use the pythagorean theorem, a^2 + b^2 = c^2

a^2 and b^2 are the legs and c^2 is the hypotenuse.

1^2 + 1^2 = c^2

1 + 1 = c^2

2 = c^2

√ 2 = √ c^2

c = ≈ 1.414

Answer:

y = (-1/2)x -3

Step-by-step explanation:

We are given

y = 2x-17

which is in slope-intercept form: y = mx +b

Where m is the slope. so, m= 2

But this is perpendicular, When a line is perpendicular then the slope become -1/m so in our case the slope m will be = -1/2

Using the point(-8,1) we can find the b i.e the y intercept

We have x = -8, y =1 and m=-1/2

y = mx + b

1 = (-1/2)(-8) + b

1 = 4 + b

=> b = 1-4

b = -3

The equation of slope intercept form will be

y = mx + b

Putting value of m= -1/2 and b = -3

y = (-1/2)x -3

Answer:

The answer is 25

Step-by-step explanation:

Answer:

4^8

Step-by-step explanation:

Because both expressions have the same base, we can add the exponents to simplify the expression:

[tex]4^5*4^3 = 4^{5+3} = 4^8[/tex]

Answer: 4^8 or 65,536

Step-by-step explanation:

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.

Answer:

Step-by-step explanation:

x + 3y = 28

Put x = 28 and solve for y:

28 + 3y = 28           subtract 28 from both sides

28 - 28 + 3y = 28 - 28

3y = 0          divide both sides by 3

3y : 3 = 0 : 3

y = 0

Answer:

Step-by-step explanation:

Compare y = (1/2)x - 3 and y = (-1/2)x - 3.

They have different slopes but the same y-intercept (0, -3).  Eliminate the first answer choice.

They have different slopes.  Eliminate the second answer choice.

Their graphs intersect, so they have a solution.  Eliminate the third choice.

They have different slopes but the same intercept, so they have one solution.  The fourth answer choice is the correct one.

Answer:

the fourth one is the corect one

Step-by-step explanation:

the fourth one is the corect one because i did the mathand i checked it twice and its right and also i asked my friend and he said it the fourth one

hope that helps you

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (10, 1) into the partial equation

1 = 30 + c ⇒ c = 1 - 30 = - 29

y = 3x - 29 ← in slope- intercept form

Subtract y from both sides

0 = 3x - y - 29 ( add 29 to both sides )

29 = 3x - y, thus

3x - y = 29 ← in standard form → B

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The dominant term of this function is x^4.  The graph of x^4 starts in Quadrant II and continues in Quadrant I.

If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV.  This is the end behavior for f(x)=-x^4+5x^3-3.

Find  the cost of the chair and desk by multiplying the total amount pent by the 70%

Chair and desk = 900 x 0.70 = $60

Subtract that cost from the total spent:

900 - 630 = $270 was spent on the other three items.

Subtract the cost of the bookshelf:

270 - 50 = 220

The two tables cost 220.

For the price of one table divide that cost by 2:

220/2 = 110

One table cost $110.

The cost of each table is $110.

Given that

There are five items i.e. chair, bookshelf, 2 tables, and a desk.

The total amount incurred for these 5 items should be $900.

And, the chair + desk = 70% of total.

The cost of the bookshelf is $50.

Since 70% of total = chair + desk

That means

Chair + desk = 0.70 of $900 = $630

So the other items cost should be

= $900 - $630

= $270

And, the cost of bookshelf is $50

So, the two tables cost should be

= $270 - $50

= $220

So for one it should be

= $220 ÷ 2

= $110

Therefore we can conclude that the cost of each table is $110.

Learn more about the cost here: brainly.com/question/5282141

Answer:

Step-by-step explanation:

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Answer:

Adjacent angles formed by two intersecting lines form a linear pair.

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect. A linear pair of angles must add up to 180 degrees.

If two angles are adjacent angles that are formed by two intersecting lines, then they are called linear.

Answer:B. vertical line symmetry

Step-by-step explanation:

Answer:

D. diagonal line symmetry

Step-by-step explanation:

Answer:

C D and E

Step-by-step explanation:

The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work

Log(4^(x + 3)) = Log(18)

(x + 3) Log(4) = log (18)

(x + 3) * 0.6021 = 1.2553

x + 3 = 1.2553/0.6021

x + 3 = 2.08496

Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.

You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy.  It does say possible first steps.

Answer:

C.Take the base-4 logarithm of each side.

D.Take the natural logarithm of each side.

E. Take the common logarithm of each side.

Step-by-step explanation: