Does this table represent a function? Why or why not?

Answer: First option. The slope is -4 and the y-intercept is 2.

Solution:

y=-4x+2

When the equation is in the form:

y=mx+b (y isolated)

The coefficient of the variable "x" is the slope "m" of the right line. In this case the coefficient of "x" is -4, then the slope "m" is -4.

The indeoendent term is the y-intercept "b". In this case the independent term is +2, then the y-intercept "b" is 2.  

Solution:

Given equation of line [tex]y=-4x+2[/tex].

The given equation is in the form of y=mx+b, y  is isolated. So the coefficient of x is the slope of the line.

The slope of the line y=-4x+2 is -4

To find the y-intercept of the equation, substitute [tex]x=0[/tex] in the equation,

[tex]\Rightarrow y=-4(0)+2\\\Rightarrow y=2[/tex]

So,  y-intercept of the equation is [tex](0,2)[/tex].

Hence, the slope is -4 and y intercept is 2. (first option)

The equation of the line through the given point parallel to the given line ...

The given line's equation is is slope-intercept form. The slope is -3, the coefficient of x.

In point-slope form, the equation of a line with slope m through point (h, k) is ...

... y -k = m(x -h)

For slope m=-3 and point (h, k) = (-4, -8) the equation of the line is ...

... y +8 = -3(x +4) . . . . equation in point-slope form

We can eliminate parentheses and add -8 to put this equation in slope-intercept form.

... y +8 = -3x -12

... y = -3x -20 . . . . equation in slope-intercept form

Answer:

Step-by-step explanation:

The answer is B

y=2x+11

2 7/8 ft

We presume no length was lost in the cut, so that ...

... (remaining length) + (cut off length) = (original length)

Then ...

... (cut off length) = (original length) - (remaining length)

... = 12 3/4 - 9 7/8

... = (12 - 9) + (3/4 - 7/8)

... = 3 + (6/8 -7/8)

... = 3 - 1/8

... = 2 7/8

The cut off length was 2 7/8 feet.

Answer:

d. (1, 3) and (-3, -1)

Step-by-step explanation:

Equating the expressions for y, we have ...

... x² +3x -1 = y = x +2

Subtracting x+2 gives ...

... x² +2x -3 = 0

... (x +3)(x -1) = 0 . . . . . factored form

... x = -3, 1 . . . . . . . . . . .values that make the factors zero

The second equation tells us, y = x+2, so

... For x = -3, y = -3 +2 = -1. The solution is (-3, -1)

... For x = 1, y = 1 +2 = 3. The solution is (1, 3)

(- 3, - 1 ) or (1, 3 )

Since both equations express y in terms of x, equate both sides

x² + 3x - 1 = x + 2 ( subtract x + 2 from both sides )

x² + 2x - 3 = 0

(x + 3 )(x - 1 ) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into either of the 2 equations for y

y = - 3 : y = - 3 + 2 = - 1 ( using y = x + 2 )

x = 1 : y = 1 + 2 = 3

solutions are (- 3, - 1 ) or (1, 3 )

Answer:

Area of the Scale drawing is [tex]72[/tex] square inches.

Step-by-step explanation:

First we need to convert feet and inches to a common unit. For that lets convert feet into inches.

1 feet = 12 inches

Therefore,

The length of the floor in inches:

[tex]36[/tex] feet = [tex]36*12[/tex] inches

                           =[tex]432[/tex] inches

The width of the floor in inches:

[tex]32[/tex] feet = [tex]32*12[/tex] inches

                           =[tex]384[/tex] inches

Now lets calculate by how many times the length has been scaled down:

432 inches of length has been reduced to 9 inches.

[tex]\frac{432}{9}=48[/tex]

So the length has been scaled down 48 times.

Now lets scale down the width 48 times:

[tex]\frac{384}{48} =8[/tex]

So the width of the Scale drawing is 8 inches.

Area of the Scale drawing = Scaled down length * Scaled down width

                                            =[tex]9*8[/tex]

                                            =[tex]72[/tex] square inches

Answer:

72 square inches.

Step-by-step explanation:

Convert feet and inches.

36 feet = 36*12  inches

                          =432 inches

Width of the floor; Converted from feet to inches:

32 feet = 32*12  inches

                          = 384 inches

Calculate how many times the length (l) has been scaled down.

432 inches of length has been reduced to 9 inches.

[tex]\frac{432}{9}=48[/tex]

Now the length has been scaled down 48 times.

Scale down the width (w) 48 times.

[tex]\frac{384}{48} =8[/tex]

The width of the scale drawing = 8 in

Area of the Scale drawing = Scaled down length * Scaled down width

                                        [tex]=9*8 =72in^{2}[/tex]

under a reflection in the y-axis

a point (x, y ) → (- x, y ), thus

R(6, 6 ) → R' (- 6, 6 )

S(3, - 6 ) → S'(- 3, - 6 )

T(0, 3 ) → T'(0, 3 )

Plot the sets of points and graph them

Answer:  The graph is attached below.

Step-by-step explanation:  Given that the co-ordinates of the vertices of ΔRST are R(6, 6), S(3, –6), and T(0, 3).

We are given to graph ΔRST and its image after a reflection over the Y-axis.

After reflection across Y-axis, the co-ordinates of the vertices of ΔRST will follow the following transformation :

(x, y)  ⇒  (-x, y), because the sign before the x-coordinates of the vertices will get reversed.

Therefore, the co-ordinates of the vertices of the image of ΔRST will be

R'(-6, 6), S'(-3, -6) and T'(0, 3).

The graphs of both the triangles, ΔRST and its image after reflection R'S'T' is drawn in the attached figure.

We see that the vertices T and T' coincide with each other.

Thus, the graph is shown below.

Note that

[tex]A_{CMD}=\dfrac{1}{2}\cdot MC\cdot h=7\ sq. ft.[/tex]

Let H be the height of triangle ABC. Since [tex]\dfrac{MD}{DB}=\dfrac{1}{2},[/tex] then

[tex]\dfrac{H}{h}=\dfrac{5}{1}, \\ \\H=5h.[/tex]

1.

[tex]A_{BDC}=A_{MBC}-A_{CMD}=\dfrac{1}{2}\cdot MC\cdot H-\dfrac{1}{2}\cdot MC\cdot h=\dfrac{1}{2}\cdot MC\cdot (5h-h)=\\ \\=4\cdot \dfrac{1}{2}\cdot MC\cdot h=4\cdot 7=28 sq. ft.[/tex]

2. M is midpoint of AC, then AM=MC.

[tex]A_{AMB}=\dfrac{1}{2}\cdot AM\cdot H=\dfrac{1}{2}\cdot MC\cdot 5h=5\cdot \dfrac{1}{2}\cdot MC\cdot h=5\cdot 7=35\ sq. ft.[/tex]

3.

[tex]A_{ABC}=\dfrac{1}{2}\cdot AC\cdot H=\dfrac{1}{2}\cdot 2MC\cdot 5h=10\cdot \dfrac{1}{2}\cdot MC\cdot h=10\cdot 7=70\ sq. ft.[/tex]

Answer:

[tex]A_{BDC}=28\ sq. ft,\ A_{AMB}=35\ sq. ft,\ A_{ABC}=70\ sq. ft.[/tex]

Answer:

28,35,70

Step-by-step explanation:

B, D and F

to test for a solution, substitute the coordinates of the given point and if the inequality is true then the point is a solution

A(- 9, 8 ) : 18 - 24 = - 6 < 8 not a solution

B(- 4, 0 ) : 8 - 0 = 8 = 8 hence a solution

C(- 2, 5) : 8- 15 = - 7 not a solution

D(0, - 3 ) : 0 + 9 = 9 hence a solution

E(7, - 1 ) : - 14 + 3 = - 11 not a solution

F(- 3, - 2 ) : 6 + 6 = 12 hence a solution

Answer:

B, D and F

Explanation:

A(- 9, 8 ) : 18 - 24 = - 6 < 8 not a solution

B(- 4, 0 ) : 8 - 0 = 8 = 8 is a solution

C(- 2, 5) : 8- 15 = - 7 not a solution

D(0, - 3 ) : 0 + 9 = 9  is a solution

E(7, - 1 ) : - 14 + 3 = - 11 not a solution

F(- 3, - 2 ) : 6 + 6 = 12  is a solution

Answer:

3.8 feet

Step-by-step explanation:

Given that the person is standing in a pool.  That means he is keeping his feet at the bottom level of the pool.  His height is 6.2 ft.  

Top of the person head above the surface of water= 2.8 feet.

Hence height of the person= Top of the person head above the surface of water+depth of the pool

6.2 = 2.8+depth of pool

Depth of pool = 6.2-2.8 = 3.4 feet.

the pool is four feet deep

(a)

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here the vertex = (6, - 2 ) and a = 1

y = (x - 6 )² - 2 ← in vertex form

(b)

to find the zeros let y = 0

(x - 6 )² - 2 = 0 ( add 2 to both sides )

(x - 6 )² = 2 ( take the square root of both sides )

x - 6 = ±√2 ← ( note plus or minus )

add 6 to both sides

x = 6 ±√2 ← zeros

(c)

to obtain standard form expand the vertex form of the equation

y = x² - 12x + 36 - 2

y = x² - 12x + 34 ← in standard form

The equation to describe the relationship between the number of lilies and roses is l/30 = r/78. This equation represents the proportion between the number of lilies and roses used in each arrangement.

The relationship between the number of lilies (l) and the number of roses (r) can be described by the equation l/30 = r/78. This equation represents the proportion between the number of lilies and roses used in each arrangement. By setting up this proportion, we can determine the ratio of lilies to roses in each arrangement.

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(a) entry fee cost

(b) the number of ride tickets James can buy (after he pays the entry fee)

(c) an equation for total cost y for purchase of x tickets

(a) We know the total cost is the cost of entry fee and ride tickets. For Jennifer, this is ...

... 30.75 = (entry fee) + 15×1.25

... 30.75 -18.75 = (entry fee)

entry fee = 12.00 . . . dollars

(b) If James spends his entire budget on entry fee and x rides, the number of ride tickets he can buy is given by ...

... 22 = 12 + 1.25x

... 10 = 1.25x

... 10/1.25 = x = 8

James can buy 8 ride tickets.

(c) The equation for total cost that we have been using is ...

... total cost = entry fee + (cost per ticket)×(number of tickets)

... y = 12 + 1.25x

The "intercept form" of the equation for a line is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively.

Dividing by -15 will put your equation into this form:

... 3x/-15 + 5y/-15 = 1

... x/(-5) + y/(-3) = 1

Your graph will go through the points (-5, 0) and (0, -3).

y = - [tex]\frac{2}{5}[/tex] x - 2

the equation of a line in slope- intercept form is

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

rearrange 2x + 5y = 10 into this form

subtract 2x from both sides

5y = - 2x + 10 ( divide all terms by 5 )

y = - [tex]\frac{2}{5}[/tex] x + 2 ← point- slope form with slope m = - [tex]\frac{2}{5}[/tex]

Parallel lines have equal slopes hence

y = - [tex]\frac{2}{5}[/tex] x + c is the partial equation of the parallel line

to find c, substitute ( 5, - 4 ) into the partial equation

- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2

y = - [tex]\frac{2}{5}[/tex] x - 2 ← equation of parallel line

The equation of the line that is parallel to 2x + 5y = 10 and passes through the point (5, -4) is y + 4 = (-2/5)x + 2.

To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope. First, let's write the given equation in slope-intercept form (y = mx + b), where m represents the slope:

2x + 5y = 10

5y = -2x + 10

y = (-2/5)x + 2

Since the given line has a slope of -2/5, the parallel line will also have a slope of -2/5. Now, we can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation. Plugging in the coordinates of the point (5, -4):

y - (-4) = (-2/5)(x - 5)

y + 4 = (-2/5)(x - 5)

y + 4 = (-2/5)x + 2

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You can use the sum of angles identities, then rearrange to put the result in the form of tangents.

[tex]\displaystyle\frac{\sin{(x+y)}}{\sin{(x-y)}}=\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}\\\\=\frac{\left(\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}{\left(\frac{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}\\\\=\frac{\tan{(x)}+\tan{(y)}}{\tan{(x)}-\tan{(y)}}[/tex]

diagonal = 9√2 ≈ 12.73

the diagonal splits the square into 2 right triangles with the hypotenuse being the diagonal of the square

using Pythagoras' identity

d = √(9² + 9²) = √162 = 9√2 ≈ 12.73 ( to 2 dec. places )

To find the diagonal of a square with side lengths of 9 inches, use the Pythagorean theorem, yielding a diagonal length approximately equal to 9√2 inches.

To calculate the diagonal of a square, you can use the Pythagorean theorem for a right triangle formed by two adjacent sides of the square and the diagonal. The formula for the diagonal (d) of a square with side length (s) is given by d = s√2. Therefore, the diagonal of the square is:

d = 9√2

d = 9 × 1.414 (approx)

d = 12.726 inches (approx)

Rounded to the nearest whole number or given options, the length of the diagonal is closer to 9√2 inches.

The complete question is:

A square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal of the square.

Hey mate!!

Answer⤵

The difference between 1,968 and 3,000 is 1,032.

3,000-1,968=1,032.

Answer confirmed= 1,032

Hope it helps you! ヅ

To find the difference between 1968 and 3000, you need to subtract the smaller number from the larger one.

Step 1: Identify the larger number. In this case, 3000 is larger than 1968.

Step 2: Subtract the smaller number from the larger number.
3000 - 1968 = 1032

So, the difference between 1968 and 3000 is 1032.

The two numbers that should replace the question marks on the given sequence are; 22 and 24

We are given the series;

19,20,21,?,?,26,28,32,33,40

From the given sequence, we see that there are two interwoven sequences.

Between 21 and second question mark, the difference is +3

Between second question mark and 28, the difference is +4

Between 28 and 33, the difference is +5

Between 20 and first question mark the difference will be +2

Between the first question mark and 26, the difference is +4

Between 26 and 32 the difference is +6.

Thus our missing numbers are 22 and 24

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Answer:

(x-4)² + (y+3)² = 9

Step-by-step explanation:

The equation of a circle of radius r centered at (h, k) is ...

... (x-h)² + (y-k)² = r²

Subsituting your given values gives ...

... (x -4)² +(y -(-3))² = 3²

... (x -4)² +(y +3)² = 9

Answer:

Step-by-step explanation:

3) Purchase price of the home is $585000

Cash down payment is $ 175000

Amount to taken for loan

[tex] = 585000-175000 = $410000[/tex]

Therefore, loan to value ratio will be

[tex]= \frac{loan amount}{value}[/tex]

[tex] =\frac{410000}{585000}[/tex]

On solving

[tex]=\frac{410}{585}[/tex]

On simplifying

[tex] =\frac{82}{117}[/tex]

The loan to value ratio will be [tex]82:117[/tex]

4) it is given that

Fixed monthly expences i.e. debt [tex]=$1836[/tex]

Total income per month [tex] =$4934[/tex]

Therefore debt to income ratio will be

[tex]= \frac{debt}{income}[/tex]

[tex]= \frac{1836}{4934}[/tex]

On simplifying we get

[tex]=\frac{918}{2467}[/tex]

Therefore debt to income ratio will be

[tex]918:2467[/tex]

answer:

1. 24

2. -6

work:

1.

[tex]5n + 3n[/tex]

[tex]5 (3) + 3 (3)[/tex]

[tex]15 + 9[/tex]

24

2.

[tex]9 (x -7) - y[/tex]

[tex]9 ( (11) -7) - 19[/tex]

[tex]9 + 4 - 19[/tex]

[tex]13 - 19[/tex]

[tex]-6[/tex]

hope this helps! ❤ from peachimin

1.  How to get answer:

2. How to get answer:

B

note that (f + g)(x) = f(x) + g(x)

f(x) + g(x) = -4x² - 6x - 1 - x² - 5x + 3 ( collect like terms )

               = - 5x² - 11x + 2

Answer:

The correct option is B.

Step-by-step explanation:

The given functions are

[tex]f(x)=-4x^2-6x-1[/tex]

[tex]g(x)=-x^2-5x+3[/tex]

Using the p addition property of functions (f + g)(x) can be written as

[tex](f+g)(x)=f(x)+g(x)[/tex]

Substitute the values of each function in the above equation.

[tex](f+g)(x)=-4x^2-6x-1-x^2-5x+3[/tex]

Combine like terms.

[tex](f+g)(x)=(-4x^2-x^2)+(-6x-5x)+(-1+2)[/tex]

[tex](f+g)(x)=-5x^2-11x+2[/tex]

Therefore the correct option is B.

Note that a:b = c:d is the same as a/b = c/d

y:1.5=0.2:0.75 same as y/1.5 = 0.2/0.75

y = 0.4

x: 1 2/3=y:3 1/3 same as x/1 2/3 = y / 3 1/3

x = y/2 = 0.2

y:1.5=0.2:0.75

so y=1.5*0.2/0.75=0.4

x:1 2 /3=y:3 1/3

so x=1 2/3*0.4/3 1/3=0.2

Step-by-step explanation:

6/8 / 3/4 = 1

I'm assuming what you mean is what can you divide 3456 by to get a natural number.

First of all every number is divisible by 1.  

Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2.  That would equal 1728.

2456 can also be divided by 3, to get 1782.  

You can also divide it by 4, to get 865.

Divided by 6, it's 576.

Divided by 8, it's 432.

And lastly, 3456 divided by 9 is 384.

So, there isn't just one single-digit number you can divide 3456 by to get a natural number.  You can divide it by 1,2,3,4,6,8, and 9.

Hope that helps!

Answer:

77.57

If we round.

78

Step-by-step explanation:

To solve this, just plugin 70 where the x is located in the equation:

y = -0,414x + 106.55

y = -0,414(70) + 106.55 = 77.57

The best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The regression equation is given by:

y = -0.414x + 106.55

Here y represents the percentage of people in an audience who finish watching a documentary.

and x represents the length of the film in minutes.

We have to determine the value of y when the value of x is: 70

Substitute the value of x = 70 in the equation,

y = -0.414x + 106.55

y = -0.414(70) + 106.55

y = 77.57

Therefore, the best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.

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First, I should point out that g(x) should be written as g(x)=(x+2)/3, otherwise the problem is confusing.  

[tex]f(x)=3x-2 \enspace g(x)=\frac{x+2}{3}[/tex]

(A) [tex]f(g(x))=3(\frac{x+2}{3})-2=x\\g(f(x))=\frac{3x-2+2}{3}=x[/tex]

(B) Since [tex]f(g(x))=x[/tex] and [tex]g(f(x))=x[/tex], it holds that

[tex]f(g(x))=g(f(x))[/tex] for all x. This means the composed functions are *identical*

A

f(g(x)) = f([tex]\frac{x+2}{3}[/tex]) = 3([tex]\frac{x+2}{3}[/tex]) - 2 = x + 2 - 2 = x

g(f(x)) = g(3x - 2) = [tex]\frac{3x-2+2}{3}[/tex] = [tex]\frac{3x}{3}[/tex] = x

B

Since both composite functions f(g(x)) and g(f(x)) equal x

This indicates that the functions f(x) and g(x) are inverse functions