Write the 2-digit number that matches the clues.my number has a ten s digit that is 8 more than the ones digit. Zero is not one of my digits

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

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

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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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]

When you replace the comparison symbol (<) with an equal sign (=), you get the equation of a line in slope-intercept form:

... y = mx + b

where m is the slope, and b is the y-intercept.

Your equation has m = -1/4 and b = -1. To graph this line, find the point (0, -1) on the y-axis. To find another point on the line, you can use the slope value (rise/run = -1/4), which tells you the line "rises" -1 for each "run" of +4. That is, another point on the line will be 4 units to the right and 1 unit down, at (4, -2). Working in the other direction (to the left, instead of to the right), the -1/4 slope tells you the point 4 units left and 1 unit up (-4, 0) will also be on the line. Draw a dashed line through these points,

The dashed line you just drew is the boundary of the solution region. It is dashed because the line itself is not part of the solution. (Those points do not meet the requirement for "less than.")

Appropriate values of y are ones that are less than those on the line, so the solution region is indicated as being the half-plane below the line. You indicate this by shading the solution region. (See the attachment for an example of the way this can be graphed.)

_____

If the comparison is ≤ instead of <, then the line is solid (not dashed), indicating it is part of the solution region. If the comparison is > or ≥, then the shaded region is above the line, where y-values are greater than those on the line.

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.

Yes ,

side ×side×side= side^3 =volume of cube  

=>side^3=30

=>side = 30^1/3-answer

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

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:

Answer:

Points (0,-3) and (-3,-1) work, I got a 100% on the test.

Answer:

  y -8 = -5(x -6)

Step-by-step explanation:

The point-slope form of the equation for a line is generally written ...

  y -k = m(x -h)

for slope m and point (h, k).

The slope of your parallel line is the same as the slope of the reference line, -5. So your equation is ...

  y -8 = -5(x -6)

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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The set of seashell weights that Mirna collected (12, 13, 16, 17, 18, 20) does not have a mode because all values appear only once.

The mode of a set of data refers to the number that appears most frequently. In the case of the weights of the seashells Mirna collected in Florida, the data set is: 12, 13, 16, 17, 18, 20. To find the mode, we look for the value that occurs the most:

Since all numbers occur only once, there is no number that appears more frequently than the others. Therefore, this set of data does not have a mode.

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:

25x²-16 is the difference of two squares, so can be written as the product ...

... (5x -4)(5x +4)

or

... (5x +4)(5x -4)

Answer:

[tex](5x+4)(5x-4)[/tex]

Step-by-step explanation:

25x^2- 16

To find out the product that is equivalent to the given expression we need to factor the given expression

we write the numbers in square form

25 = 5*5 = 5^2

16 = 4*4 = 4^2

5^2x^2 - 4^2

[tex](5x)^2- 4^2[/tex]

we apply difference in square formula

a^2 - b^2 = (a+b)(a-b)

[tex](5x)^2- 4^2=(5x+4)(5x-4)[/tex]

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]

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.

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!

Step-by-step explanation:

6/8 / 3/4 = 1

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

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.

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)

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.

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.

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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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 )

It can't be proven because it isn't so.

You can show that A'B' = C'D' because each is half of AC (from the midsegment theorem).

Answer:

See the attached.

Step-by-step explanation:

A graph of f' is a graph of the slope of the function. Your function f(x) is piecewise linear, so different sections of its graph have different constant values of slope.

In the intervals (-5, -2) and (0, 2), the slope is -1. (The graph has a "rise" of -1 for each "run" of 1.) So, in those intervals, the graph of f' looks like a graph of y=-1.

In the interval (-2, 0), the rise is 2 for a run of 2, so the slope is 2/2 = 1. The graph of f' in that interval will look like a graph of y=1.

In the interval (2, 5), the rise of f(x) is 1 for a run of 3, so the slope in that interval is 1/3. There, the graph of f' will look like a graph of y=1/3.

If you want to get technical about it, the slope is undefined at x=-2, x=0, and x=2. Therefore, the line segments that make up the graph of f' ought to have open circles at those points, indicating that f' is not defined.

Hi!

[tex]3x=18[/tex]

[tex]\frac{3x}{3}=\frac{18}{3}[/tex]

[tex]x=6[/tex]

Explanation: This question is super easy on this question. First you had to divide by 3 from both sides. And simplify, it gave us the answer is x=6 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day. -Charlie